minor fixes, updates, rebases

Author: affeldt-aist

coq-mathcomp-analysis.opam

@@ -22,7 +22,8 @@ depends: [
   "coq-mathcomp-solvable" { (>= "2.0.0") | (= "dev") }
   "coq-mathcomp-field"
   "coq-mathcomp-bigenough" { (>= "1.0.0") }
-  "coq-mathcomp-algebra-tactics" { (>= "1.1.1") }
+  "coq-mathcomp-algebra-tactics" { (>= "1.2.0") }
+  "coq-mathcomp-zify" { (>= "1.4.0") }
 ]
 
 tags: [

theories/lang_syntax.v

@@ -1,8 +1,8 @@
 Require Import String.
 From HB Require Import structures.
 From mathcomp Require Import all_ssreflect ssralg ssrnum ssrint interval.
-From mathcomp.classical Require Import mathcomp_extra boolp classical_sets.
-From mathcomp.classical Require Import functions cardinality fsbigop.
+From mathcomp Require Import mathcomp_extra boolp classical_sets.
+From mathcomp Require Import functions cardinality fsbigop.
 Require Import signed reals ereal topology normedtype sequences esum measure.
 Require Import lebesgue_measure numfun lebesgue_integral kernel prob_lang.
 Require Import lang_syntax_util.
@@ -89,7 +89,7 @@ Proof. done. Qed.
 Let mswap_sigma_additive x : semi_sigma_additive (mswap x).
 Proof. exact: measure_semi_sigma_additive. Qed.
 
-HB.instance Definition _ x := isMeasure.Build _ R _
+HB.instance Definition _ x := isMeasure.Build _ _ R
   (mswap x) (mswap0 x) (mswap_ge0 x) (@mswap_sigma_additive x).
 
 Definition mkswap : _ -> {measure set Z -> \bar R} :=
@@ -185,24 +185,22 @@ Let T0 z : (T' z) set0 = 0. Proof. by []. Qed.
 Let T_ge0 z x : 0 <= (T' z) x. Proof. by []. Qed.
 Let T_semi_sigma_additive z : semi_sigma_additive (T' z).
 Proof. exact: measure_semi_sigma_additive. Qed.
-HB.instance Definition _ z := @isMeasure.Build _ R X (T' z) (T0 z) (T_ge0 z)
+HB.instance Definition _ z := @isMeasure.Build _ X R (T' z) (T0 z) (T_ge0 z)
   (@T_semi_sigma_additive z).
 
 Let sfinT z : sfinite_measure (T' z). Proof. exact: sfinite_kernel_measure. Qed.
-HB.instance Definition _ z := @Measure_isSFinite_subdef.Build _ X R
-  (T' z) (sfinT z).
+HB.instance Definition _ z := @isSFinite.Build _ X R (T' z) (sfinT z).
 
 Definition U' z : set Y -> \bar R := u z.
 Let U0 z : (U' z) set0 = 0. Proof. by []. Qed.
 Let U_ge0 z x : 0 <= (U' z) x. Proof. by []. Qed.
 Let U_semi_sigma_additive z : semi_sigma_additive (U' z).
 Proof. exact: measure_semi_sigma_additive. Qed.
-HB.instance Definition _ z := @isMeasure.Build _ R Y (U' z) (U0 z) (U_ge0 z)
+HB.instance Definition _ z := @isMeasure.Build _ Y R (U' z) (U0 z) (U_ge0 z)
   (@U_semi_sigma_additive z).
 
 Let sfinU z : sfinite_measure (U' z). Proof. exact: sfinite_kernel_measure. Qed.
-HB.instance Definition _ z := @Measure_isSFinite_subdef.Build _ Y R
-  (U' z) (sfinU z).
+HB.instance Definition _ z := @isSFinite.Build _ Y R (U' z) (sfinU z).
 
 Lemma letin'C z A : measurable A ->
   letin' t
@@ -271,7 +269,7 @@ Inductive typ :=
 | Pair : typ -> typ -> typ
 | Prob : typ -> typ.
 
-Canonical stype_eqType := Equality.Pack (@gen_eqMixin typ).
+HB.instance Definition _ := gen_eqMixin typ.
 
 Fixpoint measurable_of_typ (t : typ) : {d & measurableType d} :=
   match t with

theories/lang_syntax_examples.v

@@ -59,7 +59,7 @@ Lemma letin'_sample_bernoulli d d' (T : measurableType d)
 Proof.
 rewrite letin'E/=.
 rewrite ge0_integral_measure_sum// 2!big_ord_recl/= big_ord0 adde0/=.
-by rewrite !ge0_integral_mscale//= !integral_dirac//= indicT 2!mul1e.
+by rewrite !ge0_integral_mscale//= !integral_dirac//= !diracT 2!mul1e.
 Qed.
 
 Section letin'_return.
@@ -81,7 +81,7 @@ Lemma letin'_retk (f : X -> Y) (mf : measurable_fun setT f)
     (k : R.-sfker Y * X ~> Z) x U :
   measurable U -> letin' (ret mf) k x U = k (f x, x) U.
 Proof.
-move=> mU; rewrite letin'E retE integral_dirac ?indicT ?mul1e//.
+move=> mU; rewrite letin'E retE integral_dirac ?diracT ?mul1e//.
 exact: (measurableT_comp (measurable_kernel k _ mU)).
 Qed.
 
@@ -209,48 +209,48 @@ Definition sample_pair_syntax : exp _ [::] _ :=
 Lemma exec_sample_pair0 (A : set (bool * bool)) :
   @execP R [::] _ sample_pair_syntax0 tt A =
   ((1 / 2)%:E *
-   ((1 / 3)%:E * ((true, true) \in A)%:R%:E +
-    (1 - 1 / 3)%:E * ((true, false) \in A)%:R%:E) +
+   ((1 / 3)%:E * \d_(true, true) A +
+    (1 - 1 / 3)%:E * \d_(true, false) A) +
    (1 - 1 / 2)%:E *
-   ((1 / 3)%:E * ((false, true) \in A)%:R%:E +
-    (1 - 1 / 3)%:E * ((false, false) \in A)%:R%:E))%E.
+   ((1 / 3)%:E * \d_(false, true) A +
+    (1 - 1 / 3)%:E * \d_(false, false) A))%E.
 Proof.
 rewrite !execP_letin !execP_sample !execD_bernoulli execP_return /=.
 rewrite execD_pair !exp_var'E (execD_var_erefl "x") (execD_var_erefl "y") /=.
 rewrite letin'E integral_measure_add//= !ge0_integral_mscale//= /onem.
-rewrite !integral_dirac//= !indicE !in_setT/= !mul1e.
+rewrite !integral_dirac//= !diracT !mul1e.
 rewrite !letin'E !integral_measure_add//= !ge0_integral_mscale//= /onem.
-by rewrite !integral_dirac//= !indicE !in_setT/= !mul1e !diracE.
+by rewrite !integral_dirac//= !diracT !mul1e.
 Qed.
 
 Lemma exec_sample_pair0_TandT :
   @execP R [::] _ sample_pair_syntax0 tt [set (true, true)] = (1 / 6)%:E.
 Proof.
-rewrite exec_sample_pair0 mem_set//; do 3 rewrite memNset//=.
+rewrite exec_sample_pair0 !diracE mem_set//; do 3 rewrite memNset//=.
 by rewrite /= !mule0 mule1 !add0e mule0 adde0; congr (_%:E); lra.
 Qed.
 
 Lemma exec_sample_pair0_TandF :
   @execP R [::] _ sample_pair_syntax0 tt [set (true, false)] = (1 / 3)%:E.
 Proof.
-rewrite exec_sample_pair0 memNset// mem_set//; do 2 rewrite memNset//.
+rewrite exec_sample_pair0 !diracE memNset// mem_set//; do 2 rewrite memNset//.
 by rewrite /= !mule0 mule1 !add0e mule0 adde0; congr (_%:E); lra.
 Qed.
 
 Lemma exec_sample_pair0_TandT' :
   @execP R [::] _ sample_pair_syntax0 tt [set p | p.1 && p.2] = (1 / 6)%:E.
 Proof.
-rewrite exec_sample_pair0 mem_set//; do 3 rewrite memNset//=.
+rewrite exec_sample_pair0 !diracE mem_set//; do 3 rewrite memNset//=.
 by rewrite /= !mule0 mule1 !add0e mule0 adde0; congr (_%:E); lra.
 Qed.
 
 Lemma exec_sample_pair_TorT :
   (projT1 (execD sample_pair_syntax)) tt [set p | p.1 || p.2] = (2 / 3)%:E.
 Proof.
 rewrite execD_normalize_pt normalizeE/= exec_sample_pair0.
-do 4 rewrite mem_set//=.
+rewrite !diracE; do 4 rewrite mem_set//=.
 rewrite eqe ifF; last by apply/negbTE/negP => /orP[/eqP|//]; lra.
-rewrite exec_sample_pair0; do 3 rewrite mem_set//; rewrite memNset//=.
+rewrite exec_sample_pair0 !diracE; do 3 rewrite mem_set//; rewrite memNset//=.
 by rewrite !mule1; congr (_%:E); field.
 Qed.
 
@@ -260,18 +260,17 @@ Definition sample_and_syntax0 : @exp R _ [::] _ :=
    return #{"x"} && #{"y"}].
 
 Lemma exec_sample_and0 (A : set bool) :
-  @execP R [::] _ sample_and_syntax0 tt A =
-  ((1 / 6)%:E * (true \in A)%:R%:E +
-  (1 - 1 / 6)%:E * (false \in A)%:R%:E)%E.
+  @execP R [::] _ sample_and_syntax0 tt A = ((1 / 6)%:E * \d_true A +
+                                             (1 - 1 / 6)%:E * \d_false A)%E.
 Proof.
 rewrite !execP_letin !execP_sample !execD_bernoulli execP_return /=.
 rewrite (@execD_bin _ _ binop_and) !exp_var'E (execD_var_erefl "x") (execD_var_erefl "y") /=.
 rewrite letin'E integral_measure_add//= !ge0_integral_mscale//= /onem.
-rewrite !integral_dirac//= !indicE !in_setT/= !mul1e.
+rewrite !integral_dirac//= !diracT !mul1e.
 rewrite !letin'E !integral_measure_add//= !ge0_integral_mscale//= /onem.
-rewrite !integral_dirac//= !indicE !in_setT/= !mul1e !diracE.
+rewrite !integral_dirac//= !diracT !mul1e.
 rewrite muleDr// -addeA; congr (_ + _)%E.
-by rewrite !muleA; congr (_%:E); congr (_ * _); field.
+  by rewrite !muleA; congr (_%:E); congr (_ * _); field.
 rewrite -muleDl// !muleA -muleDl//.
 by congr (_%:E); congr (_ * _); field.
 Qed.
@@ -283,19 +282,18 @@ Definition sample_bernoulli_and3 : @exp R _ [::] _ :=
    return #{"x"} && #{"y"} && #{"z"}].
 
 Lemma exec_sample_bernoulli_and3 t U :
-  execP sample_bernoulli_and3 t U =
-  ((1 / 8)%:E * (true \in U)%:R%:E +
-  (1 - 1 / 8)%:E * (false \in U)%:R%:E)%E.
+  execP sample_bernoulli_and3 t U = ((1 / 8)%:E * \d_true U +
+                                     (1 - 1 / 8)%:E * \d_false U)%E.
 Proof.
 rewrite !execP_letin !execP_sample !execD_bernoulli execP_return /=.
 rewrite !(@execD_bin _ _ binop_and) !exp_var'E.
 rewrite (execD_var_erefl "x") (execD_var_erefl "y") (execD_var_erefl "z") /=.
 rewrite letin'E integral_measure_add//= !ge0_integral_mscale//= /onem.
-rewrite !integral_dirac//= !indicE !in_setT/= !mul1e.
+rewrite !integral_dirac//= !diracT !mul1e.
 rewrite !letin'E !integral_measure_add//= !ge0_integral_mscale//= /onem.
-rewrite !integral_dirac//= !indicE !in_setT/= !mul1e.
+rewrite !integral_dirac//= !diracT !mul1e.
 rewrite !letin'E !integral_measure_add//= !ge0_integral_mscale//= /onem.
-rewrite !integral_dirac//= !indicE !in_setT/= !mul1e !diracE.
+rewrite !integral_dirac//= !diracT !mul1e.
 rewrite !muleDr// -!addeA.
 by congr (_ + _)%E; rewrite ?addeA !muleA -?muleDl//;
 congr (_ * _)%E; congr (_%:E); field.
@@ -307,25 +305,6 @@ Definition sample_add_syntax0 : @exp R _ [::] _ :=
    let "z" := Sample {exp_bernoulli (1 / 2)%:nng (p1S 1)} in
    return #{"x"} && #{"y"} && #{"z"}].
 
-Lemma exec_sample_bernoulli_and3 t U :
-  execP sample_bernoulli_and3 t U =
-  ((1 / 8)%:E * (true \in U)%:R%:E +
-  (1 - 1 / 8)%:E * (false \in U)%:R%:E)%E.
-Proof.
-rewrite !execP_letin !execP_sample !execD_bernoulli execP_return /=.
-rewrite !(@execD_bin _ _ binop_and) !exp_var'E.
-rewrite (execD_var_erefl "x") (execD_var_erefl "y") (execD_var_erefl "z") /=.
-rewrite letin'E integral_measure_add//= !ge0_integral_mscale//= /onem.
-rewrite !integral_dirac//= !indicE !in_setT/= !mul1e.
-rewrite !letin'E !integral_measure_add//= !ge0_integral_mscale//= /onem.
-rewrite !integral_dirac//= !indicE !in_setT/= !mul1e.
-rewrite !letin'E !integral_measure_add//= !ge0_integral_mscale//= /onem.
-rewrite !integral_dirac//= !indicE !in_setT/= !mul1e !diracE.
-rewrite !muleDr// -!addeA.
-by congr (_ + _)%E; rewrite ?addeA !muleA -?muleDl//;
-congr (_ * _)%E; congr (_%:E); field.
-Qed.
-
 End sample_pair.
 
 Section bernoulli_examples.
@@ -357,24 +336,23 @@ rewrite !integral_measure_add //=; last by move=> b _; rewrite integral_ge0.
 rewrite !ge0_integral_mscale //=; last 2 first.
   by move=> b _; rewrite integral_ge0.
   by move=> b _; rewrite integral_ge0.
-rewrite !integral_dirac// !indicE !in_setT !mul1e.
+rewrite !integral_dirac// !diracT !mul1e.
 rewrite iteE/= !ge0_integral_mscale//=.
 rewrite ger0_norm//.
 rewrite !integral_indic//= !iteE/= /mscale/=.
-rewrite setTI diracE !in_setT !mule1.
+rewrite setTI !diracT !mule1.
 rewrite ger0_norm//.
 rewrite -EFinD/= eqe ifF; last first.
   by apply/negbTE/negP => /orP[/eqP|//]; rewrite /onem; lra.
 rewrite !letin'E/= !iteE/=.
 rewrite !ge0_integral_mscale//=.
 rewrite ger0_norm//.
-rewrite !integral_dirac//= !indicE !in_setT /= !mul1e ger0_norm//.
+rewrite !integral_dirac//= !diracT !mul1e ger0_norm//.
 rewrite exp_var'E (execD_var_erefl "x")/=.
 rewrite /bernoulli/= measure_addE/= /mscale/= !mul1r.
-rewrite muleDl//; congr (_ + _)%E;
-  rewrite -!EFinM;
-  congr (_%:E);
-  by rewrite indicE /onem; case: (_ \in _); field.
+by rewrite muleDl//; congr (_ + _)%E;
+  rewrite -!EFinM; congr (_%:E);
+  rewrite !indicT !indicE /onem /=; case: (_ \in _); field.
 Qed.
 
 Definition bernoulli12_score := [Normalize
@@ -400,25 +378,25 @@ rewrite !integral_measure_add //=; last by move=> b _; rewrite integral_ge0.
 rewrite !ge0_integral_mscale //=; last 2 first.
   by move=> b _; rewrite integral_ge0.
   by move=> b _; rewrite integral_ge0.
-rewrite !integral_dirac// !indicE !in_setT !mul1e.
+rewrite !integral_dirac// !diracT !mul1e.
 rewrite iteE/= !ge0_integral_mscale//=.
 rewrite ger0_norm//.
 rewrite !integral_indic//= !iteE/= /mscale/=.
-rewrite setTI diracE !in_setT !mule1.
+rewrite setTI !diracT !mule1.
 rewrite ger0_norm//.
 rewrite -EFinD/= eqe ifF; last first.
   apply/negbTE/negP => /orP[/eqP|//].
   by rewrite /onem; lra.
 rewrite !letin'E/= !iteE/=.
 rewrite !ge0_integral_mscale//=.
 rewrite ger0_norm//.
-rewrite !integral_dirac//= !indicE !in_setT /= !mul1e ger0_norm//.
+rewrite !integral_dirac//= !diracT !mul1e ger0_norm//.
 rewrite exp_var'E (execD_var_erefl "x")/=.
 rewrite /bernoulli/= measure_addE/= /mscale/= !mul1r.
 rewrite muleDl//; congr (_ + _)%E;
   rewrite -!EFinM;
   congr (_%:E);
-  by rewrite indicE /onem; case: (_ \in _); field.
+  by rewrite !indicT !indicE /onem /=; case: (_ \in _); field.
 Qed.
 
 (* https://dl.acm.org/doi/pdf/10.1145/2933575.2935313 (Sect. 4) *)
@@ -447,26 +425,26 @@ under eq_integral.
   over.
 rewrite !integral_measure_add //=; last by move=> b _; rewrite integral_ge0.
 rewrite !ge0_integral_mscale //=; last 2 first.
-  by move=> b _; rewrite integral_ge0.
-  by move=> b _; rewrite integral_ge0.
-rewrite !integral_dirac// !indicE !in_setT !mul1e.
+  by move=> b _; exact: integral_ge0.
+  by move=> b _; exact: integral_ge0.
+rewrite !integral_dirac// !diracT !mul1e.
 rewrite iteE/= !ge0_integral_mscale//=.
 rewrite ger0_norm//.
-rewrite !integral_indic//= !iteE/= /mscale/=.
-rewrite setTI diracE !in_setT !mule1.
+rewrite !integral_cst//= !diracT !(mule1,mul1e).
+rewrite !iteE/= /mscale/= !diracT !mule1.
 rewrite ger0_norm//.
 rewrite -EFinD/= eqe ifF; last first.
   apply/negbTE/negP => /orP[/eqP|//].
   by rewrite /onem; lra.
 rewrite !letin'E/= !iteE/=.
 rewrite !ge0_integral_mscale//=.
 rewrite ger0_norm//.
-rewrite !integral_dirac//= !indicE !in_setT /= !mul1e ger0_norm//.
+rewrite !integral_dirac//= !diracT !mul1e ger0_norm//.
 rewrite /bernoulli/= measure_addE/= /mscale/= !mul1r.
 rewrite muleDl//; congr (_ + _)%E;
   rewrite -!EFinM;
   congr (_%:E);
-  by rewrite indicE /onem; case: (_ \in _); field.
+  by rewrite !indicT !indicE /onem /=; case: (_ \in _); field.
 Qed.
 
 End bernoulli_examples.
@@ -494,7 +472,7 @@ Proof.
 apply/eq_sfkernel => x U.
 rewrite letin'E/= /sample; unlock.
 rewrite integral_measure_add//= ge0_integral_mscale//= ge0_integral_mscale//=.
-rewrite integral_dirac//= integral_dirac//= !indicT/= !mul1e.
+rewrite !integral_dirac//= !diracT/= !mul1e.
 by rewrite /mscale/= iteE//= iteE//= fail'E mule0 adde0 ger0_norm.
 Qed.
 

theories/lang_syntax_toy.v

@@ -1,7 +1,7 @@
 Require Import String Classical.
 From HB Require Import structures.
 From mathcomp Require Import all_ssreflect ssralg.
-From mathcomp.classical Require Import mathcomp_extra boolp.
+From mathcomp Require Import mathcomp_extra boolp.
 Require Import signed reals topology normedtype.
 Require Import lang_syntax_util.
 
@@ -36,7 +36,7 @@ Variables (R : realType).
 
 Inductive typ := Real | Unit.
 
-Canonical typ_eqType := Equality.Pack (@gen_eqMixin typ).
+HB.instance Definition _ := gen_eqMixin typ.
 
 Definition iter_pair (l : list Type) : Type :=
   foldr (fun x y => (x * y)%type) unit l.
@@ -169,7 +169,7 @@ Implicit Types str : string.
 
 Inductive typ := Real | Unit | Pair : typ -> typ -> typ.
 
-Canonical typ_eqType := Equality.Pack (@gen_eqMixin typ).
+HB.instance Definition _ := gen_eqMixin typ.
 
 Fixpoint mtyp (t : typ) : Type :=
   match t with

theories/lang_syntax_util.v

@@ -8,8 +8,7 @@ Require Import signed.
 (*                  Shared by lang_syntax_*.v files                           *)
 (******************************************************************************)
 
-Definition string_eqMixin := @EqMixin string String.eqb eqb_spec.
-Canonical string_eqType := EqType string string_eqMixin.
+HB.instance Definition _ := hasDecEq.Build string eqb_spec.
 
 Ltac inj_ex H := revert H;
   match goal with