The Coq Standard Library

# Library Coq.extraction.ExtrOcamlZBigInt

Extraction of positive, N and Z into Ocaml's big_int
Require Import ZArith NArith.
Require Import ExtrOcamlBasic.
NB: The extracted code should be linked with nums.cm(x)a from ocaml's stdlib and with the wrapper big.ml that simplifies the use of Big_int (it can be found in the sources of Coq).
Disclaimer: trying to obtain efficient certified programs by extracting Z into big_int isn't necessarily a good idea. See the Disclaimer in ExtrOcamlNatInt.
Mapping of positive, Z, N into big_int. The last strings emulate the matching, see documentation of Extract Inductive.
Extract Inductive positive => "Big.big_int"
[ "Big.doubleplusone" "Big.double" "Big.one" ] "Big.positive_case".
Extract Inductive Z => "Big.big_int"
[ "Big.zero" "" "Big.opp" ] "Big.z_case".
Extract Inductive N => "Big.big_int"
[ "Big.zero" "" ] "Big.n_case".
Nota: the "" above is used as an identity function "(fun p->p)"
Efficient (but uncertified) versions for usual functions
Extract Constant Pos.add => "Big.add".
Extract Constant Pos.succ => "Big.succ".
Extract Constant Pos.pred => "fun n -> Big.max Big.one (Big.pred n)".
Extract Constant Pos.sub => "fun n m -> Big.max Big.one (Big.sub n m)".
Extract Constant Pos.mul => "Big.mult".
Extract Constant Pos.min => "Big.min".
Extract Constant Pos.max => "Big.max".
Extract Constant Pos.compare =>
"fun x y -> Big.compare_case Eq Lt Gt x y".
Extract Constant Pos.compare_cont =>
"fun c x y -> Big.compare_case c Lt Gt x y".
Extract Constant N.add => "Big.add".
Extract Constant N.succ => "Big.succ".
Extract Constant N.pred => "fun n -> Big.max Big.zero (Big.pred n)".
Extract Constant N.sub => "fun n m -> Big.max Big.zero (Big.sub n m)".
Extract Constant N.mul => "Big.mult".
Extract Constant N.min => "Big.min".
Extract Constant N.max => "Big.max".
Extract Constant N.div =>
"fun a b -> if Big.eq b Big.zero then Big.zero else Big.div a b".
Extract Constant N.modulo =>
"fun a b -> if Big.eq b Big.zero then Big.zero else Big.modulo a b".
Extract Constant N.compare => "Big.compare_case Eq Lt Gt".
Extract Constant Z.add => "Big.add".
Extract Constant Z.succ => "Big.succ".
Extract Constant Z.pred => "Big.pred".
Extract Constant Z.sub => "Big.sub".
Extract Constant Z.mul => "Big.mult".
Extract Constant Z.opp => "Big.opp".
Extract Constant Z.abs => "Big.abs".
Extract Constant Z.min => "Big.min".
Extract Constant Z.max => "Big.max".
Extract Constant Z.compare => "Big.compare_case Eq Lt Gt".
Extract Constant Z.of_N => "fun p -> p".
Extract Constant Z.abs_N => "Big.abs".
Z.div and Z.modulo are quite complex to define in terms of (/) and (mod). For the moment we don't even try
Test: Require Import ZArith NArith.
Extraction "/tmp/test.ml" Pos.add Pos.pred Pos.sub Pos.mul Pos.compare N.pred N.sub N.div N.modulo N.compare Z.add Z.mul Z.compare Z.of_N Z.abs_N Z.div Z.modulo.