🚀 Initial commit

.gitattributes

@@ -0,0 +1 @@
+*.elpi linguist-language=prolog

.gitignore

@@ -0,0 +1,9 @@
+.*.aux
+.lia.cache
+*.glob
+*.vo
+*.vok
+*.vos
+*~
+.*.d
+Makefile.coq*

CHANGELOG.md

@@ -0,0 +1 @@
+# Changelog

LICENSE

@@ -0,0 +1,165 @@
+                   GNU LESSER GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <https://fsf.org/>
+ Everyone is permitted to copy and distribute verbatim copies
+ of this license document, but changing it is not allowed.
+
+
+  This version of the GNU Lesser General Public License incorporates
+the terms and conditions of version 3 of the GNU General Public
+License, supplemented by the additional permissions listed below.
+
+  0. Additional Definitions.
+
+  As used herein, "this License" refers to version 3 of the GNU Lesser
+General Public License, and the "GNU GPL" refers to version 3 of the GNU
+General Public License.
+
+  "The Library" refers to a covered work governed by this License,
+other than an Application or a Combined Work as defined below.
+
+  An "Application" is any work that makes use of an interface provided
+by the Library, but which is not otherwise based on the Library.
+Defining a subclass of a class defined by the Library is deemed a mode
+of using an interface provided by the Library.
+
+  A "Combined Work" is a work produced by combining or linking an
+Application with the Library.  The particular version of the Library
+with which the Combined Work was made is also called the "Linked
+Version".
+
+  The "Minimal Corresponding Source" for a Combined Work means the
+Corresponding Source for the Combined Work, excluding any source code
+for portions of the Combined Work that, considered in isolation, are
+based on the Application, and not on the Linked Version.
+
+  The "Corresponding Application Code" for a Combined Work means the
+object code and/or source code for the Application, including any data
+and utility programs needed for reproducing the Combined Work from the
+Application, but excluding the System Libraries of the Combined Work.
+
+  1. Exception to Section 3 of the GNU GPL.
+
+  You may convey a covered work under sections 3 and 4 of this License
+without being bound by section 3 of the GNU GPL.
+
+  2. Conveying Modified Versions.
+
+  If you modify a copy of the Library, and, in your modifications, a
+facility refers to a function or data to be supplied by an Application
+that uses the facility (other than as an argument passed when the
+facility is invoked), then you may convey a copy of the modified
+version:
+
+   a) under this License, provided that you make a good faith effort to
+   ensure that, in the event an Application does not supply the
+   function or data, the facility still operates, and performs
+   whatever part of its purpose remains meaningful, or
+
+   b) under the GNU GPL, with none of the additional permissions of
+   this License applicable to that copy.
+
+  3. Object Code Incorporating Material from Library Header Files.
+
+  The object code form of an Application may incorporate material from
+a header file that is part of the Library.  You may convey such object
+code under terms of your choice, provided that, if the incorporated
+material is not limited to numerical parameters, data structure
+layouts and accessors, or small macros, inline functions and templates
+(ten or fewer lines in length), you do both of the following:
+
+   a) Give prominent notice with each copy of the object code that the
+   Library is used in it and that the Library and its use are
+   covered by this License.
+
+   b) Accompany the object code with a copy of the GNU GPL and this license
+   document.
+
+  4. Combined Works.
+
+  You may convey a Combined Work under terms of your choice that,
+taken together, effectively do not restrict modification of the
+portions of the Library contained in the Combined Work and reverse
+engineering for debugging such modifications, if you also do each of
+the following:
+
+   a) Give prominent notice with each copy of the Combined Work that
+   the Library is used in it and that the Library and its use are
+   covered by this License.
+
+   b) Accompany the Combined Work with a copy of the GNU GPL and this license
+   document.
+
+   c) For a Combined Work that displays copyright notices during
+   execution, include the copyright notice for the Library among
+   these notices, as well as a reference directing the user to the
+   copies of the GNU GPL and this license document.
+
+   d) Do one of the following:
+
+       0) Convey the Minimal Corresponding Source under the terms of this
+       License, and the Corresponding Application Code in a form
+       suitable for, and under terms that permit, the user to
+       recombine or relink the Application with a modified version of
+       the Linked Version to produce a modified Combined Work, in the
+       manner specified by section 6 of the GNU GPL for conveying
+       Corresponding Source.
+
+       1) Use a suitable shared library mechanism for linking with the
+       Library.  A suitable mechanism is one that (a) uses at run time
+       a copy of the Library already present on the user's computer
+       system, and (b) will operate properly with a modified version
+       of the Library that is interface-compatible with the Linked
+       Version.
+
+   e) Provide Installation Information, but only if you would otherwise
+   be required to provide such information under section 6 of the
+   GNU GPL, and only to the extent that such information is
+   necessary to install and execute a modified version of the
+   Combined Work produced by recombining or relinking the
+   Application with a modified version of the Linked Version. (If
+   you use option 4d0, the Installation Information must accompany
+   the Minimal Corresponding Source and Corresponding Application
+   Code. If you use option 4d1, you must provide the Installation
+   Information in the manner specified by section 6 of the GNU GPL
+   for conveying Corresponding Source.)
+
+  5. Combined Libraries.
+
+  You may place library facilities that are a work based on the
+Library side by side in a single library together with other library
+facilities that are not Applications and are not covered by this
+License, and convey such a combined library under terms of your
+choice, if you do both of the following:
+
+   a) Accompany the combined library with a copy of the same work based
+   on the Library, uncombined with any other library facilities,
+   conveyed under the terms of this License.
+
+   b) Give prominent notice with the combined library that part of it
+   is a work based on the Library, and explaining where to find the
+   accompanying uncombined form of the same work.
+
+  6. Revised Versions of the GNU Lesser General Public License.
+
+  The Free Software Foundation may publish revised and/or new versions
+of the GNU Lesser General Public License from time to time. Such new
+versions will be similar in spirit to the present version, but may
+differ in detail to address new problems or concerns.
+
+  Each version is given a distinguishing version number. If the
+Library as you received it specifies that a certain numbered version
+of the GNU Lesser General Public License "or any later version"
+applies to it, you have the option of following the terms and
+conditions either of that published version or of any later version
+published by the Free Software Foundation. If the Library as you
+received it does not specify a version number of the GNU Lesser
+General Public License, you may choose any version of the GNU Lesser
+General Public License ever published by the Free Software Foundation.
+
+  If the Library as you received it specifies that a proxy can decide
+whether future versions of the GNU Lesser General Public License shall
+apply, that proxy's public statement of acceptance of any version is
+permanent authorization for you to choose that version for the
+Library.

Makefile

@@ -0,0 +1,10 @@
+.PHONY: all
+
+all: Makefile.coq
+	$(MAKE) -f Makefile.coq all
+
+Makefile.coq:
+	coq_makefile -f _CoqProject -o Makefile.coq
+
+%:: Makefile.coq
+	$(MAKE) -f Makefile.coq $@

README.md

@@ -0,0 +1,5 @@
+# Trocq
+
+This repository contains Trocq, a modular parametricity plugin for proof transfer in Coq.
+
+NB: it relies on a [custom version of Coq-Elpi](https://github.com/ecranceMERCE/coq-elpi/tree/strat), mainly changing its behaviour regarding the translation of universe variables between Elpi and Coq.

_CoqProject

@@ -0,0 +1,22 @@
+-arg -noinit
+-arg -indices-matter
+
+-R theories/ Trocq
+-R elpi/ Trocq.Elpi
+
+theories/HoTT_additions.v
+theories/Hierarchy.v
+theories/Param_Type.v
+theories/Param_forall.v
+theories/Param_arrow.v
+theories/Database.v
+theories/Param.v
+theories/Trocq.v
+theories/Param_paths.v
+
+examples/Example.v
+examples/int_to_Zp.v
+examples/peano_bin_nat.v
+examples/setoid_rewrite.v
+examples/summable.v
+examples/trocq_setoid_rewrite.v

coq-trocq.opam

@@ -0,0 +1,39 @@
+opam-version: "2.0"
+name: "coq-trocq"
+version: "dev"
+maintainer: "Enzo Crance <[email protected]>"
+authors: [ "Cyril Cohen", "Enzo Crance", "Assia Mahboubi" ]
+homepage: "https://github.com/ecranceMERCE/trocq"
+bug-reports: "https://github.com/ecranceMERCE/trocq/issues"
+dev-repo: "https://github.com/ecranceMERCE/trocq.git"
+# doc: "https://ecranceMERCE.github.io/trocq"
+build: [ make "-j%{jobs}%" ]
+install: [ make "install" ]
+depends: [
+  "coq" {>= "8.17.0" & < "8.18~" }
+  "coq-elpi" {= "dev"}
+  "coq-hott" {>= "8.17" & < "8.18~"}
+]
+tags: [ 
+  "category:Computer Science/Decision Procedures and Certified Algorithms/Decision procedures"
+  "category:Miscellaneous/Coq Extensions"
+  "keyword:automation"
+  "keyword:elpi"
+  "date:2023-11-10"
+  "logpath:Trocq"
+]
+synopsis: "A modular parametricity plugin for proof transfer in Coq"
+description: """
+Trocq is a prototype of modular parametricity plugin for Coq, aiming to perform proof transfer by translating the goal into an associated goal featuring the target data structures as well as a rich parametricity witness from which a function justifying the goal substitution can be extracted.
+
+The plugin features a hierarchy of parametricity witness types, ranging from structure-less relations to a new formulation of type equivalence, gathering several pre-existing parametricity translations, among which univalent parametricity (*), under the same framework.
+
+This modular translation performs a fine-grained analysis and generates witnesses that are rich enough to preprocess the goal yet are not always a full-blown type equivalence, allowing to perform proof transfer with the power of univalent parametricity, but trying not to pull in the univalence axiom in cases where it is not required.
+
+The translation is implemented in Coq-Elpi and features transparent and readable code with respect to a sequent-style theoretical presentation.
+
+(*) The marriage of univalence and parametricity, Tabareau et al. (2021)
+"""
+url {
+  src: "git+https://github.com/ecranceMERCE/trocq.git"
+}

elpi/annot.elpi

@@ -0,0 +1,133 @@
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%                            %                                Trocq                                %
+%  _______                   %                       Copyright (C) 2023 MERCE                      %
+% |__   __|                  %                (Mitsubishi Electric R&D Centre Europe)              %
+%    | |_ __ ___   ___ __ _  %                   Cyril Cohen <[email protected]>                %
+%    | | '__/ _ \ / __/ _` | %                   Enzo Crance <[email protected]>                %
+%    | | | | (_) | (_| (_| | %               Assia Mahboubi <[email protected]>              %
+%    |_|_|  \___/ \___\__, | %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%                        | | %            This file is distributed under the terms of the          %
+%                        |_| %              GNU Lesser General Public License Version 3            %
+%                            %             (see LICENSE file for the text of the license)          %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+% --------------------------------------------------------------------------------------------------
+% annotated type theory
+% --------------------------------------------------------------------------------------------------
+
+% this allows to easily make sure an application is beta-reduced
+:before "subst-fun:fail"
+coq.subst-fun Args F FArgs :- !, coq.mk-app F Args FArgs.
+
+% annotate a term
+% NB: the output type is term because the annotations are encoded directly in Coq
+% see PType in Param.v
+pred term->annot-term i:term, o:term.
+term->annot-term (sort (typ U)) (app [pglobal (const PType) UI, M, N]) :- param.db.ptype PType, !,
+  coq.univ-instance UI [{coq.univ.variable U}],
+  cstr.univ-link _ M N.
+term->annot-term (fun N T F) (fun N T' F') :- !,
+  term->annot-term T T',
+  pi x\ term->annot-term (F x) (F' x).
+term->annot-term (prod N T F) (prod N T' F') :- !,
+  term->annot-term T T',
+  pi x\ term->annot-term (F x) (F' x).
+term->annot-term (app L) (app L') :- !,
+  std.map L term->annot-term L'.
+term->annot-term X X :- (name X ; X = global _ ; X = pglobal _ _), !.
+term->annot-term T _ :- coq.error "term->annot-term:" T.
+
+macro @annot-pi-decl N T F :- pi x\ annot.adecl x N T => F x.
+
+namespace annot {
+
+% typechecking a term calls Coq's typechecker, which gives back a non annotated term
+% calling term->annot-term on it will add fresh annotations
+% if we want to typecheck a variable several times and get the same type everytime, we need to
+% add some memory, which is the purpose of adecl
+pred adecl i:term, o:name, o:term.
+
+pred typecheck i:term, o:term.
+typecheck T ATy :- adecl T _ ATy, !.
+typecheck T ATy :-
+  coq.typecheck T Ty ok, !,
+  term->annot-term Ty ATy.
+
+% sub-typing predicate following the sub-typing rules in the article
+pred sub-type i:term, i:term.
+% SubUniv
+sub-type (app [pglobal (const PType) _, M1, N1]) (app [pglobal (const PType) _, M2, N2]) :-
+  param.db.ptype PType, !,
+  cstr.univ-link C1 M1 N1,
+  cstr.univ-link C2 M2 N2,
+  cstr.geq C1 C2.
+% SubPi
+sub-type (prod N T F) (prod _ T' F') :- !,
+  sub-type T' T,
+  @annot-pi-decl N T' x\ sub-type (F x) (F' x).
+% SubLam
+sub-type (fun N T F) (fun _ T F') :- !,
+  @annot-pi-decl N T x\ sub-type (F x) (F' x).
+% SubApp
+sub-type (app [F|Xs]) (app [F'|Xs']) :- !,
+  sub-type F F',
+  std.forall2 Xs Xs' eq.
+% SubConv
+sub-type X X :- (name X ; X = global _ ; X = pglobal _ _), !.
+sub-type X _ :- coq.error "annot.sub-type:" X.
+
+% syntactic term equality, taking care of adding annotation equalities in the constraint graph
+pred eq i:term, i:term.
+eq (app [pglobal (const PType) UI, M1, N1]) (app [pglobal (const PType) UI, M2, N2]) :-
+  param.db.ptype PType, !,
+  cstr.univ-link C1 M1 N1,
+  cstr.univ-link C2 M2 N2,
+  cstr.eq C1 C2.
+eq (prod _ T F) (prod _ T' F') :- !,
+  eq T T',
+  pi x\ eq (F x) (F' x).
+eq (fun _ T F) (fun _ T' F') :- !,
+  eq T T',
+  pi x\ eq (F x) (F' x).
+eq (app L) (app L') :- !,
+  std.forall2 L L' eq.
+eq X X :- (name X ; X = global _ ; X = pglobal _ _), !.
+eq X _ :- coq.error "annot.eq:" X.
+
+% get all the annotations in a type T, as well as the "output class", i.e., the parametricity class
+% of the output type of T, as an option basically returning some (A,B) for an output type PType A B,
+% and none for output types that are not sorts, because it means values of type T are not type
+% constructors, so their translation will be made at class (0,0)
+pred classes i:term, o:list param-class, o:option param-class.
+classes T Cs' Out :-
+  all-classes T Cs,
+  out-class T Out,
+  if (not (Cs = []), Out = some C, std.last Cs LastC, LastC == C) (
+    std.drop-last 1 Cs Cs'
+  ) (
+    Cs' = Cs
+  ).
+
+pred all-classes i:term, o:list param-class.
+all-classes (app [pglobal (const PType) _, M, N]) [C] :- param.db.ptype PType, !,
+  cstr.univ-link C M N.
+all-classes X Cs :- (X = prod _ T F ; X = fun _ T F), !,
+  pi x\ std.append {all-classes T} {all-classes (F x)} Cs.
+all-classes (app L) Cs :- !,
+  std.flatten {std.map L all-classes} Cs.
+all-classes X [] :- (name X ; X = global _ ; X = pglobal _ _), !.
+all-classes X _ :- coq.error "all-classes:" X.
+
+pred out-class i:term, o:option param-class.
+out-class (app [pglobal (const PType) _, M, N]) (some C) :- param.db.ptype PType, !,
+  cstr.univ-link C M N.
+out-class (prod _ _ F) Out :- !, pi x\ out-class (F x) Out.
+out-class (fun _ _ _) none :- !.
+out-class (app [F|Xs]) Out :- !,
+  coq.subst-fun Xs F App,
+  if (App = app [F|Xs]) (Out = none) (out-class App Out).
+out-class X none :- (name X ; X = global _ ; X = pglobal _ _), !.
+out-class X _ :- coq.error "out-class:" X.
+% constant applications convertible to terms having a sort as output are not supported
+
+} % annot