rebase wrt 0.6.6

Author: affeldt-aist

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} :=
@@ -185,7 +185,7 @@ 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.
@@ -197,7 +197,7 @@ 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.
@@ -271,7 +271,7 @@ 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.
 
@@ -218,9 +218,9 @@ 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 :
@@ -266,9 +266,9 @@ 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.
 rewrite -muleDl// !muleA -muleDl//.
@@ -289,11 +289,11 @@ 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.
@@ -336,24 +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
@@ -379,25 +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) *)
@@ -428,24 +427,24 @@ rewrite !integral_measure_add //=; last by move=> b _; rewrite integral_ge0.
 rewrite !ge0_integral_mscale //=; last 2 first.
   by move=> b _; exact: integral_ge0.
   by move=> b _; exact: 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 !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.
@@ -473,7 +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

theories/prob_lang.v

@@ -2,10 +2,10 @@
 From HB Require Import structures.
 From mathcomp Require Import all_ssreflect ssralg ssrnum ssrint interval finmap.
 From mathcomp Require Import rat.
-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 reals ereal signed topology normedtype sequences esum measure.
-Require Import lebesgue_measure  numfun lebesgue_integral exp kernel.
+Require Import lebesgue_measure numfun lebesgue_integral exp kernel.
 
 (******************************************************************************)
 (*  Semantics of a probabilistic programming language using s-finite kernels  *)
@@ -116,7 +116,7 @@ Lemma integral_bernoulli {R : realType}
 Proof.
 move=> f0.
 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 !mul1e.
 Qed.
 
 Section uniform_probability.
@@ -131,7 +131,7 @@ HB.instance Definition _ := Measure.on uniform_probability.
 Let uniform_probability_setT : uniform_probability [set: _] = 1.
 Proof.
 rewrite /uniform_probability /mscale/= /mrestr/=.
-rewrite setTI lebesgue_measure_itv hlength_itv/= lte_fin.
+rewrite setTI lebesgue_measure_itv/= lte_fin.
 by rewrite -subr_gt0 ab0 -EFinD -EFinM mulVf// gt_eqF// subr_gt0.
 Qed.
 
@@ -528,7 +528,7 @@ Proof.
 apply/eq_measure/funext => U.
 rewrite /ite; unlock => /=.
 rewrite /kcomp/= integral_dirac//=.
-rewrite indicT mul1e.
+rewrite diracT mul1e.
 rewrite -/(measure_add (ITE.kiteT k1 (x, f x)) (ITE.kiteF k2 (x, f x))).
 rewrite measure_addE.
 rewrite /ITE.kiteT /ITE.kiteF/=.
@@ -588,7 +588,7 @@ Lemma letin_retk
   x U : measurable U ->
   letin (ret mf) k x U = k (x, f x) U.
 Proof.
-move=> mU; rewrite letinE retE integral_dirac ?indicT ?mul1e//.
+move=> mU; rewrite letinE retE integral_dirac ?diracT ?mul1e//.
 exact: (measurableT_comp (measurable_kernel k _ mU)).
 Qed.
 
@@ -893,7 +893,7 @@ Let kcomp_scoreE d1 d2 (T1 : measurableType d1) (T2 : measurableType d2)
   (score mf \; g) r U = `|f r|%:E * g (r, tt) U.
 Proof.
 rewrite /= /kcomp /kscore /= ge0_integral_mscale//=.
-by rewrite integral_dirac// indicT mul1e.
+by rewrite integral_dirac// diracT mul1e.
 Qed.
 
 Lemma scoreE d' (T' : measurableType d') (x : T * T') (U : set T') (f : R -> R)
@@ -926,7 +926,7 @@ Proof.
 apply/eq_sfkernel => x U.
 rewrite letinE/= /sample; unlock.
 rewrite integral_measure_add//= ge0_integral_mscale//= ge0_integral_mscale//=.
-rewrite integral_dirac//= integral_dirac//= !indicT/= !mul1e.
+rewrite integral_dirac//= integral_dirac//= !diracT/= !mul1e.
 by rewrite /mscale/= iteE//= iteE//= failE mule0 adde0 ger0_norm.
 Qed.
 
@@ -1004,7 +1004,7 @@ 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.
@@ -1016,7 +1016,7 @@ 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.
@@ -1145,7 +1145,7 @@ Lemma letin_sample_bernoulli d d' (T : measurableType d)
 Proof.
 rewrite letinE/=.
 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 sample_and_return.
@@ -1327,8 +1327,8 @@ Qed.
 End staton_bus_exponential.
 
 (* X + Y is a measurableType if X and Y are *)
-Canonical sum_pointedType (X Y : pointedType) :=
-  PointedType (X + Y) (@inl X Y point).
+HB.instance Definition _ (X Y : pointedType) :=
+  isPointed.Build (X + Y)%type (@inl X Y point).
 
 Section measurable_sum.
 Context d d' (X : measurableType d) (Y : measurableType d').
@@ -1344,7 +1344,7 @@ Let sumU (F : (set (X + Y))^nat) : (forall i, measurable_sum (F i)) ->
 Proof. by []. Qed.
 
 HB.instance Definition _ := @isMeasurable.Build default_measure_display (X + Y)%type
-  (Pointed.class _) measurable_sum sum0 sumC sumU.
+  measurable_sum sum0 sumC sumU.
 
 End measurable_sum.
 
@@ -1485,7 +1485,7 @@ Proof. exact: sigma_algebra_bigcup. Qed.
 
 HB.instance Definition sum_salgebra_mixin :=
   @isMeasurable.Build (measure_sum_display (d1, d2))
-    (T1 + T2)%type (Pointed.class _) (image_classes f1 f2)
+    (T1 + T2)%type (image_classes f1 f2)
     (sum_salgebra_set0) (sum_salgebra_setC) (sum_salgebra_bigcup).
 
 End sum_salgebra_instance.

theories/prob_lang_wip.v

@@ -1,8 +1,8 @@
 From HB Require Import structures.
 From mathcomp Require Import all_ssreflect ssralg ssrnum ssrint interval finmap.
 From mathcomp Require Import rat.
-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 functions.
+From mathcomp Require Import cardinality fsbigop.
 Require Import signed reals ereal topology normedtype sequences esum measure.
 Require Import lebesgue_measure  numfun lebesgue_integral exp kernel trigo.
 Require Import prob_lang.
@@ -142,7 +142,7 @@ transitivity (\int[@mgauss01 R]_(y in U) (f1 y)%:E).
   apply: eq_integral => //= r.
   rewrite letinE/= ge0_integral_mscale//= ger0_norm//; last first.
     by rewrite invr_ge0// gauss_density_ge0.
-  by rewrite integral_dirac// indicT mul1e diracE indicE.
+  by rewrite integral_dirac// diracT mul1e diracE indicE.
 rewrite integral_mgauss01//.
 transitivity (\int[lebesgue_measure]_(x in U) (\1_U x)%:E).
   apply: eq_integral => /= y yU.