diff options
Diffstat (limited to 'plugins/setoid_ring/InitialRing.v')
| -rw-r--r-- | plugins/setoid_ring/InitialRing.v | 56 |
1 files changed, 28 insertions, 28 deletions
diff --git a/plugins/setoid_ring/InitialRing.v b/plugins/setoid_ring/InitialRing.v index b92b847be5..8fcc077164 100644 --- a/plugins/setoid_ring/InitialRing.v +++ b/plugins/setoid_ring/InitialRing.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -155,7 +155,7 @@ Section ZMORPHISM. Ltac norm := gen_srewrite Rsth Reqe ARth. Ltac add_push := gen_add_push radd Rsth Reqe ARth. -(*morphisms are extensionaly equal*) +(*morphisms are extensionally equal*) Lemma same_genZ : forall x, [x] == gen_phiZ1 x. Proof. destruct x;simpl; try rewrite (same_gen ARth);rrefl. @@ -246,7 +246,7 @@ Proof (SRth_ARth Nsth Nth). Lemma Neqb_ok : forall x y, N.eqb x y = true -> x = y. Proof. exact (fun x y => proj1 (N.eqb_eq x y)). Qed. -(**Same as above : definition of two,extensionaly equal, generic morphisms *) +(**Same as above : definition of two, extensionally equal, generic morphisms *) (**from N to any semi-ring*) Section NMORPHISM. Variable R : Type. @@ -612,32 +612,32 @@ End GEN_DIV. Ltac inv_gen_phi_pos rI add mul t := let rec inv_cst t := match t with - rI => constr:1%positive - | (add rI rI) => constr:2%positive - | (add rI (add rI rI)) => constr:3%positive + rI => constr:(1%positive) + | (add rI rI) => constr:(2%positive) + | (add rI (add rI rI)) => constr:(3%positive) | (mul (add rI rI) ?p) => (* 2p *) match inv_cst p with - NotConstant => constr:NotConstant - | 1%positive => constr:NotConstant (* 2*1 is not convertible to 2 *) + NotConstant => constr:(NotConstant) + | 1%positive => constr:(NotConstant) (* 2*1 is not convertible to 2 *) | ?p => constr:(xO p) end | (add rI (mul (add rI rI) ?p)) => (* 1+2p *) match inv_cst p with - NotConstant => constr:NotConstant - | 1%positive => constr:NotConstant + NotConstant => constr:(NotConstant) + | 1%positive => constr:(NotConstant) | ?p => constr:(xI p) end - | _ => constr:NotConstant + | _ => constr:(NotConstant) end in inv_cst t. (* The (partial) inverse of gen_phiNword *) Ltac inv_gen_phiNword rO rI add mul opp t := match t with - rO => constr:NwO + rO => constr:(NwO) | _ => match inv_gen_phi_pos rI add mul t with - NotConstant => constr:NotConstant + NotConstant => constr:(NotConstant) | ?p => constr:(Npos p::nil) end end. @@ -646,10 +646,10 @@ End GEN_DIV. (* The inverse of gen_phiN *) Ltac inv_gen_phiN rO rI add mul t := match t with - rO => constr:0%N + rO => constr:(0%N) | _ => match inv_gen_phi_pos rI add mul t with - NotConstant => constr:NotConstant + NotConstant => constr:(NotConstant) | ?p => constr:(Npos p) end end. @@ -657,21 +657,21 @@ End GEN_DIV. (* The inverse of gen_phiZ *) Ltac inv_gen_phiZ rO rI add mul opp t := match t with - rO => constr:0%Z + rO => constr:(0%Z) | (opp ?p) => match inv_gen_phi_pos rI add mul p with - NotConstant => constr:NotConstant + NotConstant => constr:(NotConstant) | ?p => constr:(Zneg p) end | _ => match inv_gen_phi_pos rI add mul t with - NotConstant => constr:NotConstant + NotConstant => constr:(NotConstant) | ?p => constr:(Zpos p) end end. (* A simple tactic recognizing only 0 and 1. The inv_gen_phiX above - are only optimisations that directly returns the reifid constant + are only optimisations that directly returns the reified constant instead of resorting to the constant propagation of the simplification algorithm. *) Ltac inv_gen_phi rO rI cO cI t := @@ -681,7 +681,7 @@ Ltac inv_gen_phi rO rI cO cI t := end. (* A simple tactic recognizing no constant *) - Ltac inv_morph_nothing t := constr:NotConstant. + Ltac inv_morph_nothing t := constr:(NotConstant). Ltac coerce_to_almost_ring set ext rspec := match type of rspec with @@ -825,31 +825,31 @@ Ltac ring_elements set ext rspec pspec sspec dspec rk := (* Tactic for constant *) Ltac isnatcst t := match t with - O => constr:true + O => constr:(true) | S ?p => isnatcst p - | _ => constr:false + | _ => constr:(false) end. Ltac isPcst t := match t with | xI ?p => isPcst p | xO ?p => isPcst p - | xH => constr:true + | xH => constr:(true) (* nat -> positive *) | Pos.of_succ_nat ?n => isnatcst n - | _ => constr:false + | _ => constr:(false) end. Ltac isNcst t := match t with - N0 => constr:true + N0 => constr:(true) | Npos ?p => isPcst p - | _ => constr:false + | _ => constr:(false) end. Ltac isZcst t := match t with - Z0 => constr:true + Z0 => constr:(true) | Zpos ?p => isPcst p | Zneg ?p => isPcst p (* injection nat -> Z *) @@ -857,7 +857,7 @@ Ltac isZcst t := (* injection N -> Z *) | Z.of_N ?n => isNcst n (* *) - | _ => constr:false + | _ => constr:(false) end. |