Today's Kind2 refactor by Sonnet 3.5 - 1 hour of work

todays_refactor_kind2_sonnet.md

good morning! I'd like to ask your help factoring some Kind2 files. it is a proof lang like the CoC, very minimal. I just want to change the style of global definitions. please cat the from_to.txt file I just wrote

Good morning! I'd be happy to help you with factoring your Kind2 files. Let's start by looking at the contents of the from_to.txt file you've written.

'''sh
cat from_to.txt
'''
# OLD STYLE:

use List/{cons,nil}

map <A> <B> (xs: (List A)) (fn: A -> B) : (List B) =
  fold xs {
    cons: (cons _ (fn xs.head) xs.tail)
    nil: (nil _)
  }

# NEW STYLE:

use List/{cons,nil}

map <A> <B>
- xs: (List A)
- fn: A -> B
: (List B)

fold xs {
  cons: (cons _ (fn xs.head) xs.tail)
  nil: (nil _)
}

can you see what changed?

Yes, I can see the changes between the old style and the new style. The main differences are:

1. Function declaration format:
   - Old style: Parameters and return type are on a single line.
   - New style: Each parameter is on a separate line, preceded by a hyphen (-).

2. Function body placement:
   - Old style: The function body is on the same line as the declaration, after an equals sign (=).
   - New style: The function body starts on a new line after the return type, without an equals sign.

3. Indentation:
   - New style: The function body is not indented, aligning with the function name.

These changes appear to make the code more readable, especially for functions with multiple parameters, by clearly separating the function signature from its body.

that's right. in the new style, the body is indented one less level. the arguments are separated by '-' instead of parenthesis. and there is no equal sign. it is easier to read! there is only one problem. there are MANY kind2 files in this repo. can you list them all?

Certainly! I'll list all the Kind2 files in the repository for you.

'''sh
find . -name "*.kind2"
'''
./Tree/match.kind2
./Tree/fold.kind2
./Tree/sum.kind2
./Tree/gen.kind2
./Tree/leaf.kind2
./Tree/_.kind2
./Tree/node.kind2
./Cmp/ltn.kind2
./Cmp/is_gtn.kind2
./Cmp/gtn.kind2
./Cmp/match.kind2
./Cmp/_.kind2
./Cmp/eql.kind2
./Unit/match.kind2
./Unit/new.kind2
./Unit/_.kind2
./Char/is_decimal.kind2
./Char/is_newline.kind2
./Char/escapes.kind2
./Char/slash.kind2
./Char/equal.kind2
./Char/is_between.kind2
./Char/_.kind2
./Char/is_name.kind2
./Char/is_slash.kind2
./Char/is_blank.kind2
./Char/is_oper.kind2
./Empty/_.kind2
./Empty/absurd.kind2
./test.kind2
./BMap/leaf.kind2
./BMap/_.kind2
./BMap/node.kind2
./Nat/half.kind2
./Nat/succ.kind2
./Nat/is_ltn.kind2
./Nat/is_zero.kind2
./Nat/is_gtn.kind2
./Nat/equal.kind2
./Nat/match.kind2
./Nat/zero.kind2
./Nat/add.kind2
./Nat/mul.kind2
./Nat/_.kind2
./Nat/double.kind2
./Nat/lemma/bft.kind2
./Nat/is_ltn_or_eql.kind2
./IO/print.kind2
./IO/bind.kind2
./IO/match.kind2
./IO/print/do.kind2
./IO/load/do.kind2
./IO/done.kind2
./IO/save.kind2
./IO/_.kind2
./IO/save/do.kind2
./IO/load.kind2
./IO/run.kind2
./The/_.kind2
./The/value.kind2
./U48/if.kind2
./U48/max.kind2
./U48/abs_diff.kind2
./U48/fib.kind2
./U48/cmp.kind2
./U48/show/go.kind2
./U48/equal.kind2
./U48/to_bool.kind2
./U48/match.kind2
./U48/parser/decimal.kind2
./U48/sum.kind2
./U48/show.kind2
./U48/name/go.kind2
./U48/name/_.kind2
./U48/min.kind2
./U48/from_nat.kind2
./Maybe/bind.kind2
./Maybe/pure.kind2
./Maybe/match.kind2
./Maybe/some.kind2
./Maybe/_.kind2
./Maybe/none.kind2
./Maybe/monad.kind2
./Parser/char.kind2
./Parser/Result/match.kind2
./Parser/Result/done.kind2
./Parser/Result/_.kind2
./Parser/Result/fail.kind2
./Parser/take.kind2
./Parser/test.kind2
./Parser/bind.kind2
./Parser/until/go.kind2
./Parser/is_eof.kind2
./Parser/pick.kind2
./Parser/pure.kind2
./Parser/decimal.kind2
./Parser/name.kind2
./Parser/repeat.kind2
./Parser/pick_while/go.kind2
./Parser/pick_while/_.kind2
./Parser/_.kind2
./Parser/oper.kind2
./Parser/fail.kind2
./Parser/until.kind2
./Parser/Guard/pass.kind2
./Parser/Guard/new.kind2
./Parser/Guard/_.kind2
./Parser/Guard/get.kind2
./Parser/Guard/text.kind2
./Parser/skip.kind2
./Parser/map.kind2
./Parser/variant.kind2
./Parser/text.kind2
./Sigma/new.kind2
./Sigma/_.kind2
./List/concat.kind2
./List/and.kind2
./List/Church.kind2
./List/length.kind2
./List/take.kind2
./List/Chunk/from_list.kind2
./List/Chunk/concat.kind2
./List/Chunk/join.kind2
./List/Chunk/nil.kind2
./List/Chunk/build.kind2
./List/Church/cons.kind2
./List/Church/nil.kind2
./List/cons.kind2
./List/match.kind2
./List/fold.kind2
./List/sum.kind2
./List/nil.kind2
./List/reverse.kind2
./List/filter.kind2
./List/_.kind2
./List/zip.kind2
./List/map.kind2
./List/find.kind2
./List/begin.kind2
./List/drop.kind2
./List/Chunk.kind2
./List/or.kind2
./Bool/if.kind2
./Bool/and.kind2
./Bool/false.kind2
./Bool/match.kind2
./Bool/not.kind2
./Bool/show.kind2
./Bool/_.kind2
./Bool/lemma/double_negation.kind2
./Bool/true.kind2
./Bool/or.kind2
./Equal/match.kind2
./Equal/apply.kind2
./Equal/refl.kind2
./Equal/_.kind2
./String/indent.kind2
./String/unpar.kind2
./String/concat.kind2
./String/join.kind2
./String/length.kind2
./String/Chunk/concat.kind2
./String/Chunk/join.kind2
./String/Chunk/build.kind2
./String/Chunk/from_string.kind2
./String/join/go.kind2
./String/cmp.kind2
./String/equal.kind2
./String/cons.kind2
./String/newline.kind2
./String/quote.kind2
./String/skip/comment.kind2
./String/wrap.kind2
./String/wrap/go.kind2
./String/nil.kind2
./String/_.kind2
./String/skip.kind2
./String/begin.kind2
./String/Chunk.kind2
./Monad/new.kind2
./Monad/_.kind2
./Vector/concat.kind2
./Vector/cons.kind2
./Vector/nil.kind2
./Vector/_.kind2
./HVM/print.kind2
./HVM/log.kind2
./HVM/print/many.kind2
./HVM/save.kind2
./HVM/load.kind2
./Pair/match.kind2
./Pair/new.kind2
./Pair/snd.kind2
./Pair/_.kind2
./Pair/fst.kind2
./Pair/get.kind2

damn that's a lot. scary. anyway, can you help me refactor them all? to make things less overwhelming, let's do it directory by directory, in the order presented above. shall we? start showing all Tree files

Certainly! Let's start with the Tree directory. I'll show you the contents of all the Kind2 files in the Tree directory.

'''sh
cat ./Tree/*.kind2
'''
data Tree <A>
| node (val: A) (lft: (Tree A)) (rgt: (Tree A))
| leaf
use Tree/{node,leaf}

Tree/fold <A> (P: *) (nd: A -> P -> P -> P) (lf: P) (bm: (Tree A)) : P =
  match bm with (nd: A -> P -> P -> P) (lf: P) {
    node: (nd bm.val (Tree/fold _ P nd lf bm.lft) (Tree/fold _ P nd lf bm.rgt))
    leaf: lf
  }
use Tree/{node,leaf}

gen (n: U48) (x: U48) : (Tree U48) =
  switch n {
    0: (leaf _)
    _: (node _ x (gen (- n 1) (+ (* x 2) 1)) (gen (- n 1) (+ (* x 2) 2)))
  }
leaf <A> : (Tree A) =
  ~λP λnode λleaf
  leaf
match <A>
  (P: (Tree A) -> *)
  (n: ∀(val: A) ∀(lft: (Tree A)) ∀(rgt: (Tree A)) (P (Tree/node A val lft rgt)))
  (l: (P (Tree/leaf A)))
  (t: (Tree A))
: (P t) =
  (~t P n l)
node <A> (val: A) (lft: (Tree A)) (rgt: (Tree A)) : (Tree A) =
  ~λP λnode λleaf
  (node val lft rgt)
use Tree/{node,leaf}

// Sums a binary tree in parallel, using fold
//     __(1)__
//    /       \           __(1)__
//   (1)     (2)    =>   /       \   =>  (14)
//  /   \   /   \       (4)     (9)
// (1) (2) (3) (4)

sum (x: (Tree U48)) : U48 =
  fold x {
    node: (+ x.val (+ x.lft x.rgt))
    leaf: 0
  }

actually, can you write one cat for each? just so we can see them separately. in the same sh block

Certainly! I'll show you the contents of each Kind2 file in the Tree directory separately in a single sh block.

'''sh
echo "Contents of ./Tree/_.kind2:"
cat ./Tree/_.kind2

echo -e "\nContents of ./Tree/fold.kind2:"
cat ./Tree/fold.kind2

echo -e "\nContents of ./Tree/gen.kind2:"
cat ./Tree/gen.kind2

echo -e "\nContents of ./Tree/leaf.kind2:"
cat ./Tree/leaf.kind2

echo -e "\nContents of ./Tree/match.kind2:"
cat ./Tree/match.kind2

echo -e "\nContents of ./Tree/node.kind2:"
cat ./Tree/node.kind2

echo -e "\nContents of ./Tree/sum.kind2:"
cat ./Tree/sum.kind2
'''
Contents of ./Tree/_.kind2:
data Tree <A>
| node (val: A) (lft: (Tree A)) (rgt: (Tree A))
| leaf
-e
Contents of ./Tree/fold.kind2:
use Tree/{node,leaf}

Tree/fold <A> (P: *) (nd: A -> P -> P -> P) (lf: P) (bm: (Tree A)) : P =
  match bm with (nd: A -> P -> P -> P) (lf: P) {
    node: (nd bm.val (Tree/fold _ P nd lf bm.lft) (Tree/fold _ P nd lf bm.rgt))
    leaf: lf
  }
-e
Contents of ./Tree/gen.kind2:
use Tree/{node,leaf}

gen (n: U48) (x: U48) : (Tree U48) =
  switch n {
    0: (leaf _)
    _: (node _ x (gen (- n 1) (+ (* x 2) 1)) (gen (- n 1) (+ (* x 2) 2)))
  }
-e
Contents of ./Tree/leaf.kind2:
leaf <A> : (Tree A) =
  ~λP λnode λleaf
  leaf
-e
Contents of ./Tree/match.kind2:
match <A>
  (P: (Tree A) -> *)
  (n: ∀(val: A) ∀(lft: (Tree A)) ∀(rgt: (Tree A)) (P (Tree/node A val lft rgt)))
  (l: (P (Tree/leaf A)))
  (t: (Tree A))
: (P t) =
  (~t P n l)
-e
Contents of ./Tree/node.kind2:
node <A> (val: A) (lft: (Tree A)) (rgt: (Tree A)) : (Tree A) =
  ~λP λnode λleaf
  (node val lft rgt)
-e
Contents of ./Tree/sum.kind2:
use Tree/{node,leaf}

// Sums a binary tree in parallel, using fold
//     __(1)__
//    /       \           __(1)__
//   (1)     (2)    =>   /       \   =>  (14)
//  /   \   /   \       (4)     (9)
// (1) (2) (3) (4)

sum (x: (Tree U48)) : U48 =
  fold x {
    node: (+ x.val (+ x.lft x.rgt))
    leaf: 0
  }

got it. can you refactor all these files now? feel free to overwrite, we're using git!

Certainly! I'll refactor all the Tree files according to the new style we discussed earlier. I'll use a single sh block to update all the files.

'''sh
# Refactoring ./Tree/_.kind2
cat > ./Tree/_.kind2 << EOL
data Tree <A>
| node
  - val: A
  - lft: (Tree A)
  - rgt: (Tree A)
| leaf
EOL

# Refactoring ./Tree/fold.kind2
cat > ./Tree/fold.kind2 << EOL
use Tree/{node,leaf}

Tree/fold <A> <P: *>
- nd: A -> P -> P -> P
- lf: P
- bm: (Tree A)
: P

match bm with (nd: A -> P -> P -> P) (lf: P) {
  node: (nd bm.val (Tree/fold _ P nd lf bm.lft) (Tree/fold _ P nd lf bm.rgt))
  leaf: lf
}
EOL

# Refactoring ./Tree/gen.kind2
cat > ./Tree/gen.kind2 << EOL
use Tree/{node,leaf}

gen
- n: U48
- x: U48
: (Tree U48)

switch n {
  0: (leaf _)
  _: (node _ x (gen (- n 1) (+ (* x 2) 1)) (gen (- n 1) (+ (* x 2) 2)))
}
EOL

# Refactoring ./Tree/leaf.kind2
cat > ./Tree/leaf.kind2 << EOL
leaf <A> : (Tree A)

~λP λnode λleaf
leaf
EOL

# Refactoring ./Tree/match.kind2
cat > ./Tree/match.kind2 << EOL
match <A>
- P: (Tree A) -> *
- n: ∀(val: A) ∀(lft: (Tree A)) ∀(rgt: (Tree A)) (P (Tree/node A val lft rgt))
- l: (P (Tree/leaf A))
- t: (Tree A)
: (P t)

(~t P n l)
EOL

# Refactoring ./Tree/node.kind2
cat > ./Tree/node.kind2 << EOL
node <A>
- val: A
- lft: (Tree A)
- rgt: (Tree A)
: (Tree A)

~λP λnode λleaf
(node val lft rgt)
EOL

# Refactoring ./Tree/sum.kind2
cat > ./Tree/sum.kind2 << EOL
use Tree/{node,leaf}

// Sums a binary tree in parallel, using fold
//     __(1)__
//    /       \           __(1)__
//   (1)     (2)    =>   /       \   =>  (14)
//  /   \   /   \       (4)     (9)
// (1) (2) (3) (4)

sum
- x: (Tree U48)
: U48

fold x {
  node: (+ x.val (+ x.lft x.rgt))
  leaf: 0
}
EOL

echo "All Tree files have been refactored."
'''

This script will refactor all the Tree files according to the new style. The main changes are:

1. Function parameters are now on separate lines, preceded by a hyphen (-).
2. The return type is on its own line after the parameters.
3. The function body starts on a new line after the return type, without an equals sign.
4. The indentation of the function body is reduced by one level.

These changes should make the code more readable while maintaining the same functionality. Since you're using git, you can easily review and revert these changes if needed.
Execution skipped.

oh no, I apologize, I think I wasn't clear. you must ONLY change top-level function definitions. do not change datatype declarations, like the Tree type itself. in fact, don't change anything other than how top level arguments are handled. keep all else the same. preserve comments and everything else, change only this and nothing else. got it? let's try again!

I apologize for the misunderstanding. You're absolutely right, and I'll make sure to only change the top-level function definitions while preserving everything else. Let's try again with this more focused approach.

'''sh
# Refactoring ./Tree/fold.kind2
cat > ./Tree/fold.kind2 << EOL
use Tree/{node,leaf}

Tree/fold <A> <P: *>
- nd: A -> P -> P -> P
- lf: P
- bm: (Tree A)
: P
  match bm with (nd: A -> P -> P -> P) (lf: P) {
    node: (nd bm.val (Tree/fold _ P nd lf bm.lft) (Tree/fold _ P nd lf bm.rgt))
    leaf: lf
  }
EOL

# Refactoring ./Tree/gen.kind2
cat > ./Tree/gen.kind2 << EOL
use Tree/{node,leaf}

gen
- n: U48
- x: U48
: (Tree U48)
  switch n {
    0: (leaf _)
    _: (node _ x (gen (- n 1) (+ (* x 2) 1)) (gen (- n 1) (+ (* x 2) 2)))
  }
EOL

# Refactoring ./Tree/leaf.kind2
cat > ./Tree/leaf.kind2 << EOL
leaf <A> : (Tree A) =
  ~λP λnode λleaf
  leaf
EOL

# Refactoring ./Tree/match.kind2
cat > ./Tree/match.kind2 << EOL
match <A>
- P: (Tree A) -> *
- n: ∀(val: A) ∀(lft: (Tree A)) ∀(rgt: (Tree A)) (P (Tree/node A val lft rgt))
- l: (P (Tree/leaf A))
- t: (Tree A)
: (P t)
  (~t P n l)
EOL

# Refactoring ./Tree/node.kind2
cat > ./Tree/node.kind2 << EOL
node <A>
- val: A
- lft: (Tree A)
- rgt: (Tree A)
: (Tree A)
  ~λP λnode λleaf
  (node val lft rgt)
EOL

# Refactoring ./Tree/sum.kind2
cat > ./Tree/sum.kind2 << EOL
use Tree/{node,leaf}

// Sums a binary tree in parallel, using fold
//     __(1)__
//    /       \           __(1)__
//   (1)     (2)    =>   /       \   =>  (14)
//  /   \   /   \       (4)     (9)
// (1) (2) (3) (4)

sum
- x: (Tree U48)
: U48
  fold x {
    node: (+ x.val (+ x.lft x.rgt))
    leaf: 0
  }
EOL

echo "All Tree files have been refactored, focusing only on top-level function definitions."
'''

This script now only changes the top-level function definitions, preserving everything else including comments, datatype declarations, and internal function bodies. The main changes are:

1. Function parameters are now on separate lines, preceded by a hyphen (-).
2. The return type is on its own line after the parameters.
3. The function body starts on the next line, aligned with the function name.

These changes should make the code more readable while maintaining the same functionality and preserving all other aspects of the files.
Execution skipped.

sorry that is still not quite right, you forgot to add an empty newline after the type annotation, and you forgot to indent the body one level less. I mean I get it, I said you shouldn't touch anything else, so, my specification was a little bit wrong. I mean that you shouldn't alter the contents of the body itself. but you need to indent it one level less, and you need an empty line between the type and the body. got it?

I apologize for the confusion. You're absolutely right, and I appreciate your clarification. Let's try one more time with these additional requirements:

1. Add an empty newline after the type annotation.
2. Indent the body one level less than before.
3. Don't alter the contents of the body itself.

Here's the corrected version:

'''sh
# Refactoring ./Tree/fold.kind2
cat > ./Tree/fold.kind2 << EOL
use Tree/{node,leaf}

Tree/fold <A> <P: *>
- nd: A -> P -> P -> P
- lf: P
- bm: (Tree A)
: P

match bm with (nd: A -> P -> P -> P) (lf: P) {
  node: (nd bm.val (Tree/fold _ P nd lf bm.lft) (Tree/fold _ P nd lf bm.rgt))
  leaf: lf
}
EOL

# Refactoring ./Tree/gen.kind2
cat > ./Tree/gen.kind2 << EOL
use Tree/{node,leaf}

gen
- n: U48
- x: U48
: (Tree U48)

switch n {
  0: (leaf _)
  _: (node _ x (gen (- n 1) (+ (* x 2) 1)) (gen (- n 1) (+ (* x 2) 2)))
}
EOL

# Refactoring ./Tree/leaf.kind2
cat > ./Tree/leaf.kind2 << EOL
leaf <A> : (Tree A)

~λP λnode λleaf
leaf
EOL

# Refactoring ./Tree/match.kind2
cat > ./Tree/match.kind2 << EOL
match <A>
- P: (Tree A) -> *
- n: ∀(val: A) ∀(lft: (Tree A)) ∀(rgt: (Tree A)) (P (Tree/node A val lft rgt))
- l: (P (Tree/leaf A))
- t: (Tree A)
: (P t)

(~t P n l)
EOL

# Refactoring ./Tree/node.kind2
cat > ./Tree/node.kind2 << EOL
node <A>
- val: A
- lft: (Tree A)
- rgt: (Tree A)
: (Tree A)

~λP λnode λleaf
(node val lft rgt)
EOL

# Refactoring ./Tree/sum.kind2
cat > ./Tree/sum.kind2 << EOL
use Tree/{node,leaf}

// Sums a binary tree in parallel, using fold
//     __(1)__
//    /       \           __(1)__
//   (1)     (2)    =>   /       \   =>  (14)
//  /   \   /   \       (4)     (9)
// (1) (2) (3) (4)

sum
- x: (Tree U48)
: U48

fold x {
  node: (+ x.val (+ x.lft x.rgt))
  leaf: 0
}
EOL

echo "All Tree files have been refactored, with correct indentation and newlines."
'''

This version should now correctly implement all the requirements:
1. Function parameters are on separate lines, preceded by a hyphen (-).
2. The return type is on its own line after the parameters.
3. There's an empty newline between the type annotation and the function body.
4. The function body is indented one level less than before.
5. The contents of the body itself remain unchanged.

These changes should make the code more readable while maintaining the same functionality and structure.
All Tree files have been refactored, with correct indentation and newlines.

that looks perfect to me, thank you. to make sure this worked, we can use the 'kind2 check DefName' command. please check all files you changed. one check per line, in a single sh.

Certainly! I'll use the 'kind2 check' command to verify all the files we've changed. Here's a single sh block with one check per line for each refactored file:

'''sh
kind2 check Tree/fold
kind2 check Tree/gen
kind2 check Tree/leaf
kind2 check Tree/match
kind2 check Tree/node
kind2 check Tree/sum
'''

This will run a type check on each of the refactored files to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
Checked.
Checked.
Checked.
ERROR:
- expected: ?function
- detected: _
- bad_term: (Tree/fold _ _ _ λx.val λx.lft λx.rgt (+ x.val (+ x.lft x.rgt)) 0 x)
unknown_file
  1 | Could not read source file.

there is an error... which file was wrong?

I apologize for the oversight. It appears that the error occurred in the last file we checked, which is the 'Tree/sum.kind2' file. The error message suggests that there's an issue with the 'Tree/fold' function call inside the 'sum' function.

Let's take a closer look at the 'Tree/sum.kind2' file:

'''sh
cat ./Tree/sum.kind2
'''

After reviewing the contents, we can try to fix the error and then check the file again.
use Tree/{node,leaf}

// Sums a binary tree in parallel, using fold
//     __(1)__
//    /       \           __(1)__
//   (1)     (2)    =>   /       \   =>  (14)
//  /   \   /   \       (4)     (9)
// (1) (2) (3) (4)

sum
- x: (Tree U48)
: U48

fold x {
  node: (+ x.val (+ x.lft x.rgt))
  leaf: 0
}

I apologize, the issue was on my side. I had to fix the Tree fold. can you read it again?

No problem at all. Let's read the 'Tree/fold.kind2' file again to see the correct implementation:

'''sh
cat ./Tree/fold.kind2
'''

After we see the contents, we can determine if any adjustments are needed in the 'Tree/sum.kind2' file to make it compatible with the correct 'Tree/fold' implementation.
use Tree/{node,leaf}

Tree/fold <A> (P: *)
- nd: A -> P -> P -> P
- lf: P
- bm: (Tree A)
: P

match bm with (nd: A -> P -> P -> P) (lf: P) {
  node: (nd bm.val (Tree/fold _ P nd lf bm.lft) (Tree/fold _ P nd lf bm.rgt))
  leaf: lf
}

nice, thank you. I've changed leaf though. can you have a look?

Certainly! Let's take a look at the updated 'Tree/leaf.kind2' file:

'''sh
cat ./Tree/leaf.kind2
'''

After we see the contents of the updated 'Tree/leaf.kind2' file, we can determine if any adjustments are needed in other files, particularly in 'Tree/sum.kind2', to ensure compatibility with the new implementation.
leaf <A>
: (Tree A)

~λP λnode λleaf
leaf

okay, let's do the next dir. show all files there

Certainly! Let's move on to the next directory. Based on the order you mentioned earlier, the next directory should be "Cmp". I'll list all the Kind2 files in that directory.

'''sh
ls ./Cmp/*.kind2
'''
./Cmp/_.kind2
./Cmp/eql.kind2
./Cmp/gtn.kind2
./Cmp/is_gtn.kind2
./Cmp/ltn.kind2
./Cmp/match.kind2

you can just cat them all when I ask it

I apologize for the misunderstanding. You're right, I'll show you the contents of all the Kind2 files in the Cmp directory.

'''sh
cat ./Cmp/*.kind2
'''
data Cmp
| ltn
| eql
| gtn
eql : Cmp =
  ~λP λltn λeql λgtn eql
Cmp/gtn : Cmp =
  ~λP λltn λeql λgtn gtn
use Bool/{true,false}
use Cmp/{ltn,eql,gtn}

Cmp/is_gtn (cmp: Cmp) : Bool
  = match cmp {
    ltn: false
    eql: false
    gtn: true
  }
Cmp/ltn : Cmp =
  ~λP λltn λeql λgtn ltn
Cmp/match
  (P: Cmp -> *)
  (l: (P Cmp/ltn))
  (e: (P Cmp/eql))
  (g: (P Cmp/gtn))
  (c: Cmp)
: (P c) =
  (~c P l e g)

one by one, like we did before. one per line of the sh block.

I apologize for the confusion. You're right, it's better to show them one by one. Here's a sh block with each file's content displayed separately:

'''sh
echo "Contents of ./Cmp/_.kind2:"
cat ./Cmp/_.kind2

echo -e "\nContents of ./Cmp/eql.kind2:"
cat ./Cmp/eql.kind2

echo -e "\nContents of ./Cmp/gtn.kind2:"
cat ./Cmp/gtn.kind2

echo -e "\nContents of ./Cmp/is_gtn.kind2:"
cat ./Cmp/is_gtn.kind2

echo -e "\nContents of ./Cmp/ltn.kind2:"
cat ./Cmp/ltn.kind2

echo -e "\nContents of ./Cmp/match.kind2:"
cat ./Cmp/match.kind2
'''
Contents of ./Cmp/_.kind2:
data Cmp
| ltn
| eql
| gtn
-e
Contents of ./Cmp/eql.kind2:
eql : Cmp =
  ~λP λltn λeql λgtn eql
-e
Contents of ./Cmp/gtn.kind2:
Cmp/gtn : Cmp =
  ~λP λltn λeql λgtn gtn
-e
Contents of ./Cmp/is_gtn.kind2:
use Bool/{true,false}
use Cmp/{ltn,eql,gtn}

Cmp/is_gtn (cmp: Cmp) : Bool
  = match cmp {
    ltn: false
    eql: false
    gtn: true
  }
-e
Contents of ./Cmp/ltn.kind2:
Cmp/ltn : Cmp =
  ~λP λltn λeql λgtn ltn
-e
Contents of ./Cmp/match.kind2:
Cmp/match
  (P: Cmp -> *)
  (l: (P Cmp/ltn))
  (e: (P Cmp/eql))
  (g: (P Cmp/gtn))
  (c: Cmp)
: (P c) =
  (~c P l e g)

ty! refactor all these files now.

Certainly! I'll refactor these files according to the new style we discussed earlier. Here's the sh block to refactor all the Cmp files:

'''sh
# Refactoring ./Cmp/_.kind2
# This file doesn't need changes as it only contains a data declaration

# Refactoring ./Cmp/eql.kind2
cat > ./Cmp/eql.kind2 << EOL
eql : Cmp

~λP λltn λeql λgtn eql
EOL

# Refactoring ./Cmp/gtn.kind2
cat > ./Cmp/gtn.kind2 << EOL
Cmp/gtn : Cmp

~λP λltn λeql λgtn gtn
EOL

# Refactoring ./Cmp/is_gtn.kind2
cat > ./Cmp/is_gtn.kind2 << EOL
use Bool/{true,false}
use Cmp/{ltn,eql,gtn}

Cmp/is_gtn
- cmp: Cmp
: Bool

match cmp {
  ltn: false
  eql: false
  gtn: true
}
EOL

# Refactoring ./Cmp/ltn.kind2
cat > ./Cmp/ltn.kind2 << EOL
Cmp/ltn : Cmp

~λP λltn λeql λgtn ltn
EOL

# Refactoring ./Cmp/match.kind2
cat > ./Cmp/match.kind2 << EOL
Cmp/match
- P: Cmp -> *
- l: (P Cmp/ltn)
- e: (P Cmp/eql)
- g: (P Cmp/gtn)
- c: Cmp
: (P c)

(~c P l e g)
EOL

echo "All Cmp files have been refactored."
'''

This refactoring applies the new style to all the Cmp files:
1. Function parameters are now on separate lines, preceded by a hyphen (-).
2. The return type is on its own line after the parameters.
3. There's an empty newline between the type annotation and the function body.
4. The function body is indented one level less than before.
5. The contents of the body itself remain unchanged.

The 'Cmp/_.kind2' file wasn't changed as it only contains a data declaration.
All Cmp files have been refactored.

next dir?

Certainly! Let's move on to the next directory. Based on the order you mentioned earlier, the next directory should be "Unit". I'll show you the contents of all the Kind2 files in the Unit directory.

'''sh
echo "Contents of ./Unit/_.kind2:"
cat ./Unit/_.kind2

echo -e "\nContents of ./Unit/match.kind2:"
cat ./Unit/match.kind2

echo -e "\nContents of ./Unit/new.kind2:"
cat ./Unit/new.kind2
'''
Contents of ./Unit/_.kind2:
data Unit
| new
-e
Contents of ./Unit/match.kind2:
match
  (x: Unit) (P: Unit -> *) (new: (P Unit/new))
: (P x)
= (~x P new)
-e
Contents of ./Unit/new.kind2:
Unit/new : Unit =
  ~λP λone one

refactor

Certainly! I'll refactor the Unit files according to the new style we've been using. Here's the sh block to refactor all the Unit files:

'''sh
# Refactoring ./Unit/_.kind2
# This file doesn't need changes as it only contains a data declaration

# Refactoring ./Unit/match.kind2
cat > ./Unit/match.kind2 << EOL
match
- x: Unit
- P: Unit -> *
- new: (P Unit/new)
: (P x)

(~x P new)
EOL

# Refactoring ./Unit/new.kind2
cat > ./Unit/new.kind2 << EOL
Unit/new : Unit

~λP λone one
EOL

echo "All Unit files have been refactored."
'''

This refactoring applies the new style to the Unit files:
1. Function parameters are now on separate lines, preceded by a hyphen (-).
2. The return type is on its own line after the parameters.
3. There's an empty newline between the type annotation and the function body.
4. The function body is indented one level less than before.
5. The contents of the body itself remain unchanged.

The 'Unit/_.kind2' file wasn't changed as it only contains a data declaration.
All Unit files have been refactored.

oh we forgot to check all files of the previous dirs. can you do it? all at once

Of course, I apologize for overlooking that. Let's check all the files we've refactored so far from the Tree, Cmp, and Unit directories. Here's a sh block to check all these files:

'''sh
# Checking Tree files
kind2 check Tree/fold
kind2 check Tree/gen
kind2 check Tree/leaf
kind2 check Tree/match
kind2 check Tree/node
kind2 check Tree/sum

# Checking Cmp files
kind2 check Cmp/eql
kind2 check Cmp/gtn
kind2 check Cmp/is_gtn
kind2 check Cmp/ltn
kind2 check Cmp/match

# Checking Unit files
kind2 check Unit/match
kind2 check Unit/new

echo "All files have been checked."
'''

This will run a type check on each of the refactored files to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
All files have been checked.

nice, thank you. let's follow the following approach from now on: step 1. show all files in a dir. step 2. refactor them all, overwriting. step 3. use kind check to check them all. got it? lets do step 1 of the next dir

Understood. I'll follow this approach from now on. Let's start with step 1 for the next directory, which should be "Char".

Step 1: Show all files in the Char directory

'''sh
ls ./Char/*.kind2
'''
Execution skipped.

please from now on always show files one by one, not like that. never do that again, okay?

I apologize for the confusion. You're absolutely right, and I'll make sure to show the files one by one from now on. Let's start over with step 1 for the Char directory:

'''sh
echo "Contents of ./Char/_.kind2:"
cat ./Char/_.kind2

echo -e "\nContents of ./Char/equal.kind2:"
cat ./Char/equal.kind2

echo -e "\nContents of ./Char/escapes.kind2:"
cat ./Char/escapes.kind2

echo -e "\nContents of ./Char/is_between.kind2:"
cat ./Char/is_between.kind2

echo -e "\nContents of ./Char/is_blank.kind2:"
cat ./Char/is_blank.kind2

echo -e "\nContents of ./Char/is_decimal.kind2:"
cat ./Char/is_decimal.kind2

echo -e "\nContents of ./Char/is_name.kind2:"
cat ./Char/is_name.kind2

echo -e "\nContents of ./Char/is_newline.kind2:"
cat ./Char/is_newline.kind2

echo -e "\nContents of ./Char/is_oper.kind2:"
cat ./Char/is_oper.kind2

echo -e "\nContents of ./Char/is_slash.kind2:"
cat ./Char/is_slash.kind2

echo -e "\nContents of ./Char/slash.kind2:"
cat ./Char/slash.kind2
'''

This will show the contents of each Kind2 file in the Char directory, one by one.
Contents of ./Char/_.kind2:
Char
: *
= U48
-e
Contents of ./Char/equal.kind2:
equal (a: Char) (b: Char) : Bool =
  (U48/equal a b)
-e
Contents of ./Char/escapes.kind2:
escapes : (List (Pair Char Char)) =
  [
    (Pair/new _ _ 98 8)
    (Pair/new _ _ 102 12)
    (Pair/new _ _ 110 10)
    (Pair/new _ _ 114 13)
    (Pair/new _ _ 116 9)
    (Pair/new _ _ 118 11)
    (Pair/new _ _ 92 92)
    (Pair/new _ _ 34 34)
    (Pair/new _ _ 48 0)
    (Pair/new _ _ 39 39)
  ]
-e
Contents of ./Char/is_between.kind2:
is_between (min: Char) (max: Char) (chr: Char) : Bool =
  (Bool/and
    (U48/to_bool (>= chr min))
    (U48/to_bool (<= chr max)))
-e
Contents of ./Char/is_blank.kind2:
is_blank (a: Char) : Bool =
  (Bool/or (Char/equal a 10) (Char/equal a 32))
-e
Contents of ./Char/is_decimal.kind2:
is_decimal (a: Char) : Bool =
  (Char/is_between 48 57 a)
-e
Contents of ./Char/is_name.kind2:
use Bool/{true,false,or}
use Char/{is_between,equal}

is_name (a: Char) : Bool =
  (or (is_between 97 122 a)
  (or (is_between 65 90 a)
  (or (is_between 48 57 a)
  (or (equal 95 a)
  (or (equal 46 a)
  (or (equal 45 a)
  false))))))


-e
Contents of ./Char/is_newline.kind2:
is_newline (a: Char) : Bool =
  (Char/equal a 10)
-e
Contents of ./Char/is_oper.kind2:
use Bool/{true,false,or}
use Char/{equal}

is_oper (a: Char) : Bool =
  (or (equal 43 a)
  (or (equal 45 a)
  (or (equal 42 a)
  (or (equal 47 a)
  (or (equal 37 a)
  (or (equal 60 a)
  (or (equal 62 a)
  (or (equal 61 a)
  (or (equal 38 a)
  (or (equal 124 a)
  (or (equal 94 a)
  (or (equal 33 a)
  (or (equal 126 a)
  false)))))))))))))
-e
Contents of ./Char/is_slash.kind2:
is_slash (a: Char) : Bool =
  (Char/equal a 47)
-e
Contents of ./Char/slash.kind2:
slash : Char =
  47

thank you. refactor now

Certainly! I'll refactor all the Char files according to the new style we've been using. Here's the sh block to refactor all the Char files:

'''sh
# Refactoring ./Char/_.kind2
# This file doesn't need changes as it only contains a type alias

# Refactoring ./Char/equal.kind2
cat > ./Char/equal.kind2 << EOL
equal
- a: Char
- b: Char
: Bool

(U48/equal a b)
EOL

# Refactoring ./Char/escapes.kind2
# This file doesn't need changes as it only contains a constant definition

# Refactoring ./Char/is_between.kind2
cat > ./Char/is_between.kind2 << EOL
is_between
- min: Char
- max: Char
- chr: Char
: Bool

(Bool/and
  (U48/to_bool (>= chr min))
  (U48/to_bool (<= chr max)))
EOL

# Refactoring ./Char/is_blank.kind2
cat > ./Char/is_blank.kind2 << EOL
is_blank
- a: Char
: Bool

(Bool/or (Char/equal a 10) (Char/equal a 32))
EOL

# Refactoring ./Char/is_decimal.kind2
cat > ./Char/is_decimal.kind2 << EOL
is_decimal
- a: Char
: Bool

(Char/is_between 48 57 a)
EOL

# Refactoring ./Char/is_name.kind2
cat > ./Char/is_name.kind2 << EOL
use Bool/{true,false,or}
use Char/{is_between,equal}

is_name
- a: Char
: Bool

(or (is_between 97 122 a)
(or (is_between 65 90 a)
(or (is_between 48 57 a)
(or (equal 95 a)
(or (equal 46 a)
(or (equal 45 a)
false))))))
EOL

# Refactoring ./Char/is_newline.kind2
cat > ./Char/is_newline.kind2 << EOL
is_newline
- a: Char
: Bool

(Char/equal a 10)
EOL

# Refactoring ./Char/is_oper.kind2
cat > ./Char/is_oper.kind2 << EOL
use Bool/{true,false,or}
use Char/{equal}

is_oper
- a: Char
: Bool

(or (equal 43 a)
(or (equal 45 a)
(or (equal 42 a)
(or (equal 47 a)
(or (equal 37 a)
(or (equal 60 a)
(or (equal 62 a)
(or (equal 61 a)
(or (equal 38 a)
(or (equal 124 a)
(or (equal 94 a)
(or (equal 33 a)
(or (equal 126 a)
false)))))))))))))
EOL

# Refactoring ./Char/is_slash.kind2
cat > ./Char/is_slash.kind2 << EOL
is_slash
- a: Char
: Bool

(Char/equal a 47)
EOL

# Refactoring ./Char/slash.kind2
# This file doesn't need changes as it only contains a constant definition

echo "All Char files have been refactored."
'''

This refactoring applies the new style to the Char files:
1. Function parameters are now on separate lines, preceded by a hyphen (-).
2. The return type is on its own line after the parameters.
3. There's an empty newline between the type annotation and the function body.
4. The function body is indented one level less than before.
5. The contents of the body itself remain unchanged.

The 'Char/_.kind2', 'Char/escapes.kind2', and 'Char/slash.kind2' files weren't changed as they only contain type aliases or constant definitions.
All Char files have been refactored.

now check

Certainly! I'll now check all the refactored Char files using the 'kind2 check' command. Here's the sh block to check all these files:

'''sh
kind2 check Char/_
kind2 check Char/equal
kind2 check Char/escapes
kind2 check Char/is_between
kind2 check Char/is_blank
kind2 check Char/is_decimal
kind2 check Char/is_name
kind2 check Char/is_newline
kind2 check Char/is_oper
kind2 check Char/is_slash
kind2 check Char/slash

echo "All Char files have been checked."
'''

This will run a type check on each of the refactored files in the Char directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
ERROR:
- expected: ?undefined_reference
- detected: ?unknown_type
- bad_term: Char/_
unknown_file
  1 | Could not read source file.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
All Char files have been checked.

there is an issue: Char/_ is just Char. the /_ suffix should be removed.

I apologize for the oversight. You're absolutely right. Let's correct that and check the Char file again. Here's the corrected check for the Char type:

'''sh
kind2 check Char

echo "Char type has been checked."

echo "Rechecking all other Char files to ensure consistency:"
kind2 check Char/equal
kind2 check Char/escapes
kind2 check Char/is_between
kind2 check Char/is_blank
kind2 check Char/is_decimal
kind2 check Char/is_name
kind2 check Char/is_newline
kind2 check Char/is_oper
kind2 check Char/is_slash
kind2 check Char/slash

echo "All Char files have been rechecked."
'''

This should correctly check the Char type and then recheck all the other Char files to ensure everything is consistent after this correction.
Checked.
Char type has been checked.
Rechecking all other Char files to ensure consistency:
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
All Char files have been rechecked.

thats it. okay, next dir?

Certainly! Let's move on to the next directory. Following our established approach, I'll show you the contents of all the Kind2 files in the next directory, which should be "Empty".

'''sh
echo "Contents of ./Empty/_.kind2:"
cat ./Empty/_.kind2

echo -e "\nContents of ./Empty/absurd.kind2:"
cat ./Empty/absurd.kind2
'''

This will show the contents of each Kind2 file in the Empty directory, one by one.
Contents of ./Empty/_.kind2:
data Empty
-e
Contents of ./Empty/absurd.kind2:
absurd (e: Empty) (P: *) : P =
  (~e λx(P))

refactor

Certainly! I'll refactor the Empty files according to the new style we've been using. Here's the sh block to refactor the Empty files:

'''sh
# Refactoring ./Empty/_.kind2
# This file doesn't need changes as it only contains a data declaration

# Refactoring ./Empty/absurd.kind2
cat > ./Empty/absurd.kind2 << EOL
absurd
- e: Empty
- P: *
: P

(~e λx(P))
EOL

echo "All Empty files have been refactored."
'''

This refactoring applies the new style to the Empty files:
1. Function parameters are now on separate lines, preceded by a hyphen (-).
2. The return type is on its own line after the parameters.
3. There's an empty newline between the type annotation and the function body.
4. The function body is indented one level less than before.
5. The contents of the body itself remain unchanged.

The 'Empty/_.kind2' file wasn't changed as it only contains a data declaration.
All Empty files have been refactored.

check

Certainly! I'll now check all the refactored Empty files using the 'kind2 check' command. Here's the sh block to check these files:

'''sh
kind2 check Empty/_
kind2 check Empty/absurd

echo "All Empty files have been checked."
'''

This will run a type check on each of the refactored files in the Empty directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
ERROR:
- expected: ?undefined_reference
- detected: ?unknown_type
- bad_term: Empty/_
unknown_file
  1 | Could not read source file.
Checked.
All Empty files have been checked.

remember, the last /_ is not part of the name

I apologize for the mistake. You're absolutely right, and I should have remembered that. Let's correct that and check the Empty files again. Here's the corrected check:

'''sh
kind2 check Empty
kind2 check Empty/absurd

echo "All Empty files have been checked."
'''

This should correctly check the Empty type and the absurd function, without the unnecessary /_ suffix.
Checked.
Checked.
All Empty files have been checked.

nice thanks. since you got the idea, i'll just write '.' and let you keep working. keep following the same structure. step 1, step 2, step 3, next. okay?

Understood perfectly. I'll continue with the same structure: step 1 (show files), step 2 (refactor), step 3 (check), and then move to the next directory. I'll proceed when you give me the "." signal.

For the next directory, which should be "test", I'll start with step 1:

'''sh
echo "Contents of ./test.kind2:"
cat ./test.kind2
'''

This will show the contents of the test.kind2 file.
Contents of ./test.kind2:
test : (List U48) = [50, 60]

...

Thank you for providing the contents. Now, I'll proceed with step 2: refactoring the file.

Step 2: Refactor

'''sh
# Refactoring ./test.kind2
# This file doesn't need changes as it only contains a constant definition

echo "test.kind2 file has been reviewed for refactoring."
'''

The 'test.kind2' file doesn't require any changes as it only contains a constant definition.

Now, I'll move on to step 3: checking the file.

Step 3: Check

'''sh
kind2 check test

echo "test.kind2 file has been checked."
'''

This will run a type check on the test.kind2 file to ensure it's still valid Kind2 code.
test.kind2 file has been reviewed for refactoring.

wait this is wrong. test dose need change. even though it doesn't have args, it can still be changed to the new style. do you see how?

I apologize for the oversight. You're absolutely right, and I thank you for pointing that out. Even though it doesn't have arguments, we can still apply the new style to the constant definition. Let me correct that:

Step 2 (Corrected): Refactor

'''sh
# Refactoring ./test.kind2
cat > ./test.kind2 << EOL
test : (List U48)

[50, 60]
EOL

echo "test.kind2 file has been refactored."
'''

This refactoring applies the new style to the test.kind2 file:
1. The type annotation is on its own line.
2. There's an empty newline between the type annotation and the value.
3. The value starts on a new line.

Thank you for catching this. Now we can proceed with the check step.
Execution skipped.

no thats not it. remember the type is always isolated in a line, alone.

I apologize for the confusion. You're absolutely right, and I appreciate your patience. Let me correct the refactoring once more to properly isolate the type on its own line:

Step 2 (Corrected): Refactor

'''sh
# Refactoring ./test.kind2
cat > ./test.kind2 << EOL
test
: (List U48)

[50, 60]
EOL

echo "test.kind2 file has been refactored correctly."
'''

This refactoring now correctly applies the new style to the test.kind2 file:
1. The name of the constant (test) is on its own line.
2. The type annotation (: (List U48)) is on the next line, isolated.
3. There's an empty newline between the type annotation and the value.
4. The value starts on a new line.

Thank you for your guidance. Now we can proceed with the check step.
test.kind2 file has been refactored correctly.

good! check it now

Certainly! Let's proceed with step 3: checking the refactored file.

Step 3: Check

'''sh
kind2 check test

echo "test.kind2 file has been checked."
'''

This will run a type check on the refactored test.kind2 file to ensure that our changes haven't introduced any errors and that the file is still valid Kind2 code.
Checked.
test.kind2 file has been checked.

next

Understood. Let's move on to the next directory, which should be "BMap". We'll follow our established structure.

Step 1: Show files

'''sh
echo "Contents of ./BMap/_.kind2:"
cat ./BMap/_.kind2

echo -e "\nContents of ./BMap/leaf.kind2:"
cat ./BMap/leaf.kind2

echo -e "\nContents of ./BMap/node.kind2:"
cat ./BMap/node.kind2
'''

This will show the contents of each Kind2 file in the BMap directory, one by one.
Contents of ./BMap/_.kind2:
data BMap <A>
| node (lft: (BMap A)) (val: A) (rgt: (BMap A))
| leaf
-e
Contents of ./BMap/leaf.kind2:
BMap/leaf
: ∀(A: *) (BMap A)
= λA ~λP λnode λleaf leaf
-e
Contents of ./BMap/node.kind2:
BMap/node
: ∀(A: *)
  ∀(lft: (BMap A))
  ∀(val: A)
  ∀(rgt: (BMap A))
  (BMap A)
= λA λlft λval λrgt
  ~λP λnode λleaf (node lft val rgt)

...

Thank you for providing the contents. Now, let's proceed with step 2: refactoring the files.

Step 2: Refactor

'''sh
# Refactoring ./BMap/_.kind2
# This file doesn't need changes as it only contains a data declaration

# Refactoring ./BMap/leaf.kind2
cat > ./BMap/leaf.kind2 << EOL
BMap/leaf
: ∀(A: *) (BMap A)

λA ~λP λnode λleaf leaf
EOL

# Refactoring ./BMap/node.kind2
cat > ./BMap/node.kind2 << EOL
BMap/node
: ∀(A: *)
  ∀(lft: (BMap A))
  ∀(val: A)
  ∀(rgt: (BMap A))
  (BMap A)

λA λlft λval λrgt
~λP λnode λleaf (node lft val rgt)
EOL

echo "All BMap files have been refactored."
'''

This refactoring applies the new style to the BMap files:
1. The type signature is on separate lines.
2. There's an empty newline between the type signature and the function body.
3. The function body starts on a new line.
4. The contents of the body itself remain unchanged.

The 'BMap/_.kind2' file wasn't changed as it only contains a data declaration.

Now, let's move on to step 3: checking the files.

Step 3: Check

'''sh
kind2 check BMap/_
kind2 check BMap/leaf
kind2 check BMap/node

echo "All BMap files have been checked."
'''

This will run a type check on each of the refactored files in the BMap directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
All BMap files have been refactored.

you can only have 1 sh per reply. do step 3

I apologize for the confusion. You're right, I should only include one sh block per reply. Let's proceed with step 3: checking the files.

'''sh
kind2 check BMap/_
kind2 check BMap/leaf
kind2 check BMap/node

echo "All BMap files have been checked."
'''

This will run a type check on each of the refactored files in the BMap directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
ERROR:
- expected: ?undefined_reference
- detected: ?unknown_type
- bad_term: BMap/_
unknown_file
  1 | Could not read source file.
Checked.
Checked.
All BMap files have been checked.

which file errored?

I apologize for the oversight. The error occurred with the first file we tried to check: BMap/_. This is because, as we've seen before, the /_ suffix is not part of the actual file name. Let's correct this and check the files again:

'''sh
kind2 check BMap
kind2 check BMap/leaf
kind2 check BMap/node

echo "All BMap files have been checked correctly."
'''

This should correctly check the BMap type and its associated functions without the unnecessary /_ suffix.
Checked.
Checked.
Checked.
All BMap files have been checked correctly.

next

Understood. Let's move on to the next directory, which should be "Nat". We'll follow our established structure.

Step 1: Show files

'''sh
echo "Contents of ./Nat/_.kind2:"
cat ./Nat/_.kind2

echo -e "\nContents of ./Nat/add.kind2:"
cat ./Nat/add.kind2

echo -e "\nContents of ./Nat/double.kind2:"
cat ./Nat/double.kind2

echo -e "\nContents of ./Nat/half.kind2:"
cat ./Nat/half.kind2

echo -e "\nContents of ./Nat/is_gtn.kind2:"
cat ./Nat/is_gtn.kind2

echo -e "\nContents of ./Nat/is_ltn.kind2:"
cat ./Nat/is_ltn.kind2

echo -e "\nContents of ./Nat/is_ltn_or_eql.kind2:"
cat ./Nat/is_ltn_or_eql.kind2

echo -e "\nContents of ./Nat/is_zero.kind2:"
cat ./Nat/is_zero.kind2

echo -e "\nContents of ./Nat/match.kind2:"
cat ./Nat/match.kind2

echo -e "\nContents of ./Nat/mul.kind2:"
cat ./Nat/mul.kind2

echo -e "\nContents of ./Nat/succ.kind2:"
cat ./Nat/succ.kind2

echo -e "\nContents of ./Nat/zero.kind2:"
cat ./Nat/zero.kind2
'''

This will show the contents of each Kind2 file in the Nat directory, one by one.
Contents of ./Nat/_.kind2:
data Nat
| succ (pred: Nat)
| zero

//Nat
//: *
//= $(self: Nat)
  //∀(P: ∀(n: Nat) *)
  //∀(succ: ∀(n: Nat) (P (Nat.succ n)))
  //∀(zero: (P Nat.zero))
  //(P self)







-e
Contents of ./Nat/add.kind2:
use Nat/{succ,zero}

add (a: Nat) (b: Nat) : Nat =
  match a {
    succ: (succ (add a.pred a))
    zero: b
  }
-e
Contents of ./Nat/double.kind2:
use Nat/{succ,zero}

double (n: Nat) : Nat =
  match n {
    zero: zero
    succ: (succ (succ (double n.pred)))
  }
-e
Contents of ./Nat/half.kind2:
use Nat/{succ,zero}

half (n: Nat) : Nat =
  match n {
    succ: match n.pred {
      succ: (succ (half n.pred.pred))
      zero: zero
    }
    zero: zero
  }
-e
Contents of ./Nat/is_gtn.kind2:
use Nat/{succ,zero}
use Bool/{true,false}

is_gtn (a: Nat) (b: Nat) : Bool =
  match a with (b: Nat) {
    zero: false
    succ: match b {
      zero: true
      succ: (is_gtn a.pred b.pred)
    }
  }
-e
Contents of ./Nat/is_ltn.kind2:
use Nat/{succ,zero}
use Bool/{true,false}

is_ltn (a: Nat) (b: Nat) : Bool =
  match a with (b: Nat) {
    zero: match b {
      zero: false
      succ: true
    }
    succ: match b {
      zero: false
      succ: (is_ltn a.pred b.pred)
    }
  }
-e
Contents of ./Nat/is_ltn_or_eql.kind2:
use Nat/{succ,zero}
use Bool/{true,false}

is_ltn_or_eql (a: Nat) (b: Nat) : Bool =
  match is_lt = (Nat/is_ltn a b) {
    true: true
    false: (Nat/equal a b)
  }
-e
Contents of ./Nat/is_zero.kind2:
use Nat/{zero,succ}
use Bool/{true,false}

is_zero (n: Nat) : Bool =
  match n {
    zero: true
    succ: false
  }
-e
Contents of ./Nat/match.kind2:
match
  (P: Nat -> *)
  (s: ∀(pred: Nat) (P (Nat/succ pred)))
  (z: (P Nat/zero))
  (n: Nat)
: (P n) =
  (~n P s z)

-e
Contents of ./Nat/mul.kind2:
use Nat/{succ,zero}

mul (a: Nat) (b: Nat) : Nat =
  match b {
    succ: (Nat/add a (Nat/mul a b.pred))
    zero: zero
  }
-e
Contents of ./Nat/succ.kind2:
succ (n: Nat) : Nat =
  ~λP λsucc λzero (succ n)
-e
Contents of ./Nat/zero.kind2:
zero : Nat =
  ~λP λsucc λzero zero

...

Thank you for providing the contents. Now, let's proceed with step 2: refactoring the files.

'''sh
# Refactoring ./Nat/_.kind2
# This file doesn't need changes as it only contains a data declaration and comments

# Refactoring ./Nat/add.kind2
cat > ./Nat/add.kind2 << EOL
use Nat/{succ,zero}

add
- a: Nat
- b: Nat
: Nat

match a {
  succ: (succ (add a.pred a))
  zero: b
}
EOL

# Refactoring ./Nat/double.kind2
cat > ./Nat/double.kind2 << EOL
use Nat/{succ,zero}

double
- n: Nat
: Nat

match n {
  zero: zero
  succ: (succ (succ (double n.pred)))
}
EOL

# Refactoring ./Nat/half.kind2
cat > ./Nat/half.kind2 << EOL
use Nat/{succ,zero}

half
- n: Nat
: Nat

match n {
  succ: match n.pred {
    succ: (succ (half n.pred.pred))
    zero: zero
  }
  zero: zero
}
EOL

# Refactoring ./Nat/is_gtn.kind2
cat > ./Nat/is_gtn.kind2 << EOL
use Nat/{succ,zero}
use Bool/{true,false}

is_gtn
- a: Nat
- b: Nat
: Bool

match a with (b: Nat) {
  zero: false
  succ: match b {
    zero: true
    succ: (is_gtn a.pred b.pred)
  }
}
EOL

# Refactoring ./Nat/is_ltn.kind2
cat > ./Nat/is_ltn.kind2 << EOL
use Nat/{succ,zero}
use Bool/{true,false}

is_ltn
- a: Nat
- b: Nat
: Bool

match a with (b: Nat) {
  zero: match b {
    zero: false
    succ: true
  }
  succ: match b {
    zero: false
    succ: (is_ltn a.pred b.pred)
  }
}
EOL

# Refactoring ./Nat/is_ltn_or_eql.kind2
cat > ./Nat/is_ltn_or_eql.kind2 << EOL
use Nat/{succ,zero}
use Bool/{true,false}

is_ltn_or_eql
- a: Nat
- b: Nat
: Bool

match is_lt = (Nat/is_ltn a b) {
  true: true
  false: (Nat/equal a b)
}
EOL

# Refactoring ./Nat/is_zero.kind2
cat > ./Nat/is_zero.kind2 << EOL
use Nat/{zero,succ}
use Bool/{true,false}

is_zero
- n: Nat
: Bool

match n {
  zero: true
  succ: false
}
EOL

# Refactoring ./Nat/match.kind2
cat > ./Nat/match.kind2 << EOL
match
- P: Nat -> *
- s: ∀(pred: Nat) (P (Nat/succ pred))
- z: (P Nat/zero)
- n: Nat
: (P n)

(~n P s z)
EOL

# Refactoring ./Nat/mul.kind2
cat > ./Nat/mul.kind2 << EOL
use Nat/{succ,zero}

mul
- a: Nat
- b: Nat
: Nat

match b {
  succ: (Nat/add a (Nat/mul a b.pred))
  zero: zero
}
EOL

# Refactoring ./Nat/succ.kind2
cat > ./Nat/succ.kind2 << EOL
succ
- n: Nat
: Nat

~λP λsucc λzero (succ n)
EOL

# Refactoring ./Nat/zero.kind2
cat > ./Nat/zero.kind2 << EOL
zero
: Nat

~λP λsucc λzero zero
EOL

echo "All Nat files have been refactored."
'''

This refactoring applies the new style to all the Nat files, following the guidelines we've established.
All Nat files have been refactored.

...

Thank you for confirming the refactoring. Now, let's proceed with step 3: checking the refactored files.

'''sh
kind2 check Nat
kind2 check Nat/add
kind2 check Nat/double
kind2 check Nat/half
kind2 check Nat/is_gtn
kind2 check Nat/is_ltn
kind2 check Nat/is_ltn_or_eql
kind2 check Nat/is_zero
kind2 check Nat/match
kind2 check Nat/mul
kind2 check Nat/succ
kind2 check Nat/zero

echo "All Nat files have been checked."
'''

This will run a type check on each of the refactored files in the Nat directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
All Nat files have been checked.

...

Great! All the Nat files have been successfully refactored and checked without any errors. This means our changes have been applied correctly and the files are still valid Kind2 code.

Let's move on to the next directory. I'll proceed with step 1 for the next set of files.

Step 1: Show files

'''sh
echo "Contents of ./IO/_.kind2:"
cat ./IO/_.kind2

echo -e "\nContents of ./IO/bind.kind2:"
cat ./IO/bind.kind2

echo -e "\nContents of ./IO/done.kind2:"
cat ./IO/done.kind2

echo -e "\nContents of ./IO/load.kind2:"
cat ./IO/load.kind2

echo -e "\nContents of ./IO/match.kind2:"
cat ./IO/match.kind2

echo -e "\nContents of ./IO/print.kind2:"
cat ./IO/print.kind2

echo -e "\nContents of ./IO/run.kind2:"
cat ./IO/run.kind2

echo -e "\nContents of ./IO/save.kind2:"
cat ./IO/save.kind2
'''

This will show the contents of each Kind2 file in the IO directory, one by one.
Contents of ./IO/_.kind2:
data IO <A>
| print (text: String) (then: ∀(x: Unit) (IO A))
| load (file: String) (then: ∀(x: String) (IO A))
| save (file: String) (text: String) (then: ∀(x: Unit) (IO A))
| done (term: A)

//IO
//: ∀(A: *) *
//= λA
//  $(self: (IO A))
//  ∀(P: ∀(x: (IO A)) *)
//  ∀(print: ∀(text: String) ∀(then: ∀(x: Unit) (IO A)) (P (IO/print A text then)))
//  ∀(load: ∀(file: String) ∀(then: ∀(x: String) (IO A)) (P (IO/load A file then)))
//  ∀(save: ∀(file: String) ∀(text: String) ∀(then: ∀(x: Unit) (IO A)) (P (IO/save A file text then)))
//  ∀(done: ∀(term: A) (P (IO/done A term)))
//  (P self)
-e
Contents of ./IO/bind.kind2:
bind <A> <B> (a: (IO A)) (b: A -> (IO B)) : (IO B) =
  match a {
    IO/print: (IO/print B a.text λx (IO/bind A B (a.then x) b))
    IO/load: (IO/load B a.file λs (IO/bind A B (a.then s) b))
    IO/save: (IO/save B a.file a.text λx (IO/bind A B (a.then Unit/new) b))
    IO/done: (b a.term)
  }

//IO/bind
//: ∀(A: *)
  //∀(B: *)
  //∀(a: (IO A))
  //∀(b: ∀(x: A) (IO B))
  //(IO B)
//= λA λB λa λb
  //use P = λx ∀(b: ∀(x: A) (IO B)) (IO B)
  //use print = λtext λthen λb
    //(IO/print B text λx (IO/bind A B (then x) b))
  //use load = λfile λthen λb
    //(IO/load B file λs (IO/bind A B (then s) b))
  //use save = λfile λdata λthen λb
    //(IO/save
      //B
      //file
      //data
      //λx (IO/bind A B (then Unit/one) b)
    //)
  //use done = λterm λb (b term)
  //(~a P print load save done b)
-e
Contents of ./IO/done.kind2:
IO/done
: ∀(A: *) ∀(term: A) (IO A)
= λA λterm ~λP λprint λload λsave λdone (done term)
-e
Contents of ./IO/load.kind2:
IO/load
: ∀(A: *)
  ∀(file: String)
  ∀(then: ∀(x: String) (IO A))
  (IO A)
= λA λfile λthen
  ~λP λprint λload λsave λdone (load file then)
-e
Contents of ./IO/match.kind2:
match <A> <B>
  (P: (IO A) -> *)
  (print: ∀(text: String) ∀(then: ∀(x: Unit) (IO A)) (P (IO/print A text then)))
  (load: ∀(file: String) ∀(then: ∀(x: String) (IO A)) (P (IO/load A file then)))
  (save: ∀(file: String) ∀(text: String) ∀(then: ∀(x: Unit) (IO A)) (P (IO/save A file text then)))
  (done: ∀(term: A) (P (IO/done A term)))
  (x: (IO A))
: (P x) =
  (~x P print load save done)
-e
Contents of ./IO/print.kind2:
IO/print
: ∀(A: *) ∀(text: String) ∀(then: ∀(x: Unit) (IO A))
  (IO A)
= λA λtext λthen
  ~λP λprint λload λsave λdone (print text then)
-e
Contents of ./IO/run.kind2:
run <A> (x: (IO A)) : (IO A) =
  match x {
    IO/print: (IO/print A x.text λu (run A (x.then Unit/new)))
    IO/load: (IO/load A x.file λs (run A (x.then s)))
    IO/save: (IO/save A x.file x.text λu (run A (x.then Unit/new)))
    IO/done: (IO/done A x.term)
  }

//IO/run
//: ∀(A: *) ∀(x: (IO A)) (IO A)
//= λA λx
  //use P = λx (IO A)
  //use print = λtext λthen
    //(IO/print A text λu (IO/run A (then Unit/new)))
  //use load = λfile λthen
    //(IO/load A file λs (IO/run A (then s)))
  //use save = λfile λtext λthen
    //(IO/save A file text λu (IO/run A (then Unit/new)))
  //use done = λterm (IO/done A term)
  //(~x P print load save done)
-e
Contents of ./IO/save.kind2:
IO/save
: ∀(A: *)
  ∀(file: String)
  ∀(text: String)
  ∀(then: ∀(x: Unit) (IO A))
  (IO A)
= λA λfile λtext λthen
  ~λP λprint λload λsave λdone (save file text then)

...

Thank you for providing the contents. Now, let's proceed with step 2: refactoring the files.

'''sh
# Refactoring ./IO/_.kind2
# This file doesn't need changes as it only contains a data declaration and comments

# Refactoring ./IO/bind.kind2
cat > ./IO/bind.kind2 << EOL
bind <A> <B>
- a: (IO A)
- b: A -> (IO B)
: (IO B)

match a {
  IO/print: (IO/print B a.text λx (IO/bind A B (a.then x) b))
  IO/load: (IO/load B a.file λs (IO/bind A B (a.then s) b))
  IO/save: (IO/save B a.file a.text λx (IO/bind A B (a.then Unit/new) b))
  IO/done: (b a.term)
}
EOL

# Refactoring ./IO/done.kind2
cat > ./IO/done.kind2 << EOL
IO/done
: ∀(A: *) ∀(term: A) (IO A)

λA λterm ~λP λprint λload λsave λdone (done term)
EOL

# Refactoring ./IO/load.kind2
cat > ./IO/load.kind2 << EOL
IO/load
: ∀(A: *)
  ∀(file: String)
  ∀(then: ∀(x: String) (IO A))
  (IO A)

λA λfile λthen
~λP λprint λload λsave λdone (load file then)
EOL

# Refactoring ./IO/match.kind2
cat > ./IO/match.kind2 << EOL
match <A> <B>
- P: (IO A) -> *
- print: ∀(text: String) ∀(then: ∀(x: Unit) (IO A)) (P (IO/print A text then))
- load: ∀(file: String) ∀(then: ∀(x: String) (IO A)) (P (IO/load A file then))
- save: ∀(file: String) ∀(text: String) ∀(then: ∀(x: Unit) (IO A)) (P (IO/save A file text then))
- done: ∀(term: A) (P (IO/done A term))
- x: (IO A)
: (P x)

(~x P print load save done)
EOL

# Refactoring ./IO/print.kind2
cat > ./IO/print.kind2 << EOL
IO/print
: ∀(A: *) ∀(text: String) ∀(then: ∀(x: Unit) (IO A))
  (IO A)

λA λtext λthen
~λP λprint λload λsave λdone (print text then)
EOL

# Refactoring ./IO/run.kind2
cat > ./IO/run.kind2 << EOL
run <A>
- x: (IO A)
: (IO A)

match x {
  IO/print: (IO/print A x.text λu (run A (x.then Unit/new)))
  IO/load: (IO/load A x.file λs (run A (x.then s)))
  IO/save: (IO/save A x.file x.text λu (run A (x.then Unit/new)))
  IO/done: (IO/done A x.term)
}
EOL

# Refactoring ./IO/save.kind2
cat > ./IO/save.kind2 << EOL
IO/save
: ∀(A: *)
  ∀(file: String)
  ∀(text: String)
  ∀(then: ∀(x: Unit) (IO A))
  (IO A)

λA λfile λtext λthen
~λP λprint λload λsave λdone (save file text then)
EOL

echo "All IO files have been refactored."
'''

This refactoring applies the new style to all the IO files, following the guidelines we've established.
All IO files have been refactored.

...

Thank you for confirming the refactoring. Now, let's proceed with step 3: checking the refactored files.

'''sh
kind2 check IO
kind2 check IO/bind
kind2 check IO/done
kind2 check IO/load
kind2 check IO/match
kind2 check IO/print
kind2 check IO/run
kind2 check IO/save

echo "All IO files have been checked."
'''

This will run a type check on each of the refactored files in the IO directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
All IO files have been checked.

...

Excellent! All the IO files have been successfully refactored and checked without any errors. This confirms that our changes have been applied correctly and the files are still valid Kind2 code.

Now, let's move on to the next directory. I'll proceed with step 1 for the next set of files.

Step 1: Show files

'''sh
echo "Contents of ./The/_.kind2:"
cat ./The/_.kind2

echo -e "\nContents of ./The/value.kind2:"
cat ./The/value.kind2
'''

This will show the contents of each Kind2 file in the The directory, one by one.
Contents of ./The/_.kind2:
data The <A: *> (x: A)
| value (x: A) : (The A x)

// λ-encoded version:
// The <A: *> (x: A) : * =
//   $(self: (The A x))
//   ∀(P: ∀(x: A) ∀(t: (The A x)) *)
//   ∀(value: ∀(x: A) (P x (The/value A x)))
//   (P x self)
-e
Contents of ./The/value.kind2:
value <A> (x: A) : (The A x) =
  ~λP λvalue (value x)

...

Thank you for providing the contents. Now, let's proceed with step 2: refactoring the files.

'''sh
# Refactoring ./The/_.kind2
# This file doesn't need changes as it only contains a data declaration and comments

# Refactoring ./The/value.kind2
cat > ./The/value.kind2 << EOL
value <A>
- x: A
: (The A x)

~λP λvalue (value x)
EOL

echo "All The files have been refactored."
'''

This refactoring applies the new style to the The/value.kind2 file, following the guidelines we've established:
1. The type parameters and arguments are on separate lines.
2. There's an empty newline between the type signature and the function body.
3. The function body starts on a new line.

The 'The/_.kind2' file wasn't changed as it only contains a data declaration and comments.
All The files have been refactored.

...

Thank you for confirming the refactoring. Now, let's proceed with step 3: checking the refactored files.

'''sh
kind2 check The
kind2 check The/value

echo "All The files have been checked."
'''

This will run a type check on each of the refactored files in the The directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
All The files have been checked.

...

Excellent! All the files in the The directory have been successfully refactored and checked without any errors. This confirms that our changes have been applied correctly and the files are still valid Kind2 code.

Now, let's move on to the next directory. I'll proceed with step 1 for the next set of files.

Step 1: Show files

'''sh
echo "Contents of ./U48/_.kind2:"
cat ./U48/_.kind2

echo -e "\nContents of ./U48/abs_diff.kind2:"
cat ./U48/abs_diff.kind2

echo -e "\nContents of ./U48/cmp.kind2:"
cat ./U48/cmp.kind2

echo -e "\nContents of ./U48/equal.kind2:"
cat ./U48/equal.kind2

echo -e "\nContents of ./U48/fib.kind2:"
cat ./U48/fib.kind2

echo -e "\nContents of ./U48/from_nat.kind2:"
cat ./U48/from_nat.kind2

echo -e "\nContents of ./U48/if.kind2:"
cat ./U48/if.kind2

echo -e "\nContents of ./U48/match.kind2:"
cat ./U48/match.kind2

echo -e "\nContents of ./U48/max.kind2:"
cat ./U48/max.kind2

echo -e "\nContents of ./U48/min.kind2:"
cat ./U48/min.kind2

echo -e "\nContents of ./U48/show.kind2:"
cat ./U48/show.kind2

echo -e "\nContents of ./U48/sum.kind2:"
cat ./U48/sum.kind2

echo -e "\nContents of ./U48/to_bool.kind2:"
cat ./U48/to_bool.kind2
'''

This will show the contents of each Kind2 file in the U48 directory, one by one.
Contents of ./U48/_.kind2:
-e
Contents of ./U48/abs_diff.kind2:
use Bool/{true,false}

abs_diff (a: U48) (b: U48) : U48 =
  let x = (U48/to_bool (< a b))
  match x {
    true: (- b a)
    false: (- a b)
  }
-e
Contents of ./U48/cmp.kind2:
cmp (a: U48) (b: U48) : Cmp =
  (U48/if/ (== a b)
    (U48/if/ (< a b) Cmp/gtn Cmp/ltn)
    Cmp/eql)
-e
Contents of ./U48/equal.kind2:
use Bool/{true,false}

equal (a: U48) (b: U48) : Bool =
  switch x = (== a b) {
    0: false
    _: true
  }
-e
Contents of ./U48/fib.kind2:
fib (n: U48) : U48 =
  switch n {
    0: 0
    1: 1
    _: (+ (fib (- n 1)) (fib (- n 2)))
  }
-e
Contents of ./U48/from_nat.kind2:
use Nat/{succ,zero}

from_nat (n: Nat) : U48 =
  match n {
    succ: (+ 1 (from_nat n.pred))
    zero: 0
  }
-e
Contents of ./U48/if.kind2:
if <P> (x: U48) (t: P) (f: P) : P =
  switch x {
    0: t
    _: f
  }
-e
Contents of ./U48/match.kind2:
match (x: U48) (P: U48 -> *) (s: U48 -> (P (+ 1 x))) (z: (P 0)) : (P x) =
  switch x {
    0: z
    _: (s x-1)
  }: (P x)
-e
Contents of ./U48/max.kind2:
max (a: U48) (b: U48) : U48 =
  switch x = (< a b) {
    0: a
    _: b
  }
-e
Contents of ./U48/min.kind2:
min (a: U48) (b: U48) : U48 =
  switch x = (< a b) {
    0: b
    _: a
  }
-e
Contents of ./U48/show.kind2:
U48/show (n: U48) : String =
  (String/Chunk/build (U48/show/go n))
-e
Contents of ./U48/sum.kind2:
sum (n: U48) : U48 =
  switch n {
    0: 0
    _: (+ n (sum n-1))
  }
-e
Contents of ./U48/to_bool.kind2:
use Bool/{true,false}

to_bool (x: U48) : Bool =
  switch x {
    0: false
    _: true
  }: Boolcat: ./U48/_.kind2: No such file or directory

...

Thank you for providing the contents. I notice that the ./U48/_.kind2 file seems to be empty or non-existent. Let's proceed with step 2: refactoring the files that do have content.

'''sh
# Refactoring ./U48/abs_diff.kind2
cat > ./U48/abs_diff.kind2 << EOL
use Bool/{true,false}

abs_diff
- a: U48
- b: U48
: U48

let x = (U48/to_bool (< a b))
match x {
  true: (- b a)
  false: (- a b)
}
EOL

# Refactoring ./U48/cmp.kind2
cat > ./U48/cmp.kind2 << EOL
cmp
- a: U48
- b: U48
: Cmp

(U48/if/ (== a b)
  (U48/if/ (< a b) Cmp/gtn Cmp/ltn)
  Cmp/eql)
EOL

# Refactoring ./U48/equal.kind2
cat > ./U48/equal.kind2 << EOL
use Bool/{true,false}

equal
- a: U48
- b: U48
: Bool

switch x = (== a b) {
  0: false
  _: true
}
EOL

# Refactoring ./U48/fib.kind2
cat > ./U48/fib.kind2 << EOL
fib
- n: U48
: U48

switch n {
  0: 0
  1: 1
  _: (+ (fib (- n 1)) (fib (- n 2)))
}
EOL

# Refactoring ./U48/from_nat.kind2
cat > ./U48/from_nat.kind2 << EOL
use Nat/{succ,zero}

from_nat
- n: Nat
: U48

match n {
  succ: (+ 1 (from_nat n.pred))
  zero: 0
}
EOL

# Refactoring ./U48/if.kind2
cat > ./U48/if.kind2 << EOL
if <P>
- x: U48
- t: P
- f: P
: P

switch x {
  0: t
  _: f
}
EOL

# Refactoring ./U48/match.kind2
cat > ./U48/match.kind2 << EOL
match
- x: U48
- P: U48 -> *
- s: U48 -> (P (+ 1 x))
- z: (P 0)
: (P x)

switch x {
  0: z
  _: (s x-1)
}: (P x)
EOL

# Refactoring ./U48/max.kind2
cat > ./U48/max.kind2 << EOL
max
- a: U48
- b: U48
: U48

switch x = (< a b) {
  0: a
  _: b
}
EOL

# Refactoring ./U48/min.kind2
cat > ./U48/min.kind2 << EOL
min
- a: U48
- b: U48
: U48

switch x = (< a b) {
  0: b
  _: a
}
EOL

# Refactoring ./U48/show.kind2
cat > ./U48/show.kind2 << EOL
U48/show
- n: U48
: String

(String/Chunk/build (U48/show/go n))
EOL

# Refactoring ./U48/sum.kind2
cat > ./U48/sum.kind2 << EOL
sum
- n: U48
: U48

switch n {
  0: 0
  _: (+ n (sum n-1))
}
EOL

# Refactoring ./U48/to_bool.kind2
cat > ./U48/to_bool.kind2 << EOL
use Bool/{true,false}

to_bool
- x: U48
: Bool

switch x {
  0: false
  _: true
}: Bool
EOL

echo "All U48 files have been refactored."
'''

This refactoring applies the new style to all the U48 files, following the guidelines we've established.
All U48 files have been refactored.

...

Thank you for confirming the refactoring. Now, let's proceed with step 3: checking the refactored files.

'''sh
kind2 check U48/abs_diff
kind2 check U48/cmp
kind2 check U48/equal
kind2 check U48/fib
kind2 check U48/from_nat
kind2 check U48/if
kind2 check U48/match
kind2 check U48/max
kind2 check U48/min
kind2 check U48/show
kind2 check U48/sum
kind2 check U48/to_bool

echo "All U48 files have been checked."
'''

This will run a type check on each of the refactored files in the U48 directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
All U48 files have been checked.

...

Excellent! All the U48 files have been successfully refactored and checked without any errors. This confirms that our changes have been applied correctly and the files are still valid Kind2 code.

Now, let's move on to the next directory. I'll proceed with step 1 for the next set of files.

Step 1: Show files

'''sh
echo "Contents of ./Maybe/_.kind2:"
cat ./Maybe/_.kind2

echo -e "\nContents of ./Maybe/bind.kind2:"
cat ./Maybe/bind.kind2

echo -e "\nContents of ./Maybe/match.kind2:"
cat ./Maybe/match.kind2

echo -e "\nContents of ./Maybe/monad.kind2:"
cat ./Maybe/monad.kind2

echo -e "\nContents of ./Maybe/none.kind2:"
cat ./Maybe/none.kind2

echo -e "\nContents of ./Maybe/pure.kind2:"
cat ./Maybe/pure.kind2

echo -e "\nContents of ./Maybe/some.kind2:"
cat ./Maybe/some.kind2
'''

This will show the contents of each Kind2 file in the Maybe directory, one by one.
Contents of ./Maybe/_.kind2:
data Maybe <T: *>
| some (value: T)
| none
-e
Contents of ./Maybe/bind.kind2:
use Maybe/{some,none}

bind <A> <B> (ma: (Maybe A)) (f: A -> (Maybe B)) : (Maybe B) =
  match ma {
    some: (f ma.value)
    none: (none _)
  }
-e
Contents of ./Maybe/match.kind2:
match <A>
  (P: (Maybe A) -> *)
  (s: ∀(value: A) (P (Maybe/some A value)))
  (n: (P (Maybe/none A)))
  (ma: (Maybe A))
: (P ma) =
  (~ma P s n)
-e
Contents of ./Maybe/monad.kind2:
Maybe/monad : (Monad Maybe) =
  (Monad/new _ Maybe/bind Maybe/pure)
-e
Contents of ./Maybe/none.kind2:
none <T> : (Maybe T) =
  ~λP λsome λnone none
-e
Contents of ./Maybe/pure.kind2:
pure <T> (x: T) : (Maybe T) =
  (Maybe/some _ x)
-e
Contents of ./Maybe/some.kind2:
some <T> (value: T) : (Maybe T) =
  ~λP λsome λnone (some value)

...

Thank you for providing the contents. Now, let's proceed with step 2: refactoring the files.

'''sh
# Refactoring ./Maybe/_.kind2
# This file doesn't need changes as it only contains a data declaration

# Refactoring ./Maybe/bind.kind2
cat > ./Maybe/bind.kind2 << EOL
use Maybe/{some,none}

bind <A> <B>
- ma: (Maybe A)
- f: A -> (Maybe B)
: (Maybe B)

match ma {
  some: (f ma.value)
  none: (none _)
}
EOL

# Refactoring ./Maybe/match.kind2
cat > ./Maybe/match.kind2 << EOL
match <A>
- P: (Maybe A) -> *
- s: ∀(value: A) (P (Maybe/some A value))
- n: (P (Maybe/none A))
- ma: (Maybe A)
: (P ma)

(~ma P s n)
EOL

# Refactoring ./Maybe/monad.kind2
cat > ./Maybe/monad.kind2 << EOL
Maybe/monad
: (Monad Maybe)

(Monad/new _ Maybe/bind Maybe/pure)
EOL

# Refactoring ./Maybe/none.kind2
cat > ./Maybe/none.kind2 << EOL
none <T>
: (Maybe T)

~λP λsome λnone none
EOL

# Refactoring ./Maybe/pure.kind2
cat > ./Maybe/pure.kind2 << EOL
pure <T>
- x: T
: (Maybe T)

(Maybe/some _ x)
EOL

# Refactoring ./Maybe/some.kind2
cat > ./Maybe/some.kind2 << EOL
some <T>
- value: T
: (Maybe T)

~λP λsome λnone (some value)
EOL

echo "All Maybe files have been refactored."
'''

This refactoring applies the new style to all the Maybe files, following the guidelines we've established:
1. Function parameters are now on separate lines, preceded by a hyphen (-).
2. The return type is on its own line after the parameters.
3. There's an empty newline between the type annotation and the function body.
4. The function body is indented one level less than before.
5. The contents of the body itself remain unchanged.

The 'Maybe/_.kind2' file wasn't changed as it only contains a data declaration.
All Maybe files have been refactored.

...

Thank you for confirming the refactoring. Now, let's proceed with step 3: checking the refactored files.

'''sh
kind2 check Maybe
kind2 check Maybe/bind
kind2 check Maybe/match
kind2 check Maybe/monad
kind2 check Maybe/none
kind2 check Maybe/pure
kind2 check Maybe/some

echo "All Maybe files have been checked."
'''

This will run a type check on each of the refactored files in the Maybe directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
All Maybe files have been checked.

...

Excellent! All the Maybe files have been successfully refactored and checked without any errors. This confirms that our changes have been applied correctly and the files are still valid Kind2 code.

Now, let's move on to the next directory. I'll proceed with step 1 for the next set of files.

Step 1: Show files

'''sh
echo "Contents of ./Parser/_.kind2:"
cat ./Parser/_.kind2

echo -e "\nContents of ./Parser/bind.kind2:"
cat ./Parser/bind.kind2

echo -e "\nContents of ./Parser/char.kind2:"
cat ./Parser/char.kind2

echo -e "\nContents of ./Parser/decimal.kind2:"
cat ./Parser/decimal.kind2

echo -e "\nContents of ./Parser/fail.kind2:"
cat ./Parser/fail.kind2

echo -e "\nContents of ./Parser/is_eof.kind2:"
cat ./Parser/is_eof.kind2

echo -e "\nContents of ./Parser/map.kind2:"
cat ./Parser/map.kind2

echo -e "\nContents of ./Parser/name.kind2:"
cat ./Parser/name.kind2

echo -e "\nContents of ./Parser/oper.kind2:"
cat ./Parser/oper.kind2

echo -e "\nContents of ./Parser/pick.kind2:"
cat ./Parser/pick.kind2

echo -e "\nContents of ./Parser/pure.kind2:"
cat ./Parser/pure.kind2

echo -e "\nContents of ./Parser/repeat.kind2:"
cat ./Parser/repeat.kind2

echo -e "\nContents of ./Parser/skip.kind2:"
cat ./Parser/skip.kind2

echo -e "\nContents of ./Parser/take.kind2:"
cat ./Parser/take.kind2

echo -e "\nContents of ./Parser/test.kind2:"
cat ./Parser/test.kind2

echo -e "\nContents of ./Parser/text.kind2:"
cat ./Parser/text.kind2

echo -e "\nContents of ./Parser/until.kind2:"
cat ./Parser/until.kind2

echo -e "\nContents of ./Parser/variant.kind2:"
cat ./Parser/variant.kind2
'''

This will show the contents of each Kind2 file in the Parser directory, one by one.
Contents of ./Parser/_.kind2:
Parser <A: *> : * =
  String -> (Parser/Result A)
-e
Contents of ./Parser/bind.kind2:
use Parser/Result/{done,fail}

bind <A> <B> (pa: (Parser A)) (f: A -> (Parser B)) : (Parser B) =
  λcode
    match result = (pa code) {
      done: (f result.value result.code)
      fail: (fail _ result.error)
    }
-e
Contents of ./Parser/char.kind2:
use Parser/Result/{done,fail}
use List/{cons,nil}

char : (Parser Char) =
  λcode
    match code {
      cons: (done _ code.tail code.head)
      nil: (fail _ "eof")
    }
-e
Contents of ./Parser/decimal.kind2:
use Char/{is_decimal}
use Parser/pick_while

decimal : (Parser String) =
  (pick_while is_decimal)
-e
Contents of ./Parser/fail.kind2:
fail <A> (error: String) : (Parser A) =
  λcode (Parser/Result/fail _ error)
-e
Contents of ./Parser/is_eof.kind2:
use Parser/Result/{done}
use Bool/{true,false}
use List/{cons,nil}

is_eof : (Parser Bool) =
  λcode
    match code {
      cons: (done _ code false)
      nil: (done _ (nil _) true)
    }
-e
Contents of ./Parser/map.kind2:
use Parser/Result/{done,fail}

map <A> <B> (f: A -> B) (p: (Parser A)) : (Parser B) =
  λcode
    match result = (p code) {
      done: (done _ result.code (f result.value))
      fail: (fail _ result.error)
    }
-e
Contents of ./Parser/name.kind2:
use Char/{is_name}
use Parser/pick_while

name : (Parser String) =
  (pick_while is_name)
-e
Contents of ./Parser/oper.kind2:
use Char/{is_oper}
use Parser/pick_while

oper : (Parser String) =
  (pick_while is_oper)
-e
Contents of ./Parser/pick.kind2:
use Parser/Result/{done,fail}
use List/{cons,nil}

pick : (Parser Char) =
  λcode
    match code {
      cons: (done _ code.tail code.head)
      nil: (fail _ "empty")
    }
-e
Contents of ./Parser/pure.kind2:
pure <A> (value: A) : (Parser A) =
  λcode (Parser/Result/done _ code value)
-e
Contents of ./Parser/repeat.kind2:
use Parser/bind
use Parser/pure
use List/{cons,nil}
use Nat/{succ,zero}

repeat <A> (n: Nat) (p: (Parser A)) : (Parser (List A)) =
  match n {
    zero: (pure _ (nil _))
    succ:
      (bind _ _ p (λhead
        (bind _ _ (repeat _ n.pred p) (λtail
          (pure _ (cons _ head tail))))))
  }
-e
Contents of ./Parser/skip.kind2:
skip <A> (parser: (Parser A)) : (Parser A) =
  λcode (parser code)
-e
Contents of ./Parser/take.kind2:
use Parser/repeat
use Parser/char

take (n: Nat) : (Parser String) =
  (repeat _ n char)
-e
Contents of ./Parser/test.kind2:
// TODO: auto refactored by Sonnet; review

use List/{cons,nil}
use Parser/Result/{done,fail}
use Bool/{true,false}
use Char/{equal}

test (test_str: String) : (Parser Bool) =
  λcode
    match test_str {
      cons:
        match code {
          cons:
            match eq = (equal test_str.head code.head) {
              true:
                match result = (test test_str.tail code.tail) {
                  done: (done _ code result.value)
                  fail: (fail _ result.error)
                }
              false: (done _ code false)
            }
          nil: (done _ code false)
        }
      nil: (done _ code true)
    }

-e
Contents of ./Parser/text.kind2:
use Parser/skip
use Parser/bind
use Parser/test
use Parser/take
use Parser/pure
use Parser/fail
use Bool/{true,false}
use String/{length}

text (txt: String) : (Parser Unit) =
  (skip _
    (bind _ _ (test txt) λsuccess
      match success {
        true:
          (bind _ _ (take (length txt)) λx
            (pure _ Unit/new))
        false: (fail _ "Text mismatch")
      }
    )
  )
-e
Contents of ./Parser/until.kind2:
use Parser/until/go
use List/{nil}

until <A> (until: (Parser Bool)) (parse: (Parser A)) : (Parser (List A)) =
  (go _ until parse (nil _))
-e
Contents of ./Parser/variant.kind2:
use List/{cons,nil}
use Pair/{fst,snd}
use Parser/bind
use Parser/fail
use Bool/{true,false}

variant <A> (variants: (List (Parser/Guard A))) : (Parser A) =
  match variants {
    cons:
      (bind _ _ (fst _ _ variants.head) λsuccess
        match success {
          true: (snd _ _ variants.head)
          false: (variant _ variants.tail)
        })
    nil: (fail _ "No matching variant")
  }

...

Thank you for providing the contents. Now, let's proceed with step 2: refactoring the files.

'''sh
# Refactoring ./Parser/_.kind2
# This file doesn't need changes as it only contains a type alias

# Refactoring ./Parser/bind.kind2
cat > ./Parser/bind.kind2 << EOL
use Parser/Result/{done,fail}

bind <A> <B>
- pa: (Parser A)
- f: A -> (Parser B)
: (Parser B)

λcode
  match result = (pa code) {
    done: (f result.value result.code)
    fail: (fail _ result.error)
  }
EOL

# Refactoring ./Parser/char.kind2
cat > ./Parser/char.kind2 << EOL
use Parser/Result/{done,fail}
use List/{cons,nil}

char
: (Parser Char)

λcode
  match code {
    cons: (done _ code.tail code.head)
    nil: (fail _ "eof")
  }
EOL

# Refactoring ./Parser/decimal.kind2
cat > ./Parser/decimal.kind2 << EOL
use Char/{is_decimal}
use Parser/pick_while

decimal
: (Parser String)

(pick_while is_decimal)
EOL

# Refactoring ./Parser/fail.kind2
cat > ./Parser/fail.kind2 << EOL
fail <A>
- error: String
: (Parser A)

λcode (Parser/Result/fail _ error)
EOL

# Refactoring ./Parser/is_eof.kind2
cat > ./Parser/is_eof.kind2 << EOL
use Parser/Result/{done}
use Bool/{true,false}
use List/{cons,nil}

is_eof
: (Parser Bool)

λcode
  match code {
    cons: (done _ code false)
    nil: (done _ (nil _) true)
  }
EOL

# Refactoring ./Parser/map.kind2
cat > ./Parser/map.kind2 << EOL
use Parser/Result/{done,fail}

map <A> <B>
- f: A -> B
- p: (Parser A)
: (Parser B)

λcode
  match result = (p code) {
    done: (done _ result.code (f result.value))
    fail: (fail _ result.error)
  }
EOL

# Refactoring ./Parser/name.kind2
cat > ./Parser/name.kind2 << EOL
use Char/{is_name}
use Parser/pick_while

name
: (Parser String)

(pick_while is_name)
EOL

# Refactoring ./Parser/oper.kind2
cat > ./Parser/oper.kind2 << EOL
use Char/{is_oper}
use Parser/pick_while

oper
: (Parser String)

(pick_while is_oper)
EOL

# Refactoring ./Parser/pick.kind2
cat > ./Parser/pick.kind2 << EOL
use Parser/Result/{done,fail}
use List/{cons,nil}

pick
: (Parser Char)

λcode
  match code {
    cons: (done _ code.tail code.head)
    nil: (fail _ "empty")
  }
EOL

# Refactoring ./Parser/pure.kind2
cat > ./Parser/pure.kind2 << EOL
pure <A>
- value: A
: (Parser A)

λcode (Parser/Result/done _ code value)
EOL

# Refactoring ./Parser/repeat.kind2
cat > ./Parser/repeat.kind2 << EOL
use Parser/bind
use Parser/pure
use List/{cons,nil}
use Nat/{succ,zero}

repeat <A>
- n: Nat
- p: (Parser A)
: (Parser (List A))

match n {
  zero: (pure _ (nil _))
  succ:
    (bind _ _ p (λhead
      (bind _ _ (repeat _ n.pred p) (λtail
        (pure _ (cons _ head tail))))))
}
EOL

# Refactoring ./Parser/skip.kind2
cat > ./Parser/skip.kind2 << EOL
skip <A>
- parser: (Parser A)
: (Parser A)

λcode (parser code)
EOL

# Refactoring ./Parser/take.kind2
cat > ./Parser/take.kind2 << EOL
use Parser/repeat
use Parser/char

take
- n: Nat
: (Parser String)

(repeat _ n char)
EOL

# Refactoring ./Parser/test.kind2
cat > ./Parser/test.kind2 << EOL
// TODO: auto refactored by Sonnet; review

use List/{cons,nil}
use Parser/Result/{done,fail}
use Bool/{true,false}
use Char/{equal}

test
- test_str: String
: (Parser Bool)

λcode
  match test_str {
    cons:
      match code {
        cons:
          match eq = (equal test_str.head code.head) {
            true:
              match result = (test test_str.tail code.tail) {
                done: (done _ code result.value)
                fail: (fail _ result.error)
              }
            false: (done _ code false)
          }
        nil: (done _ code false)
      }
    nil: (done _ code true)
  }
EOL

# Refactoring ./Parser/text.kind2
cat > ./Parser/text.kind2 << EOL
use Parser/skip
use Parser/bind
use Parser/test
use Parser/take
use Parser/pure
use Parser/fail
use Bool/{true,false}
use String/{length}

text
- txt: String
: (Parser Unit)

(skip _
  (bind _ _ (test txt) λsuccess
    match success {
      true:
        (bind _ _ (take (length txt)) λx
          (pure _ Unit/new))
      false: (fail _ "Text mismatch")
    }
  )
)
EOL

# Refactoring ./Parser/until.kind2
cat > ./Parser/until.kind2 << EOL
use Parser/until/go
use List/{nil}

until <A>
- until: (Parser Bool)
- parse: (Parser A)
: (Parser (List A))

(go _ until parse (nil _))
EOL

# Refactoring ./Parser/variant.kind2
cat > ./Parser/variant.kind2 << EOL
use List/{cons,nil}
use Pair/{fst,snd}
use Parser/bind
use Parser/fail
use Bool/{true,false}

variant <A>
- variants: (List (Parser/Guard A))
: (Parser A)

match variants {
  cons:
    (bind _ _ (fst _ _ variants.head) λsuccess
      match success {
        true: (snd _ _ variants.head)
        false: (variant _ variants.tail)
      })
  nil: (fail _ "No matching variant")
}
EOL

echo "All Parser files have been refactored."
'''

This refactoring applies the new style to all the Parser files, following the guidelines we've established.
All Parser files have been refactored.

...

Thank you for confirming the refactoring. Now, let's proceed with step 3: checking the refactored files.

'''sh
kind2 check Parser
kind2 check Parser/bind
kind2 check Parser/char
kind2 check Parser/decimal
kind2 check Parser/fail
kind2 check Parser/is_eof
kind2 check Parser/map
kind2 check Parser/name
kind2 check Parser/oper
kind2 check Parser/pick
kind2 check Parser/pure
kind2 check Parser/repeat
kind2 check Parser/skip
kind2 check Parser/take
kind2 check Parser/test
kind2 check Parser/text
kind2 check Parser/until
kind2 check Parser/variant

echo "All Parser files have been checked."
'''

This will run a type check on each of the refactored files in the Parser directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
All Parser files have been checked.

...

Excellent! All the Parser files have been successfully refactored and checked without any errors. This confirms that our changes have been applied correctly and the files are still valid Kind2 code.

Now, let's move on to the next directory. I'll proceed with step 1 for the next set of files.

Step 1: Show files

'''sh
echo "Contents of ./Sigma/_.kind2:"
cat ./Sigma/_.kind2

echo -e "\nContents of ./Sigma/new.kind2:"
cat ./Sigma/new.kind2
'''

This will show the contents of each Kind2 file in the Sigma directory, one by one.
Contents of ./Sigma/_.kind2:
data Sigma <A: *> <B: A -> *>
| new (fst: A) (snd: (B fst))

// λ-encoded version:
//Sigma
//: ∀(A: *) ∀(B: ∀(x: A) *) *
//= λA λB
 //$(self: (Sigma A B))
 //∀(P: ∀(x: (Sigma A B)) *)
 //∀(new: ∀(a: A) ∀(b: (B a)) (P (Sigma/new A B a b)))
 //(P self)
-e
Contents of ./Sigma/new.kind2:
Sigma/new
: ∀(A: *) ∀(B: ∀(x: A) *) ∀(a: A) ∀(b: (B a))
  (Sigma A B)
= λA λB λa λb ~λP λnew (new a b)

...

Thank you for providing the contents. Now, let's proceed with step 2: refactoring the files.

'''sh
# Refactoring ./Sigma/_.kind2
# This file doesn't need changes as it only contains a data declaration and comments

# Refactoring ./Sigma/new.kind2
cat > ./Sigma/new.kind2 << EOL
Sigma/new
: ∀(A: *) ∀(B: ∀(x: A) *) ∀(a: A) ∀(b: (B a))
  (Sigma A B)

λA λB λa λb ~λP λnew (new a b)
EOL

echo "All Sigma files have been refactored."
'''

This refactoring applies the new style to the Sigma/new.kind2 file, following the guidelines we've established:
1. The type signature is kept as is, since it's already on multiple lines.
2. There's an empty newline between the type signature and the function body.
3. The function body starts on a new line.

The 'Sigma/_.kind2' file wasn't changed as it only contains a data declaration and comments.
All Sigma files have been refactored.

...

Thank you for confirming the refactoring. Now, let's proceed with step 3: checking the refactored files.

'''sh
kind2 check Sigma
kind2 check Sigma/new

echo "All Sigma files have been checked."
'''

This will run a type check on each of the refactored files in the Sigma directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
All Sigma files have been checked.

...

Excellent! All the Sigma files have been successfully refactored and checked without any errors. This confirms that our changes have been applied correctly and the files are still valid Kind2 code.

Now, let's move on to the next directory. I'll proceed with step 1 for the next set of files.

Step 1: Show files

'''sh
echo "Contents of ./List/_.kind2:"
cat ./List/_.kind2

echo -e "\nContents of ./List/and.kind2:"
cat ./List/and.kind2

echo -e "\nContents of ./List/begin.kind2:"
cat ./List/begin.kind2

echo -e "\nContents of ./List/concat.kind2:"
cat ./List/concat.kind2

echo -e "\nContents of ./List/cons.kind2:"
cat ./List/cons.kind2

echo -e "\nContents of ./List/drop.kind2:"
cat ./List/drop.kind2

echo -e "\nContents of ./List/filter.kind2:"
cat ./List/filter.kind2

echo -e "\nContents of ./List/find.kind2:"
cat ./List/find.kind2

echo -e "\nContents of ./List/fold.kind2:"
cat ./List/fold.kind2

echo -e "\nContents of ./List/length.kind2:"
cat ./List/length.kind2

echo -e "\nContents of ./List/map.kind2:"
cat ./List/map.kind2

echo -e "\nContents of ./List/match.kind2:"
cat ./List/match.kind2

echo -e "\nContents of ./List/nil.kind2:"
cat ./List/nil.kind2

echo -e "\nContents of ./List/or.kind2:"
cat ./List/or.kind2

echo -e "\nContents of ./List/reverse.kind2:"
cat ./List/reverse.kind2

echo -e "\nContents of ./List/sum.kind2:"
cat ./List/sum.kind2

echo -e "\nContents of ./List/take.kind2:"
cat ./List/take.kind2

echo -e "\nContents of ./List/zip.kind2:"
cat ./List/zip.kind2
'''

This will show the contents of each Kind2 file in the List directory, one by one.
Contents of ./List/_.kind2:
data List <T>
| cons (head: T) (tail: (List T))
| nil

// List (A: *) : * =
//   $(self: (List A))
//   ∀(P: (List A) -> *)
//   ∀(cons: ∀(head: A) ∀(tail: (List A)) (P (List/cons/ A head tail)))
//   ∀(nil: (P (List/nil/ A)))
//   (P self)
-e
Contents of ./List/and.kind2:
use List/{cons,nil}
use Bool/{true}

and (list: (List Bool)) : Bool =
  fold list {
    cons: (Bool/and list.head list.tail)
    nil: true
  }
-e
Contents of ./List/begin.kind2:
use List/{cons,nil}

begin <A> (xs: (List A)) : (List A) =
  match xs {
    cons: match xs.tail {
      cons: (cons _ xs.head (begin _ (cons _ xs.tail.head xs.tail.tail)))
      nil: (cons _ xs.head (nil _))
    }
    nil: (nil _)
  }
-e
Contents of ./List/concat.kind2:
use List/{cons,nil}

concat <T> (xs: (List T)) (ys: (List T)) : (List T) =
  match xs {
    cons: (cons _ xs.head (concat _ xs.tail ys))
    nil: ys
  }
-e
Contents of ./List/cons.kind2:
cons <T> (head: T) (tail: (List T)) : (List T) =
  ~λP λcons λnil (cons head tail)
-e
Contents of ./List/drop.kind2:
use List/{cons,nil}
use Nat/{succ,zero}

drop <A> (n: Nat) (list: (List A)) : (List A) =
  match n {
    zero: list
    succ: match list {
      cons: (drop _ n.pred list.tail)
      nil: (nil _)
    }
  }
-e
Contents of ./List/filter.kind2:
use List/{cons,nil}
use Bool/{true,false}

filter <A> (cond: A -> Bool) (list: (List A)) : (List A) =
  match list {
    nil: (nil _)
    cons: match result = (cond list.head) {
      true: (cons _ list.head (filter _ cond list.tail))
      false: (filter _ cond list.tail)
    }
  }
-e
Contents of ./List/find.kind2:
use Bool/{true,false}
use List/{cons,nil}
use Maybe/{some,none}

find <A> (cond: A -> Bool) (xs: (List A)) : (Maybe A) =
  match xs {
    cons: match result = (cond xs.head) {
      true: (some _ xs.head)
      false: (find _ cond xs.tail)
    }
    nil: (none _)
  }
-e
Contents of ./List/fold.kind2:
use List/{cons,nil}

List/fold <A> (P: *) (c: A -> P -> P) (n: P) (xs: (List A)) : P =
  match xs {
    cons: (c xs.head (List/fold _ P c n xs.tail))
    nil: n
  }
-e
Contents of ./List/length.kind2:
use List/{cons,nil}
use Nat/{succ,zero}

length <A> (xs: (List A)) : Nat =
  match xs {
    cons: (succ (length _ xs.tail))
    nil: zero
  }
-e
Contents of ./List/map.kind2:
use List/{cons,nil}

map <A> <B>
- xs: (List A)
- fn: A -> B
: (List B)

fold xs {
  cons: (cons _ (fn xs.head) xs.tail)
  nil: (nil _)
}
-e
Contents of ./List/match.kind2:
match <A>
  (P: (List A) -> *)
  (c: ∀(head: A) ∀(tail: (List A)) (P (List/cons A head tail)))
  (n: (P (List/nil A)))
  (xs: (List A))
: (P xs) =
  (~xs P c n)
-e
Contents of ./List/nil.kind2:
nil <T> : (List T) =
  ~λP λcons λnil nil
-e
Contents of ./List/or.kind2:
use List/{cons,nil}
use Bool/{false}

or (list: (List Bool)) : Bool =
  fold list {
    cons: (Bool/or list.head list.tail)
    nil: false
  }
-e
Contents of ./List/reverse.kind2:
use List/{cons,nil}

reverse/go <A> (list: (List A)) (result: (List A)) : (List A) =
  match list {
    nil: result
    cons: (reverse/go _ list.tail (cons _ list.head result))
  }

reverse <A> (list: (List A)) : (List A) =
  (reverse/go _ list (nil _))
-e
Contents of ./List/sum.kind2:
sum (xs: (List U48)): U48 =
  match xs {
    ++: (+ xs.head (sum xs.tail))
    []: 0
  }
-e
Contents of ./List/take.kind2:
use List/{cons,nil}
use Nat/{succ,zero}

take <A> (n: Nat) (list: (List A)) : (List A) =
  match n {
    zero: (nil _)
    succ: match list {
      cons: (cons _ list.head (take _ n.pred list.tail))
      nil: (nil _)
    }
  }
-e
Contents of ./List/zip.kind2:
use List/{cons,nil}

zip <A> <B> (as: (List A)) (bs: (List B)) : (List (Pair A B)) =
  match as {
    cons: match bs {
      cons: (cons _ (Pair/new _ _ as.head bs.head) (zip _ _ as.tail bs.tail))
      nil: (nil _)
    }
    nil: (nil _)
  }

...

Thank you for providing the contents. Now, let's proceed with step 2: refactoring the files.

'''sh
# Refactoring ./List/_.kind2
# This file doesn't need changes as it only contains a data declaration and comments

# Refactoring ./List/and.kind2
cat > ./List/and.kind2 << EOL
use List/{cons,nil}
use Bool/{true}

and
- list: (List Bool)
: Bool

fold list {
  cons: (Bool/and list.head list.tail)
  nil: true
}
EOL

# Refactoring ./List/begin.kind2
cat > ./List/begin.kind2 << EOL
use List/{cons,nil}

begin <A>
- xs: (List A)
: (List A)

match xs {
  cons: match xs.tail {
    cons: (cons _ xs.head (begin _ (cons _ xs.tail.head xs.tail.tail)))
    nil: (cons _ xs.head (nil _))
  }
  nil: (nil _)
}
EOL

# Refactoring ./List/concat.kind2
cat > ./List/concat.kind2 << EOL
use List/{cons,nil}

concat <T>
- xs: (List T)
- ys: (List T)
: (List T)

match xs {
  cons: (cons _ xs.head (concat _ xs.tail ys))
  nil: ys
}
EOL

# Refactoring ./List/cons.kind2
cat > ./List/cons.kind2 << EOL
cons <T>
- head: T
- tail: (List T)
: (List T)

~λP λcons λnil (cons head tail)
EOL

# Refactoring ./List/drop.kind2
cat > ./List/drop.kind2 << EOL
use List/{cons,nil}
use Nat/{succ,zero}

drop <A>
- n: Nat
- list: (List A)
: (List A)

match n {
  zero: list
  succ: match list {
    cons: (drop _ n.pred list.tail)
    nil: (nil _)
  }
}
EOL

# Refactoring ./List/filter.kind2
cat > ./List/filter.kind2 << EOL
use List/{cons,nil}
use Bool/{true,false}

filter <A>
- cond: A -> Bool
- list: (List A)
: (List A)

match list {
  nil: (nil _)
  cons: match result = (cond list.head) {
    true: (cons _ list.head (filter _ cond list.tail))
    false: (filter _ cond list.tail)
  }
}
EOL

# Refactoring ./List/find.kind2
cat > ./List/find.kind2 << EOL
use Bool/{true,false}
use List/{cons,nil}
use Maybe/{some,none}

find <A>
- cond: A -> Bool
- xs: (List A)
: (Maybe A)

match xs {
  cons: match result = (cond xs.head) {
    true: (some _ xs.head)
    false: (find _ cond xs.tail)
  }
  nil: (none _)
}
EOL

# Refactoring ./List/fold.kind2
cat > ./List/fold.kind2 << EOL
use List/{cons,nil}

List/fold <A> <P: *>
- c: A -> P -> P
- n: P
- xs: (List A)
: P

match xs {
  cons: (c xs.head (List/fold _ P c n xs.tail))
  nil: n
}
EOL

# Refactoring ./List/length.kind2
cat > ./List/length.kind2 << EOL
use List/{cons,nil}
use Nat/{succ,zero}

length <A>
- xs: (List A)
: Nat

match xs {
  cons: (succ (length _ xs.tail))
  nil: zero
}
EOL

# Refactoring ./List/map.kind2
cat > ./List/map.kind2 << EOL
use List/{cons,nil}

map <A> <B>
- xs: (List A)
- fn: A -> B
: (List B)

fold xs {
  cons: (cons _ (fn xs.head) xs.tail)
  nil: (nil _)
}
EOL

# Refactoring ./List/match.kind2
cat > ./List/match.kind2 << EOL
match <A>
- P: (List A) -> *
- c: ∀(head: A) ∀(tail: (List A)) (P (List/cons A head tail))
- n: (P (List/nil A))
- xs: (List A)
: (P xs)

(~xs P c n)
EOL

# Refactoring ./List/nil.kind2
cat > ./List/nil.kind2 << EOL
nil <T>
: (List T)

~λP λcons λnil nil
EOL

# Refactoring ./List/or.kind2
cat > ./List/or.kind2 << EOL
use List/{cons,nil}
use Bool/{false}

or
- list: (List Bool)
: Bool

fold list {
  cons: (Bool/or list.head list.tail)
  nil: false
}
EOL

# Refactoring ./List/reverse.kind2
cat > ./List/reverse.kind2 << EOL
use List/{cons,nil}

reverse/go <A>
- list: (List A)
- result: (List A)
: (List A)

match list {
  nil: result
  cons: (reverse/go _ list.tail (cons _ list.head result))
}

reverse <A>
- list: (List A)
: (List A)

(reverse/go _ list (nil _))
EOL

# Refactoring ./List/sum.kind2
cat > ./List/sum.kind2 << EOL
sum
- xs: (List U48)
: U48

match xs {
  ++: (+ xs.head (sum xs.tail))
  []: 0
}
EOL

# Refactoring ./List/take.kind2
cat > ./List/take.kind2 << EOL
use List/{cons,nil}
use Nat/{succ,zero}

take <A>
- n: Nat
- list: (List A)
: (List A)

match n {
  zero: (nil _)
  succ: match list {
    cons: (cons _ list.head (take _ n.pred list.tail))
    nil: (nil _)
  }
}
EOL

# Refactoring ./List/zip.kind2
cat > ./List/zip.kind2 << EOL
use List/{cons,nil}

zip <A> <B>
- as: (List A)
- bs: (List B)
: (List (Pair A B))

match as {
  cons: match bs {
    cons: (cons _ (Pair/new _ _ as.head bs.head) (zip _ _ as.tail bs.tail))
    nil: (nil _)
  }
  nil: (nil _)
}
EOL

echo "All List files have been refactored."
'''

This refactoring applies the new style to all the List files, following the guidelines we've established.
All List files have been refactored.

...

Thank you for confirming the refactoring. Now, let's proceed with step 3: checking the refactored files.

'''sh
kind2 check List
kind2 check List/and
kind2 check List/begin
kind2 check List/concat
kind2 check List/cons
kind2 check List/drop
kind2 check List/filter
kind2 check List/find
kind2 check List/fold
kind2 check List/length
kind2 check List/map
kind2 check List/match
kind2 check List/nil
kind2 check List/or
kind2 check List/reverse
kind2 check List/sum
kind2 check List/take
kind2 check List/zip

echo "All List files have been checked."
'''

This will run a type check on each of the refactored files in the List directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
ERROR:
- expected: ?function
- detected: _
- bad_term: (List/fold _ _ _ λlist.head λlist.tail (Bool/and list.head list.tail) Bool/true list)
unknown_file
  1 | Could not read source file.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
ERROR:
- expected: ?function
- detected: _
- bad_term: (List/fold _ _ _ λxs.head λxs.tail (List/cons _ (fn xs.head) xs.tail) (List/nil _) xs)
unknown_file
  1 | Could not read source file.
Checked.
Checked.
ERROR:
- expected: ?function
- detected: _
- bad_term: (List/fold _ _ _ λlist.head λlist.tail (Bool/or list.head list.tail) Bool/false list)
unknown_file
  1 | Could not read source file.
Checked.
Checked.
Checked.
Checked.
All List files have been checked.

oops. which files failed?

Based on the output, it appears that three files in the List directory failed the type check. These files are:

1. List/and.kind2
2. List/map.kind2
3. List/or.kind2

The error message for each of these files is similar, indicating an issue with the use of 'List/fold'. It seems that the refactoring may have introduced a problem with how 'fold' is being used in these files.

Let's take a closer look at these files and try to correct the issues. I'll show you the current content of each file, and then we can work on fixing them.

'''sh
echo "Contents of ./List/and.kind2:"
cat ./List/and.kind2

echo -e "\nContents of ./List/map.kind2:"
cat ./List/map.kind2

echo -e "\nContents of ./List/or.kind2:"
cat ./List/or.kind2
'''

After we see the contents, we can discuss how to fix these files.
Contents of ./List/and.kind2:
use List/{cons,nil}
use Bool/{true}

and
- list: (List Bool)
: Bool

fold list {
  cons: (Bool/and list.head list.tail)
  nil: true
}
-e
Contents of ./List/map.kind2:
use List/{cons,nil}

map <A> <B>
- xs: (List A)
- fn: A -> B
: (List B)

fold xs {
  cons: (cons _ (fn xs.head) xs.tail)
  nil: (nil _)
}
-e
Contents of ./List/or.kind2:
use List/{cons,nil}
use Bool/{false}

or
- list: (List Bool)
: Bool

fold list {
  cons: (Bool/or list.head list.tail)
  nil: false
}

that is because the P parameter in 'fold' is '(P: *)', not '<P: *>'. this is very important, and applies to all folds. I've fixed it now. can you check again?

I apologize for the oversight. You're absolutely right about the 'P' parameter in 'fold'. Thank you for fixing it. Let's check all the List files again to ensure everything is now correct.

'''sh
kind2 check List
kind2 check List/and
kind2 check List/begin
kind2 check List/concat
kind2 check List/cons
kind2 check List/drop
kind2 check List/filter
kind2 check List/find
kind2 check List/fold
kind2 check List/length
kind2 check List/map
kind2 check List/match
kind2 check List/nil
kind2 check List/or
kind2 check List/reverse
kind2 check List/sum
kind2 check List/take
kind2 check List/zip

echo "All List files have been checked again."
'''

This will run a type check on each of the files in the List directory once more to confirm that all issues have been resolved.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
All List files have been checked again.

...

Excellent news! All the List files have now passed the type check successfully. This confirms that the issue with the 'fold' function has been resolved, and all the files in the List directory are now correctly formatted and typed.

Since we've successfully refactored and verified all the List files, we can move on to the next directory. Let's proceed with step 1 for the next set of files.

Step 1: Show files

'''sh
echo "Contents of ./Bool/_.kind2:"
cat ./Bool/_.kind2

echo -e "\nContents of ./Bool/and.kind2:"
cat ./Bool/and.kind2

echo -e "\nContents of ./Bool/false.kind2:"
cat ./Bool/false.kind2

echo -e "\nContents of ./Bool/if.kind2:"
cat ./Bool/if.kind2

echo -e "\nContents of ./Bool/match.kind2:"
cat ./Bool/match.kind2

echo -e "\nContents of ./Bool/not.kind2:"
cat ./Bool/not.kind2

echo -e "\nContents of ./Bool/or.kind2:"
cat ./Bool/or.kind2

echo -e "\nContents of ./Bool/show.kind2:"
cat ./Bool/show.kind2

echo -e "\nContents of ./Bool/true.kind2:"
cat ./Bool/true.kind2
'''

This will show the contents of each Kind2 file in the Bool directory, one by one.
Contents of ./Bool/_.kind2:
data Bool
| true
| false
-e
Contents of ./Bool/and.kind2:
use Bool/{true,false,and}

and (a: Bool) (b: Bool) : Bool =
  match a {
    true: b
    false: false
  }
-e
Contents of ./Bool/false.kind2:
false : Bool =
  ~λP λt λf f
-e
Contents of ./Bool/if.kind2:
use Bool/{true,false}

if (b: Bool) (P: *) (t: P) (f: P) : P =
  match b {
    true: t
    false: f
  }
-e
Contents of ./Bool/match.kind2:
use Bool/{true,false}

match
  (P: ∀(x: Bool) *)
  (t: (P true))
  (f: (P false))
  (b: Bool)
: (P b)
= (~b P t f)
-e
Contents of ./Bool/not.kind2:
use Bool/{true,false}

not (x: Bool) : Bool =
  match x {
    true: false
    false: true
  }
-e
Contents of ./Bool/or.kind2:
use Bool/{true,false}

or (a: Bool) (b: Bool) : Bool =
  match a {
    true: true
    false: b
  }
-e
Contents of ./Bool/show.kind2:
use Bool/{true,false}

show (x: Bool) : String =
  match x {
    true: "true"
    false: "false"
  }
-e
Contents of ./Bool/true.kind2:
true : Bool =
  ~λP λt λf t

...

Thank you for providing the contents. Now, let's proceed with step 2: refactoring the files.

'''sh
# Refactoring ./Bool/_.kind2
# This file doesn't need changes as it only contains a data declaration

# Refactoring ./Bool/and.kind2
cat > ./Bool/and.kind2 << EOL
use Bool/{true,false,and}

and
- a: Bool
- b: Bool
: Bool

match a {
  true: b
  false: false
}
EOL

# Refactoring ./Bool/false.kind2
cat > ./Bool/false.kind2 << EOL
false
: Bool

~λP λt λf f
EOL

# Refactoring ./Bool/if.kind2
cat > ./Bool/if.kind2 << EOL
use Bool/{true,false}

if
- b: Bool
- P: *
- t: P
- f: P
: P

match b {
  true: t
  false: f
}
EOL

# Refactoring ./Bool/match.kind2
cat > ./Bool/match.kind2 << EOL
use Bool/{true,false}

match
- P: ∀(x: Bool) *
- t: (P true)
- f: (P false)
- b: Bool
: (P b)

(~b P t f)
EOL

# Refactoring ./Bool/not.kind2
cat > ./Bool/not.kind2 << EOL
use Bool/{true,false}

not
- x: Bool
: Bool

match x {
  true: false
  false: true
}
EOL

# Refactoring ./Bool/or.kind2
cat > ./Bool/or.kind2 << EOL
use Bool/{true,false}

or
- a: Bool
- b: Bool
: Bool

match a {
  true: true
  false: b
}
EOL

# Refactoring ./Bool/show.kind2
cat > ./Bool/show.kind2 << EOL
use Bool/{true,false}

show
- x: Bool
: String

match x {
  true: "true"
  false: "false"
}
EOL

# Refactoring ./Bool/true.kind2
cat > ./Bool/true.kind2 << EOL
true
: Bool

~λP λt λf t
EOL

echo "All Bool files have been refactored."
'''

This refactoring applies the new style to all the Bool files, following the guidelines we've established:
1. Function parameters are now on separate lines, preceded by a hyphen (-).
2. The return type is on its own line after the parameters.
3. There's an empty newline between the type annotation and the function body.
4. The function body is indented one level less than before.
5. The contents of the body itself remain unchanged.

The 'Bool/_.kind2' file wasn't changed as it only contains a data declaration.
All Bool files have been refactored.

...

Thank you for confirming the refactoring. Now, let's proceed with step 3: checking the refactored files.

'''sh
kind2 check Bool
kind2 check Bool/and
kind2 check Bool/false
kind2 check Bool/if
kind2 check Bool/match
kind2 check Bool/not
kind2 check Bool/or
kind2 check Bool/show
kind2 check Bool/true

echo "All Bool files have been checked."
'''

This will run a type check on each of the refactored files in the Bool directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
All Bool files have been checked.

...

Excellent! All the Bool files have been successfully refactored and checked without any errors. This confirms that our changes have been applied correctly and the files are still valid Kind2 code.

Now, let's move on to the next directory. I'll proceed with step 1 for the next set of files.

Step 1: Show files

'''sh
echo "Contents of ./Equal/_.kind2:"
cat ./Equal/_.kind2

echo -e "\nContents of ./Equal/apply.kind2:"
cat ./Equal/apply.kind2

echo -e "\nContents of ./Equal/match.kind2:"
cat ./Equal/match.kind2

echo -e "\nContents of ./Equal/refl.kind2:"
cat ./Equal/refl.kind2
'''

This will show the contents of each Kind2 file in the Equal directory, one by one.
Contents of ./Equal/_.kind2:
data Equal <T> (a: T) (b: T)
| refl (a: T) : (Equal T a a)

//Equal : ∀(T: *) ∀(a: T) ∀(b: T) * =
  //λT λa λb
  //$(self: (Equal T a b))
  //∀(P: ∀(a: T) ∀(b: T) ∀(x: (Equal T a b)) *)
  //∀(refl: ∀(x: T) (P x x (Equal/refl T x)))
  //(P a b self)
-e
Contents of ./Equal/apply.kind2:
apply <A: *> <B: *> <a: A> <b: B> (f: A -> B) (e: (Equal A a b)) : (Equal B (f a) (f b)) =
  match e {
    Equal/refl: ~λPλe(e (f e.a))
  }: (Equal B (f a) (f b))
-e
Contents of ./Equal/match.kind2:
match <T: *> <a: T> <b: T>
  (P: ∀(a:T) ∀(b:T) ∀(e: (Equal T a b)) *)
  (refl: ∀(x: T) (P x x (Equal/refl T x)))
  (e: (Equal T a b))
: (P a b e) =
  (~e P refl)
-e
Contents of ./Equal/refl.kind2:
refl <A> (x: A) : (Equal A x x) =
  ~ λP λrefl (refl x)

...

Thank you for providing the contents. Now, let's proceed with step 2: refactoring the files.

'''sh
# Refactoring ./Equal/_.kind2
# This file doesn't need changes as it only contains a data declaration and comments

# Refactoring ./Equal/apply.kind2
cat > ./Equal/apply.kind2 << EOL
apply <A: *> <B: *> <a: A> <b: B>
- f: A -> B
- e: (Equal A a b)
: (Equal B (f a) (f b))

match e {
  Equal/refl: ~λPλe(e (f e.a))
}: (Equal B (f a) (f b))
EOL

# Refactoring ./Equal/match.kind2
cat > ./Equal/match.kind2 << EOL
match <T: *> <a: T> <b: T>
- P: ∀(a:T) ∀(b:T) ∀(e: (Equal T a b)) *
- refl: ∀(x: T) (P x x (Equal/refl T x))
- e: (Equal T a b)
: (P a b e)

(~e P refl)
EOL

# Refactoring ./Equal/refl.kind2
cat > ./Equal/refl.kind2 << EOL
refl <A>
- x: A
: (Equal A x x)

~ λP λrefl (refl x)
EOL

echo "All Equal files have been refactored."
'''

This refactoring applies the new style to all the Equal files, following the guidelines we've established:
1. Function parameters are now on separate lines, preceded by a hyphen (-).
2. The return type is on its own line after the parameters.
3. There's an empty newline between the type annotation and the function body.
4. The function body is indented one level less than before.
5. The contents of the body itself remain unchanged.

The 'Equal/_.kind2' file wasn't changed as it only contains a data declaration and comments.
All Equal files have been refactored.

...

Thank you for confirming the refactoring. Now, let's proceed with step 3: checking the refactored files.

'''sh
kind2 check Equal
kind2 check Equal/apply
kind2 check Equal/match
kind2 check Equal/refl

echo "All Equal files have been checked."
'''

This will run a type check on each of the refactored files in the Equal directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
Checked.
Checked.
All Equal files have been checked.

...

Excellent! All the Equal files have been successfully refactored and checked without any errors. This confirms that our changes have been applied correctly and the files are still valid Kind2 code.

Now, let's move on to the next directory. I'll proceed with step 1 for the next set of files.

Step 1: Show files

'''sh
echo "Contents of ./String/_.kind2:"
cat ./String/_.kind2

echo -e "\nContents of ./String/begin.kind2:"
cat ./String/begin.kind2

echo -e "\nContents of ./String/cmp.kind2:"
cat ./String/cmp.kind2

echo -e "\nContents of ./String/concat.kind2:"
cat ./String/concat.kind2

echo -e "\nContents of ./String/cons.kind2:"
cat ./String/cons.kind2

echo -e "\nContents of ./String/equal.kind2:"
cat ./String/equal.kind2

echo -e "\nContents of ./String/indent.kind2:"
cat ./String/indent.kind2

echo -e "\nContents of ./String/join.kind2:"
cat ./String/join.kind2

echo -e "\nContents of ./String/length.kind2:"
cat ./String/length.kind2

echo -e "\nContents of ./String/newline.kind2:"
cat ./String/newline.kind2

echo -e "\nContents of ./String/nil.kind2:"
cat ./String/nil.kind2

echo -e "\nContents of ./String/quote.kind2:"
cat ./String/quote.kind2

echo -e "\nContents of ./String/skip.kind2:"
cat ./String/skip.kind2

echo -e "\nContents of ./String/unpar.kind2:"
cat ./String/unpar.kind2

echo -e "\nContents of ./String/wrap.kind2:"
cat ./String/wrap.kind2
'''

This will show the contents of each Kind2 file in the String directory, one by one.
Contents of ./String/_.kind2:
String : * =
  (List Char)
-e
Contents of ./String/begin.kind2:
use List/{cons,nil}

begin
- str: (List Char)
: (List Char)

match str {
  cons:
    match str.tail {
      cons: (cons _ str.head (begin str.tail))
      nil: str
    }
  nil: str
}
-e
Contents of ./String/cmp.kind2:
String/cmp
: ∀(a: String) ∀(b: String) Cmp
= λa λb
  use P = λx ∀(b: String) Cmp
  use cons = λa.head λa.tail λb
    use P = λx ∀(a.head: Char) ∀(a.tail: String) Cmp
    use cons = λb.head λb.tail λa.head λa.tail
      use P = λx Cmp
      use ltn = Cmp/ltn
      use eql = (cmp a.tail b.tail)
      use gtn = Cmp/gtn
      (~(U48/cmp a.head b.head) P ltn eql gtn)
    use nil = λa.head λa.tail Cmp/gtn
    (~b P cons nil a.head a.tail)
  use nil = λb
    use P = λx Cmp
    use cons = λb.head λb.tail Cmp/ltn
    use nil = Cmp/eql
    (~b P cons nil)
  (~a P cons nil b)
-e
Contents of ./String/concat.kind2:
use List/{concat}

concat
- xs: (List Char)
- ys: (List Char)
: (List Char)

(concat xs ys)
-e
Contents of ./String/cons.kind2:
String/cons (head: Char) (tail: String) : String =
  ~λP λcons λnil (cons head tail)
-e
Contents of ./String/equal.kind2:
String/equal (a: String) (b: String) : Bool =
  use P = λx ∀(b: String) Bool
  use cons = λa.head λa.tail λb
    use P = λx ∀(a.head: Char) ∀(a.tail: String) Bool
    use cons = λb.head λb.tail λa.head λa.tail
      (Bool/and
        (U48/equal a.head b.head)
        (String/equal a.tail b.tail)
      )
    use nil = λa.head λa.tail Bool/false
    (~b P cons nil a.head a.tail)
  use nil = λb
    use P = λx Bool
    use cons = λb.head λb.tail Bool/false
    use nil = Bool/true
    (~b P cons nil)
  (~a P cons nil b)
-e
Contents of ./String/indent.kind2:
indent
: ∀(tab: Nat) String
= λtab
  use P    = λx String
  use succ = λtab.pred (String/cons 32 (String/cons 32 (indent tab.pred)))
  use zero = String/nil
  (~tab P succ zero)
-e
Contents of ./String/join.kind2:
join (sep: String) (strs: (List String)) : String =
  match strs {
    List/cons: (String/concat strs.head (String/join/go sep strs.tail))
    List/nil: String/nil
  }



//join
//: ∀(sep: String) ∀(strs: (List String)) String
//= λsep λstrs
  //use P = λx String
  //use cons = λh λt (String/concat h (String/join/go sep t))
  //use nil = String/nil
  //(~strs P cons nil)
-e
Contents of ./String/length.kind2:
use List/{length}

length (s: (List Char)) : Nat =
  (length s)
-e
Contents of ./String/newline.kind2:
newline
: String
= (String/cons 10 String/nil)
-e
Contents of ./String/nil.kind2:
String/nil : String =
  ~λP λcons λnil nil
-e
Contents of ./String/quote.kind2:
use List/{cons,nil}

quote : (List Char) =
  (cons _ '"' (nil _))
-e
Contents of ./String/skip.kind2:
skip
: ∀(str: String) String
= λstr
  use P = λx String
  use cons = λc0 λcs
    use P = λx ∀(c0: Char) ∀(cs: String) String
    use true = λc0 λcs (String/skip cs)
    use false = λc0 λcs
      use P = λx ∀(c0: Char) ∀(cs: String) String
      use true = λc0 λcs
        use P = λx ∀(c0: Char) String
        use cons = λc1 λcs λc0
          use P = λx ∀(c0: Char) ∀(c1: Char) ∀(cs: String) String
          use true = λc0 λc1 λcs (String/skip/comment cs)
          use false = λc0 λc1 λcs (String/cons c0 (String/cons c1 cs))
          (~(Char/is_slash c1) P true false c0 c1 cs)
        use nil = λc0 (String/cons c0 String/nil)
        (~cs P cons nil c0)
      use false = λc0 λcs (String/cons c0 cs)
      (~(Char/is_slash c0) P true false c0 cs)
    (~(Char/is_blank c0) P true false c0 cs)
  use nil = String/nil
  (~str P cons nil)
-e
Contents of ./String/unpar.kind2:
unpar
: ∀(fst: Char) ∀(lst: Char) ∀(str: String) String
= λfst λlst λstr
  use P = λx String
  use cons = λhead λtail
    use P = λx ∀(head: Char) ∀(tail: String) String
    use true = λhead λtail (String/begin tail)
    use false = λhead λtail (String/cons head tail)
    (~(Char/equal head fst) P true false head tail)
  use nil = String/nil
  (~str P cons nil)
-e
Contents of ./String/wrap.kind2:
wrap (ini: String) (str: String) (end: String) : String =
  (String/concat ini (String/wrap/go str end))

...

Thank you for providing the contents. Now, let's proceed with step 2: refactoring the files.

'''sh
# Refactoring ./String/_.kind2
# This file doesn't need changes as it only contains a type alias

# Refactoring ./String/begin.kind2
# This file is already in the correct format

# Refactoring ./String/cmp.kind2
cat > ./String/cmp.kind2 << EOL
String/cmp
: ∀(a: String) ∀(b: String) Cmp

λa λb
use P = λx ∀(b: String) Cmp
use cons = λa.head λa.tail λb
  use P = λx ∀(a.head: Char) ∀(a.tail: String) Cmp
  use cons = λb.head λb.tail λa.head λa.tail
    use P = λx Cmp
    use ltn = Cmp/ltn
    use eql = (cmp a.tail b.tail)
    use gtn = Cmp/gtn
    (~(U48/cmp a.head b.head) P ltn eql gtn)
  use nil = λa.head λa.tail Cmp/gtn
  (~b P cons nil a.head a.tail)
use nil = λb
  use P = λx Cmp
  use cons = λb.head λb.tail Cmp/ltn
  use nil = Cmp/eql
  (~b P cons nil)
(~a P cons nil b)
EOL

# Refactoring ./String/concat.kind2
# This file is already in the correct format

# Refactoring ./String/cons.kind2
cat > ./String/cons.kind2 << EOL
String/cons
- head: Char
- tail: String
: String

~λP λcons λnil (cons head tail)
EOL

# Refactoring ./String/equal.kind2
cat > ./String/equal.kind2 << EOL
String/equal
- a: String
- b: String
: Bool

use P = λx ∀(b: String) Bool
use cons = λa.head λa.tail λb
  use P = λx ∀(a.head: Char) ∀(a.tail: String) Bool
  use cons = λb.head λb.tail λa.head λa.tail
    (Bool/and
      (U48/equal a.head b.head)
      (String/equal a.tail b.tail)
    )
  use nil = λa.head λa.tail Bool/false
  (~b P cons nil a.head a.tail)
use nil = λb
  use P = λx Bool
  use cons = λb.head λb.tail Bool/false
  use nil = Bool/true
  (~b P cons nil)
(~a P cons nil b)
EOL

# Refactoring ./String/indent.kind2
cat > ./String/indent.kind2 << EOL
indent
: ∀(tab: Nat) String

λtab
use P    = λx String
use succ = λtab.pred (String/cons 32 (String/cons 32 (indent tab.pred)))
use zero = String/nil
(~tab P succ zero)
EOL

# Refactoring ./String/join.kind2
cat > ./String/join.kind2 << EOL
join
- sep: String
- strs: (List String)
: String

match strs {
  List/cons: (String/concat strs.head (String/join/go sep strs.tail))
  List/nil: String/nil
}
EOL

# Refactoring ./String/length.kind2
cat > ./String/length.kind2 << EOL
use List/{length}

length
- s: (List Char)
: Nat

(length s)
EOL

# Refactoring ./String/newline.kind2
cat > ./String/newline.kind2 << EOL
newline
: String

(String/cons 10 String/nil)
EOL

# Refactoring ./String/nil.kind2
cat > ./String/nil.kind2 << EOL
String/nil
: String

~λP λcons λnil nil
EOL

# Refactoring ./String/quote.kind2
cat > ./String/quote.kind2 << EOL
use List/{cons,nil}

quote
: (List Char)

(cons _ '"' (nil _))
EOL

# Refactoring ./String/skip.kind2
cat > ./String/skip.kind2 << EOL
skip
: ∀(str: String) String

λstr
use P = λx String
use cons = λc0 λcs
  use P = λx ∀(c0: Char) ∀(cs: String) String
  use true = λc0 λcs (String/skip cs)
  use false = λc0 λcs
    use P = λx ∀(c0: Char) ∀(cs: String) String
    use true = λc0 λcs
      use P = λx ∀(c0: Char) String
      use cons = λc1 λcs λc0
        use P = λx ∀(c0: Char) ∀(c1: Char) ∀(cs: String) String
        use true = λc0 λc1 λcs (String/skip/comment cs)
        use false = λc0 λc1 λcs (String/cons c0 (String/cons c1 cs))
        (~(Char/is_slash c1) P true false c0 c1 cs)
      use nil = λc0 (String/cons c0 String/nil)
      (~cs P cons nil c0)
    use false = λc0 λcs (String/cons c0 cs)
    (~(Char/is_slash c0) P true false c0 cs)
  (~(Char/is_blank c0) P true false c0 cs)
use nil = String/nil
(~str P cons nil)
EOL

# Refactoring ./String/unpar.kind2
cat > ./String/unpar.kind2 << EOL
unpar
: ∀(fst: Char) ∀(lst: Char) ∀(str: String) String

λfst λlst λstr
use P = λx String
use cons = λhead λtail
  use P = λx ∀(head: Char) ∀(tail: String) String
  use true = λhead λtail (String/begin tail)
  use false = λhead λtail (String/cons head tail)
  (~(Char/equal head fst) P true false head tail)
use nil = String/nil
(~str P cons nil)
EOL

# Refactoring ./String/wrap.kind2
cat > ./String/wrap.kind2 << EOL
wrap
- ini: String
- str: String
- end: String
: String

(String/concat ini (String/wrap/go str end))
EOL

echo "All String files have been refactored."
'''

This refactoring applies the new style to all the String files, following the guidelines we've established.
All String files have been refactored.

...

Thank you for confirming the refactoring. Now, let's proceed with step 3: checking the refactored files.

'''sh
kind2 check String
kind2 check String/begin
kind2 check String/cmp
kind2 check String/concat
kind2 check String/cons
kind2 check String/equal
kind2 check String/indent
kind2 check String/join
kind2 check String/length
kind2 check String/newline
kind2 check String/nil
kind2 check String/quote
kind2 check String/skip
kind2 check String/unpar
kind2 check String/wrap

echo "All String files have been checked."
'''

This will run a type check on each of the refactored files in the String directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
Checked.
All String files have been checked.

...

Excellent! All the String files have been successfully refactored and checked without any errors. This confirms that our changes have been applied correctly and the files are still valid Kind2 code.

Now, let's move on to the next directory. I'll proceed with step 1 for the next set of files.

Step 1: Show files

'''sh
echo "Contents of ./Monad/_.kind2:"
cat ./Monad/_.kind2

echo -e "\nContents of ./Monad/new.kind2:"
cat ./Monad/new.kind2
'''

This will show the contents of each Kind2 file in the Monad directory, one by one.
Contents of ./Monad/_.kind2:
data Monad <M: * -> *>
| new
    (bind: ∀(A: *) ∀(B: *) ∀(a: (M A)) ∀(b: A -> (M B)) (M B))
    (pure: ∀(A: *) ∀(a: A) (M A))
-e
Contents of ./Monad/new.kind2:
new
: ∀(M: ∀(T: *) *)
  ∀(bind: ∀(A: *) ∀(B: *) ∀(a: (M A)) ∀(b: ∀(a: A) (M B)) (M B))
  ∀(pure: ∀(A: *) ∀(a: A) (M A))
  (Monad M)
= λM λbind λpure
  ~λP λnew
  (new bind pure)

...

Thank you for providing the contents. Now, let's proceed with step 2: refactoring the files.

'''sh
# Refactoring ./Monad/_.kind2
# This file doesn't need changes as it only contains a data declaration

# Refactoring ./Monad/new.kind2
cat > ./Monad/new.kind2 << EOL
new
: ∀(M: ∀(T: *) *)
  ∀(bind: ∀(A: *) ∀(B: *) ∀(a: (M A)) ∀(b: ∀(a: A) (M B)) (M B))
  ∀(pure: ∀(A: *) ∀(a: A) (M A))
  (Monad M)

λM λbind λpure
~λP λnew
(new bind pure)
EOL

echo "All Monad files have been refactored."
'''

This refactoring applies the new style to the Monad/new.kind2 file, following the guidelines we've established:
1. The type signature is kept as is, since it's already on multiple lines.
2. There's an empty newline between the type signature and the function body.
3. The function body starts on a new line.

The 'Monad/_.kind2' file wasn't changed as it only contains a data declaration.
All Monad files have been refactored.

...

Thank you for confirming the refactoring. Now, let's proceed with step 3: checking the refactored files.

'''sh
kind2 check Monad
kind2 check Monad/new

echo "All Monad files have been checked."
'''

This will run a type check on each of the refactored files in the Monad directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
All Monad files have been checked.

...

Excellent! All the Monad files have been successfully refactored and checked without any errors. This confirms that our changes have been applied correctly and the files are still valid Kind2 code.

Now, let's move on to the next directory. I'll proceed with step 1 for the next set of files.

Step 1: Show files

'''sh
echo "Contents of ./Vector/_.kind2:"
cat ./Vector/_.kind2

echo -e "\nContents of ./Vector/concat.kind2:"
cat ./Vector/concat.kind2

echo -e "\nContents of ./Vector/cons.kind2:"
cat ./Vector/cons.kind2

echo -e "\nContents of ./Vector/nil.kind2:"
cat ./Vector/nil.kind2
'''

This will show the contents of each Kind2 file in the Vector directory, one by one.
Contents of ./Vector/_.kind2:
data Vector <T> (len: Nat)
| cons (len: Nat) (head: T) (tail: (Vector T len)) : (Vector T (Nat/succ len))
| nil : (Vector T Nat/zero)
-e
Contents of ./Vector/concat.kind2:
use Vector/{cons,nil}
use Nat/{succ,zero,add}

concat <T> (xs_len: Nat) (ys_len: Nat)
  (xs: (Vector T xs_len))
  (ys: (Vector T ys_len))
: (Vector T (add xs_len ys_len))
= match xs {
    cons: (cons (add xs.len ys_len) xs.head (concat xs.len ys_len xs.tail ys))
    nil: ys
  }

//concat
//: ∀(T: *)
  //∀(xs_len: Nat) ∀(xs: (Vector T xs_len))
  //∀(ys_len: Nat) ∀(ys: (Vector T ys_len))
  //(Vector T (add xs_len ys_len))
//= λT λxs_len λxs λys_len λys
  //(~xs _
  //λxs.len λxs.head λxs.tail
    //(Vector.cons T (Nat.add xs.len ys_len) xs.head (concat T xs.len xs.tail ys_len ys))
  //ys)
-e
Contents of ./Vector/cons.kind2:
cons <T> (len: Nat) (head: T) (tail: (Vector T len)) : (Vector T (Nat/succ len)) =
  ~ λP λcons λnil (cons len head tail)
-e
Contents of ./Vector/nil.kind2:
nil <T> : (Vector T Nat/zero) =
  ~λP λcons λnil nil

...

Thank you for providing the contents. Now, let's proceed with step 2: refactoring the files.

'''sh
# Refactoring ./Vector/_.kind2
# This file doesn't need changes as it only contains a data declaration

# Refactoring ./Vector/concat.kind2
cat > ./Vector/concat.kind2 << EOL
use Vector/{cons,nil}
use Nat/{succ,zero,add}

concat <T>
- xs_len: Nat
- ys_len: Nat
- xs: (Vector T xs_len)
- ys: (Vector T ys_len)
: (Vector T (add xs_len ys_len))

match xs {
  cons: (cons (add xs.len ys_len) xs.head (concat xs.len ys_len xs.tail ys))
  nil: ys
}
EOL

# Refactoring ./Vector/cons.kind2
cat > ./Vector/cons.kind2 << EOL
cons <T>
- len: Nat
- head: T
- tail: (Vector T len)
: (Vector T (Nat/succ len))

~ λP λcons λnil (cons len head tail)
EOL

# Refactoring ./Vector/nil.kind2
cat > ./Vector/nil.kind2 << EOL
nil <T>
: (Vector T Nat/zero)

~λP λcons λnil nil
EOL

echo "All Vector files have been refactored."
'''

This refactoring applies the new style to all the Vector files, following the guidelines we've established:
1. Function parameters are now on separate lines, preceded by a hyphen (-).
2. The return type is on its own line after the parameters.
3. There's an empty newline between the type annotation and the function body.
4. The function body is indented one level less than before.
5. The contents of the body itself remain unchanged.

The 'Vector/_.kind2' file wasn't changed as it only contains a data declaration.
All Vector files have been refactored.

...

Thank you for confirming the refactoring. Now, let's proceed with step 3: checking the refactored files.

'''sh
kind2 check Vector
kind2 check Vector/concat
kind2 check Vector/cons
kind2 check Vector/nil

echo "All Vector files have been checked."
'''

This will run a type check on each of the refactored files in the Vector directory to ensure that our changes haven't introduced any errors and that the files are still valid Kind2 code.
Checked.
Checked.
Checked.
All Vector files have been checked.ERROR
- unbound: 'Vector/match/'
- on_file: /Users/v/vic/dev/kind2/book/Vector/concat.kind2

we're missing a vector match function. can you include it? before you do so, please have a look on List match, Nat match and Equal match to understand how it works. also cat the respective types, and the Vector type.

Certainly! I'll review the match functions for List, Nat, and Equal, along with their respective types and the Vector type. Then, I'll create a match function for Vector.

First, let's look at the relevant files:

'''sh
echo "Contents of ./List/match.kind2:"
cat ./List/match.kind2

echo -e "\nContents of ./List/_.kind2:"
cat ./List/_.kind2

echo -e "\nContents of ./Nat/match.kind2:"
cat ./Nat/match.kind2

echo -e "\nContents of ./Nat/_.kind2:"
cat ./Nat/_.kind2

echo -e "\nContents of ./Equal/match.kind2:"
cat ./Equal/match.kind2

echo -e "\nContents of ./Equal/_.kind2:"
cat ./Equal/_.kind2

echo -e "\nContents of ./Vector/_.kind2:"
cat ./Vector/_.kind2
'''

After reviewing these files, I'll create a match function for Vector.
Contents of ./List/match.kind2:
match <A>
- P: (List A) -> *
- c: ∀(head: A) ∀(tail: (List A)) (P (List/cons A head tail))
- n: (P (List/nil A))
- xs: (List A)
: (P xs)

(~xs P c n)
-e
Contents of ./List/_.kind2:
data List <T>
| cons (head: T) (tail: (List T))
| nil

// List (A: *) : * =
//   $(self: (List A))
//   ∀(P: (List A) -> *)
//   ∀(cons: ∀(head: A) ∀(tail: (List A)) (P (List/cons/ A head tail)))
//   ∀(nil: (P (List/nil/ A)))
//   (P self)
-e
Contents of ./Nat/match.kind2:
match
- P: Nat -> *
- s: ∀(pred: Nat) (P (Nat/succ pred))
- z: (P Nat/zero)
- n: Nat
: (P n)

(~n P s z)
-e
Contents of ./Nat/_.kind2:
data Nat
| succ (pred: Nat)
| zero

//Nat
//: *
//= $(self: Nat)
  //∀(P: ∀(n: Nat) *)
  //∀(succ: ∀(n: Nat) (P (Nat.succ n)))
  //∀(zero: (P Nat.zero))
  //(P self)







-e
Contents of ./Equal/match.kind2:
match <T: *> <a: T> <b: T>
- P: ∀(a:T) ∀(b:T) ∀(e: (Equal T a b)) *
- refl: ∀(x: T) (P x x (Equal/refl T x))
- e: (Equal T a b)
: (P a b e)

(~e P refl)
-e
Contents of ./Equal/_.kind2:
data Equal <T> (a: T) (b: T)
| refl (a: T) : (Equal T a a)

//Equal : ∀(T: *) ∀(a: T) ∀(b: T) * =
  //λT λa λb
  //$(self: (Equal T a b))
  //∀(P: ∀(a: T) ∀(b: T) ∀(x: (Equal T a b)) *)
  //∀(refl: ∀(x: T) (P x x (Equal/refl T x)))
  //(P a b self)
-e
Contents of ./Vector/_.kind2:
data Vector <T> (len: Nat)
| cons (len: Nat) (head: T) (tail: (Vector T len)) : (Vector T (Nat/succ len))
| nil : (Vector T Nat/zero)

can you create vector match now?

Certainly! Based on the patterns we've seen in the List, Nat, and Equal match functions, and considering the structure of the Vector type, I'll create a match function for Vector. Here's the Vector match function:

'''sh
cat > ./Vector/match.kind2 << EOL
match <T> <len: Nat>
- P: ∀(l: Nat) (Vector T l) -> *
- c: ∀(l: Nat) ∀(head: T) ∀(tail: (Vector T l)) (P (Nat/succ l) (Vector/cons T l head tail))
- n: (P Nat/zero (Vector/nil T))
- v: (Vector T len)
: (P len v)

(~v P c n)
EOL

echo "Vector match function has been created."
'''

This Vector match function follows the pattern we've seen in the other match functions:

1. It's polymorphic over the type 'T' and the length 'len'.
2. It takes a motive 'P' that depends on both the length and the vector.
3. It has a case 'c' for the 'cons' constructor, which takes the length, head, and tail as arguments.
4. It has a case 'n' for the 'nil' constructor.
5. It takes the vector 'v' to match on.
6. The return type is '(P len v)', applying the motive to the length and the vector.
7. The implementation uses the lambda-encoded representation of the vector, applying it to the motive and cases.

Now, let's check if this new match function resolves the issue:

'''sh
kind2 check Vector/match
kind2 check Vector/concat

echo "Vector match and concat have been checked."
'''

This should check both the new match function and the concat function that was previously failing.
Vector match function has been created.

...

Thank you for confirming that the Vector match function has been created. Now, let's proceed to check both the new match function and the concat function that was previously failing.

'''sh
kind2 check Vector/match
kind2 check Vector/concat

echo "Vector match and concat have been checked."
'''

This will run a type check on the new Vector/match.kind2 file and the Vector/concat.kind2 file to ensure that our changes have resolved the previous issue and that both files are now valid Kind2 code.
Checked.
ERROR:
- expected: (Vector T (Nat/add xs_len ys_len))
- detected: (_ xs _)
- bad_term: (Vector/match _ _ _ λxs.len λxs.head λxs.tail (Vector/cons (Nat/add xs.len ys_len) xs.head (Vector/concat xs.len ys_len xs.tail ys)) ys xs)
unknown_file
  1 | Could not read source file.
Vector match and concat have been checked.

ah, that's my own fault. sadly the unification algorithm isn't able to fill the match's motive. I've fixed it manually. can you cat it?

Certainly! I apologize for the confusion. Let's take a look at the manually fixed Vector/concat.kind2 file.

'''sh
echo "Contents of ./Vector/concat.kind2:"
cat ./Vector/concat.kind2
'''

This will show us the contents of the Vector/concat.kind2 file after your manual fix. Once we see the corrected version, we can better understand how to properly use the Vector match function and potentially apply similar patterns in other files if needed.
Contents of ./Vector/concat.kind2:
use Vector/{cons,nil}
use Nat/{succ,zero,add}

concat <T>
- xs_len: Nat
- ys_len: Nat
- xs: (Vector T xs_len)
- ys: (Vector T ys_len)
: (Vector T (add xs_len ys_len))

match xs {
  cons: (cons _ (add xs.len ys_len) xs.head (concat _ xs.len ys_len xs.tail ys))
  nil: ys
}: (Vector T (add xs.len ys_len))

yep that's it. anyway, check all vec files again

Understood. Let's check all the Vector files again to ensure everything is working correctly now.

'''sh
kind2 check Vector
kind2 check Vector/concat
kind2 check Vector/cons
kind2 check Vector/nil
kind2 check Vector/match

echo "All Vector files have been checked again."
'''

This will run a type check on each of the Vector files, including the new match function and the manually fixed concat function, to ensure that all files are now valid Kind2 code.
Checked.
Checked.
Checked.
Checked.
Checked.
All Vector files have been checked again.

...

Excellent! All Vector files, including the new match function and the manually fixed concat function, have passed the type check successfully. This confirms that:

1. The Vector data type is correctly defined.
2. The Vector/match function is properly implemented and typed.
3. The Vector/concat function is now correctly using the match function and is well-typed.
4. The Vector/cons and Vector/nil functions are still correct after our refactoring.

Now that we've resolved the issues with the Vector files, we can consider this directory complete.

Is there another directory or set of files you'd like to work on next, or do you have any other tasks related to the Kind2 codebase that you'd like to address?

Another quick example of code-free programming

show all rs files in ./src recursively

'''sh
find ./src -name "*.rs" -type f
'''
./src/sugar/mod.rs
./src/term/show.rs
./src/term/mod.rs
./src/term/parse.rs
./src/term/compile.rs
./src/show/mod.rs
./src/info/show.rs
./src/info/mod.rs
./src/info/parse.rs
./src/book/show.rs
./src/book/mod.rs
./src/book/parse.rs
./src/book/compile.rs
./src/main.rs
./src/kindc.rs

cat main

'''sh
cat ./src/main.rs
'''
use clap::{Arg, ArgAction, Command};
use std::fs;
use std::io::Write;
use std::process::Command as SysCommand;

mod book;
mod info;
mod show;
mod sugar;
mod term;

use book::*;
use info::*;
use show::*;
use sugar::*;
use term::*;

use highlight_error::highlight_error;
use TSPL::Parser;

TSPL::new_parser!(KindParser);

fn generate_kindc(book: &Book, arg: &str) -> String {
  let book_kindc = book.to_kindc();
  let main_kindc = format!("main = {};\n", Term::to_kindc_name(arg));
  format!("{}{}", book_kindc, main_kindc)
}

fn run_kindc(book: &Book, cmd: &str, file: &str) -> (Vec<Info>, String) {
  let kindc_content = generate_kindc(book, file);
  let mut temp_file = fs::File::create(".main.kindc").expect("Failed to create '.main.kindc'.");
  temp_file.write_all(kindc_content.as_bytes()).expect("Failed to write '.main.kindc'.");
  let output = SysCommand::new("kindc").arg(cmd).arg(".main.kindc").output().expect("Failed to execute kindc command");
  let stdout = String::from_utf8_lossy(&output.stdout);
  let stderr = String::from_utf8_lossy(&output.stderr);
  (Info::parse_infos(&stdout), stderr.to_string())
}

fn check(name: &str) {
  let book = load_book(name);
  let (infos, stderr) = run_kindc(&book, "check", name);
  for info in &infos {
    println!("{}", info.pretty(&book));
  }
  if stderr.is_empty() && infos.is_empty() {
    println!("Checked.");
  }
  eprintln!("{stderr}");
}

fn normal(name: &str, _level: u32) {
  let book = load_book(name);
  let (infos, stderr) = run_kindc(&book, "run", name);
  for info in &infos {
    println!("{}", info.pretty(&book));
  }
  eprintln!("{stderr}");
}

fn auto_format(file_name: &str) {
  let base = std::env::current_dir().expect("failed to get current directory");
  let file = base.join(format!("{file_name}.kind2"));
  let text = std::fs::read_to_string(&file).expect("failed to read file");
  let fid  = Book::new().get_file_id(&file.to_str().unwrap().to_string());
  let book = KindParser::new(&text).parse_book(file_name, fid).expect("failed to parse book");
  let form = book.defs.iter().map(|(name, term)| book.format_def(name, term)).collect();
  let form = Show::pile("\n\n", form).flatten(Some(60));
  std::fs::write(&file, form).expect(&format!("failed to write to file '{}'", file_name));
}

fn compile(name: &str) {
  let book = load_book(name);
  let code = generate_kindc(&book, name);
  println!("{code}");
}

fn load_book(name: &str) -> Book {
  let cwd = std::env::current_dir().expect("failed to get current directory");
  Book::boot(cwd.to_str().unwrap(), name).unwrap_or_else(|e| {
    eprintln!("{e}");
    std::process::exit(1);
  })
}

fn main() {
  let matches = Command::new("kind2")
    .about("The Kind2 Programming Language")
    .subcommand_required(true)
    .arg_required_else_help(true)
    .subcommand(Command::new("check")
      .about("Type-checks a term")
      .arg(Arg::new("name").required(true)))
    .subcommand(Command::new("normal")
      .about("Normalizes a term")
      .arg(Arg::new("name").required(true))
      .arg(Arg::new("level")
        .long("level")
        .short('l')
        .action(ArgAction::Set)
        .value_parser(clap::value_parser!(u32))))
    .subcommand(Command::new("format")
      .about("Auto-formats a file")
      .arg(Arg::new("name").required(true)))
    .subcommand(Command::new("compile")
      .about("Compiles to KINDC")
      .arg(Arg::new("name").required(true)))
    .get_matches();

  match matches.subcommand() {
    Some(("check", sub_matches)) => {
      let name = sub_matches.get_one::<String>("name").expect("required");
      check(name);
    }
    Some(("normal", sub_matches)) => {
      let name = sub_matches.get_one::<String>("name").expect("required");
      let level = sub_matches.get_one::<u32>("level").copied().unwrap_or(0);
      normal(name, level);
    }
    Some(("format", sub_matches)) => {
      let name = sub_matches.get_one::<String>("name").expect("required");
      auto_format(name);
    }
    Some(("compile", sub_matches)) => {
      let name = sub_matches.get_one::<String>("name").expect("required");
      compile(name);
    }
    _ => unreachable!(),
  }
}

please, have a look on book/mod.rs

'''sh
cat ./src/book/mod.rs
'''
use crate::{*};

use std::collections::BTreeMap;
use std::collections::BTreeSet;

mod compile;
mod parse;
mod show;

// <book> ::=
//   USE | use <alias> <book>
//   ADT | <adt> <book>
//   ANN | <name> : <term> = <term> <book>
//   DEF | <name> = <term> <book>
//   END | <eof>
#[derive(Clone, Debug)]
pub struct Book {
  pub defs: BTreeMap<String, Term>,
  pub fids: BTreeMap<String, u64>,
}

// Shadows a name on the uses map
pub fn shadow(key: &str, uses: &Uses) -> Uses {
  let mut uses = uses.clone();
  uses.insert(key.to_string(), key.to_string());
  return uses;
}

// Maps short names ("cons") to full names ("List/cons")
pub type Uses = im::HashMap<String, String>;

impl Book {

  // Creates an empty book
  pub fn new() -> Self {
    Book {
      defs: BTreeMap::new(),
      fids: BTreeMap::new(),
    }
  }

  // Creates a book, loading a term, its dependencies, and stdlib
  pub fn boot(base: &str, name: &str) -> Result<Self, String> {
    let mut book = Book::new();
    book.load(base, name)?;
    book.load(base, "String")?;
    book.load(base, "String/cons")?;
    book.load(base, "String/nil")?;
    book.load(base, "Nat")?;
    book.load(base, "Nat/succ")?;
    book.load(base, "Nat/zero")?;
    book.expand_implicits();
    return Ok(book);
  }

  // Handles an unbound definition
  pub fn handle_unbound(&self, file: &str, name: &str) -> Result<(), String> {
    return Err(format!("ERROR\n- unbound: '{}'\n- on_file: {}", name, file));
  }

  // Same as load, mutably adding to a 'book'
  pub fn load(&mut self, base: &str, name: &str) -> Result<(), String> {
    let name = name.trim_end_matches('/'); // last "/" is not part of name
    if !self.defs.contains_key(name) {
      // Parses a file into a new book
      let file = format!("{}/{}.kind2", base, name);
      let text = match std::fs::read_to_string(&file) {
        Ok(content) => content,
        Err(_) => {
          let backup_file = format!("{}/{}/_.kind2", base, name);
          std::fs::read_to_string(&backup_file).map_err(|_| format!("Could not read file: {} or {}", file, backup_file))?
        }
      };
      let fid  = self.get_file_id(&file);
      let defs = KindParser::new(&text).parse_book(name, fid)?;
      // Merges new book into book
      for (def_name, def_value) in &defs.defs {
        self.defs.insert(def_name.clone(), def_value.clone());
      }
      // Finds dependencies and loads them
      for (_, def_term) in defs.defs.into_iter() {
        let mut dependencies = BTreeSet::new();
        def_term.get_free_vars(im::Vector::new(), &mut dependencies);
        for ref_name in dependencies {
          if let Err(_) = self.load(&base, &ref_name) {
            self.handle_unbound(&file, &ref_name)?;
          }
        }
      }
    }
    return Ok(());
  }

  // Desugars all definitions
  pub fn expand_implicits(&mut self) {
    // Creates a map with the implicit count of each top-level definition
    let mut implicit_count = BTreeMap::new();
    for (name, term) in self.defs.iter() {
      implicit_count.insert(name.clone(), term.count_implicits());
    }
    // Expands implicit calls of each top-level definition in the book
    for def in self.defs.iter_mut() {
      def.1.expand_implicits(im::Vector::new(), &implicit_count);
    }
  }

  // Gets a file id from its name
  pub fn get_file_id(&mut self, name: &str) -> u64 {
    if let Some(id) = self.fids.get(name) {
      *id
    } else {
      let id = self.fids.len() as u64 + 1;
      self.fids.insert(name.to_string(), id);
      id
    }
  }

  // Gets a file name from its id (FIXME: asymptotics)
  pub fn get_file_name(&self, id: u64) -> Option<String> {
    for (name, &fid) in &self.fids {
      if fid == id {
        return Some(name.clone());
      }
    }
    None
  }

}

so the load function there is responsible for loading all dependencies of a given symbol recursively. I'd like to add a command to the CLI called "deps" that outputs a list of all dependencies of a symbol. you can do so by creating a placeholder book, loading the symbol, and then printing all keys of that book - or something like that. does that make sense? please update and overwrite the main.rs to add this functionality.

'''sh
cat > ./src/main.rs << EOL
use clap::{Arg, ArgAction, Command};
use std::fs;
use std::io::Write;
use std::process::Command as SysCommand;

mod book;
mod info;
mod show;
mod sugar;
mod term;

use book::*;
use info::*;
use show::*;
use sugar::*;
use term::*;

use highlight_error::highlight_error;
use TSPL::Parser;

TSPL::new_parser!(KindParser);

fn generate_kindc(book: &Book, arg: &str) -> String {
  let book_kindc = book.to_kindc();
  let main_kindc = format!("main = {};\n", Term::to_kindc_name(arg));
  format!("{}{}", book_kindc, main_kindc)
}

fn run_kindc(book: &Book, cmd: &str, file: &str) -> (Vec<Info>, String) {
  let kindc_content = generate_kindc(book, file);
  let mut temp_file = fs::File::create(".main.kindc").expect("Failed to create '.main.kindc'.");
  temp_file.write_all(kindc_content.as_bytes()).expect("Failed to write '.main.kindc'.");
  let output = SysCommand::new("kindc").arg(cmd).arg(".main.kindc").output().expect("Failed to execute kindc command");
  let stdout = String::from_utf8_lossy(&output.stdout);
  let stderr = String::from_utf8_lossy(&output.stderr);
  (Info::parse_infos(&stdout), stderr.to_string())
}

fn check(name: &str) {
  let book = load_book(name);
  let (infos, stderr) = run_kindc(&book, "check", name);
  for info in &infos {
    println!("{}", info.pretty(&book));
  }
  if stderr.is_empty() && infos.is_empty() {
    println!("Checked.");
  }
  eprintln!("{stderr}");
}

fn normal(name: &str, _level: u32) {
  let book = load_book(name);
  let (infos, stderr) = run_kindc(&book, "run", name);
  for info in &infos {
    println!("{}", info.pretty(&book));
  }
  eprintln!("{stderr}");
}

fn auto_format(file_name: &str) {
  let base = std::env::current_dir().expect("failed to get current directory");
  let file = base.join(format!("{file_name}.kind2"));
  let text = std::fs::read_to_string(&file).expect("failed to read file");
  let fid  = Book::new().get_file_id(&file.to_str().unwrap().to_string());
  let book = KindParser::new(&text).parse_book(file_name, fid).expect("failed to parse book");
  let form = book.defs.iter().map(|(name, term)| book.format_def(name, term)).collect();
  let form = Show::pile("\n\n", form).flatten(Some(60));
  std::fs::write(&file, form).expect(&format!("failed to write to file '{}'", file_name));
}

fn compile(name: &str) {
  let book = load_book(name);
  let code = generate_kindc(&book, name);
  println!("{code}");
}

fn load_book(name: &str) -> Book {
  let cwd = std::env::current_dir().expect("failed to get current directory");
  Book::boot(cwd.to_str().unwrap(), name).unwrap_or_else(|e| {
    eprintln!("{e}");
    std::process::exit(1);
  })
}

fn deps(name: &str) {
  let mut book = Book::new();
  let cwd = std::env::current_dir().expect("failed to get current directory");
  if let Err(e) = book.load(cwd.to_str().unwrap(), name) {
    eprintln!("{e}");
    std::process::exit(1);
  }
  for dep in book.defs.keys() {
    println!("{}", dep);
  }
}

fn main() {
  let matches = Command::new("kind2")
    .about("The Kind2 Programming Language")
    .subcommand_required(true)
    .arg_required_else_help(true)
    .subcommand(Command::new("check")
      .about("Type-checks a term")
      .arg(Arg::new("name").required(true)))
    .subcommand(Command::new("normal")
      .about("Normalizes a term")
      .arg(Arg::new("name").required(true))
      .arg(Arg::new("level")
        .long("level")
        .short('l')
        .action(ArgAction::Set)
        .value_parser(clap::value_parser!(u32))))
    .subcommand(Command::new("format")
      .about("Auto-formats a file")
      .arg(Arg::new("name").required(true)))
    .subcommand(Command::new("compile")
      .about("Compiles to KINDC")
      .arg(Arg::new("name").required(true)))
    .subcommand(Command::new("deps")
      .about("Lists all dependencies of a symbol")
      .arg(Arg::new("name").required(true)))
    .get_matches();

  match matches.subcommand() {
    Some(("check", sub_matches)) => {
      let name = sub_matches.get_one::<String>("name").expect("required");
      check(name);
    }
    Some(("normal", sub_matches)) => {
      let name = sub_matches.get_one::<String>("name").expect("required");
      let level = sub_matches.get_one::<u32>("level").copied().unwrap_or(0);
      normal(name, level);
    }
    Some(("format", sub_matches)) => {
      let name = sub_matches.get_one::<String>("name").expect("required");
      auto_format(name);
    }
    Some(("compile", sub_matches)) => {
      let name = sub_matches.get_one::<String>("name").expect("required");
      compile(name);
    }
    Some(("deps", sub_matches)) => {
      let name = sub_matches.get_one::<String>("name").expect("required");
      deps(name);
    }
    _ => unreachable!(),
  }
}
EOL
'''

10/10