einblicker
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| |- let rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2) in | |
| fib 5 | |
| evalto 5 by E-LetRec { | |
| fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)] |- | |
| fib 5 | |
| evalto 5 by E-AppRec { | |
| fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)] |- | |
| fib | |
| evalto ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)] |
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| |- let rec sum = fun f -> fun n -> | |
| if n < 1 then 0 else f n + sum f (n - 1) in | |
| sum (fun x -> x * x) 2 | |
| evalto 5 | |
| by E-LetRec { | |
| sum = ()[rec sum = fun f -> fun n -> | |
| if n < 1 then 0 else f n + sum f (n - 1)] |- | |
| ((sum (fun x -> x * x)) 2) | |
| evalto 5 | |
| by E-App { |
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| |- let fact = fun self -> fun n -> | |
| if n < 2 then 1 else n * self self (n - 1) in | |
| fact fact 3 | |
| evalto 6 | |
| by E-Let { | |
| |- fun self -> fun n -> | |
| if n < 2 then 1 else n * self self (n - 1) | |
| evalto ()[fun self -> fun n -> | |
| if n < 2 then 1 else n * self self (n - 1)] | |
| by E-Fun {}; |
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| |- let rec . = fun . -> | |
| if #1 < 2 then 1 else #1 * #2 (#1 - 1) in #1 3 | |
| evalto 6 by E-LetRec { | |
| ()[rec . = fun . -> | |
| if #1 < 2 then 1 else #1 * #2 (#1 - 1)] |- #1 3 evalto 6 by E-AppRec { | |
| ()[rec . = fun . -> | |
| if #1 < 2 then 1 else #1 * #2 (#1 - 1)] |- #1 | |
| evalto ()[rec . = fun . -> | |
| if #1 < 2 then 1 else #1 * #2 (#1 - 1)] by E-Var {}; | |
| ()[rec . = fun . -> |
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| |- let f = fun x -> match x with [] -> 0 | a :: b -> a in | |
| f (4::[]) + f [] + f (1 :: 2 :: 3 :: []) | |
| evalto 5 by E-Let { | |
| |- fun x -> match x with [] -> 0 | a :: b -> a | |
| evalto ()[fun x -> match x with [] -> 0 | a :: b -> a] | |
| by E-Fun {}; | |
| f = ()[fun x -> match x with [] -> 0 | a :: b -> a] |- | |
| ((f (4::[])) + (f [])) + (f (1 :: 2 :: 3 :: [])) | |
| evalto 5 by E-Plus { | |
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| |- let rec f = fun x -> if x < 1 then [] else x :: f (x - 1) in | |
| f 3 evalto 3 :: 2 :: 1 :: [] | |
| by E-LetRec { | |
| f = ()[rec f = fun x -> if x < 1 then [] else x :: f (x - 1)] |- | |
| f 3 evalto 3 :: 2 :: 1 :: [] | |
| by E-AppRec { | |
| f = ()[rec f = fun x -> if x < 1 then [] else x :: f (x - 1)] |- | |
| f evalto ()[rec f = fun x -> if x < 1 then [] else x :: f (x - 1)] | |
| by E-Var {}; |
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| |- let rec length = fun l -> match l with [] -> 0 | x :: y -> 1 + length y in | |
| length (1 :: 2 :: 3 :: []) evalto 3 | |
| by E-LetRec { | |
| length = ()[rec length = fun l -> match l with [] -> 0 | x :: y -> 1 + length y] |- | |
| length (1 :: 2 :: 3 :: []) evalto 3 | |
| by E-AppRec { | |
| length = ()[rec length = fun l -> match l with [] -> 0 | x :: y -> 1 + length y] |- | |
| length evalto ()[rec length = fun l -> match l with [] -> 0 | x :: y -> 1 + length y] | |
| by E-Var {}; |
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| |- let rec length = fun l -> match l with [] -> 0 | x :: y -> 1 + length y in | |
| length ((1 :: 2 :: []) :: (3 :: 4 :: 5 :: []) :: []) evalto 2 | |
| by E-LetRec { | |
| length = ()[rec length = fun l -> match l with [] -> 0 | x :: y -> 1 + length y] |- | |
| length ((1 :: 2 :: []) :: (3 :: 4 :: 5 :: []) :: []) evalto 2 | |
| by E-AppRec { | |
| length = ()[rec length = fun l -> match l with [] -> 0 | x :: y -> 1 + length y] |- | |
| length evalto ()[rec length = fun l -> match l with [] -> 0 | x :: y -> 1 + length y] | |
| by E-Var {}; |
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| |- let rec apply = fun l -> fun x -> | |
| match l with [] -> x | f :: l -> f (apply l x) in | |
| apply ((fun x -> x * x) :: (fun y -> y + 3) :: []) 4 | |
| evalto 49 | |
| by E-LetRec { | |
| apply = ()[rec apply = fun l -> fun x -> | |
| match l with [] -> x | f :: l -> f (apply l x)] |- | |
| (apply ((fun x -> x * x) :: (fun y -> y + 3) :: [])) 4 | |
| evalto 49 | |
| by E-App { |
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| |- let rec apply = fun l -> fun x -> | |
| match l with [] -> x | f :: l -> apply l (f x) in | |
| apply ((fun x -> x * x) :: (fun y -> y + 3) :: []) 4 | |
| evalto 19 | |
| by E-LetRec { | |
| apply = ()[rec apply = fun l -> fun x -> | |
| match l with [] -> x | f :: l -> apply l (f x)] |- | |
| apply ((fun x -> x * x) :: (fun y -> y + 3) :: []) 4 | |
| evalto 19 | |
| by E-App { |