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einblicker/gist:1156445

Created August 19, 2011 09:31
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CoPL problem 51
Raw
gistfile1.txt
|- 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)]
by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)] |-
5
evalto 5 by E-Int {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
if n < 3 then 1 else fib (n - 1) + fib (n - 2)
evalto 5 by E-IfF {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
n < 3
evalto false by E-Lt {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
n evalto 5 by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
3 evalto 3 by E-Int {};
5 less than 3 is false by B-Lt {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
fib (n - 1) + fib (n - 2)
evalto 5 by E-Plus {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
fib (n - 1)
evalto 3 by E-AppRec {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
fib
evalto ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)]
by E-Var2 {
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)]
by E-Var1 {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
n - 1 evalto 4
by E-Minus {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
n evalto 5 by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
1 evalto 1 by E-Int {};
5 minus 1 is 4 by B-Minus {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
if n < 3 then 1 else fib (n - 1) + fib (n - 2)
evalto 3 by E-IfF {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
n < 3 evalto false
by E-Lt {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
n evalto 4 by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
3 evalto 3 by E-Int {};
4 less than 3 is false by B-Lt {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
fib (n - 1) + fib (n - 2)
evalto 3 by E-Plus {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
fib (n - 1)
evalto 2 by E-AppRec {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
fib evalto ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)]
by E-Var2 {
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)]
by E-Var1 {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
n - 1 evalto 3
by E-Minus {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
n evalto 4
by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
1 evalto 1 by E-Int {};
4 minus 1 is 3 by B-Minus {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
if n < 3 then 1 else fib (n - 1) + fib (n - 2)
evalto 2 by E-IfF {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
n < 3 evalto false
by E-Lt {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
n evalto 3 by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
3 evalto 3 by E-Int {};
3 less than 3 is false by B-Lt {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
fib (n - 1) + fib (n - 2)
evalto 2 by E-Plus {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
fib (n - 1) evalto 1
by E-AppRec {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
fib evalto ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)]
by E-Var2 {
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)]
by E-Var1 {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
n - 1 evalto 2
by E-Minus {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
n evalto 3
by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
1 evalto 1
by E-Int {};
3 minus 1 is 2 by B-Minus {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
if n < 3 then 1 else fib (n - 1) + fib (n - 2)
evalto 1
by E-IfT {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
n < 3 evalto true
by E-Lt {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
n evalto 2 by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
3 evalto 3 by E-Int {};
2 less than 3 is true by B-Lt {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
1 evalto 1
by E-Int {}
}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
fib (n - 2) evalto 1
by E-AppRec {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
fib evalto ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)]
by E-Var2 {
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)]
by E-Var1 {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
n - 2 evalto 1
by E-Minus {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
n evalto 3 by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
2 evalto 2 by E-Int {};
3 minus 2 is 1 by B-Minus {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 1 |-
if n < 3 then 1 else fib (n - 1) + fib (n - 2)
evalto 1
by E-IfT {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 1 |-
n < 3 evalto true
by E-Lt {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 1 |-
n evalto 1 by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 1 |-
3 evalto 3 by E-Int {};
1 less than 3 is true by B-Lt {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 1 |-
1 evalto 1 by E-Int {}
}
};
1 plus 1 is 2 by B-Plus {}
}
}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
fib (n - 2)
evalto 1 by E-AppRec {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
fib evalto ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)]
by E-Var2 {
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)]
by E-Var1 {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
n - 2 evalto 2
by E-Minus {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
n evalto 4
by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 4 |-
2 evalto 2
by E-Int {};
4 minus 2 is 2 by B-Minus {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
if n < 3 then 1 else fib (n - 1) + fib (n - 2)
evalto 1
by E-IfT {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
n < 3 evalto true
by E-Lt {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
n evalto 2
by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
3 evalto 3
by E-Int {};
2 less than 3 is true by B-Lt {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
1 evalto 1
by E-Int {}
}
};
2 plus 1 is 3 by B-Plus {}
}
}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
fib (n - 2)
evalto 2 by E-AppRec {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
fib evalto ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)]
by E-Var2 {
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)]
by E-Var1 {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
n - 2 evalto 3
by E-Minus {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
n evalto 5 by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 5 |-
2 evalto 2 by E-Int {};
5 minus 2 is 3 by B-Minus {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
if n < 3 then 1 else fib (n - 1) + fib (n - 2)
evalto 2
by E-IfF {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
n < 3 evalto false
by E-Lt {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
n evalto 3
by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
3 evalto 3
by E-Int {};
3 less than 3 is false by B-Lt {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
fib (n - 1) + fib (n - 2)
evalto 2
by E-Plus {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
fib (n - 1)
evalto 1
by E-AppRec {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
fib evalto ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)]
by E-Var2 {
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)]
by E-Var1 {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
n - 1 evalto 2
by E-Minus {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
n evalto 3
by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
1 evalto 1
by E-Int {};
3 minus 1 is 2 by B-Minus {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
if n < 3 then 1 else fib (n - 1) + fib (n - 2)
evalto 1
by E-IfT {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
n < 3 evalto true
by E-Lt {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
n evalto 2
by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
3 evalto 3
by E-Int {};
2 less than 3 is true by B-Lt {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 2 |-
1 evalto 1
by E-Int {}
}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
fib (n - 2)
evalto 1
by E-AppRec {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
fib evalto ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)]
by E-Var2 {
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)]
by E-Var1 {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
n - 2 evalto 1
by E-Minus {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
n evalto 3
by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 3 |-
2 evalto 2
by E-Int {};
3 minus 2 is 1 by B-Minus {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 1 |-
if n < 3 then 1 else fib (n - 1) + fib (n - 2)
evalto 1
by E-IfT {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 1 |-
n < 3 evalto true
by E-Lt {
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 1 |-
n evalto 1
by E-Var1 {};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 1 |-
3 evalto 3
by E-Int {};
1 less than 3 is true by B-Lt {}
};
fib = ()[rec fib = fun n -> if n < 3 then 1 else fib (n - 1) + fib (n - 2)],
n = 1 |-
1 evalto 1
by E-Int {}
}
};
1 plus 1 is 2 by B-Plus {}
}
}
};
3 plus 2 is 5 by B-Plus {}
}
}
}
}
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