99 lines
2.8 KiB
Text
99 lines
2.8 KiB
Text
/- Benchmark for new code generator -/
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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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partial 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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partial 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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partial 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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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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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 → UInt32
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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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def nestAux (s : Nat) (f : Nat → Expr → IO Expr) : Nat → Expr → IO Expr
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| 0, x => pure x
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| m@(n+1), x => f (s - m) x >>= nestAux n
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def nest (f : Nat → Expr → IO Expr) (n : Nat) (e : Expr) : IO Expr :=
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nestAux n f n e
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def deriv (i : Nat) (f : Expr) : IO Expr :=
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do
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let d := d "x" f;
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IO.println (toString (i+1) ++ " count: " ++ (toString $ count d));
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pure d
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unsafe def main : List String → IO UInt32
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| [s] => do
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let n := s.toNat;
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let x := Var "x";
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let f := pow x x;
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nest deriv n f;
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pure 0
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| _ => pure 1
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