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July 13, 2014 02:36
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Learn more about bidirectional Unicode charactersOriginal file line number Diff line number Diff line change @@ -0,0 +1,112 @@ |- let twice = fun f -> fun x -> f (f x) in twice twice (fun x -> x * x) 2 evalto 65536 by E-Let { |- fun f -> fun x -> f (f x) evalto ()[fun f -> fun x -> f (f x)] by E-Fun {}; twice = ()[fun f -> fun x -> f (f x)] |- twice twice (fun x -> x * x) 2 evalto 65536 by E-App { twice = ()[fun f -> fun x -> f (f x)] |- twice twice (fun x -> x * x) evalto (f = (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)])[fun x -> f (f x)] by E-App { twice = ()[fun f -> fun x -> f (f x)] |- twice twice evalto (f = ()[fun f -> fun x -> f (f x)])[fun x -> f (f x)] by E-App { twice = ()[fun f -> fun x -> f (f x)] |- twice evalto ()[fun f -> fun x -> f (f x)] by E-Var1 {}; twice = ()[fun f -> fun x -> f (f x)] |- twice evalto ()[fun f -> fun x -> f (f x)] by E-Var1 {}; f = ()[fun f -> fun x -> f (f x)] |- fun x -> f (f x) evalto (f = ()[fun f -> fun x -> f (f x)])[fun x -> f (f x)] by E-Fun {}; }; twice = ()[fun f -> fun x -> f (f x)] |- fun x -> x * x evalto (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] by E-Fun {}; f = ()[fun f -> fun x -> f (f x)], x = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] |- f (f x) evalto (f = (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)])[fun x -> f (f x)] by E-App { f = ()[fun f -> fun x -> f (f x)], x = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] |- f evalto ()[fun f -> fun x -> f (f x)] by E-Var2 { f = ()[fun f -> fun x -> f (f x)] |- f evalto ()[fun f -> fun x -> f (f x)] by E-Var1 {}; }; f = ()[fun f -> fun x -> f (f x)], x = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] |- f x evalto (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)] by E-App { f = ()[fun f -> fun x -> f (f x)], x = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] |- f evalto ()[fun f -> fun x -> f (f x)] by E-Var2 { f = ()[fun f -> fun x -> f (f x)] |- f evalto ()[fun f -> fun x -> f (f x)] by E-Var1 {}; }; f = ()[fun f -> fun x -> f (f x)], x = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] |- x evalto (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] by E-Var1 {}; f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] |- fun x -> f (f x) evalto (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)] by E-Fun {}; }; f = (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)] |- fun x -> f (f x) evalto (f = (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)])[fun x -> f (f x)] by E-Fun {}; } }; twice = ()[fun f -> fun x -> f (f x)] |- 2 evalto 2 by E-Int {}; f = (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)], x = 2 |- f (f x) evalto 65536 by E-App { f = (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)], x = 2 |- f evalto (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)] by E-Var2 { f = (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)] |- f evalto (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)] by E-Var1 {}; }; f = (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)], x = 2 |- f x evalto 16 by E-App { f = (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)], x = 2 |- f evalto (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)] by E-Var2 { f = (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)] |- f evalto (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)] by E-Var1 {}; }; f = (f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x])[fun x -> f (f x)], x = 2 |- x evalto 2 by E-Var1 {}; f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x], x = 2 |- f (f x) evalto 16 by E-App { f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x], x = 2 |- f evalto (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] by E-Var2 { f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] |- f evalto (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] by E-Var1 {}; }; f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x], x = 2 |- f x evalto 4 by E-App { f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x], x = 2 |- f evalto (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] by E-Var2 { f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] |- f evalto (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] by E-Var1 {}; }; f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x], x = 2 |- x evalto 2 by E-Var1 {}; twice = ()[fun f -> fun x -> f (f x)], x = 2 |- x * x evalto 4 by E-Times { twice = ()[fun f -> fun x -> f (f x)], x = 2 |- x evalto 2 by E-Var1{}; twice = ()[fun f -> fun x -> f (f x)], x = 2 |- x evalto 2 by E-Var1{}; 2 times 2 is 4 by B-Times {}; }; }; twice = ()[fun f -> fun x -> f (f x)], x = 4 |- x * x evalto 16 by E-Times { twice = ()[fun f -> fun x -> f (f x)], x = 4 |- x evalto 4 by E-Var1{}; twice = ()[fun f -> fun x -> f (f x)], x = 4 |- x evalto 4 by E-Var1{}; 4 times 4 is 16 by B-Times {}; }; } }; f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x], x = 16 |- f (f x) evalto 65536 by E-App { f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x], x = 16 |- f evalto (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] by E-Var2 { f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] |- f evalto (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] by E-Var1 {}; }; f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x], x = 16 |- f x evalto 256 by E-App { f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x], x = 16 |- f evalto (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] by E-Var2 { f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] |- f evalto (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x] by E-Var1 {}; }; f = (twice = ()[fun f -> fun x -> f (f x)])[fun x -> x * x], x = 16 |- x evalto 16 by E-Var1 {}; twice = ()[fun f -> fun x -> f (f x)], x = 16 |- x * x evalto 256 by E-Times { twice = ()[fun f -> fun x -> f (f x)], x = 16 |- x evalto 16 by E-Var1{}; twice = ()[fun f -> fun x -> f (f x)], x = 16 |- x evalto 16 by E-Var1{}; 16 times 16 is 256 by B-Times {}; }; }; twice = ()[fun f -> fun x -> f (f x)], x = 256 |- x * x evalto 65536 by E-Times { twice = ()[fun f -> fun x -> f (f x)], x = 256 |- x evalto 256 by E-Var1{}; twice = ()[fun f -> fun x -> f (f x)], x = 256 |- x evalto 256 by E-Var1{}; 256 times 256 is 65536 by B-Times {}; }; } } } } }