Application of s-finite kernels to program semantics

.github/workflows/nix-action-8.19.yml

@@ -187,6 +187,10 @@ jobs:
       name: 'Building/fetching previous CI target: mathcomp-bigenough'
       run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.19" --argstr
         job "mathcomp-bigenough"
+    - if: steps.stepCheck.outputs.status == 'built'
+      name: 'Building/fetching previous CI target: mathcomp-algebra-tactics'
+      run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.19" --argstr
+        job "mathcomp-algebra-tactics"
     - if: steps.stepCheck.outputs.status == 'built'
       name: 'Building/fetching previous CI target: hierarchy-builder'
       run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.19" --argstr
@@ -263,6 +267,10 @@ jobs:
       name: 'Building/fetching previous CI target: mathcomp-bigenough'
       run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.19" --argstr
         job "mathcomp-bigenough"
+    - if: steps.stepCheck.outputs.status == 'built'
+      name: 'Building/fetching previous CI target: mathcomp-algebra-tactics'
+      run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.19" --argstr
+        job "mathcomp-algebra-tactics"
     - if: steps.stepCheck.outputs.status == 'built'
       name: 'Building/fetching previous CI target: hierarchy-builder'
       run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.19" --argstr

.github/workflows/nix-action-8.20.yml

@@ -187,6 +187,10 @@ jobs:
       name: 'Building/fetching previous CI target: mathcomp-bigenough'
       run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
         job "mathcomp-bigenough"
+    - if: steps.stepCheck.outputs.status == 'built'
+      name: 'Building/fetching previous CI target: mathcomp-algebra-tactics'
+      run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
+        job "mathcomp-algebra-tactics"
     - if: steps.stepCheck.outputs.status == 'built'
       name: 'Building/fetching previous CI target: hierarchy-builder'
       run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
@@ -263,6 +267,10 @@ jobs:
       name: 'Building/fetching previous CI target: mathcomp-bigenough'
       run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
         job "mathcomp-bigenough"
+    - if: steps.stepCheck.outputs.status == 'built'
+      name: 'Building/fetching previous CI target: mathcomp-algebra-tactics'
+      run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr
+        job "mathcomp-algebra-tactics"
     - if: steps.stepCheck.outputs.status == 'built'
       name: 'Building/fetching previous CI target: hierarchy-builder'
       run: NIXPKGS_ALLOW_UNFREE=1 nix-build --no-out-link --argstr bundle "8.20" --argstr

.github/workflows/nix-action-master.yml

@@ -311,6 +311,7 @@ jobs:
     needs:
     - coq
     - mathcomp-finmap
+    - hierarchy-builder
     - mathcomp-bigenough
     - mathcomp-bigenough
     - hierarchy-builder

.github/workflows/nix-action.yml

@@ -0,0 +1,46 @@
+# This file was generated from `meta.yml`, please do not edit manually.
+# Follow the instructions on https://github.com/coq-community/templates to regenerate.
+name: Nix CI
+
+on:
+  push:
+    branches:
+      - master
+  pull_request:
+    paths:
+    - .github/workflows/**
+  pull_request_target:
+
+jobs:
+  build:
+    runs-on: ubuntu-latest
+    strategy:
+      matrix:
+        overrides:
+          - 'coq = "master"'
+      fail-fast: false
+    steps:
+      - name: Determine which commit to test
+        run: |
+          if [[ ${{ github.event_name }} =~ "pull_request" ]]; then
+            merge_commit=$(git ls-remote ${{ github.event.repository.html_url }} refs/pull/${{ github.event.number }}/merge | cut -f1)
+            if [ -z "$merge_commit" ]; then
+              echo "tested_commit=${{ github.event.pull_request.head.sha }}" >> $GITHUB_ENV
+            else
+              echo "tested_commit=$merge_commit" >> $GITHUB_ENV
+            fi
+          else
+            echo "tested_commit=${{ github.sha }}" >> $GITHUB_ENV
+          fi
+      - uses: cachix/install-nix-action@v14
+        with:
+          nix_path: nixpkgs=channel:nixpkgs-unstable
+      - uses: cachix/cachix-action@v10
+        with:
+          name: coq-community
+          extraPullNames: coq, math-comp
+      - uses: actions/checkout@v2
+        with:
+          ref: ${{ env.tested_ref }}
+      - run: >
+          nix-build https://coq.inria.fr/nix/toolbox --argstr job analysis --arg override '{ ${{ matrix.overrides }}; analysis = builtins.filterSource (path: _: baseNameOf path != ".git") ./.; }'

.nix/coq-overlays/mathcomp-analysis/default.nix

@@ -0,0 +1,93 @@
+{ lib,
+  mkCoqDerivation, recurseIntoAttrs,
+  mathcomp, mathcomp-finmap, mathcomp-bigenough,
+  hierarchy-builder, mathcomp-algebra-tactics,
+  single ? false,
+  coqPackages, coq, version ? null }@args:
+with builtins // lib;
+let
+  repo  = "analysis";
+  owner = "math-comp";
+
+  release."0.6.1".sha256 = "sha256-1VyNXu11/pDMuH4DmFYSUF/qZ4Bo+/Zl3Y0JkyrH/r0=";
+  release."0.6.0".sha256 = "sha256-0msICcIrK6jbOSiBu0gIVU3RHwoEEvB88CMQqW/06rg=";
+  release."0.5.3".sha256 = "sha256-1NjFsi5TITF8ZWx1NyppRmi8g6YaoUtTdS9bU/sUe5k=";
+  release."0.5.2".sha256 = "0yx5p9zyl8jv1vg7rgkyq8dqzkdnkqv969mi62whmhkvxbavgzbw";
+  release."0.5.1".sha256 = "1hnzqb1gxf88wgj2n1b0f2xm6sxg9j0735zdsv6j12hlvx5lwk68";
+  release."0.3.13".sha256 = "sha256-Yaztew79KWRC933kGFOAUIIoqukaZOdNOdw4XszR1Hg=";
+  release."0.3.10".sha256 = "sha256-FBH2c8QRibq5Ycw/ieB8mZl0fDiPrYdIzZ6W/A3pIhI=";
+  release."0.3.9".sha256 = "sha256-uUU9diBwUqBrNRLiDc0kz0CGkwTZCUmigPwLbpDOeg4=";
+  release."0.3.6".sha256 = "0g2j7b2hca4byz62ssgg90bkbc8wwp7xkb2d3225bbvihi92b4c5";
+  release."0.3.4".sha256 = "18mgycjgg829dbr7ps77z6lcj03h3dchjbj5iir0pybxby7gd45c";
+  release."0.3.3".sha256 = "1m2mxcngj368vbdb8mlr91hsygl430spl7lgyn9qmn3jykack867";
+  release."0.3.1".sha256 = "1iad288yvrjv8ahl9v18vfblgqb1l5z6ax644w49w9hwxs93f2k8";
+  release."0.2.3".sha256 = "0p9mr8g1qma6h10qf7014dv98ln90dfkwn76ynagpww7qap8s966";
+
+  defaultVersion = with versions; lib.switch [ coq.version mathcomp.version ]  [
+      { cases = [ (isGe "8.14") (isGe "1.13.0") ];               out = "0.6.1"; }
+      { cases = [ (isGe "8.14") (range "1.13" "1.15") ];         out = "0.5.2"; }
+      { cases = [ (range "8.13" "8.15") (range "1.13" "1.14") ]; out = "0.5.1"; }
+      { cases = [ (range "8.13" "8.15") (range "1.12" "1.14") ]; out = "0.3.13"; }
+      { cases = [ (range "8.11" "8.14") (range "1.12" "1.13") ]; out = "0.3.10"; }
+      { cases = [ (range "8.11" "8.12") "1.11.0" ];              out = "0.3.4"; }
+      { cases = [ (range "8.10" "8.12") "1.11.0" ];              out = "0.3.3"; }
+      { cases = [ (range "8.10" "8.11") "1.11.0" ];              out = "0.3.1"; }
+      { cases = [ (range "8.8"  "8.11") (range "1.8" "1.10") ];  out = "0.2.3"; }
+    ] null;
+
+  # list of analysis packages sorted by dependency order
+  packages = [ "classical" "analysis" ];
+
+  mathcomp_ = package: let
+      classical-deps = [ mathcomp.algebra mathcomp-finmap hierarchy-builder ];
+      analysis-deps = [ mathcomp.field mathcomp-bigenough ];
+      intra-deps = if package == "single" then []
+        else map mathcomp_ (head (splitList (lib.pred.equal package) packages));
+      pkgpath = if package == "single" then "."
+        else if package == "analysis" then "theories" else "${package}";
+      pname = if package == "single" then "mathcomp-analysis-single"
+        else "mathcomp-${package}";
+      derivation = mkCoqDerivation ({
+        inherit version pname defaultVersion release repo owner;
+
+        namePrefix = [ "coq" "mathcomp" ];
+
+        propagatedBuildInputs =
+          intra-deps
+          ++ optionals (elem package [ "classical" "single" ]) classical-deps
+          ++ optionals (elem package [ "analysis" "single" ]) analysis-deps
+          ++ optionals (elem package [ "analysis" "single" ]) [mathcomp-algebra-tactics];
+
+        preBuild = ''
+          cd ${pkgpath}
+        '';
+
+        meta = {
+          description = "Analysis library compatible with Mathematical Components";
+          maintainers = [ maintainers.cohencyril ];
+          license     = licenses.cecill-c;
+        };
+
+        passthru = genAttrs packages mathcomp_;
+      });
+    # split packages didn't exist before 0.6, so bulding nothing in that case
+    patched-derivation1 = derivation.overrideAttrs (o:
+      optionalAttrs (o.pname != null && o.pname != "mathcomp-analysis" &&
+         o.version != null && o.version != "dev" && versions.isLt "0.6" o.version)
+      { preBuild = ""; buildPhase = "echo doing nothing"; installPhase = "echo doing nothing"; }
+    );
+    patched-derivation2 = patched-derivation1.overrideAttrs (o:
+      optionalAttrs (o.pname != null && o.pname == "mathcomp-analysis" &&
+         o.version != null && o.version != "dev" && versions.isLt "0.6" o.version)
+      { preBuild = ""; }
+    );
+    patched-derivation = patched-derivation2.overrideAttrs (o:
+      optionalAttrs (o.version != null
+        && (o.version == "dev" || versions.isGe "0.3.4" o.version))
+      {
+        propagatedBuildInputs = o.propagatedBuildInputs ++ [ hierarchy-builder ];
+      }
+    );
+    in patched-derivation;
+in
+mathcomp_ (if single then "single" else "analysis")

_CoqProject

@@ -92,3 +92,10 @@ theories/kernel.v
 theories/showcase/summability.v
 analysis_stdlib/Rstruct_topology.v
 analysis_stdlib/showcase/uniform_bigO.v
+theories/prob_lang.v
+theories/prob_lang_wip.v
+theories/lang_syntax_util.v
+theories/lang_syntax_toy.v
+theories/lang_syntax.v
+theories/lang_syntax_examples.v
+theories/lang_syntax_table_game.v

coq-mathcomp-analysis.opam

@@ -19,6 +19,8 @@ depends: [
   "coq-mathcomp-solvable"
   "coq-mathcomp-field"
   "coq-mathcomp-bigenough" { (>= "1.0.0") }
+  "coq-mathcomp-algebra-tactics" { (>= "1.2.3") }
+  "coq-mathcomp-zify" { (>= "1.5.0") }
 ]
 
 tags: [

theories/Make

@@ -58,3 +58,10 @@ charge.v
 kernel.v
 all_analysis.v
 showcase/summability.v
+prob_lang.v
+prob_lang_wip.v
+lang_syntax_util.v
+lang_syntax_toy.v
+lang_syntax.v
+lang_syntax_examples.v
+lang_syntax_table_game.v

theories/ftc.v

@@ -35,6 +35,24 @@ Notation mu := (@lebesgue_measure R).
 Local Open Scope ereal_scope.
 Implicit Types (f : R -> R) (a : itv_bound R).
 
+Let integrable_locally f (A : set R) : measurable A ->
+  mu.-integrable A (EFin \o f) -> locally_integrable [set: R] (f \_ A).
+Proof.
+move=> mA intf; split.
+- move/integrableP : intf => [mf _].
+  by apply/(measurable_restrictT _ _).1 => //; exact/EFin_measurable_fun.
+- exact: openT.
+- move=> K _ cK.
+  move/integrableP : intf => [mf].
+  rewrite integral_mkcond/=.
+  under eq_integral do rewrite restrict_EFin restrict_normr.
+  apply: le_lt_trans.
+  apply: ge0_subset_integral => //=; first exact: compact_measurable.
+  apply/EFin_measurable_fun/measurableT_comp/EFin_measurable_fun => //=.
+  move/(measurable_restrictT _ _).1 : mf => /=.
+  by rewrite restrict_EFin; exact.
+Qed.
+
 Let FTC0 f a : mu.-integrable setT (EFin \o f) ->
   let F x := (\int[mu]_(t in [set` Interval a (BRight x)]) f t)%R in
   forall x, a < BRight x -> lebesgue_pt f x ->
@@ -679,7 +697,6 @@ Qed.
 
 End Rintegration_by_parts.
 
-(* TODO: move to realfun.v? *)
 Section integration_by_substitution_preliminaries.
 Context {R : realType}.
 Notation mu := lebesgue_measure.

theories/kernel.v

@@ -767,7 +767,6 @@ HB.instance Definition _ (P : probability Y R):=
 
 End knormalize.
 
-(* TODO: useful? *)
 Lemma measurable_fun_mnormalize d d' (X : measurableType d)
     (Y : measurableType d') (R : realType) (k : R.-ker X ~> Y) :
   measurable_fun [set: X] (fun x =>