The Coq Proof Assistant

# Library Coq.extraction.ExtrOcamlZBigInt

Extraction of positive, N, and Z, into Zarith's Z.t
Require Coq.extraction.Extraction.
Require Import ZArith NArith.
Require Import ExtrOcamlBasic.
Extraction Blacklist Z Big_int_Z.
NB: The extracted code depends on zarith package.
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 Z. The last strings emulate the matching, see documentation of Extract Inductive.
Extract Inductive positive => "Big_int_Z.big_int"
[ "(fun x -> Big_int_Z.succ_big_int (Big_int_Z.mult_int_big_int 2 x))"
"Big_int_Z.mult_int_big_int 2" "Big_int_Z.unit_big_int" ]
"(fun f2p1 f2p f1 p -> if Big_int_Z.le_big_int p Big_int_Z.unit_big_int then f1 () else let (q,r) = Big_int_Z.quomod_big_int p (Big_int_Z.big_int_of_int 2) in if Big_int_Z.eq_big_int r Big_int_Z.zero_big_int then f2p q else f2p1 q)".
Extract Inductive Z => "Big_int_Z.big_int"
[ "Big_int_Z.zero_big_int" "" "Big_int_Z.minus_big_int" ]
"(fun fO fp fn z -> let s = Big_int_Z.sign_big_int z in if s = 0 then fO () else if s > 0 then fp z else fn (Big_int_Z.minus_big_int z))".
Extract Inductive N => "Big_int_Z.big_int"
[ "Big_int_Z.zero_big_int" "" ]
"(fun fO fp n -> if Big_int_Z.sign_big_int n <= 0 then fO () 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 => "Big_int_Z.add_big_int".
Extract Constant Pos.succ => "Big_int_Z.succ_big_int".
Extract Constant Pos.pred =>
"(fun n -> Big_int_Z.max_big_int Big_int_Z.unit_big_int (Big_int_Z.pred_big_int n))".
Extract Constant Pos.sub =>
"(fun n m -> Big_int_Z.max_big_int Big_int_Z.unit_big_int (Big_int_Z.sub_big_int n m))".
Extract Constant Pos.mul => "Big_int_Z.mult_big_int".
Extract Constant Pos.min => "Big_int_Z.min_big_int".
Extract Constant Pos.max => "Big_int_Z.max_big_int".
Extract Constant Pos.compare =>
"(fun x y -> let s = Big_int_Z.compare_big_int x y in if s = 0 then Eq else if s < 0 then Lt else Gt)".
Extract Constant Pos.compare_cont =>
"(fun c x y -> let s = Big_int_Z.compare_big_int x y in if s = 0 then c else if s < 0 then Lt else Gt)".
Extract Constant N.add => "Big_int_Z.add_big_int".
Extract Constant N.succ => "Big_int_Z.succ_big_int".
Extract Constant N.pred =>
"(fun n -> Big_int_Z.max_big_int Big_int_Z.zero_big_int (Big_int_Z.pred_big_int n))".
Extract Constant N.sub =>
"(fun n m -> Big_int_Z.max_big_int Big_int_Z.zero_big_int (Big_int_Z.sub_big_int n m))".
Extract Constant N.mul => "Big_int_Z.mult_big_int".
Extract Constant N.min => "Big_int_Z.min_big_int".
Extract Constant N.max => "Big_int_Z.max_big_int".
Extract Constant N.div_eucl =>
"Big_int_Z.(fun x y -> if eq_big_int zero_big_int y then (zero_big_int, x) else quomod_big_int x y)".
Extract Constant N.div =>
"(fun a b -> if Big_int_Z.eq_big_int b Big_int_Z.zero_big_int then Big_int_Z.zero_big_int else Big_int_Z.div_big_int a b)".
Extract Constant N.modulo =>
"(fun a b -> if Big_int_Z.eq_big_int b Big_int_Z.zero_big_int then a else Big_int_Z.mod_big_int a b)".
Extract Constant Z.eqb => "Big_int_Z.eq_big_int".
Extract Constant Z.eq_dec => "Big_int_Z.eq_big_int".
Extract Constant N.compare =>
"(fun x y -> let s = Big_int_Z.compare_big_int x y in if s = 0 then Eq else if s < 0 then Lt else Gt)".
Extract Constant N.shiftl => "Big_int_Z.(fun x y -> shift_left_big_int x (int_of_big_int y))".
Extract Constant N.shiftr => "Big_int_Z.(fun x y -> shift_right_big_int x (int_of_big_int y))".
Extract Constant Z.add => "Big_int_Z.add_big_int".
Extract Constant Z.succ => "Big_int_Z.succ_big_int".
Extract Constant Z.pred => "Big_int_Z.pred_big_int".
Extract Constant Z.sub => "Big_int_Z.sub_big_int".
Extract Constant Z.mul => "Big_int_Z.mult_big_int".
Extract Constant Z.opp => "Big_int_Z.minus_big_int".
Extract Constant Z.abs => "Big_int_Z.abs_big_int".
Extract Constant Z.min => "Big_int_Z.min_big_int".
Extract Constant Z.max => "Big_int_Z.max_big_int".
Extract Constant Z.compare =>
"(fun x y -> let s = Big_int_Z.compare_big_int x y in if s = 0 then Eq else if s < 0 then Lt else Gt)".
Extract Constant Z.eqb => "Big_int_Z.eq_big_int".
Extract Constant Z.eq_dec => "Big_int_Z.eq_big_int".
Extract Constant Z.to_N => "Big_int_Z.(fun p -> if sign_big_int p < 0 then zero_big_int else p)".
Extract Constant Z.of_N => "(fun p -> p)".
Extract Constant Z.abs_N => "Big_int_Z.abs_big_int".
Extract Constant Z.div_eucl => "Big_int_Z.(fun x y -> match sign_big_int y with | 0 -> (zero_big_int, x) | 1 -> quomod_big_int x y | _ -> let (q, r) = quomod_big_int (add_int_big_int (-1) x) y in (add_int_big_int (-1) q, add_big_int (add_int_big_int 1 y) r))".
Extract Constant Z.div => "Big_int_Z.(fun x y -> match sign_big_int y with | 0 -> zero_big_int | 1 -> div_big_int x y | _ -> add_int_big_int (-1) (div_big_int (add_int_big_int (-1) x) y))".
Extract Constant Z.modulo => "Big_int_Z.(fun x y -> match sign_big_int y with | 0 -> x | 1 -> mod_big_int x y | _ -> add_big_int y (add_int_big_int 1 (mod_big_int (add_int_big_int (-1) x) y)))".
Extract Constant Z.shiftl => "Big_int_Z.(fun x y -> let y = int_of_big_int y in if y < 0 then shift_right_big_int x (-y) else shift_left_big_int x y)".
Extract Constant Z.shiftr => "Big_int_Z.(fun x y -> let y = int_of_big_int y in if y < 0 then shift_left_big_int x (-y) else shift_right_big_int x y)".
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.