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einblicker/gist:1156043

Created August 19, 2011 04:34
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CoPL problem 48
Raw
gistfile1.txt
|- let compose = fun f -> fun g -> fun x -> f (g x) in
let p = fun x -> x * x in
let q = fun x -> x + 4 in
compose p q 4
evalto 64 by E-Let {
|- fun f -> fun g -> fun x -> f (g x) evalto ()[fun f -> fun g -> fun x -> f (g x)] by E-Fun {};
compose = ()[fun f -> fun g -> fun x -> f (g x)]
|- let p = fun x -> x * x in
let q = fun x -> x + 4 in
compose p q 4
evalto 64 by E-Let {
compose = ()[fun f -> fun g -> fun x -> f (g x)] |- fun x -> x * x evalto (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x] by E-Fun {};
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x]
|- let q = fun x -> x + 4 in
compose p q 4
evalto 64 by E-Let {
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x]|- fun x -> x + 4 evalto (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4] by E-Fun {};
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], q = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4]
|- compose p q 4
evalto 64 by E-App {
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], q = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4] |- ((compose p) q) evalto (f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], g = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4])[fun x -> f (g x)] by E-App {
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], q = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4]
|- compose p evalto (f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun g -> fun x -> f (g x)] by E-App {
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], q = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4]
|- compose evalto ()[fun f -> fun g -> fun x -> f (g x)] by E-Var2 {
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x]
|- compose evalto ()[fun f -> fun g -> fun x -> f (g x)] by E-Var2 {
compose = ()[fun f -> fun g -> fun x -> f (g x)]
|- compose evalto ()[fun f -> fun g -> fun x -> f (g x)] by E-Var1 {}
}
};
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], q = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4]
|- p evalto (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x] by E-Var2 {
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x]
|- p evalto (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x] by E-Var1 {}
};
f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x]
|- fun g -> fun x -> f (g x) evalto (f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun g -> fun x -> f (g x)] by E-Fun {}
};
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], q = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4]|-
q evalto (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4] by E-Var1 {};
f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x],g = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4] |- fun x -> f (g x) evalto (f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], g = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4])[fun x -> f (g x)] by E-Fun {}
};
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], q = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4]
|- 4 evalto 4 by E-Int {};
f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], g = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4], x = 4 |- f (g x) evalto 64 by E-App {
f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], g = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4], x = 4 |- f evalto (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x] by E-Var2 {
f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], g = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4]|- f evalto (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x] by E-Var2 {
f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x] |- f evalto (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x] by E-Var1 {}
}
};
f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], g = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4], x = 4 |- g x evalto 8 by E-App {
f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], g = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4], x = 4|- g evalto (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4] by E-Var2 {
f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], g = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4]|- g evalto (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4] by E-Var1 {}
};
f = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], g = (compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x])[fun x -> x + 4], x = 4|- x evalto 4 by E-Var1 {};
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], x = 4|- x + 4 evalto 8 by E-Plus {
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], x = 4|- x evalto 4 by E-Var1 {};
compose = ()[fun f -> fun g -> fun x -> f (g x)], p = (compose = ()[fun f -> fun g -> fun x -> f (g x)])[fun x -> x * x], x = 4|- 4 evalto 4 by E-Int {};
4 plus 4 is 8 by B-Plus {}
}
};
compose = ()[fun f -> fun g -> fun x -> f (g x)], x = 8 |- x * x evalto 64 by E-Times {
compose = ()[fun f -> fun g -> fun x -> f (g x)], x = 8 |- x evalto 8 by E-Var1 {};
compose = ()[fun f -> fun g -> fun x -> f (g x)], x = 8 |- x evalto 8 by E-Var1 {};
8 times 8 is 64 by B-Times {}
}
}
}
}
}
}
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