Library Coq.extraction.ExtrHaskellNatNum

Efficient (but uncertified) extraction of usual nat functions

into equivalent versions in Haskell's Prelude that are defined

for any Num typeclass instances. Useful in combination with

Extract Inductive nat that maps nat onto a Haskell type that

implements Num.


Require Coq.extraction.Extraction.

Require Import Arith.
Require Import EqNat.

Extract Inlined Constant Nat.add => "(Prelude.+)".
Extract Inlined Constant Nat.mul => "(Prelude.*)".
Extract Inlined Constant Nat.max => "Prelude.max".
Extract Inlined Constant Nat.min => "Prelude.min".
Extract Inlined Constant Init.Nat.add => "(Prelude.+)".
Extract Inlined Constant Init.Nat.mul => "(Prelude.*)".
Extract Inlined Constant Init.Nat.max => "Prelude.max".
Extract Inlined Constant Init.Nat.min => "Prelude.min".
Extract Inlined Constant Compare_dec.lt_dec => "(Prelude.<)".
Extract Inlined Constant Compare_dec.leb => "(Prelude.<=)".
Extract Inlined Constant Compare_dec.le_lt_dec => "(Prelude.<=)".
Extract Inlined Constant Nat.eqb => "(Prelude.==)".
Extract Inlined Constant EqNat.eq_nat_decide => "(Prelude.==)".
Extract Inlined Constant Peano_dec.eq_nat_dec => "(Prelude.==)".

Extract Constant Nat.pred => "(\n -> Prelude.max 0 (Prelude.pred n))".
Extract Constant Nat.sub => "(\n m -> Prelude.max 0 (n Prelude.- m))".
Extract Constant Init.Nat.pred => "(\n -> Prelude.max 0 (Prelude.pred n))".
Extract Constant Init.Nat.sub => "(\n m -> Prelude.max 0 (n Prelude.- m))".

Extract Constant Nat.div => "(\n m -> if m Prelude.== 0 then 0 else Prelude.div n m)".
Extract Constant Nat.modulo => "(\n m -> if m Prelude.== 0 then n else Prelude.mod n m)".
Extract Constant Init.Nat.div => "(\n m -> if m Prelude.== 0 then 0 else Prelude.div n m)".
Extract Constant Init.Nat.modulo => "(\n m -> if m Prelude.== 0 then n else Prelude.mod n m)".