diff options
Diffstat (limited to 'plugins/omega/PreOmega.v')
| -rw-r--r-- | plugins/omega/PreOmega.v | 46 |
1 files changed, 32 insertions, 14 deletions
diff --git a/plugins/omega/PreOmega.v b/plugins/omega/PreOmega.v index 5f5f548f..59fd9b80 100644 --- a/plugins/omega/PreOmega.v +++ b/plugins/omega/PreOmega.v @@ -1,9 +1,11 @@ (************************************************************************) -(* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) +(* * The Coq Proof Assistant / The Coq Development Team *) +(* v * INRIA, CNRS and contributors - Copyright 1999-2018 *) +(* <O___,, * (see CREDITS file for the list of authors) *) (* \VV/ **************************************************************) -(* // * This file is distributed under the terms of the *) -(* * GNU Lesser General Public License Version 2.1 *) +(* // * This file is distributed under the terms of the *) +(* * GNU Lesser General Public License Version 2.1 *) +(* * (see LICENSE file for the text of the license) *) (************************************************************************) Require Import Arith Max Min BinInt BinNat Znat Nnat. @@ -26,7 +28,7 @@ Local Open Scope Z_scope. - on Z: Z.min, Z.max, Z.abs, Z.sgn are translated in term of <= < = - on nat: + * - S O pred min max Pos.to_nat N.to_nat Z.abs_nat - on positive: Zneg Zpos xI xO xH + * - Pos.succ Pos.pred Pos.min Pos.max Pos.of_succ_nat - - on N: N0 Npos + * - N.succ N.min N.max N.of_nat Z.abs_N + - on N: N0 Npos + * - N.pred N.succ N.min N.max N.of_nat Z.abs_N *) @@ -48,10 +50,13 @@ Ltac zify_unop_var_or_term t thm a := (remember a as za; zify_unop_core t thm za). Ltac zify_unop t thm a := - (* if a is a scalar, we can simply reduce the unop *) + (* If a is a scalar, we can simply reduce the unop. *) + (* Note that simpl wasn't enough to reduce [Z.max 0 0] (#5439) *) let isz := isZcst a in match isz with - | true => simpl (t a) in * + | true => + let u := eval compute in (t a) in + change (t a) with u in * | _ => zify_unop_var_or_term t thm a end. @@ -165,21 +170,31 @@ Ltac zify_nat_op := rewrite (Nat2Z.inj_mul a b) in * (* O -> Z0 *) - | H : context [ Z.of_nat O ] |- _ => simpl (Z.of_nat O) in H - | |- context [ Z.of_nat O ] => simpl (Z.of_nat O) + | H : context [ Z.of_nat O ] |- _ => change (Z.of_nat O) with Z0 in H + | |- context [ Z.of_nat O ] => change (Z.of_nat O) with Z0 (* S -> number or Z.succ *) | H : context [ Z.of_nat (S ?a) ] |- _ => let isnat := isnatcst a in match isnat with - | true => simpl (Z.of_nat (S a)) in H + | true => + let t := eval compute in (Z.of_nat (S a)) in + change (Z.of_nat (S a)) with t in H | _ => rewrite (Nat2Z.inj_succ a) in H + | _ => (* if the [rewrite] fails (most likely a dependent occurence of [Z.of_nat (S a)]), + hide [Z.of_nat (S a)] in this one hypothesis *) + change (Z.of_nat (S a)) with (Z_of_nat' (S a)) in H end | |- context [ Z.of_nat (S ?a) ] => let isnat := isnatcst a in match isnat with - | true => simpl (Z.of_nat (S a)) + | true => + let t := eval compute in (Z.of_nat (S a)) in + change (Z.of_nat (S a)) with t | _ => rewrite (Nat2Z.inj_succ a) + | _ => (* if the [rewrite] fails (most likely a dependent occurence of [Z.of_nat (S a)]), + hide [Z.of_nat (S a)] in the goal *) + change (Z.of_nat (S a)) with (Z_of_nat' (S a)) end (* atoms of type nat : we add a positivity condition (if not already there) *) @@ -258,8 +273,8 @@ Ltac zify_positive_op := | |- context [ Zpos (Pos.max ?a ?b) ] => rewrite (Pos2Z.inj_max a b) (* Pos.sub -> Z.max 1 (Z.sub ... ...) *) - | H : context [ Zpos (Pos.sub ?a ?b) ] |- _ => rewrite (Pos2Z.inj_sub a b) in H - | |- context [ Zpos (Pos.sub ?a ?b) ] => rewrite (Pos2Z.inj_sub a b) + | H : context [ Zpos (Pos.sub ?a ?b) ] |- _ => rewrite (Pos2Z.inj_sub_max a b) in H + | |- context [ Zpos (Pos.sub ?a ?b) ] => rewrite (Pos2Z.inj_sub_max a b) (* Pos.succ -> Z.succ *) | H : context [ Zpos (Pos.succ ?a) ] |- _ => rewrite (Pos2Z.inj_succ a) in H @@ -378,6 +393,10 @@ Ltac zify_N_op := | H : context [ Z.of_N (N.sub ?a ?b) ] |- _ => rewrite (N2Z.inj_sub_max a b) in H | |- context [ Z.of_N (N.sub ?a ?b) ] => rewrite (N2Z.inj_sub_max a b) + (* pred -> minus ... -1 -> Z.max (Z.sub ... -1) 0 *) + | H : context [ Z.of_N (N.pred ?a) ] |- _ => rewrite (N.pred_sub a) in H + | |- context [ Z.of_N (N.pred ?a) ] => rewrite (N.pred_sub a) + (* N.succ -> Z.succ *) | H : context [ Z.of_N (N.succ ?a) ] |- _ => rewrite (N2Z.inj_succ a) in H | |- context [ Z.of_N (N.succ ?a) ] => rewrite (N2Z.inj_succ a) @@ -401,4 +420,3 @@ Ltac zify_N := repeat zify_N_rel; repeat zify_N_op; unfold Z_of_N' in *. (** The complete Z-ification tactic *) Ltac zify := repeat (zify_nat; zify_positive; zify_N); zify_op. - |