96 lines
2.6 KiB
Text
96 lines
2.6 KiB
Text
/- Benchmark for new code generator -/
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import init.system.io
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inductive Expr
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| Val : Int → Expr
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| Var : String → Expr
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| Add : Expr → Expr → Expr
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| Mul : Expr → Expr → Expr
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| Pow : Expr → Expr → Expr
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| Ln : Expr → Expr
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open Expr
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unsafe def pown : Int → Int → Int
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| a 0 := 1
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| a 1 := a
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| a n :=
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let b := pown a (n / 2);
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b * b * (if n % 2 = 0 then 1 else a)
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unsafe def add : Expr → Expr → Expr
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| (Val n) (Val m) := Val (n + m)
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| (Val 0) f := f
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| f (Val 0) := f
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| f (Val n) := add (Val n) f
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| (Val n) (Add (Val m) f) := add (Val (n+m)) f
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| f (Add (Val n) g) := add (Val n) (add f g)
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| (Add f g) h := add f (add g h)
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| f g := Add f g
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unsafe def mul : Expr → Expr → Expr
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| (Val n) (Val m) := Val (n*m)
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| (Val 0) _ := Val 0
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| _ (Val 0) := Val 0
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| (Val 1) f := f
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| f (Val 1) := f
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| f (Val n) := mul (Val n) f
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| (Val n) (Mul (Val m) f) := mul (Val (n*m)) f
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| f (Mul (Val n) g) := mul (Val n) (mul f g)
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| (Mul f g) h := mul f (mul g h)
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| f g := Mul f g
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unsafe def pow : Expr → Expr → Expr
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| (Val m) (Val n) := Val (pown m n)
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| _ (Val 0) := Val 1
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| f (Val 1) := f
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| (Val 0) _ := Val 0
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| f g := Pow f g
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def ln : Expr → Expr
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| (Val 1) := Val 0
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| f := Ln f
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unsafe def d (x : String) : Expr → Expr
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| (Val _) := Val 0
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| (Var y) := if x = y then Val 1 else Val 0
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| (Add f g) := add (d f) (d g)
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| (Mul f g) := add (mul f (d g)) (mul g (d f))
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| (Pow f g) := mul (pow f g) (add (mul (mul g (d f)) (pow f (Val (-1)))) (mul (ln f) (d g)))
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| (Ln f) := mul (d f) (pow f (Val (-1)))
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def count : Expr → Nat
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| (Val _) := 1
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| (Var _) := 1
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| (Add f g) := count f + count g
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| (Mul f g) := count f + count g
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| (Pow f g) := count f + count g
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| (Ln f) := count f
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def Expr.toString : Expr → String
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| (Val n) := toString n
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| (Var x) := x
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| (Add f g) := "(" ++ Expr.toString f ++ " + " ++ Expr.toString g ++ ")"
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| (Mul f g) := "(" ++ Expr.toString f ++ " * " ++ Expr.toString g ++ ")"
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| (Pow f g) := "(" ++ Expr.toString f ++ " ^ " ++ Expr.toString g ++ ")"
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| (Ln f) := "ln(" ++ Expr.toString f ++ ")"
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instance : HasToString Expr :=
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⟨Expr.toString⟩
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unsafe def nest (f : Expr → IO Expr) : Nat → Expr → IO Expr
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| 0 x := pure x
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| (n+1) x := f x >>= nest n
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unsafe def deriv (f : Expr) : IO Expr :=
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do
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let d := d "x" f;
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IO.print "count: ";
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IO.println (count f);
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pure d
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unsafe def main : IO Unit :=
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do let x := Var "x";
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let f := pow x x;
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nest deriv 9 f;
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pure ()
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