# Library Coq.extraction.ExtrOcamlZInt

Extraction of positive, N and Z into Ocaml's int

Require Coq.extraction.Extraction.

Require Import ZArith NArith.
Require Import ExtrOcamlBasic.

Disclaimer: trying to obtain efficient certified programs by extracting Z into int is definitively *not* a good idea. See the Disclaimer in ExtrOcamlNatInt.
Mapping of positive, Z, N into int. The last strings emulate the matching, see documentation of Extract Inductive.

Extract Inductive positive => int
[ "(fun p->1+2*p)" "(fun p->2*p)" "1" ]
"(fun f2p1 f2p f1 p -> if p<=1 then f1 () else if p mod 2 = 0 then f2p (p/2) else f2p1 (p/2))".

Extract Inductive Z => int [ "0" "" "(~-)" ]
"(fun f0 fp fn z -> if z=0 then f0 () else if z>0 then fp z else fn (-z))".

Extract Inductive N => int [ "0" "" ]
"(fun f0 fp n -> if n=0 then f0 () else fp n)".

Nota: the "" above is used as an identity function "(fun p->p)"
Efficient (but uncertified) versions for usual functions

Extract Constant Pos.add => "(+)".
Extract Constant Pos.succ => "Pervasives.succ".
Extract Constant Pos.pred => "fun n -> Pervasives.max 1 (n-1)".
Extract Constant Pos.sub => "fun n m -> Pervasives.max 1 (n-m)".
Extract Constant Pos.mul => "( * )".
Extract Constant Pos.min => "Pervasives.min".
Extract Constant Pos.max => "Pervasives.max".
Extract Constant Pos.compare =>
"fun x y -> if x=y then Eq else if x<y then Lt else Gt".
Extract Constant Pos.compare_cont =>
"fun c x y -> if x=y then c else if x<y then Lt else Gt".

Extract Constant N.add => "(+)".
Extract Constant N.succ => "Pervasives.succ".
Extract Constant N.pred => "fun n -> Pervasives.max 0 (n-1)".
Extract Constant N.sub => "fun n m -> Pervasives.max 0 (n-m)".
Extract Constant N.mul => "( * )".
Extract Constant N.min => "Pervasives.min".
Extract Constant N.max => "Pervasives.max".
Extract Constant N.div => "fun a b -> if b=0 then 0 else a/b".
Extract Constant N.modulo => "fun a b -> if b=0 then a else a mod b".
Extract Constant N.compare =>
"fun x y -> if x=y then Eq else if x<y then Lt else Gt".

Extract Constant Z.add => "(+)".
Extract Constant Z.succ => "Pervasives.succ".
Extract Constant Z.pred => "Pervasives.pred".
Extract Constant Z.sub => "(-)".
Extract Constant Z.mul => "( * )".
Extract Constant Z.opp => "(~-)".
Extract Constant Z.abs => "Pervasives.abs".
Extract Constant Z.min => "Pervasives.min".
Extract Constant Z.max => "Pervasives.max".
Extract Constant Z.compare =>
"fun x y -> if x=y then Eq else if x<y then Lt else Gt".

Extract Constant Z.of_N => "fun p -> p".
Extract Constant Z.abs_N => "Pervasives.abs".

Z.div and Z.modulo are quite complex to define in terms of (/) and (mod). For the moment we don't even try