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einblicker/gist:1158965

Created August 20, 2011 11:04
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CoPL problem 76
Raw
gistfile1.txt
|- 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 {
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) :: [])
evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [])[
fun x ->
match l with [] -> x | f :: l -> f (apply l x)]
by E-AppRec {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)] |-
apply evalto ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)]
by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)] |-
(fun x -> x * x) :: ((fun y -> y + 3) :: [])
evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: []
by E-Cons {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)] |-
(fun x -> x * x)
evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x]
by E-Fun {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)] |-
(fun y -> y + 3) :: []
evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: []
by E-Cons {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)] |-
(fun y -> y + 3)
evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3]
by E-Fun {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)] |-
[] evalto [] by E-Nil {}
}
};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [] |-
fun x ->
match l with [] -> x | f :: l -> f (apply l x)
evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [])[
fun x ->
match l with [] -> x | f :: l -> f (apply l x)]
by E-Fun {}
};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)] |-
4 evalto 4 by E-Int {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4 |-
match l with [] -> x | f :: l -> f (apply l x)
evalto 49
by E-MatchCons {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4 |-
l evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: []
by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [] |-
f (apply l x)
evalto 49
by E-App {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [] |-
f evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x]
by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [] |-
((apply l) x)
evalto 7
by E-App {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [] |-
(apply l) evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [])[
fun x ->
match l with [] -> x | f :: l -> f (apply l x)]
by E-AppRec {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [] |-
apply evalto ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)]
by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [] |-
l evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: []
by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [] |-
fun x ->
match l with [] -> x | f :: l -> f (apply l x)
evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [] )[
fun x ->
match l with [] -> x | f :: l -> f (apply l x)]
by E-Fun {}
};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x] :: (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun x -> x * x],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [] |-
x evalto 4 by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4 |-
match l with [] -> x | f :: l -> f (apply l x)
evalto 7
by E-MatchCons {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4 |-
l evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: []
by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3],
l = [] |-
f (apply l x)
evalto 7
by E-App {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3],
l = [] |-
f evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3]
by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3],
l = [] |-
(apply l) x
evalto 4
by E-App {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3],
l = [] |-
apply l
evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = [])[
fun x ->
match l with [] -> x | f :: l -> f (apply l x)]
by E-AppRec {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3],
l = [] |-
apply
evalto ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)]
by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3],
l = [] |-
l evalto []
by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = [] |-
fun x ->
match l with [] -> x | f :: l -> f (apply l x)
evalto (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = [])[
fun x ->
match l with [] -> x | f :: l -> f (apply l x)]
by E-Fun {}
};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3] :: [],
x = 4,
f = (apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)])[
fun y -> y + 3],
l = [] |-
x evalto 4 by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = [],
x = 4 |-
match l with [] -> x | f :: l -> f (apply l x)
evalto 4 by E-MatchNil {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = [],
x = 4 |-
l evalto []
by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
l = [],
x = 4 |-
x evalto 4 by E-Var {}
}
};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
y = 4 |-
y + 3 evalto 7
by E-Plus {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
y = 4 |-
y evalto 4 by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
y = 4 |-
3 evalto 3 by E-Int {};
4 plus 3 is 7 by B-Plus {}
}
}
}
};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
x = 7 |-
x * x evalto 49
by E-Times {
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
x = 7 |-
x evalto 7
by E-Var {};
apply = ()[rec apply = fun l -> fun x ->
match l with [] -> x | f :: l -> f (apply l x)],
x = 7 |-
x evalto 7
by E-Var {};
7 times 7 is 49 by B-Times {}
}
}
}
}
}
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