diff options
Diffstat (limited to 'plugins/setoid_ring')
| -rw-r--r-- | plugins/setoid_ring/Field_theory.v | 30 | ||||
| -rw-r--r-- | plugins/setoid_ring/InitialRing.v | 74 | ||||
| -rw-r--r-- | plugins/setoid_ring/Ring_polynom.v | 16 | ||||
| -rw-r--r-- | plugins/setoid_ring/Ring_tac.v | 2 | ||||
| -rw-r--r-- | plugins/setoid_ring/Ring_theory.v | 45 | ||||
| -rw-r--r-- | plugins/setoid_ring/newring.ml | 4 |
6 files changed, 121 insertions, 50 deletions
diff --git a/plugins/setoid_ring/Field_theory.v b/plugins/setoid_ring/Field_theory.v index 56b985aa34..462ffde313 100644 --- a/plugins/setoid_ring/Field_theory.v +++ b/plugins/setoid_ring/Field_theory.v @@ -56,11 +56,16 @@ Let rI_neq_rO := AFth.(AF_1_neq_0). Let rdiv_def := AFth.(AFdiv_def). Let rinv_l := AFth.(AFinv_l). -Add Morphism radd : radd_ext. Proof. exact (Radd_ext Reqe). Qed. -Add Morphism rmul : rmul_ext. Proof. exact (Rmul_ext Reqe). Qed. -Add Morphism ropp : ropp_ext. Proof. exact (Ropp_ext Reqe). Qed. -Add Morphism rsub : rsub_ext. Proof. exact (ARsub_ext Rsth Reqe ARth). Qed. -Add Morphism rinv : rinv_ext. Proof. exact SRinv_ext. Qed. +Add Morphism radd with signature (req ==> req ==> req) as radd_ext. +Proof. exact (Radd_ext Reqe). Qed. +Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext. +Proof. exact (Rmul_ext Reqe). Qed. +Add Morphism ropp with signature (req ==> req) as ropp_ext. +Proof. exact (Ropp_ext Reqe). Qed. +Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext. +Proof. exact (ARsub_ext Rsth Reqe ARth). Qed. +Add Morphism rinv with signature (req ==> req) as rinv_ext. +Proof. exact SRinv_ext. Qed. Let eq_trans := Setoid.Seq_trans _ _ Rsth. Let eq_sym := Setoid.Seq_sym _ _ Rsth. @@ -1607,11 +1612,18 @@ Section Complete. Notation "x / y " := (rdiv x y). Notation "/ x" := (rinv x). Notation "x == y" := (req x y) (at level 70, no associativity). Variable Rsth : Setoid_Theory R req. - Add Setoid R req Rsth as R_setoid3. + Add Parametric Relation : R req + reflexivity proved by Rsth.(@Equivalence_Reflexive _ _) + symmetry proved by Rsth.(@Equivalence_Symmetric _ _) + transitivity proved by Rsth.(@Equivalence_Transitive _ _) + as R_setoid3. Variable Reqe : ring_eq_ext radd rmul ropp req. - Add Morphism radd : radd_ext3. exact (Radd_ext Reqe). Qed. - Add Morphism rmul : rmul_ext3. exact (Rmul_ext Reqe). Qed. - Add Morphism ropp : ropp_ext3. exact (Ropp_ext Reqe). Qed. + Add Morphism radd with signature (req ==> req ==> req) as radd_ext3. + Proof. exact (Radd_ext Reqe). Qed. + Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext3. + Proof. exact (Rmul_ext Reqe). Qed. + Add Morphism ropp with signature (req ==> req) as ropp_ext3. + Proof. exact (Ropp_ext Reqe). Qed. Section AlmostField. diff --git a/plugins/setoid_ring/InitialRing.v b/plugins/setoid_ring/InitialRing.v index 98ffff4322..8aa0b1c91f 100644 --- a/plugins/setoid_ring/InitialRing.v +++ b/plugins/setoid_ring/InitialRing.v @@ -48,12 +48,19 @@ Section ZMORPHISM. Notation "x - y " := (rsub x y). Notation "- x" := (ropp x). Notation "x == y" := (req x y). Variable Rsth : Setoid_Theory R req. - Add Setoid R req Rsth as R_setoid3. + Add Parametric Relation : R req + reflexivity proved by Rsth.(@Equivalence_Reflexive _ _) + symmetry proved by Rsth.(@Equivalence_Symmetric _ _) + transitivity proved by Rsth.(@Equivalence_Transitive _ _) + as R_setoid3. Ltac rrefl := gen_reflexivity Rsth. Variable Reqe : ring_eq_ext radd rmul ropp req. - Add Morphism radd : radd_ext3. exact (Radd_ext Reqe). Qed. - Add Morphism rmul : rmul_ext3. exact (Rmul_ext Reqe). Qed. - Add Morphism ropp : ropp_ext3. exact (Ropp_ext Reqe). Qed. + Add Morphism radd with signature (req ==> req ==> req) as radd_ext3. + Proof. exact (Radd_ext Reqe). Qed. + Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext3. + Proof. exact (Rmul_ext Reqe). Qed. + Add Morphism ropp with signature (req ==> req) as ropp_ext3. + Proof. exact (Ropp_ext Reqe). Qed. Fixpoint gen_phiPOS1 (p:positive) : R := match p with @@ -103,7 +110,8 @@ Section ZMORPHISM. Section ALMOST_RING. Variable ARth : almost_ring_theory 0 1 radd rmul rsub ropp req. - Add Morphism rsub : rsub_ext3. exact (ARsub_ext Rsth Reqe ARth). Qed. + Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext3. + Proof. exact (ARsub_ext Rsth Reqe ARth). Qed. Ltac norm := gen_srewrite Rsth Reqe ARth. Ltac add_push := gen_add_push radd Rsth Reqe ARth. @@ -151,7 +159,8 @@ Section ZMORPHISM. Variable Rth : ring_theory 0 1 radd rmul rsub ropp req. Let ARth := Rth_ARth Rsth Reqe Rth. - Add Morphism rsub : rsub_ext4. exact (ARsub_ext Rsth Reqe ARth). Qed. + Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext4. + Proof. exact (ARsub_ext Rsth Reqe ARth). Qed. Ltac norm := gen_srewrite Rsth Reqe ARth. Ltac add_push := gen_add_push radd Rsth Reqe ARth. @@ -255,7 +264,11 @@ Section NMORPHISM. Notation "0" := rO. Notation "1" := rI. Notation "x + y" := (radd x y). Notation "x * y " := (rmul x y). Variable Rsth : Setoid_Theory R req. - Add Setoid R req Rsth as R_setoid4. + Add Parametric Relation : R req + reflexivity proved by Rsth.(@Equivalence_Reflexive _ _) + symmetry proved by Rsth.(@Equivalence_Symmetric _ _) + transitivity proved by Rsth.(@Equivalence_Transitive _ _) + as R_setoid4. Ltac rrefl := gen_reflexivity Rsth. Variable SReqe : sring_eq_ext radd rmul req. Variable SRth : semi_ring_theory 0 1 radd rmul req. @@ -265,8 +278,10 @@ Section NMORPHISM. Let rsub := (@SRsub R radd). Notation "x - y " := (rsub x y). Notation "- x" := (ropp x). Notation "x == y" := (req x y). - Add Morphism radd : radd_ext4. exact (Radd_ext Reqe). Qed. - Add Morphism rmul : rmul_ext4. exact (Rmul_ext Reqe). Qed. + Add Morphism radd with signature (req ==> req ==> req) as radd_ext4. + Proof. exact (Radd_ext Reqe). Qed. + Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext4. + Proof. exact (Rmul_ext Reqe). Qed. Ltac norm := gen_srewrite_sr Rsth Reqe ARth. Definition gen_phiN1 x := @@ -374,15 +389,23 @@ Section NWORDMORPHISM. Notation "x - y " := (rsub x y). Notation "- x" := (ropp x). Notation "x == y" := (req x y). Variable Rsth : Setoid_Theory R req. - Add Setoid R req Rsth as R_setoid5. + Add Parametric Relation : R req + reflexivity proved by Rsth.(@Equivalence_Reflexive _ _) + symmetry proved by Rsth.(@Equivalence_Symmetric _ _) + transitivity proved by Rsth.(@Equivalence_Transitive _ _) + as R_setoid5. Ltac rrefl := gen_reflexivity Rsth. Variable Reqe : ring_eq_ext radd rmul ropp req. - Add Morphism radd : radd_ext5. exact (Radd_ext Reqe). Qed. - Add Morphism rmul : rmul_ext5. exact (Rmul_ext Reqe). Qed. - Add Morphism ropp : ropp_ext5. exact (Ropp_ext Reqe). Qed. + Add Morphism radd with signature (req ==> req ==> req) as radd_ext5. + Proof. exact (Radd_ext Reqe). Qed. + Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext5. + Proof. exact (Rmul_ext Reqe). Qed. + Add Morphism ropp with signature (req ==> req) as ropp_ext5. + Proof. exact (Ropp_ext Reqe). Qed. Variable ARth : almost_ring_theory 0 1 radd rmul rsub ropp req. - Add Morphism rsub : rsub_ext7. exact (ARsub_ext Rsth Reqe ARth). Qed. + Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext7. + Proof. exact (ARsub_ext Rsth Reqe ARth). Qed. Ltac norm := gen_srewrite Rsth Reqe ARth. Ltac add_push := gen_add_push radd Rsth Reqe ARth. @@ -555,12 +578,20 @@ Section GEN_DIV. Variable morph : ring_morph rO rI radd rmul rsub ropp req cO cI cadd cmul csub copp ceqb phi. (* Useful tactics *) - Add Setoid R req Rsth as R_set1. + Add Parametric Relation : R req + reflexivity proved by Rsth.(@Equivalence_Reflexive _ _) + symmetry proved by Rsth.(@Equivalence_Symmetric _ _) + transitivity proved by Rsth.(@Equivalence_Transitive _ _) + as R_set1. Ltac rrefl := gen_reflexivity Rsth. - Add Morphism radd : radd_ext. exact (Radd_ext Reqe). Qed. - Add Morphism rmul : rmul_ext. exact (Rmul_ext Reqe). Qed. - Add Morphism ropp : ropp_ext. exact (Ropp_ext Reqe). Qed. - Add Morphism rsub : rsub_ext. exact (ARsub_ext Rsth Reqe ARth). Qed. + Add Morphism radd with signature (req ==> req ==> req) as radd_ext. + Proof. exact (Radd_ext Reqe). Qed. + Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext. + Proof. exact (Rmul_ext Reqe). Qed. + Add Morphism ropp with signature (req ==> req) as ropp_ext. + Proof. exact (Ropp_ext Reqe). Qed. + Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext. + Proof. exact (ARsub_ext Rsth Reqe ARth). Qed. Ltac rsimpl := gen_srewrite Rsth Reqe ARth. Definition triv_div x y := @@ -859,8 +890,3 @@ Ltac isZcst t := (* *) | _ => constr:(false) end. - - - - - diff --git a/plugins/setoid_ring/Ring_polynom.v b/plugins/setoid_ring/Ring_polynom.v index ac54d862c9..a94f8d8df6 100644 --- a/plugins/setoid_ring/Ring_polynom.v +++ b/plugins/setoid_ring/Ring_polynom.v @@ -59,10 +59,18 @@ Section MakeRingPol. Infix "?=!" := ceqb. Notation "[ x ]" := (phi x). (* Useful tactics *) - Add Morphism radd : radd_ext. exact (Radd_ext Reqe). Qed. - Add Morphism rmul : rmul_ext. exact (Rmul_ext Reqe). Qed. - Add Morphism ropp : ropp_ext. exact (Ropp_ext Reqe). Qed. - Add Morphism rsub : rsub_ext. exact (ARsub_ext Rsth Reqe ARth). Qed. + Add Morphism radd with signature (req ==> req ==> req) as radd_ext. + Proof. exact (Radd_ext Reqe). Qed. + + Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext. + Proof. exact (Rmul_ext Reqe). Qed. + + Add Morphism ropp with signature (req ==> req) as ropp_ext. + Proof. exact (Ropp_ext Reqe). Qed. + + Add Morphism rsub with signature (req ==> req ==> req) as rsub_ext. + Proof. exact (ARsub_ext Rsth Reqe ARth). Qed. + Ltac rsimpl := gen_srewrite Rsth Reqe ARth. Ltac add_push := gen_add_push radd Rsth Reqe ARth. diff --git a/plugins/setoid_ring/Ring_tac.v b/plugins/setoid_ring/Ring_tac.v index 329fa0ee81..36d1e7c542 100644 --- a/plugins/setoid_ring/Ring_tac.v +++ b/plugins/setoid_ring/Ring_tac.v @@ -460,4 +460,4 @@ Tactic Notation "ring_simplify" "["constr_list(lH)"]" constr_list(rl) "in" hyp(H intro H'; move H' after H; clear H;rename H' into H; - unfold g;clear g.
\ No newline at end of file + unfold g;clear g. diff --git a/plugins/setoid_ring/Ring_theory.v b/plugins/setoid_ring/Ring_theory.v index 8dda5ecd34..776ebd808d 100644 --- a/plugins/setoid_ring/Ring_theory.v +++ b/plugins/setoid_ring/Ring_theory.v @@ -254,8 +254,12 @@ Section ALMOST_RING. Section SEMI_RING. Variable SReqe : sring_eq_ext radd rmul req. - Add Morphism radd : radd_ext1. exact (SRadd_ext SReqe). Qed. - Add Morphism rmul : rmul_ext1. exact (SRmul_ext SReqe). Qed. + Add Morphism radd with signature (req ==> req ==> req) as radd_ext1. + Proof. exact (SRadd_ext SReqe). Qed. + + Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext1. + Proof. exact (SRmul_ext SReqe). Qed. + Variable SRth : semi_ring_theory 0 1 radd rmul req. (** Every semi ring can be seen as an almost ring, by taking : @@ -323,9 +327,15 @@ Section ALMOST_RING. Notation "- x" := (ropp x). Variable Reqe : ring_eq_ext radd rmul ropp req. - Add Morphism radd : radd_ext2. exact (Radd_ext Reqe). Qed. - Add Morphism rmul : rmul_ext2. exact (Rmul_ext Reqe). Qed. - Add Morphism ropp : ropp_ext2. exact (Ropp_ext Reqe). Qed. + + Add Morphism radd with signature (req ==> req ==> req) as radd_ext2. + Proof. exact (Radd_ext Reqe). Qed. + + Add Morphism rmul with signature (req ==> req ==> req) as rmul_ext2. + Proof. exact (Rmul_ext Reqe). Qed. + + Add Morphism ropp with signature (req ==> req) as ropp_ext2. + Proof. exact (Ropp_ext Reqe). Qed. Section RING. Variable Rth : ring_theory 0 1 radd rmul rsub ropp req. @@ -393,14 +403,29 @@ Section ALMOST_RING. Notation "?=!" := ceqb. Notation "[ x ]" := (phi x). Variable Csth : Equivalence ceq. Variable Ceqe : ring_eq_ext cadd cmul copp ceq. - Add Setoid C ceq Csth as C_setoid. - Add Morphism cadd : cadd_ext. exact (Radd_ext Ceqe). Qed. - Add Morphism cmul : cmul_ext. exact (Rmul_ext Ceqe). Qed. - Add Morphism copp : copp_ext. exact (Ropp_ext Ceqe). Qed. + + Add Parametric Relation : C ceq + reflexivity proved by Csth.(@Equivalence_Reflexive _ _) + symmetry proved by Csth.(@Equivalence_Symmetric _ _) + transitivity proved by Csth.(@Equivalence_Transitive _ _) + as C_setoid. + + Add Morphism cadd with signature (ceq ==> ceq ==> ceq) as cadd_ext. + Proof. exact (Radd_ext Ceqe). Qed. + + Add Morphism cmul with signature (ceq ==> ceq ==> ceq) as cmul_ext. + Proof. exact (Rmul_ext Ceqe). Qed. + + Add Morphism copp with signature (ceq ==> ceq) as copp_ext. + Proof. exact (Ropp_ext Ceqe). Qed. + Variable Cth : ring_theory cO cI cadd cmul csub copp ceq. Variable Smorph : semi_morph 0 1 radd rmul req cO cI cadd cmul ceqb phi. Variable phi_ext : forall x y, ceq x y -> [x] == [y]. - Add Morphism phi : phi_ext1. exact phi_ext. Qed. + + Add Morphism phi with signature (ceq ==> req) as phi_ext1. + Proof. exact phi_ext. Qed. + Lemma Smorph_opp x : [-!x] == -[x]. Proof. rewrite <- (Rth.(Radd_0_l) [-!x]). diff --git a/plugins/setoid_ring/newring.ml b/plugins/setoid_ring/newring.ml index 0f996c65aa..b8fae2494f 100644 --- a/plugins/setoid_ring/newring.ml +++ b/plugins/setoid_ring/newring.ml @@ -131,7 +131,7 @@ let closed_term_ast l = let l = List.map (fun gr -> ArgArg(Loc.tag gr)) l in TacFun([Name(Id.of_string"t")], TacML(Loc.tag (tacname, - [TacGeneric (Genarg.in_gen (Genarg.glbwit Stdarg.wit_constr) (CAst.make @@ GVar(Id.of_string"t"),None)); + [TacGeneric (Genarg.in_gen (Genarg.glbwit Stdarg.wit_constr) (DAst.make @@ GVar(Id.of_string"t"),None)); TacGeneric (Genarg.in_gen (Genarg.glbwit (Genarg.wit_list Stdarg.wit_ref)) l)]))) (* let _ = add_tacdef false ((Loc.ghost,Id.of_string"ring_closed_term" @@ -220,7 +220,7 @@ let exec_tactic env evd n f args = let gls = Proofview.V82.of_tactic (Tacinterp.eval_tactic_ist ist (ltac_call f (args@[getter]))) gl in let evd, nf = Evarutil.nf_evars_and_universes (Refiner.project gls) in let nf c = nf (constr_of c) in - Array.map nf !tactic_res, snd (Evd.universe_context evd) + Array.map nf !tactic_res, snd (Evd.universe_context ~names:[] ~extensible:true evd) let stdlib_modules = [["Coq";"Setoids";"Setoid"]; |