Created
October 10, 2015 22:00
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Staged Fixed-point combinator
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| open Microsoft.FSharp.Quotations | |
| // <@ fun x -> (% <@ x @> ) @> ~ lambda (fun x -> x) | |
| let lambda (f : Expr<'T> -> Expr<'R>) : Expr<'T -> 'R> = | |
| let var = new Var("__temp__", typeof<'T>) | |
| Expr.Cast<_>(Expr.Lambda(var, f (Expr.Cast<_>(Expr.Var var)))) | |
| // fixed-point combinator | |
| let rec fix : (('Τ -> 'R) -> ('Τ -> 'R)) -> 'Τ -> 'R = fun f x -> | |
| f (fix f) x | |
| let power x f = | |
| fun n -> | |
| match n with | |
| | 0 -> <@ 1 @> | |
| | n -> <@ %x * (% f (n - 1) ) @> | |
| let power2 = fix (power <@ 2 @>) | |
| power2 10 // loop unroll 10 times | |
| // Staged fixed-point combinator | |
| let fix' : (Expr<'T -> 'R> -> Expr<'T -> 'R>) -> Expr<'T -> 'R> = fun f -> | |
| <@ fun x -> let rec loop x = (% lambda (fun f' -> f f') ) loop x in loop x @> | |
| let power' x f = | |
| <@ fun n -> | |
| match n with | |
| | 0 -> 1 | |
| | n -> %x * (%f) (n - 1) @> | |
| let power2' = fix' (power' <@ 2 @>) |
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