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einblicker/gist:1156613

Created August 19, 2011 11:29
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CoPL problem 52
Raw
gistfile1.txt
|- 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 {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)] |-
(sum (fun x -> x * x)) evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x])[
fun n ->
if n < 1 then 0 else f n + sum f (n - 1)]
by E-AppRec {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)] |-
sum evalto ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)]
by E-Var1 {};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)] |-
(fun x -> x * x) evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x]
by E-Fun {};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x] |-
fun n -> if n < 1 then 0 else f n + sum f (n - 1)
evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x])[
fun n ->
if n < 1 then 0 else f n + sum f (n - 1)]
by E-Fun {}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)] |-
2 evalto 2 by E-Int {};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
if n < 1 then 0 else f n + sum f (n - 1)
evalto 5
by E-IfF {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
n < 1 evalto false
by E-Lt {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
n evalto 2 by E-Var1 {};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
1 evalto 1 by E-Int {};
2 less than 1 is false by B-Lt {}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
f n + sum f (n - 1)
evalto 5
by E-Plus {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
f n evalto 4
by E-App {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
f evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x]
by E-Var2 {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x] |-
f evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x]
by E-Var1 {}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
n evalto 2 by E-Var1 {};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
x = 2 |-
x * x evalto 4 by E-Times {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
x = 2 |-
x evalto 2 by E-Var1 {};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
x = 2 |-
x evalto 2 by E-Var1 {};
2 times 2 is 4 by B-Times {}
}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
((sum f) (n - 1))
evalto 1
by E-App {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
sum f evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x])[
fun n ->
if n < 1 then 0 else f n + sum f (n - 1)]
by E-AppRec {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
sum evalto ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)]
by E-Var2 {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x] |-
sum evalto ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)]
by E-Var2 {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)] |-
sum evalto ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)]
by E-Var1 {}
}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
f evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x]
by E-Var2 {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x] |-
f evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x]
by E-Var1 {}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x] |-
fun n ->
if n < 1 then 0 else f n + sum f (n - 1)
evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x])[
fun n ->
if n < 1 then 0 else f n + sum f (n - 1)]
by E-Fun {}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
n - 1 evalto 1
by E-Minus {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
n evalto 2 by E-Var1 {};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 2 |-
1 evalto 1 by E-Int {};
2 minus 1 is 1 by B-Minus {}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
if n < 1 then 0 else f n + sum f (n - 1)
evalto 1
by E-IfF {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
n < 1 evalto false
by E-Lt {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
n evalto 1
by E-Var1 {};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
1 evalto 1
by E-Int {};
1 less than 1 is false by B-Lt {}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
f n + sum f (n - 1)
evalto 1
by E-Plus {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
f n evalto 1
by E-App {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
f evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x]
by E-Var2 {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x] |-
f evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x]
by E-Var1 {}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
n evalto 1
by E-Var1 {};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
x = 1 |-
x * x evalto 1
by E-Times {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
x = 1 |-
x evalto 1 by E-Var1 {};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
x = 1 |-
x evalto 1 by E-Var1 {};
1 times 1 is 1 by B-Times {}
}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
((sum f) (n - 1)) evalto 0
by E-App {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
sum f evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x])[
fun n ->
if n < 1 then 0 else f n + sum f (n - 1)]
by E-AppRec {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
sum evalto ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)]
by E-Var2 {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x] |-
sum evalto ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)]
by E-Var2 {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)] |-
sum evalto ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)]
by E-Var1 {}
}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
f evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x]
by E-Var2 {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x] |-
f evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x]
by E-Var1 {}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x] |-
fun n ->
if n < 1 then 0 else f n + sum f (n - 1)
evalto (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x])[
fun n ->
if n < 1 then 0 else f n + sum f (n - 1)]
by E-Fun {}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
n - 1 evalto 0
by E-Minus {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
n evalto 1
by E-Var1 {};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 1 |-
1 evalto 1
by E-Int {};
1 minus 1 is 0 by B-Minus {}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 0 |-
if n < 1 then 0 else f n + sum f (n - 1)
evalto 0
by E-IfT {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 0 |-
n < 1 evalto true
by E-Lt {
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 0 |-
n evalto 0 by E-Var1 {};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 0 |-
1 evalto 1 by E-Int {};
0 less than 1 is true by B-Lt {}
};
sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)],
f = (sum = ()[rec sum = fun f -> fun n ->
if n < 1 then 0 else f n + sum f (n - 1)])[fun x -> x * x],
n = 0 |-
0 evalto 0 by E-Int {}
}
};
1 plus 0 is 1 by B-Plus {}
}
}
};
4 plus 1 is 5 by B-Plus {}
}
}
}
}
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