pax_global_header00006660000000000000000000000064130106117550014511gustar00rootroot0000000000000052 comment=feeae2d259ceaa0a1c254bc66816e04a3754629f ocplib-simplex-0.3/000077500000000000000000000000001301061175500143025ustar00rootroot00000000000000ocplib-simplex-0.3/.gitignore000066400000000000000000000002441301061175500162720ustar00rootroot00000000000000_obuild .gitignore _olint .ocplint *~ #* autom4te.cache configure config.status .depend *.cm* *.o *.annot *.a src/coreSig.ml src/extSigs.ml config.log Makefile METAocplib-simplex-0.3/.ocplint000066400000000000000000000137141301061175500157610ustar00rootroot00000000000000 (*************************************) (* Never edit options files while *) (* the program is running *) (*************************************) (* SECTION : Header *) (* These options must be read first *) (*************************************) (* Module to ignore during the lint. *) ignored_files = [ ] plugin_typedtree = { (* A plugin with linters on typed tree. *) 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{ (* Enable/Disable linter "Checks on module type name.". *) enabled = true (* Module to ignore durint the lint of "Checks on module type name." *) ignored_files = [ ] (* Enable/Disable warnings from "Checks on module type name." *) warnings = "+A" } } ocplib-simplex-0.3/CHANGES.md000066400000000000000000000020531301061175500156740ustar00rootroot00000000000000(!!! = may break code that uses previous versions) verion 0.3, November 09, 2016 =============================== * bugfix in maximization verion 0.2, August 24, 2016 =============================== * add support for linear optimization (!!!). An minimal example is given in tests/standalone_minimal_maximization.ml * some bugfixes when assuming inconsistent bounds * improve build and testing first public 0.1, July 11, 2016 =============================== * A functor called `Basic` provides three modules: - `Core`: provides some basic functions, and a function `empty` to create an empty environment - `Assert`: exports two functions `var` and `polys` to assert bounds on variables and polynomials, respectively - `Solve`: exports a function `solve` that tries to find a solution for the constrains * two flags can be set when creating an empty environment to activate debug mode and some invariants verification * implementation is fully functional, incremental and backtrackable * linear optimization is not supported yet ocplib-simplex-0.3/LICENSE000066400000000000000000000632571301061175500153240ustar00rootroot00000000000000ocplib-simplex is distributed under the terms of the GNU Lesser General Public License (LGPL) version 2.1 (see below), with some exceptions as defined for the OCaml Core System (see https://github.com/ocaml/ocaml/blob/trunk/LICENSE) ---------------------------------------------------------------------- GNU LESSER GENERAL PUBLIC LICENSE Version 2.1, February 1999 Copyright (C) 1991, 1999 Free Software Foundation, Inc. 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 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Here is a sample; alter the names: Yoyodyne, Inc., hereby disclaims all copyright interest in the library `Frob' (a library for tweaking knobs) written by James Random Hacker. signature of Ty Coon, 1 April 1990 Ty Coon, President of Vice That's all there is to it! -------------------------------------------------- ocplib-simplex-0.3/Makefile.in000066400000000000000000000150511301061175500163510ustar00rootroot00000000000000# sample Makefile for Objective Caml # Copyright (C) 2001 Jean-Christophe FILLIATRE # # This library is free software; you can redistribute it and/or # modify it under the terms of the GNU Library General Public # License version 2, as published by the Free Software Foundation. # # This library is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. # # See the GNU Library General Public License version 2 for more details # (enclosed in the file LGPL). # where to install the binaries # DESTDIR= # prefix=@prefix@ # exec_prefix=@exec_prefix@ # BINDIR=$(DESTDIR)@bindir@ # LIBDIR=$(DESTDIR)@libdir@/ocplib-simplex # DATADIR=$(DESTDIR)@datadir@/ocplib-simplex # where to install the man page MANDIR=$(DESTDIR)@mandir@ # other variables set by ./configure OCAMLC = @OCAMLC@ OCAMLOPT = @OCAMLOPT@ OCAMLDEP = @OCAMLDEP@ OCAMLBEST = @OCAMLBEST@ OCAMLVERSION = @OCAMLVERSION@ OCAMLWIN32 = @OCAMLWIN32@ OCAMLLIB = @OCAMLLIB@ LIBNAME=ocplibSimplex EXE =@EXE@ ARCH = $(shell uname -m) VERSION=$(shell grep "=" src/version.ml | cut -d"=" -f2 | head -n 1) LOCAL_INC = -I src INCLUDES = $(LOCAL_INC) #for coverage # -I /usr/local/lib/ocaml/3.12.1/bisect -pp "camlp4o str.cma /usr/local/lib/ocaml/3.12.1/bisect/bisect_pp.cmo" OFLAGS_LIGHT = -annot -absname -bin-annot -short-paths -strict-sequence -w +A -g -inline 100 $(INCLUDES) BFLAGS_LIGHT = -annot -absname -bin-annot -short-paths -strict-sequence -w +A -g $(INCLUDES) BFLAGS = $(BFLAGS_LIGHT) -for-pack OcplibSimplex OFLAGS = $(OFLAGS_LIGHT) -for-pack OcplibSimplex BIBBYTE = # for coverage bisect.cma BIBOPT = $(BIBBYTE:.cma=.cmxa) GENERATED = src/extSigs.ml src/coreSig.ml #src/ocplibSimplex.mli CMO = src/version.cmo src/rat2.cmo src/extSigs.cmo src/polys.cmo src/coreSig.cmo src/core.cmo \ src/result.cmo src/assertBounds.cmo src/solveBounds.cmo src/basic.cmo CMX = $(CMO:.cmo=.cmx) # Build ######### all: $(OCAMLBEST) byte: src/$(LIBNAME).cma opt: src/$(LIBNAME).cma src/$(LIBNAME).cmxa src/$(LIBNAME).cmxs src/$(LIBNAME).cma: src/$(LIBNAME).cmo $(OCAMLC) -a $(BFLAGS_LIGHT) -o $@ $^ src/$(LIBNAME).cmxa: src/$(LIBNAME).cmx $(OCAMLOPT) -a $(OFLAGS_LIGHT) -o $@ $^ src/$(LIBNAME).cmxs: src/$(LIBNAME).cmx $(OCAMLOPT) -shared $(OFLAGS_LIGHT) -o $@ $^ src/$(LIBNAME).cmo: $(CMO) # src/$(LIBNAME).cmi $(OCAMLC) $(BFLAGS_LIGHT) -pack -o src/$(LIBNAME).cmo $^ src/$(LIBNAME).cmx: $(CMX) # src/$(LIBNAME).cmi $(OCAMLOPT) $(OFLAGS_LIGHT) -pack -o src/$(LIBNAME).cmx $^ src/extSigs.ml: src/extSigs.mli cp src/extSigs.mli src/extSigs.ml src/coreSig.ml: src/coreSig.mli cp src/coreSig.mli src/coreSig.ml .PHONY: all META: config.status @echo "description = \"ocplib-simplex: A library implementing a simplex algorithm, in a functional style, for solving systems of linear inequalities\"" > META @echo "version = \""$(VERSION)"\"" >> META @echo "archive(byte) = \"$(LIBNAME).cma\"" >> META @echo "archive(native) = \"$(LIBNAME).cmxa\"" >> META @echo "archive(native, plugin) = \"$(LIBNAME).cmxs\"" >> META @echo "archive(byte, plugin) = \"$(LIBNAME).cma\"" >> META @echo "requires = \"\"" >> META @echo "exists_if = \"$(LIBNAME).cma\"" >> META # installation ############## install: all META ocamlfind install ocplib-simplex src/$(LIBNAME).* src/*.mli META uninstall: ocamlfind remove ocplib-simplex # generic rules ############### .SUFFIXES: .mli .ml .cmi .cmo .cmx .mll .mly .tex .dvi .ps .html .mli.cmi: $(OCAMLC) -c $(BFLAGS) $< .ml.cmo: $(OCAMLC) -c $(BFLAGS) $< .ml.o: $(OCAMLOPT) -c $(OFLAGS) $< .ml.cmx: $(OCAMLOPT) -c $(OFLAGS) $< .mll.ml: $(OCAMLLEX) $< > /dev/null .mly.ml: $(OCAMLYACC) -v $< .mly.mli: $(OCAMLYACC) -v $< # clean ####### clean: @for dd in . src tests; do \ rm -f $$dd/*.cm* $$dd/*.a $$dd/*.o $$dd/*~ $$dd/*.annot $$dd/*.owz $(GENERATED) *.byte *.opt;\ done @rm -rf META # depend ######## .depend depend: $(GENERATED) $(OCAMLDEP) $(LOCAL_INC) src/*.ml* > .depend include .depend #show-dest-dirs: # @echo INSTALL DIR = $(INSTALLDIR) # Makefile.configurable is rebuilt whenever Makefile.configurable.in # or configure.in is modified ###################################################################### configure: configure.in autoconf ./configure Makefile.configurable: Makefile.in configure.in ./config.status config.status: configure ./config.status --recheck archi: depend ocamldot .depend > archi.dot && dot -Tpdf archi.dot > archi.pdf && evince archi.pdf & lint: ocp-lint --path /home/omig/Bureau/pro/alt-ergo/ocplib-simplex/src --disable-plugin-indent edit: emacs src/*ml* & opam-deps: opam install ocamlfind repin: opam remove ocplib-simplex opam pin add . --y local-tests: all ## minimal example with solve: byte and opt >> lib is local $(OCAMLC) -o standalone_minimal_local.byte -I src -I tests ocplibSimplex.cma nums.cma tests/standalone_minimal.ml ./standalone_minimal_local.byte 2> /dev/null $(OCAMLOPT) -o standalone_minimal_local.opt -I src -I tests ocplibSimplex.cmxa nums.cmxa tests/standalone_minimal.ml ./standalone_minimal_local.opt 2> /dev/null ## minimal example with maximization: byte and opt >> lib is local $(OCAMLC) -o standalone_minimal_maximization_local.byte -I src -I tests ocplibSimplex.cma nums.cma tests/standalone_minimal_maximization.ml ./standalone_minimal_maximization_local.byte 2> /dev/null $(OCAMLOPT) -o standalone_minimal_maximization_local.opt -I src -I tests ocplibSimplex.cmxa nums.cmxa tests/standalone_minimal_maximization.ml ./standalone_minimal_maximization_local.opt 2> /dev/null opam-installed-tests: repin ## minimal example with solve: byte and opt >> lib is pinned with OPAM $(OCAMLC) -o standalone_minimal_opam.byte -I `ocamlfind query ocplib-simplex` -I tests ocplibSimplex.cma nums.cma tests/standalone_minimal.ml ./standalone_minimal_opam.byte 2> /dev/null $(OCAMLOPT) -o standalone_minimal_opam.opt -I `ocamlfind query ocplib-simplex` -I tests ocplibSimplex.cmxa nums.cmxa tests/standalone_minimal.ml ./standalone_minimal_opam.opt 2> /dev/null ## minimal example with maximization: byte and opt >> lib is pinned with OPAM $(OCAMLC) -o standalone_minimal_maximization_opam.byte -I `ocamlfind query ocplib-simplex` -I tests ocplibSimplex.cma nums.cma tests/standalone_minimal_maximization.ml ./standalone_minimal_maximization_opam.byte 2> /dev/null $(OCAMLOPT) -o standalone_minimal_maximization_opam.opt -I `ocamlfind query ocplib-simplex` -I tests ocplibSimplex.cmxa nums.cmxa tests/standalone_minimal_maximization.ml ./standalone_minimal_maximization_opam.opt 2> /dev/null tests: local-tests opam-installed-tests ocplib-simplex-0.3/README.md000066400000000000000000000035321301061175500155640ustar00rootroot00000000000000# ocplib-simplex A library implementing a simplex algorithm, in a functional style, for solving systems of linear inequalities and optimizing linear objective functions ## Overview `ocplib-simplex` is a (fully) functional OCaml implementation of the simplex algorithm for solving systems of linear inequalities. The implementation is incremental and backtrackable. It is able to extract unsat-cores for unsatisfiable problems. Versions `> 0.1` also support linear optimization ## Dependencies `ocplib-simplex` requires `4.01.0` or higher and `ocamlfind`. You can use `make opam-deps` to install dependencies in the current switch. ## Build and Install Instructions The easiest way to install ocplib-simplex is to use OPAM: $ opam install ocplib-simplex If you want to install ocplib-simplex from sources, use the following instructions: $ autoconf (if configure is not present) $ ./configure $ make opam-deps (if you are using OPAM and some deps are missing) $ make $ make install to compile and install `ocplib-simplex` on your system. You can uninstall the library with `make uninstall`. ## Minimal Examples Solving a system of linear inequalities: see the file `tests/standalone_minimal.ml` Linear optimization: see the file `tests/standalone_minimal_maximization.ml` ## Contributing Don't hesitate to report encountered bugs on this Git repo's issues tracker. ## TODO - the code is not (well) documented, - some parts of the code need factorization/simplification, - some invariants (check unsat-core, linear optimization) are missing. ## Licensing `ocplib-simplex` is Copyright (C) --- OCamlPro. it is distributed under the terms of the GNU Lesser General Public License (LGPL) version 2.1 (see LICENSE file), with some exceptions as defined for the OCaml Core System (see https://github.com/ocaml/ocaml/blob/trunk/LICENSE).ocplib-simplex-0.3/configure.in000066400000000000000000000107041301061175500166150ustar00rootroot00000000000000# autoconf input for Objective Caml programs # Copyright (C) 2001 Jean-Christophe Filliātre # from a first script by Georges Mariano # # This library is free software; you can redistribute it and/or # modify it under the terms of the GNU Library General Public # License version 2, as published by the Free Software Foundation. # # This library is distributed in the hope that it will be useful, # but WITHOUT ANY WARRANTY; without even the implied warranty of # MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. # # See the GNU Library General Public License version 2 for more details # (enclosed in the file LGPL). # the script generated by autoconf from this input will set the following # variables: # OCAMLC "ocamlc" if present in the path, or a failure # or "ocamlc.opt" if present with same version number as ocamlc # OCAMLOPT "ocamlopt" (or "ocamlopt.opt" if present), or "no" # OCAMLBEST either "byte" if no native compiler was found, # or "opt" otherwise # OCAMLDEP "ocamldep" # OCAMLLEX "ocamllex" (or "ocamllex.opt" if present) # OCAMLYACC "ocamlyac" # OCAMLLIB the path to the ocaml standard library # OCAMLVERSION the ocaml version number # OCAMLWEB "ocamlweb" (not mandatory) # OCAMLWIN32 "yes"/"no" depending on Sys.os_type = "Win32" # EXE ".exe" if OCAMLWIN32=yes, "" otherwise # check for one particular file of the sources # ADAPT THE FOLLOWING LINE TO YOUR SOURCES! AC_INIT(src/core.ml) # Check for Ocaml compilers # we first look for ocamlc in the path; if not present, we fail AC_CHECK_PROGS(OCAMLC,ocamlc,no) if test "$OCAMLC" = no ; then AC_MSG_ERROR(Cannot find ocamlc.) fi # we extract Ocaml version number and library path OCAMLVERSION=`$OCAMLC -v | sed -n -e 's|.*version *\(.*\)$|\1|p' ` echo "ocaml version is $OCAMLVERSION" OCAMLLIB=`$OCAMLC -v | tail -1 | cut -f 4 -d " " | tr -d '\\r'` echo "ocaml library path is $OCAMLLIB" # we look for ocamlfind; if not present, we just don't use it to find # libraries AC_CHECK_PROG(USEOCAMLFIND,ocamlfind,yes,no) if test "$USEOCAMLFIND" = yes; then OCAMLFINDLIB=$(ocamlfind printconf stdlib) OCAMLFIND=$(which ocamlfind) if test "$OCAMLFINDLIB" != "$OCAMLLIB"; then USEOCAMLFIND=no; echo "but your ocamlfind is not compatible with your ocamlc:" echo "ocamlfind : $OCAMLFINDLIB, ocamlc : $OCAMLLIB" fi fi # then we look for ocamlopt; if not present, we issue a warning # if the version is not the same, we also discard it # we set OCAMLBEST to "opt" or "byte", whether ocamlopt is available or not AC_CHECK_PROGS(OCAMLOPT,ocamlopt,no) OCAMLBEST=byte if test "$OCAMLOPT" = no ; then AC_MSG_WARN(Cannot find ocamlopt; bytecode compilation only.) else AC_MSG_CHECKING(ocamlopt version) TMPVERSION=`$OCAMLOPT -v | sed -n -e 's|.*version *\(.*\)$|\1|p' ` if test "$TMPVERSION" != "$OCAMLVERSION" ; then AC_MSG_RESULT(differs from ocamlc; ocamlopt discarded.) OCAMLOPT=no else AC_MSG_RESULT(ok) OCAMLBEST=opt fi fi # checking for ocamlc.opt AC_CHECK_PROGS(OCAMLCDOTOPT,ocamlc.opt,no) if test "$OCAMLCDOTOPT" != no ; then AC_MSG_CHECKING(ocamlc.opt version) TMPVERSION=`$OCAMLCDOTOPT -v | sed -n -e 's|.*version *\(.*\)$|\1|p' ` if test "$TMPVERSION" != "$OCAMLVERSION" ; then AC_MSG_RESULT(differs from ocamlc; ocamlc.opt discarded.) else AC_MSG_RESULT(ok) OCAMLC=$OCAMLCDOTOPT fi fi # checking for ocamlopt.opt if test "$OCAMLOPT" != no ; then AC_CHECK_PROGS(OCAMLOPTDOTOPT,ocamlopt.opt,no) if test "$OCAMLOPTDOTOPT" != no ; then AC_MSG_CHECKING(ocamlopt.opt version) TMPVER=`$OCAMLOPTDOTOPT -v | sed -n -e 's|.*version *\(.*\)$|\1|p' ` if test "$TMPVER" != "$OCAMLVERSION" ; then AC_MSG_RESULT(differs from ocamlc; ocamlopt.opt discarded.) else AC_MSG_RESULT(ok) OCAMLOPT=$OCAMLOPTDOTOPT fi fi fi # ocamldep should also be present in the path AC_CHECK_PROG(OCAMLDEP,ocamldep,ocamldep,no) if test "$OCAMLDEP" = no ; then AC_MSG_ERROR(Cannot find ocamldep.) fi # platform AC_MSG_CHECKING(platform) if echo "let _ = Sys.os_type;;" | ocaml | grep -q Win32; then AC_MSG_RESULT(Win32) OCAMLWIN32=yes EXE=.exe else OCAMLWIN32=no EXE= fi # substitutions to perform AC_SUBST(OCAMLC) AC_SUBST(OCAMLOPT) AC_SUBST(OCAMLDEP) AC_SUBST(OCAMLBEST) AC_SUBST(OCAMLVERSION) AC_SUBST(OCAMLLIB) AC_SUBST(OCAMLWIN32) AC_SUBST(EXE) # Finally create the Makefile.configurable from Makefile.configurable.in AC_OUTPUT(Makefile) chmod a-w Makefile ocplib-simplex-0.3/extra/000077500000000000000000000000001301061175500154255ustar00rootroot00000000000000ocplib-simplex-0.3/extra/TODO.txt000066400000000000000000000011351301061175500167330ustar00rootroot00000000000000global: ------- - put some documentation in .mli files - try some more heuristics to extract models for simplexes over ints. - add the ability to do some encoding (with a flag): (eg. cubes-test for LIA) - add optimization capabilities assertBounds.ml: ---------------- - assert_var and assert_poly should ignore bounds when Pb is UNSAT - assert_var and assert_poly should ignore bounds that are implied by those of the simplex - add a mode for assert_var and assert_poly to ignore previously asserted bounds ? (i.e. mode force_bounds) useful for assertUI.ml ? - deduce bounds from the simplex ? ocplib-simplex-0.3/extra/simplex_invariants.txt000066400000000000000000000050451301061175500221110ustar00rootroot00000000000000Basic formulation: ---------------- version 0.1 has the following env. type value_status = ValueOK | LowerKO | UpperKO type var_info = { mini : bound; maxi : bound; min_ex : Ex.t; max_ex : Ex.t; value : R.t * R.t; vstatus : value_status; is_slake : bool; } type t = { basic : (var_info * P.t) MX.t; non_basic : (var_info * SX.t) MX.t; slake_cache : Var.t SLAKE.t; fixme : SX.t; is_int : bool; status : simplex_status; debug : int; check_invariants : bool } (1) forall x in basic U non_basic U used_by U polys(basic) U slake_cache U polys(slake_cache) U fixeme. is_int <=> Var.is_int x (2) basic intersect non_basic = empty (3) forall p in polys(basic) U polys(slake_cache). forall (x, c) in p. (x in basic xor x in non_basic) and c <> 0 (4) used_by intersect non_basic = empty (5) forall y. forall x in used_by(y). (*y is no_basic and x is basic*) let _, p = basic(x) y in vars(p) (* i.e. with a coef != 0 *) (6) forall s. forall p such that basic(s) = _, p. forall x in vars(p). s in used_by(x) (* 5 and 6 mean that used_by contain exactly what needed *) (7) forall x in non_basic. min_bound <= val(x) <= max_bound (8) status = SAT => forall x in basic. min_bound <= val(x) <= max_bound (9) status = IntSAT => (8) and forall x. val(x) is an integer (10) is_int => (* ie simplex on integers *) coefs of delta_i's in min and max bounds are equal to zero (11) not is_int => (* ie simplex on rationnals *) coefs of delta_i's in min bounds are in {0, 1} and coefs of delta_i's in max bounds are in {0, -1} (12) status = SAT (sol) => sol satisfies the bounds of every constraints and sol satisfies every equality s = p, with (s, p) in basic. (13) status = UNSAT ({x_i, ex_i)} => /\ min_bound_i <= x_i <= max_bound_i in UNSAT on rationnals (* use FM to check this ? *) (14). fixme subset basic (15) forall x. x in fixme => ( val(x) < min_bound_x or val(x) > max_bound_x ) (16) status != UNSAT => forall x. x not in fixme => min_bound_x <= val(x) <= max_bound_x (17) status != Unknown => fixme = empty (* When UNSAT is deduced, we empty fixme *) (18) forall (s, p) in basic. val(s) = eval(p) (19) forall (x, i) in basic U non_basic min_bound_x <= val(x) <= max_bound_x => i.vstatus = ValueOK) and val(x) < min_bound_x => i.vstatus = LowerKO and max_bound_x < val(x) => i.vstatus = UpperKO (20) status != Unsat => forall (x, i) in basic U non_basic (min_bound_x <= max_bound_x) ocplib-simplex-0.3/opam000066400000000000000000000012651301061175500151650ustar00rootroot00000000000000opam-version: "1.2" name: "ocplib-simplex" version: "0.2+" authors: "Mohamed Iguernlala " maintainer: "Mohamed Iguernlala " license: "LGPL version 2.1" homepage: "https://github.com/OCamlPro-Iguernlala/ocplib-simplex" bug-reports: "https://github.com/OCamlPro-Iguernlala/ocplib-simplex/issues" dev-repo: "https://github.com/OCamlPro-Iguernlala/ocplib-simplex.git" build:[ ["autoconf"] ["./configure"] [make] ] install:[ [make "install"] ] remove:[ ["ocamlfind" "remove" "ocplib-simplex"] ] depends: [ "ocamlfind" {build} "conf-autoconf" {build} ] available: [ ocaml-version >= "4.01.0" ]ocplib-simplex-0.3/src/000077500000000000000000000000001301061175500150715ustar00rootroot00000000000000ocplib-simplex-0.3/src/assertBounds.ml000066400000000000000000000205551301061175500201060ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module type SIG = sig module Core : CoreSig.SIG val var : Core.t -> Core.Var.t -> Core.bound -> Core.Ex.t -> Core.bound -> Core.Ex.t -> Core.t val poly : Core.t -> Core.P.t -> Core.Var.t -> Core.bound -> Core.Ex.t -> Core.bound -> Core.Ex.t -> Core.t end module Make(Core : CoreSig.SIG) : SIG with module Core = Core = struct module Core = Core module Result = Result.Make(Core) open Core let new_status_basic stt fixme s info consistent_bnds = let has_bad_value = info.vstatus != ValueOK in match stt, consistent_bnds with | UNSAT _, _ -> stt, fixme | _, false -> UNSAT s, SX.empty | UNK, true -> stt, if has_bad_value then SX.add s fixme else SX.remove s fixme | SAT, _ -> assert (fixme == SX.empty); if has_bad_value then UNK, SX.add s fixme else stt, fixme let assert_basic_var env x mini min_ex maxi max_ex = let info, poly = try let info, poly = MX.find x env.basic in let info = set_min_bound info mini min_ex in let info = set_max_bound info maxi max_ex in info, poly with Not_found -> assert false in let status, fixme = new_status_basic env.status env.fixme x info (consistent_bounds info) in {env with basic = MX.add x (info, poly) env.basic; status; fixme} (* *) let new_status_non_basic x stt fixme ({mini; maxi; value; _} as info) = match stt with | UNSAT _ -> stt, fixme | SAT | UNK when consistent_bounds info -> assert (not (violates_min_bound value mini)); assert (not (violates_max_bound value maxi)); assert (stt != SAT || fixme == SX.empty); stt, fixme | SAT | UNK -> UNSAT x, SX.empty let adapt_values_of_basic_vars env _old _new x use = let {basic; _} = env in let diff = R2.sub _new _old in SX.fold (fun s env -> let info, p = try MX.find s basic with Not_found -> assert false in let c_x = try P.find x p with Not_found -> assert false in let info = {info with value = R2.add info.value (R2.mult_by_const c_x diff)} in let info = ajust_status_of_basic info in let status, fixme = new_status_basic env.status env.fixme s info true in {env with status; fixme; basic = MX.add s (info, p) env.basic} )use env let assert_non_basic_var env x mini min_ex maxi max_ex = let info, use = try MX.find x env.non_basic with Not_found -> empty_info, SX.empty in let info = set_min_bound info mini min_ex in let info = set_max_bound info maxi max_ex in let old_val = info.value in let info, changed = ajust_value_of_non_basic info in let status, fixme = new_status_non_basic x env.status env.fixme info in let env = {env with non_basic = MX.add x (info, use) env.non_basic; status; fixme} in if not changed then env else adapt_values_of_basic_vars env old_val info.value x use (* exported function: check_invariants called before and after *) let var env x mini ex_min maxi ex_max = debug "[entry of assert_var]" env (Result.get None); check_invariants env (Result.get None); let env = if MX.mem x env.basic then assert_basic_var env x mini ex_min maxi ex_max else assert_non_basic_var env x mini ex_min maxi ex_max in debug "[exit of assert_var]" env (Result.get None); check_invariants env (Result.get None); env let register_slake slk p env = if MX.mem slk env.slake then env, false else {env with slake = MX.add slk p env.slake}, true let update_use is_fresh_slk x_status slk use = match x_status with | P.Exists -> assert (SX.mem slk use); use | P.Removed -> assert (SX.mem slk use); SX.remove slk use | P.New -> assert (not is_fresh_slk || not (SX.mem slk use)); SX.add slk use let update_use_list is_fresh modified_stt slk non_basic = List.fold_left (fun non_basic (x, x_status) -> try let i, u = MX.find x non_basic in MX.add x (i, update_use is_fresh x_status slk u) non_basic with Not_found -> assert false )non_basic modified_stt let normalize_polynomial is_fresh slk p env = P.fold (fun x c (q, env) -> try let info, use = MX.find x env.non_basic in let new_q, x_status = P.accumulate x c q in let use = update_use is_fresh x_status slk use in new_q, {env with non_basic = MX.add x (info, use) env.non_basic} with Not_found -> try let _ , p_of_x = MX.find x env.basic in let new_q, modified_stt = P.append q c p_of_x in new_q, {env with non_basic = update_use_list is_fresh modified_stt slk env.non_basic} with Not_found -> (* var not initied -> new non_basic *) let env = assert_non_basic_var env x None Ex.empty None Ex.empty in let new_q, x_status = P.replace x c q in assert (x_status == P.New); let info, use = try MX.find x env.non_basic with Not_found -> assert false in let use = update_use is_fresh x_status slk use in new_q, { env with non_basic = MX.add x (info, use) env.non_basic} )p (P.empty, env) (* exported function: check_invariants called before and after *) let poly env p slk mini min_ex maxi max_ex = debug "[entry of assert_poly]" env (Result.get None); check_invariants env (Result.get None); assert (P.is_polynomial p); let env, is_fresh = register_slake slk p env in let info, is_basic, env = try (* non basic existing var ? *) let info, use = MX.find slk env.non_basic in assert ( let np, _ = normalize_polynomial is_fresh slk p env in let zp, _ = P.accumulate slk R.m_one np in P.is_empty zp ); let info = set_min_bound info mini min_ex in let info = set_max_bound info maxi max_ex in let old_val = info.value in let info, changed = ajust_value_of_non_basic info in let env = {env with non_basic = MX.add slk (info, use) env.non_basic} in info, false, if not changed then env else adapt_values_of_basic_vars env old_val info.value slk use with Not_found -> try (* basic existing var ? *) let info, poly = MX.find slk env.basic in assert ( let np, _ = normalize_polynomial is_fresh slk p env in P.equal np poly ); let info = set_min_bound info mini min_ex in let info = set_max_bound info maxi max_ex in info, true, {env with basic = MX.add slk (info, poly) env.basic} with Not_found -> (* fresh basic var *) assert (is_fresh); let np, env = normalize_polynomial is_fresh slk p env in let info = {empty_info with value = evaluate_poly env np} in let info = set_min_bound info mini min_ex in let info = set_max_bound info maxi max_ex in info, true, {env with basic = MX.add slk (info, np) env.basic} in let status, fixme = if is_basic then new_status_basic env.status env.fixme slk info (consistent_bounds info) else new_status_non_basic slk env.status env.fixme info in let env = {env with status; fixme } in debug "[exit of assert_poly]" env (Result.get None); check_invariants env (Result.get None); env end (* end of functor Make *) ocplib-simplex-0.3/src/assertBounds.mli000066400000000000000000000014321301061175500202500ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module type SIG = sig module Core : CoreSig.SIG val var : Core.t -> Core.Var.t -> Core.bound -> Core.Ex.t -> Core.bound -> Core.Ex.t -> Core.t val poly : Core.t -> Core.P.t -> Core.Var.t -> Core.bound -> Core.Ex.t -> Core.bound -> Core.Ex.t -> Core.t end module Make(Core : CoreSig.SIG) : SIG with module Core = Core ocplib-simplex-0.3/src/basic.ml000066400000000000000000000016441301061175500165110ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module Make (Var : ExtSigs.VAR_SIG)(R : ExtSigs.R_SIG)(Ex : ExtSigs.EX_SIG) : sig module Core : CoreSig.SIG with module Var=Var and module R=R and module Ex=Ex module Assert : AssertBounds.SIG with module Core := Core module Solve : SolveBounds.SIG with module Core := Core module Result : Result.SIG with module Core := Core end = struct module Core = Core.Make(Var)(R)(Ex) module Assert = AssertBounds.Make(Core) module Solve = SolveBounds.Make(Core) module Result = Result.Make(Core) end ocplib-simplex-0.3/src/basic.mli000066400000000000000000000013671301061175500166640ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module Make (Var : ExtSigs.VAR_SIG)(R : ExtSigs.R_SIG)(Ex : ExtSigs.EX_SIG) : sig module Core : CoreSig.SIG with module Var=Var and module R=R and module Ex=Ex module Assert : AssertBounds.SIG with module Core := Core module Solve : SolveBounds.SIG with module Core := Core module Result : Result.SIG with module Core := Core end ocplib-simplex-0.3/src/build.ocp000066400000000000000000000011111301061175500166650ustar00rootroot00000000000000comp += [ "-g" ] link += [ "-g" ] comp += [ "-bin-annot" ] comp += [ "-annot" ] comp += [ "-w" "+A" ] comp += [ "-absname" ] comp += [ "-short-paths" ] comp += [ "-strict-sequence" ] begin library "ocplibSimplex" files = [ "version.mli" "version.ml" "extSigs.mli" "rat2.mli" "rat2.ml" "polys.mli" "polys.ml" "coreSig.mli" "core.mli" "core.ml" "result.mli" "result.ml" "assertBounds.mli" "assertBounds.ml" "solveBounds.mli" "solveBounds.ml" "basic.mli" "basic.ml" ] end ocplib-simplex-0.3/src/core.ml000066400000000000000000000434421301061175500163620ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) open Format module Make (Var : ExtSigs.VAR_SIG) (R : ExtSigs.R_SIG) (Ex : ExtSigs.EX_SIG) : CoreSig.SIG with module Var=Var and module R=R and module Ex=Ex = struct module Var = Var module R = R module Ex = Ex module R2 = Rat2.Make(R) module P : Polys.SIG with module Var = Var and module R = R = Polys.Make(Var) (R) module MX : Map.S with type key = Var.t = Map.Make(Var) module SX : Set.S with type elt = Var.t = Set.Make(Var) module SP : Set.S with type elt = P.t = Set.Make(P) type bound = R2.t option type value_status = ValueOK | LowerKO | UpperKO type var_info = { mini : bound; maxi : bound; min_ex : Ex.t; max_ex : Ex.t; value : R2.t; vstatus : value_status; empty_dom : bool; } type solution = { main_vars : (Var.t * R.t) list; slake_vars : (Var.t * R.t) list; int_sol : bool (* always set to false for rational simplexes*) } type maximum = { max_v : R.t; is_le : bool; (* bool = true <-> large bound *) reason: Ex.t } type result = | Unknown | Unsat of Ex.t Lazy.t | Sat of solution Lazy.t | Unbounded of solution Lazy.t | Max of maximum Lazy.t * solution Lazy.t type simplex_status = UNK | UNSAT of Var.t | SAT type t = { basic : (var_info * P.t) MX.t; non_basic : (var_info * SX.t) MX.t; slake : P.t MX.t; fixme : SX.t; is_int : bool; status : simplex_status; debug : int; check_invs: bool; } let empty_info = { mini = None; maxi = None; min_ex = Ex.empty; max_ex = Ex.empty; value = R2.zero; vstatus = ValueOK; empty_dom = false; } let empty ~is_int ~check_invs ~debug = { basic = MX.empty; non_basic = MX.empty; slake = MX.empty; fixme = SX.empty; status = UNK; is_int; check_invs; debug } let on_integers env = env.is_int let equals_optimum v opt = match opt with | None -> false | Some opt -> R2.compare v opt = 0 let violates_min_bound value mn = match mn with | None -> false (* min is -infinity *) | Some min -> R2.compare value min < 0 let violates_max_bound value mx = match mx with | None -> false (* max is +infinity *) | Some max -> R2.compare value max > 0 let consistent_bounds_aux mini maxi = match mini, maxi with | None, None | Some _, None | None, Some _ -> true | Some min, Some max -> R2.compare min max <= 0 let consistent_bounds info = consistent_bounds_aux info.mini info.maxi let set_min_bound info bnd ex = match bnd with | None -> info | Some _new -> if violates_min_bound _new info.mini then info else let empty_dom = not (consistent_bounds_aux bnd info.maxi) in if violates_min_bound info.value bnd then {info with mini = bnd; min_ex = ex; vstatus = LowerKO; empty_dom} else {info with mini = bnd; min_ex = ex; empty_dom} let set_max_bound info bnd ex = match bnd with | None -> info | Some _new -> if violates_max_bound _new info.maxi then info else let empty_dom = not (consistent_bounds_aux info.mini bnd) in if violates_max_bound info.value bnd then {info with maxi = bnd; max_ex = ex; vstatus = UpperKO; empty_dom} else {info with maxi = bnd; max_ex = ex; empty_dom} let ajust_value_of_non_basic info = if info.empty_dom then begin assert (info.vstatus != ValueOK); info, false (* not changed if not sat_bnds *) end else match info.vstatus with | ValueOK -> info, false | UpperKO -> {info with vstatus = ValueOK; value = match info.maxi with | None -> assert false | Some bnd -> bnd}, true | LowerKO -> {info with vstatus = ValueOK; value = match info.mini with | None -> assert false | Some bnd -> bnd}, true let ajust_status_of_basic info = let _new = if violates_min_bound info.value info.mini then LowerKO else if violates_max_bound info.value info.maxi then UpperKO else ValueOK in if info.vstatus == _new then info else {info with vstatus = _new} let evaluate_poly {non_basic; _} p = P.fold (fun x c acc -> let {value = v; _}, _ = try MX.find x non_basic with Not_found -> assert false in R2.add acc (R2.mult_by_const c v) )p R2.zero let poly_of_slake env slk = try Some (MX.find slk env.slake) with Not_found -> None (* debug functions *) module Debug = struct let string_of_status = function | ValueOK -> "OK " | UpperKO -> "KO(Upper)" | LowerKO -> "KO(Lower)" let print_min_bound fmt i = match i.mini with | None -> fprintf fmt "-inf <" | Some (re, im) -> fprintf fmt "%a <%s" R.print re (if R.equal im R.zero then "=" else "") let print_max_bound fmt i = match i.maxi with | None -> fprintf fmt "< +inf" | Some (re, im) -> fprintf fmt "<%s %a" (if R.equal im R.zero then "=" else "") R.print re let re_computed_status_of_info v = if violates_min_bound v.value v.mini then LowerKO else if violates_max_bound v.value v.maxi then UpperKO else ValueOK let print_bounds_and_values fmt mx = MX.iter (fun x (info, _) -> let re, im = info.value in let comp_status = re_computed_status_of_info info in Format.fprintf fmt "%a [ %a == (%4a , %4a) ] %a (computed %s) (flag %s)@." print_min_bound info Var.print x R.print re R.print im print_max_bound info (string_of_status comp_status) (string_of_status info.vstatus); assert (info.empty_dom || comp_status == info.vstatus); )mx let print_uses fmt non_basic = MX.iter (fun x (_, use_x) -> Format.fprintf fmt "variables that use %a are: %a@." Var.print x (fun fmt s -> SX.iter(fprintf fmt "%a , " Var.print) s) use_x; )non_basic let print_solution = let aux fmt l = List.iter (fun (x, q) -> fprintf fmt " %a --> %a@." Var.print x R.print q; )l in fun is_int fmt s -> if is_int then fprintf fmt " (int solution ? %b)@." s.int_sol; aux fmt s.main_vars; aux fmt s.slake_vars let print_result is_int fmt status = match status with | Unknown -> fprintf fmt "Unknown" | Sat s -> fprintf fmt "Sat:@.%a@." (print_solution is_int) (Lazy.force s) | Unsat ex -> fprintf fmt "Unsat:%a@." Ex.print (Lazy.force ex) | Unbounded s -> fprintf fmt "Unbounded:@.%a@." (print_solution is_int) (Lazy.force s) | Max(mx, s) -> let mx = Lazy.force mx in fprintf fmt "Max: (v=%a, is_le=%b, ex=%a)@.%a@." R.print mx.max_v mx.is_le Ex.print mx.reason (print_solution is_int) (Lazy.force s) let print_fixme fmt sx = match SX.elements sx with | [] -> fprintf fmt " (fixme is empty)@."; | l -> List.iter (fprintf fmt " >> %a@." Var.print) l let print_matrix fmt env = MX.iter (fun x (_, p) ->fprintf fmt "%4a = %a@." Var.print x P.print p) env.basic let print result fmt env = Format.fprintf fmt "== begin ========================================@."; fprintf fmt "on integers ? %b@." env.is_int; fprintf fmt "--- values of non-basic ---------------------------@."; print_bounds_and_values fmt env.non_basic; fprintf fmt "---------------------------------------------------@."; fprintf fmt "--- values of basic -------------------------------@."; fprintf fmt "---------------------------------------------------@."; print_bounds_and_values fmt env.basic; fprintf fmt "--- matrix ----------------------------------------@."; print_matrix fmt env; fprintf fmt "---------------------------------------------------@."; fprintf fmt "--- sets of uses ----------------------------------@."; print_uses fmt env.non_basic; fprintf fmt "---------------------------------------------------@."; fprintf fmt "--- basic variables in fixme ----------------------@."; print_fixme fmt env.fixme; fprintf fmt "---------------------------------------------------@."; fprintf fmt "--- simplex status --------------------------------@."; fprintf fmt "%a@." (print_result env.is_int) result; fprintf fmt "== end ==========================================@."; end (* end of module Debug *) let print = Debug.print let debug msg env get_result = if env.debug > 0 then let result = get_result env in Format.eprintf "@.%s@.%a@." msg (print result) env (* check invariants of the simplex: these invariants are listed in extra/simplexe_invariants.txt *) let get_all_polys env = let sp = MX.fold (fun _ (_,p) sp -> SP.add p sp) env.basic SP.empty in MX.fold (fun _ p sp -> SP.add p sp) env.slake sp let get_all_vars env all_polys = let sx = env.fixme in let sx = MX.fold (fun x _ sx -> SX.add x sx) env.basic sx in let sx = MX.fold (fun x (_, use) sx -> SX.union use (SX.add x sx)) env.non_basic sx in let sx = MX.fold (fun x _ sx -> SX.add x sx) env.slake sx in SP.fold (P.fold (fun x _ sx -> SX.add x sx)) all_polys sx let info_of x env = try fst (MX.find x env.non_basic) with Not_found -> try fst (MX.find x env.basic) with Not_found -> assert false let _01__check_type is_int all_vars = SX.iter (fun x -> assert (is_int == Var.is_int x)) all_vars let _02__check_basic_non_basic_disjoint env = MX.iter (fun x _ -> assert (not (MX.mem x env.non_basic))) env.basic; MX.iter (fun x _ -> assert (not (MX.mem x env.basic))) env.non_basic let _03__check_vars_of_polys env polys = SP.iter (P.iter (fun x c -> assert (R.sign c <> 0); assert (MX.mem x env.basic || MX.mem x env.non_basic) ))polys let _04_05_06__check_use env = MX.iter (fun x (_, use) -> SX.iter (fun s -> assert (not (MX.mem s env.non_basic)); (* 04 *) try assert (P.mem x (snd (MX.find s env.basic))) (*05*) with Not_found -> assert false ) use )env.non_basic; MX.iter (fun s (_, p) -> P.iter (fun x _ -> try assert (SX.mem s (snd (MX.find x env.non_basic))); (*06*) with Not_found -> assert false )p; )env.basic let _07__values_ok_for_non_basic_vars env = MX.iter (fun _ (info, _) -> if consistent_bounds info then begin assert (not (violates_min_bound info.value info.mini)); assert (not (violates_max_bound info.value info.maxi)); end else match env.status with | UNSAT _ -> () | SAT | UNK -> assert false )env.non_basic let _08_09__values_ok_when_sat env result = let check mx int_sol = MX.iter (fun _ (info, _) -> let r, i = info.value in assert (not (violates_min_bound info.value info.mini)); assert (not (violates_max_bound info.value info.maxi)); assert (not int_sol || R.is_int r && R.is_zero i) )mx in match result with | Sat s | Unbounded s | Max(_,s) -> let s = Lazy.force s in check env.basic s.int_sol; check env.non_basic s.int_sol | Unsat _ | Unknown -> () let _10_11__check_handling_strict_ineqs env = let is_int = env.is_int in let aux _ (info, _) = begin match info.mini with | None -> () | Some (_, i) -> assert (not is_int || R.is_zero i); assert (is_int || R.is_zero i || R.is_one i); end; begin match info.maxi with | None -> () | Some (_, i) -> assert (not is_int || R.is_zero i); assert (is_int || R.is_zero i || R.is_m_one i); end in MX.iter aux env.basic; MX.iter aux env.non_basic let _12__check_solution_when_sat = let aux l env = List.iter (fun (x, v) -> let info = info_of x env in let v2 = v, R.zero in assert (not (violates_min_bound v2 info.mini)); assert (not (violates_max_bound v2 info.maxi)); )l in fun env result -> match result with | Unsat _ | Unknown -> () | Sat s | Unbounded s | Max(_,s) -> let s = Lazy.force s in let v = List.length s.main_vars + List.length s.slake_vars in let w = MX.cardinal env.non_basic + MX.cardinal env.basic in assert ( if v <> w then eprintf "model length = %d, but basic + non_basic = %d@." v w; v = w); aux s.main_vars env; aux s.slake_vars env let _13__check_reason_when_unsat env = if env.debug > 0 then Format.eprintf "@.[check-invariants] _13__check_reason_when_unsat: TODO@.@." let _14_15__fixme_is_subset_of_basic env = SX.iter (fun x -> try let info, _ = MX.find x env.basic in assert ((violates_min_bound info.value info.mini) || (violates_max_bound info.value info.maxi)); (*15*) with Not_found -> assert false (*14*) ) env.fixme let _16__fixme_containts_basic_with_bad_values_if_not_unsat env all_vars result = match result with | Unsat _ | Unbounded _ | Max _ -> () | Unknown | Sat _ -> SX.iter (fun x -> if not (SX.mem x env.fixme) then let info = info_of x env in assert (not (violates_min_bound info.value info.mini)); assert (not (violates_max_bound info.value info.maxi)) )all_vars let _17__fixme_is_empty_if_not_unknown env result = match result with | Unknown -> () | Unsat _ | Sat _ | Unbounded _ | Max _ -> assert (SX.is_empty env.fixme) let _18__vals_of_basic_vars_computation env = MX.iter (fun _ ({value = s; _}, p) -> let vp = evaluate_poly env p in assert (R2.compare vp s = 0); )env.basic let _19__check_that_vstatus_are_well_set env = let aux _ (info, _) = if info.empty_dom then assert (info.vstatus != ValueOK) else let vmin = violates_min_bound info.value info.mini in let vmax = violates_max_bound info.value info.maxi in match info.vstatus with | ValueOK -> assert (not vmin); assert(not vmax); | UpperKO -> assert (not vmin); assert(vmax); | LowerKO -> assert (vmin); assert(not vmax); in MX.iter aux env.basic; MX.iter aux env.non_basic let _20__bounds_are_consistent_if_not_unsat env result = match result with | Unsat _ -> () | Unknown | Sat _ | Unbounded _ | Max _ -> let aux _ (info, _) = assert (consistent_bounds info) in MX.iter aux env.basic; MX.iter aux env.non_basic let _21__check_coherence_of_empty_dom = let aux mx = MX.iter (fun _ (info, _) -> assert (consistent_bounds info == not info.empty_dom); if info.empty_dom then assert (violates_min_bound info.value info.mini || violates_max_bound info.value info.maxi); )mx in fun env -> aux env.non_basic; aux env.basic let check_invariants env get_result = if env.check_invs then let polys = get_all_polys env in let all_vars = get_all_vars env polys in let result = get_result env in _01__check_type env.is_int all_vars; _02__check_basic_non_basic_disjoint env; _03__check_vars_of_polys env polys; _04_05_06__check_use env; _07__values_ok_for_non_basic_vars env; _08_09__values_ok_when_sat env result; _10_11__check_handling_strict_ineqs env; _12__check_solution_when_sat env result; _13__check_reason_when_unsat env; _14_15__fixme_is_subset_of_basic env; _16__fixme_containts_basic_with_bad_values_if_not_unsat env all_vars result; _17__fixme_is_empty_if_not_unknown env result; _18__vals_of_basic_vars_computation env; _19__check_that_vstatus_are_well_set env; _20__bounds_are_consistent_if_not_unsat env result; (*_21__check_coherence_of_empty_dom env;*) end ocplib-simplex-0.3/src/core.mli000066400000000000000000000010671301061175500165300ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module Make (Var : ExtSigs.VAR_SIG) (R : ExtSigs.R_SIG) (Ex : ExtSigs.EX_SIG) : CoreSig.SIG with module Var = Var and module R = R and module Ex = Ex ocplib-simplex-0.3/src/coreSig.mli000066400000000000000000000053671301061175500172020ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) (** Interface of the main types and auxiliary of the simplex *) module type SIG = sig module Var : ExtSigs.VAR_SIG module Ex : ExtSigs.EX_SIG module R : ExtSigs.R_SIG module R2 : Rat2.SIG with module R = R module P : Polys.SIG with module Var = Var and module R = R module MX : Map.S with type key = Var.t module SX : Set.S with type elt = Var.t (*module SLAKE : Map.S with type key = P.t*) type bound = R2.t option type value_status = ValueOK | LowerKO | UpperKO type var_info = { mini : bound; maxi : bound; min_ex : Ex.t; max_ex : Ex.t; value : R2.t; vstatus : value_status; empty_dom : bool; } type solution = { main_vars : (Var.t * R.t) list; slake_vars : (Var.t * R.t) list; int_sol : bool (* always set to false for rational simplexes*) } type maximum = { max_v : R.t; is_le : bool; (* bool = true <-> large bound *) reason: Ex.t } type result = | Unknown | Unsat of Ex.t Lazy.t | Sat of solution Lazy.t | Unbounded of solution Lazy.t | Max of maximum Lazy.t * solution Lazy.t type simplex_status = UNK | UNSAT of Var.t | SAT type t = { basic : (var_info * P.t) MX.t; non_basic : (var_info * SX.t) MX.t; slake : P.t MX.t; fixme : SX.t; is_int : bool; status : simplex_status; debug : int; check_invs: bool; } val empty_info : var_info val empty : is_int : bool -> check_invs : bool -> debug : int -> t val on_integers : t -> bool val equals_optimum : R2.t -> bound -> bool val consistent_bounds : var_info -> bool val violates_min_bound : R2.t -> bound -> bool val violates_max_bound : R2.t -> bound -> bool val set_min_bound : var_info -> bound -> Ex.t -> var_info val set_max_bound : var_info -> bound -> Ex.t -> var_info (* vstatus is supposed to be well set *) val ajust_value_of_non_basic: var_info -> var_info * bool (* valuation is supposed to be well computed *) val ajust_status_of_basic : var_info -> var_info val evaluate_poly : t -> P.t -> R2.t val poly_of_slake : t -> Var.t -> P.t option (* debug functions and invariants *) val check_invariants : t -> (t -> result) -> unit val print : result -> Format.formatter -> t -> unit val debug : string -> t -> (t -> result) -> unit end ocplib-simplex-0.3/src/extSigs.mli000066400000000000000000000034561301061175500172320ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) (*----------------------------------------------------------------------------*) (** Interface required for variables *) module type VAR_SIG = sig (** type of variables used in the simplex *) type t (** compare function on vars *) val compare : t -> t -> int (** [is_int v] returns true if the variable has integer type, and false otherwise *) val is_int : t -> bool (** [print fmt v] prints the given var *) val print : Format.formatter -> t -> unit end (*----------------------------------------------------------------------------*) (** Interface required for rationnals *) module type R_SIG = sig (** type of rationnal numbers *) type t val zero : t val one : t val m_one : t val sign : t -> int (* can be used to quickly compare with zero *) val compare : t -> t -> int val equal : t -> t -> bool val is_zero : t -> bool val is_one : t -> bool val is_m_one : t -> bool val add : t -> t -> t val sub : t -> t -> t val div : t -> t -> t val mult : t -> t -> t val abs : t -> t val is_int : t -> bool val print : Format.formatter -> t -> unit val to_string : t -> string val min : t -> t -> t val minus : t -> t end (*----------------------------------------------------------------------------*) (** Interface of explanations *) module type EX_SIG = sig type t val empty : t val union : t -> t -> t val print : Format.formatter -> t -> unit end ocplib-simplex-0.3/src/polys.ml000066400000000000000000000064641301061175500166030ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module type SIG = sig module Var : ExtSigs.VAR_SIG module R : ExtSigs.R_SIG type t type var_status = New | Exists | Removed val empty : t val is_polynomial : t -> bool val is_empty : t -> bool val replace : Var.t -> R.t -> t -> t * var_status val accumulate : Var.t -> R.t -> t -> t * var_status val append : t -> R.t -> t -> t * (Var.t * var_status) list val subst : Var.t -> t -> t -> t * (Var.t * var_status) list val from_list : (Var.t * R.t) list -> t val print : Format.formatter -> t -> unit val fold: (Var.t -> R.t -> 'a -> 'a) -> t -> 'a -> 'a val iter: (Var.t -> R.t -> unit) -> t -> unit val partition: (Var.t -> R.t -> bool) -> t -> t * t val compare : t -> t -> int val mem : Var.t -> t -> bool val equal : t -> t -> bool val bindings : t -> (Var.t * R.t) list val find : Var.t -> t -> R.t val remove : Var.t -> t -> t end module Make(Var: ExtSigs.VAR_SIG)(R : ExtSigs.R_SIG) : SIG with module Var = Var and module R = R = struct module Var = Var module R = R module MV = Map.Make(Var) type t = R.t MV.t type var_status = New | Exists | Removed let empty = MV.empty let fold = MV.fold let iter = MV.iter let compare = MV.compare R.compare let partition = MV.partition let remove = MV.remove let find = MV.find let bindings = MV.bindings let equal = MV.equal R.equal let mem = MV.mem let is_empty = MV.is_empty let is_polynomial p = try let cpt = ref 0 in iter (fun _ _ -> incr cpt; if !cpt > 1 then raise Exit) p; false with Exit -> true let replace v q t = if R.is_zero q then MV.remove v t, Removed else MV.add v q t, (if MV.mem v t then Exists else New) let accumulate v q t = let new_q = try R.add q (find v t) with Not_found -> q in replace v new_q t (* TODO: We can maybe replace mp with a list, since keys are unique ... *) let append_aux p coef q = fold (fun x c (p, mp) -> let p, x_status = accumulate x (R.mult coef c) p in p, MV.add x x_status mp ) q (p, MV.empty) let append p coef q = let p, mp = append_aux p coef q in p, MV.bindings mp let subst v p q = try let new_q, modified = append_aux (remove v q) (find v q) p in new_q, MV.bindings (MV.add v Removed modified) with Not_found -> (* This will oblige us to enforce strong invariants !! We should know exactly where we have to substitute !! *) assert false let from_list l = List.fold_left (fun p (x, c) -> fst (accumulate x c p)) empty l let print fmt p = let l = MV.bindings p in match l with | [] -> Format.fprintf fmt "(empty-poly)" | (x, q)::l -> Format.fprintf fmt "(%a) * %a" R.print q Var.print x; List.iter (fun (x,q) -> Format.fprintf fmt " + (%a) * %a" R.print q Var.print x) l end ocplib-simplex-0.3/src/polys.mli000066400000000000000000000025671301061175500167540ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module type SIG = sig module Var : ExtSigs.VAR_SIG module R : ExtSigs.R_SIG type t type var_status = New | Exists | Removed val empty : t val is_polynomial : t -> bool val is_empty : t -> bool val replace : Var.t -> R.t -> t -> t * var_status val accumulate : Var.t -> R.t -> t -> t * var_status val append : t -> R.t -> t -> t * (Var.t * var_status) list val subst : Var.t -> t -> t -> t * (Var.t * var_status) list val from_list : (Var.t * R.t) list -> t val print : Format.formatter -> t -> unit val fold: (Var.t -> R.t -> 'a -> 'a) -> t -> 'a -> 'a val iter: (Var.t -> R.t -> unit) -> t -> unit val partition: (Var.t -> R.t -> bool) -> t -> t * t val compare : t -> t -> int val mem : Var.t -> t -> bool val equal : t -> t -> bool val bindings : t -> (Var.t * R.t) list val find : Var.t -> t -> R.t val remove : Var.t -> t -> t end module Make(Var: ExtSigs.VAR_SIG)(R : ExtSigs.R_SIG) : SIG with module Var = Var and module R = R ocplib-simplex-0.3/src/rat2.ml000066400000000000000000000025621301061175500163000ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module type SIG = sig module R : ExtSigs.R_SIG type t = R.t * R.t val zero : t val minus : t -> t val add : t -> t -> t val sub : t -> t -> t val mult : t -> t -> t val mult_by_const : R.t -> t -> t val div_by_const : R.t -> t -> t val compare : t -> t -> int val is_zero : t -> bool end module Make(R : ExtSigs.R_SIG) : SIG with module R = R = struct module R = R type t = R.t * R.t let zero = R.zero, R.zero let add (a, b) (x, y) = R.add a x, R.add b y let sub (a, b) (x, y) = R.sub a x, R.sub b y let mult (a, b) (x, y) = R.mult a x, R.mult b y let mult_by_const c e = if R.is_one c then e else let a, b = e in R.mult a c, R.mult b c let div_by_const c e = if R.is_one c then e else let a, b = e in R.div a c, R.div b c let compare (a, b) (x, y) = let c = R.compare a x in if c <> 0 then c else R.compare b y let is_zero (a, b) = R.is_zero a && R.is_zero b let minus (a, b) = R.minus a, R.minus b end ocplib-simplex-0.3/src/rat2.mli000066400000000000000000000014051301061175500164440ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module type SIG = sig module R : ExtSigs.R_SIG type t = R.t * R.t val zero : t val minus : t -> t val add : t -> t -> t val sub : t -> t -> t val mult : t -> t -> t val mult_by_const : R.t -> t -> t val div_by_const : R.t -> t -> t val compare : t -> t -> int val is_zero : t -> bool end module Make(R : ExtSigs.R_SIG) : SIG with module R = R ocplib-simplex-0.3/src/result.ml000066400000000000000000000124261301061175500167460ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module type SIG = sig module Core : CoreSig.SIG val get : (Core.P.t * bool) option -> Core.t -> Core.result end module Make(Core : CoreSig.SIG) : SIG with module Core = Core = struct module Core = Core open Core let explain_poly non_basic p ex is_lower = let invert_sign = if is_lower then 1 else -1 in P.fold (fun x coef ex -> let c = invert_sign * R.sign coef in assert (c <> 0); let xi, _ = try MX.find x non_basic with Not_found -> assert false in let ex, optimum = if c > 0 then Ex.union ex xi.max_ex, xi.maxi else Ex.union ex xi.min_ex, xi.mini in assert (equals_optimum xi.value optimum); ex )p ex let get_unsat_core s env = try let si, p = MX.find s env.basic in if not (consistent_bounds si) then Ex.union si.min_ex si.max_ex else match si.vstatus with | ValueOK -> assert false | LowerKO -> explain_poly env.non_basic p si.min_ex true | UpperKO -> explain_poly env.non_basic p si.max_ex false with Not_found -> let si, _ = MX.find s env.non_basic in if not (consistent_bounds si) then Ex.union si.min_ex si.max_ex else assert false let get_int_solution env = let is_int_sol = ref true in let sol = MX.fold (fun x (xi,_) sol -> let re, im = xi.value in assert (R.sign im = 0); is_int_sol := !is_int_sol && R.is_int re; (x, re) :: sol ) env.non_basic [] in let sol = MX.fold (fun x (xi, _) sol -> let re, im = xi.value in assert (R.sign im = 0); is_int_sol := !is_int_sol && R.is_int re; (x, re) :: sol )env.basic sol in let slake = env.slake in let sol_slk, sol = List.partition (fun (x, _) -> MX.mem x slake) sol in { main_vars = sol; slake_vars = sol_slk; int_sol = !is_int_sol } let eval_eps eps inf_r inf_d sup_r sup_d = let c = R.compare inf_r sup_r in assert (c <= 0); if c = 0 || R.compare inf_d sup_d <= 0 then eps else R.min eps (R.div (R.sub sup_r inf_r) (R.sub inf_d sup_d)) let get_rat_solution = let compute_epsilon mp eps = MX.fold (fun _ (i, _) eps -> match i.mini , i.maxi with | None, None -> eps | Some (min_r, min_d), None -> let q1,q2 = i.value in assert (R.equal min_d R.zero || R.equal min_d R.one); let eps = eval_eps eps min_r min_d q1 q2 in assert (R.compare eps R.zero > 0); eps | None, Some (max_r, max_d) -> let q1,q2 = i.value in assert (R.equal max_d R.zero || R.equal max_d R.m_one); let eps = eval_eps eps q1 q2 max_r max_d in assert (R.compare eps R.zero > 0); eps | Some (min_r, min_d), Some (max_r, max_d) -> let q1,q2 = i.value in assert (R.equal min_d R.zero || R.equal min_d R.one); assert (R.equal max_d R.zero || R.equal max_d R.m_one); let eps = eval_eps eps min_r min_d q1 q2 in let eps = eval_eps eps q1 q2 max_r max_d in assert (R.compare eps R.zero > 0); eps ) mp eps in let compute_solution slake mp eps acc = MX.fold (fun x (info, _) (m, s) -> let q1,q2 = info.value in let q = R.add q1 (R.mult q2 eps) in assert (not (violates_min_bound (q, R.zero) info.mini)); assert (not (violates_max_bound (q, R.zero) info.maxi)); if MX.mem x slake then m, (x, q) :: s else (x,q) :: m, s )mp acc in fun env -> let eps = compute_epsilon env.basic R.one in let eps = compute_epsilon env.non_basic eps in let acc = compute_solution env.slake env.basic eps ([], []) in let m,s = compute_solution env.slake env.non_basic eps acc in { main_vars = m ; slake_vars = s; int_sol = false } let get_solution env = if env.is_int then get_int_solution env else get_rat_solution env let get_max_info {non_basic; _} p = let (max_v, symb), reason = Core.P.fold (fun x c (max_v, reason) -> let xi, _ = try MX.find x non_basic with Not_found -> assert false in let ex, bnd = if R.sign c > 0 then xi.max_ex, xi.maxi else xi.min_ex, xi.mini in let value = xi.value in assert (equals_optimum value bnd); R2.add max_v (R2.mult_by_const c value), Ex.union reason ex )p (R2.zero, Ex.empty) in {max_v; is_le = R.is_zero symb; reason} let get opt env = match env.status with | UNK -> Unknown | UNSAT s -> Unsat (lazy (get_unsat_core s env)) | SAT -> match opt with | None -> Sat (lazy (get_solution env)) | Some(_, false) -> Unbounded (lazy (get_solution env)) | Some(p, true) -> Max (lazy(get_max_info env p), lazy(get_solution env)) end ocplib-simplex-0.3/src/result.mli000066400000000000000000000011111301061175500171040ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module type SIG = sig module Core : CoreSig.SIG val get : (Core.P.t * bool) option -> Core.t -> Core.result end module Make(Core : CoreSig.SIG) : SIG with module Core = Core ocplib-simplex-0.3/src/solveBounds.ml000066400000000000000000000426331301061175500177360ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module type SIG = sig module Core : CoreSig.SIG val solve : Core.t -> Core.t val maximize : Core.t -> Core.P.t -> Core.t * (Core.P.t * bool) option end module Make(Core : CoreSig.SIG) : SIG with module Core = Core = struct module Core = Core module Result = Result.Make(Core) open Core let gauss_pivot s p x c = let p, _ = P.replace s R.m_one (P.remove x p) in let c = R.div R.m_one c in if R.is_one c then p else P.fold (fun y d q -> fst (P.replace y (R.mult c d) q)) p P.empty exception Out of Var.t * R.t * var_info * SX.t let look_for_next_pivot si pi non_basic = let status = si.vstatus in let is_lower = match status with | ValueOK -> assert false | LowerKO -> 1 | UpperKO -> -1 in try P.iter (fun x coef -> let xi,use = try MX.find x non_basic with Not_found -> assert false in let c = is_lower * R.sign coef in assert (c <> 0); if c > 0 && not (equals_optimum xi.value xi.maxi) then raise (Out (x, coef, xi, use)); if c < 0 && not (equals_optimum xi.value xi.mini) then raise (Out (x, coef, xi, use)); )pi; None with Out (x, c, xi, use) -> Some (x, c, xi, use) let adapt_valuation_of_newly_basic old_si new_si old_xi c_x = let diff = R2.div_by_const c_x (R2.sub new_si.value old_si.value) in { old_xi with value = R2.add diff old_xi.value } (* let string_of_var_status stt = match stt with | P.Removed -> "Removed" | P.New -> "New" | P.Exists -> "Exists" *) (* TODO : review and improve this function *) let rec solve_rec env round = Core.debug (Format.sprintf "[solve] round %d" round) env (Result.get None); Core.check_invariants env (Result.get None); if SX.is_empty env.fixme then {env with status = SAT} else let s = SX.choose env.fixme in let fixme = SX.remove s env.fixme in let si, p = try MX.find s env.basic with Not_found -> assert false in match look_for_next_pivot si p env.non_basic with | None -> {env with fixme = SX.empty; status = UNSAT s} | Some(x, c, xi, use_x) -> if env.debug > 1 then Format.eprintf "[solve_rec] pivot basic %a and non-basic %a@." Var.print s Var.print x; let basic = MX.remove s env.basic in let non_basic = MX.remove x env.non_basic in let q = gauss_pivot s p x c in assert (SX.mem s use_x); let use_x = SX.remove s use_x in let old_si = si in let si, changed = Core.ajust_value_of_non_basic si in assert (changed); let old_xi = xi in let xi = adapt_valuation_of_newly_basic old_si si xi c in let xi = ajust_status_of_basic xi in let diff_xi_val = R2.sub xi.value old_xi.value in let fixme = (* do this earlier to detect bad pivots *) if xi.vstatus == ValueOK then fixme else SX.add x fixme in let non_basic = P.fold (fun y _ non_basic -> let yi, use_y = try MX.find y non_basic with Not_found -> assert false in MX.add y (yi, SX.add x (SX.remove s use_y)) non_basic )(P.remove s q) non_basic in let non_basic = MX.add s (si, SX.add x use_x) non_basic in let basic, non_basic, fixme = SX.fold (fun t (basic, non_basic, fixme) -> let ti0, r = try MX.find t basic with Not_found -> assert false in let cx = try P.find x r with Not_found -> assert false in (*should update_ti*) let diff_cx = R2.mult_by_const cx diff_xi_val in let ti = {ti0 with value = R2.add ti0.value diff_cx} in let ti = ajust_status_of_basic ti in let r', changed = P.subst x q r in (* Format.eprintf "update poly of basic %a@." Var.print t; List.iter (fun (v, vstt) -> Format.eprintf " %a ---> %s@." Var.print v (string_of_var_status vstt); )changed; *) let non_basic = List.fold_left (fun non_basic (z, vstt) -> match vstt with | P.Exists -> non_basic | P.New -> let zi, use_z = try MX.find z non_basic with Not_found -> assert false in MX.add z (zi, SX.add t use_z) non_basic | P.Removed -> if Var.compare z x = 0 then non_basic else let zi, use_z = try MX.find z non_basic with Not_found -> assert false in MX.add z (zi, SX.remove t use_z) non_basic )non_basic changed in (*val subst : Var.t -> t -> t -> t * (Var.t * var_status) list*) let basic = MX.add t (ti, r') basic in let fixme = if ti.vstatus == ValueOK then if ti0.vstatus == ValueOK then fixme else SX.remove t fixme else SX.add t fixme in basic, non_basic, fixme )use_x (basic, non_basic, fixme) in (* ... *) let basic = MX.add x (xi, q) basic in (* ... *) let env = {env with fixme; basic; non_basic} in solve_rec env (round + 1) let solve env = Core.debug "[entry of solve]" env (Result.get None); Core.check_invariants env (Result.get None); let env = match env.Core.status with | Core.UNSAT _ | Core.SAT -> env | Core.UNK -> solve_rec env 1 in Core.debug "[exit of solve]" env (Result.get None); Core.check_invariants env (Result.get None); env let non_basic_to_maximize {non_basic=n_b; _} opt = let acc = ref None in try P.iter (fun x c -> let xi, use = try MX.find x n_b with Not_found -> assert false in let sg = R.sign c in if sg > 0 && not (equals_optimum xi.value xi.maxi) || sg < 0 && not (equals_optimum xi.value xi.mini) then begin acc := Some (x, c, xi, use, sg > 0); raise Exit end )opt; !acc with Exit -> !acc type 'a maximiza_basic = | Free | Stuck | Progress of 'a let basic_var_to_pivot_for_maximization = let choose_best_pivot acc s si p c_px bnd_opt is_min = match bnd_opt with | None -> if !acc = Stuck then acc := Free (* !!! to check *) | Some bnd -> let tmp = if is_min then R2.sub si.value bnd else R2.sub bnd si.value in let ratio = R2.div_by_const (R.abs c_px) tmp in begin match !acc with | Free | Stuck -> acc := Progress (ratio, s, si, p, c_px, bnd, is_min) | Progress (r_old,_,_,_,_,_,_) -> if R2.compare r_old ratio > 0 then acc := Progress (ratio, s, si, p, c_px, bnd, is_min) end; if R2.is_zero ratio then raise Exit (* in the case, the pivot is found*) in fun {basic; _} x use_x should_incr_x -> (* Initially, we assume that we are stuck, unless, use_x is empty *) let acc = ref (if SX.is_empty use_x then Free else Stuck) in try SX.iter (fun s -> let si, p = try MX.find s basic with Not_found -> assert false in let c_px = try P.find x p with Not_found -> assert false in let sg = R.sign c_px in assert (sg <> 0); match should_incr_x, sg > 0, si.mini, si.maxi with | true , true , _, mx_opt -> (* by increasing x, s will increase and max(s) <> +infty *) choose_best_pivot acc s si p c_px mx_opt false | true , false, mn_opt, _ -> (* by increasing x, s will decrease and min(s) <> -infty *) choose_best_pivot acc s si p c_px mn_opt true | false, true , mn_opt, _ -> (* by decreasing x, s will decreease and min(s) <> -infty *) choose_best_pivot acc s si p c_px mn_opt true | false, false, _, mx_opt -> (* by decreasning x, s will increase and max(s) <> +infty *) choose_best_pivot acc s si p c_px mx_opt false (*| true, true, _, None | true, false, None, _ | false, true, None, _ | false, false, _, None -> (* for the cases where max or max = infty, we keep acc unchanged. if acc = None at the end, the problem is unbounded *) () *) )use_x; !acc with Exit -> !acc let can_fix_valuation_without_pivot should_incr xi ratio_opt = if should_incr then match xi.maxi, ratio_opt with | None, _ -> None | Some bnd, Some ratio -> let diff = R2.sub bnd xi.value in if R2.compare diff ratio < 0 then Some ({xi with value = bnd}, diff) else None | Some bnd, None -> let diff = R2.sub bnd xi.value in Some ({xi with value = bnd}, diff) else match xi.mini, ratio_opt with | None, _ -> None | Some bnd, Some ratio -> let diff = R2.sub xi.value bnd in if R2.compare diff ratio < 0 then Some ({xi with value = bnd}, diff) else None | Some bnd, None -> let diff = R2.sub xi.value bnd in Some ({xi with value = bnd}, diff) let update_valuation_without_pivot ({basic; non_basic; _ } as env) x use_x new_xi diff _should_incr = let non_basic = MX.add x (new_xi, use_x) non_basic in let diff = if _should_incr then diff else R2.minus diff in let basic = SX.fold (fun s basic -> let si, p = try MX.find s basic with Not_found -> assert false in let cx = try P.find x p with Not_found -> assert false in assert (not (R.is_zero cx)); let delta = R2.mult_by_const cx diff in let si = {si with value = R2.add si.value delta} in MX.add s (si, p) basic )use_x basic in {env with basic; non_basic} let rec maximize_rec env opt rnd = if env.debug > 1 then Format.eprintf "[maximize_rec] round %d // OPT = %a@." rnd P.print opt; Core.debug (Format.sprintf "[maximize_rec] round %d" rnd) env (Result.get None); Core.check_invariants env (Result.get None); match non_basic_to_maximize env opt with | None -> if env.debug > 1 then Format.eprintf "max reached@."; rnd, env, Some (opt, true) (* max reached *) | Some (_x, _c, _xi, _use_x, _should_incr) -> if env.debug > 1 then Format.eprintf "pivot non basic var %a ?@." Var.print _x; match basic_var_to_pivot_for_maximization env _x _use_x _should_incr with | Free -> if env.debug > 1 then Format.eprintf "non basic %a not constrained by basic vars: Set it to max@." Var.print _x; begin match can_fix_valuation_without_pivot _should_incr _xi None with | Some (new_xi, diff) -> if env.debug > 1 then Format.eprintf "No --> I can set value of %a to min/max WO pivot@." Var.print _x; let env, opt = update_valuation_without_pivot env _x _use_x new_xi diff _should_incr, opt in maximize_rec env opt (rnd + 1) | None -> if env.debug > 1 then Format.eprintf "no pivot finally(no upper bnd), pb unbounded@."; rnd, env, Some (opt, false) (* unbounded *) end | Stuck -> if env.debug > 1 then Format.eprintf "no pivot finally, pb unbounded@."; rnd, env, Some (opt, false) (* unbounded *) | Progress (ratio, s, si, p, c_px, bnd, _is_min) -> if env.debug > 1 then Format.eprintf "pivot with basic var %a ?@." Var.print s; let env, opt = match can_fix_valuation_without_pivot _should_incr _xi (Some ratio) with | Some (new_xi, diff) -> if env.debug > 1 then Format.eprintf "No --> I can set value of %a to min/max WO pivot@." Var.print _x; update_valuation_without_pivot env _x _use_x new_xi diff _should_incr, opt | None -> let x = _x in let c = c_px in let use_x = _use_x in let xi = _xi in if env.debug > 1 then Format.eprintf "[maximize_rec] pivot basic %a and non-basic %a@." Var.print s Var.print x; let basic = MX.remove s env.basic in let non_basic = MX.remove x env.non_basic in let q = gauss_pivot s p x c in assert (SX.mem s use_x); let use_x = SX.remove s use_x in let old_si = si in let si = {si with value = bnd} in (* difference wrt solve *) (* because the code of solve below, assumes that value in si violotas a bound let si, changed = Core.ajust_value_of_non_basic si in assert (changed); *) let old_xi = xi in let xi = adapt_valuation_of_newly_basic old_si si xi c in let xi = ajust_status_of_basic xi in let diff_xi_val = R2.sub xi.value old_xi.value in assert(xi.vstatus == ValueOK); let non_basic = P.fold (fun y _ non_basic -> let yi, use_y = try MX.find y non_basic with Not_found -> assert false in MX.add y (yi, SX.add x (SX.remove s use_y)) non_basic )(P.remove s q) non_basic in let non_basic = MX.add s (si, SX.add x use_x) non_basic in let basic, non_basic = SX.fold (fun t (basic, non_basic) -> let ti0, r = try MX.find t basic with Not_found -> assert false in let cx = try P.find x r with Not_found -> assert false in (*should update_ti*) let diff_cx = R2.mult_by_const cx diff_xi_val in let ti = {ti0 with value = R2.add ti0.value diff_cx} in let ti = ajust_status_of_basic ti in let r', changed = P.subst x q r in let non_basic = List.fold_left (fun non_basic (z, vstt) -> match vstt with | P.Exists -> non_basic | P.New -> let zi, use_z = try MX.find z non_basic with Not_found -> assert false in MX.add z (zi, SX.add t use_z) non_basic | P.Removed -> if Var.compare z x = 0 then non_basic else let zi, use_z = try MX.find z non_basic with Not_found -> assert false in MX.add z (zi, SX.remove t use_z) non_basic )non_basic changed in let basic = MX.add t (ti, r') basic in assert(ti.vstatus == ValueOK); basic, non_basic )use_x (basic, non_basic) in (* ... *) let basic = MX.add x (xi, q) basic in (* ... *) {env with basic; non_basic}, (fst (P.subst x q opt)) in maximize_rec env opt (rnd + 1) let maximize env opt0 = let env = solve env in match env.status with | UNK -> assert false | UNSAT _ -> env, None | SAT -> if env.debug > 1 then Format.eprintf "[maximize] pb SAT! try to maximize %a@." P.print opt0; let {basic; non_basic; _} = env in let unbnd = ref false in let opt = P.fold (fun x c acc -> if MX.mem x non_basic then fst (P.accumulate x c acc) else try fst (P.append acc c (snd (MX.find x basic))) with Not_found -> unbnd := true; fst (P.accumulate x c acc) )opt0 P.empty in if !unbnd then env, Some (opt, false) (* unbounded *) else begin if env.debug > 1 then Format.eprintf "start maximization@."; let rnd, env, is_max = maximize_rec env opt 1 in Core.check_invariants env (Result.get is_max); if env.debug > 1 then Format.eprintf "[maximize] pb SAT! Max found ? %b for %a == %a@." (is_max != None) P.print opt0 P.print opt; if env.debug > 1 then Format.eprintf "maximization done after %d steps@." rnd; env, is_max end end ocplib-simplex-0.3/src/solveBounds.mli000066400000000000000000000011631301061175500201000ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module type SIG = sig module Core : CoreSig.SIG val solve : Core.t -> Core.t val maximize : Core.t -> Core.P.t -> Core.t * (Core.P.t * bool) option end module Make(Core : CoreSig.SIG) : SIG with module Core = Core ocplib-simplex-0.3/src/version.ml000066400000000000000000000006501301061175500171110ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) let version="0.3" ocplib-simplex-0.3/src/version.mli000066400000000000000000000006531301061175500172650ustar00rootroot00000000000000(******************************************************************************) (* ocplib-simplex *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) val version : string ocplib-simplex-0.3/tests/000077500000000000000000000000001301061175500154445ustar00rootroot00000000000000ocplib-simplex-0.3/tests/ex.ml000066400000000000000000000001771301061175500164170ustar00rootroot00000000000000type t = unit let empty = () let union _ _ = () let print fmt _ = Format.fprintf fmt "[no explanations for this example]" ocplib-simplex-0.3/tests/instantiateBasicFunctor.ml000066400000000000000000000010161301061175500226220ustar00rootroot00000000000000(******************************************************************************) (* ocp-fun-sim *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) module Ty = Core.Make(Var)(Rat)(Ex) module AB = AssertBounds.Make(Ty) module Basic = OcpFunSim.MakeBasic(Var)(Rat)(Ex) ocplib-simplex-0.3/tests/rat.ml000066400000000000000000000006471301061175500165730ustar00rootroot00000000000000open Num type t = num let add = ( +/ ) let mult = ( */ ) let compare = compare_num let equal = ( =/ ) let zero = Int 0 let one = Int 1 let m_one = Int (-1) let is_zero n = n =/ zero let to_string = string_of_num let print fmt t = Format.fprintf fmt "%s" (to_string t) let is_int = is_integer_num let div = (//) let sub = (-/) let is_one v = v =/ Int 1 let is_m_one v = v =/ Int (-1) let sign = sign_num let min = min_num ocplib-simplex-0.3/tests/solveEmpty.ml000066400000000000000000000005431301061175500201470ustar00rootroot00000000000000module Sim = InstantiateBasicFunctor.Basic let () = let sim = Sim.Core.empty ~is_int:false ~check_invs:true ~debug:1 in let sim = Sim.Solve.solve sim in ignore (sim); match Sim.Result.get sim with | Sim.Core.Unknown -> assert false | Sim.Core.Unsat _ -> assert false | Sim.Core.Sat _ -> Format.printf "[test solveEmpty]: result is Sat@." ocplib-simplex-0.3/tests/standalone_minimal.ml000066400000000000000000000044401301061175500216360ustar00rootroot00000000000000(*== Build the example with: "ocamlopt -o standalone_minimal -I `ocamlfind query ocplib-simplex` \ ocplibSimplex.cmxa nums.cmxa standalone_minimal.ml" if the lib is installed, or with: "ocamlopt -o standalone_minimal -I ../src ocplibSimplex.cmxa \ nums.cmxa standalone_minimal.ml" if the lib is built but not installed ==*) module Var = struct type t = string let print fmt s = Format.fprintf fmt "%s" s let compare = String.compare let is_int _ = true end module Ex = struct module S = Set.Make(String) include S let print fmt s = match elements s with | [] -> Format.fprintf fmt "()" | e::l -> Format.fprintf fmt "%s" e; List.iter (Format.fprintf fmt ", %s") l end module Rat = struct open Num type t = num let add = ( +/ ) let mult = ( */ ) let compare = compare_num let equal = ( =/ ) let zero = Int 0 let one = Int 1 let m_one = Int (-1) let is_zero n = n =/ zero let to_string = string_of_num let print fmt t = Format.fprintf fmt "%s" (to_string t) let is_int = is_integer_num let div = (//) let sub = (-/) let is_one v = v =/ Int 1 let is_m_one v = v =/ Int (-1) let sign = sign_num let min = min_num let abs = abs_num let minus = minus_num end module Sim = OcplibSimplex.Basic.Make(Var)(Rat)(Ex) let () = let sim = Sim.Core.empty ~is_int:true ~check_invs:true ~debug:1 in let zero = Some (Rat.zero, Rat.zero) in let m_one = Some (Rat.m_one, Rat.zero) in (* x >= 0 *) let sim = Sim.Assert.var sim "x" zero (Ex.singleton "x>=0") None Ex.empty in (* y >= 0 *) let sim = Sim.Assert.var sim "y" zero (Ex.singleton "y>=0") None Ex.empty in let x_y = Sim.Core.P.from_list ["x", Rat.one; "y", Rat.one] in (* z == x + y <= -1 *) let sim = Sim.Assert.poly sim x_y "z" None Ex.empty m_one (Ex.singleton "x+y<=-1") in let sim = Sim.Solve.solve sim in match Sim.Result.get None sim with | Sim.Core.Unknown -> assert false | Sim.Core.Sat _ -> assert false | Sim.Core.Max _ -> assert false | Sim.Core.Unbounded _ -> assert false | Sim.Core.Unsat ex -> Format.printf "-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+@."; Format.printf "The problem is unsat! reason: %a@." Ex.print (Lazy.force ex); Format.printf "-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+@.@." ocplib-simplex-0.3/tests/standalone_minimal_maximization.ml000066400000000000000000000053701301061175500244320ustar00rootroot00000000000000(*== Build the example with: "ocamlopt -o standalone_minimal_maximization \ -I `ocamlfind query ocplib-simplex` ocplibSimplex.cmxa nums.cmxa \ standalone_minimal_maximization.ml" if the lib is installed, or with: "ocamlopt -o standalone_minimal_maximization -I ../src ocplibSimplex.cmxa \ nums.cmxa standalone_minimal_maximization.ml" if the lib is built but not installed ==*) module Var = struct type t = string let print fmt s = Format.fprintf fmt "%s" s let compare = String.compare let is_int _ = true end module Ex = struct module S = Set.Make(String) include S let print fmt s = match elements s with | [] -> Format.fprintf fmt "()" | e::l -> Format.fprintf fmt "%s" e; List.iter (Format.fprintf fmt ", %s") l end module Rat = struct open Num type t = num let add = ( +/ ) let mult = ( */ ) let compare = compare_num let equal = ( =/ ) let zero = Int 0 let one = Int 1 let m_one = Int (-1) let is_zero n = n =/ zero let to_string = string_of_num let print fmt t = Format.fprintf fmt "%s" (to_string t) let is_int = is_integer_num let div = (//) let sub = (-/) let is_one v = v =/ Int 1 let is_m_one v = v =/ Int (-1) let sign = sign_num let min = min_num let abs = abs_num let minus = minus_num end module Sim = OcplibSimplex.Basic.Make(Var)(Rat)(Ex) let sep () = Format.printf "-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+-+@." let aux sim opt_p = let sim, opt = Sim.Solve.maximize sim opt_p in sep (); Format.printf "The problem 'max %a' ...@." Sim.Core.P.print opt_p; begin match Sim.Result.get opt sim with | Sim.Core.Unknown -> assert false | Sim.Core.Sat _ -> assert false | Sim.Core.Unsat ex -> Format.printf " is unsat (reason = %a)@." Ex.print (Lazy.force ex); | Sim.Core.Unbounded _ -> Format.printf " is unbounded@." | Sim.Core.Max (mx,_) -> let {Sim.Core.max_v; is_le; reason} = Lazy.force mx in Format.printf " has an upper bound: %a (is_le = %b)(reason: %a)@." Rat.print max_v is_le Ex.print reason; end; sep (); Format.printf "@." let () = let sim = Sim.Core.empty ~is_int:true ~check_invs:true ~debug:0 in let x_y = Sim.Core.P.from_list ["x", Rat.one; "y", Rat.one] in let ten = Some (Num.Int (10), Num.Int 0) in let three = Some (Num.Int (3), Num.Int 0) in (* s == x + y >= 10 let sim = Sim.Assert.poly sim x_y "s" ten Ex.empty None Ex.empty in *) (* x <= 5 *) let sim = Sim.Assert.var sim "x" three (Ex.singleton "x>=3") None Ex.empty in (* s == x + y <= 10 *) let sim = Sim.Assert.poly sim x_y "s" None Ex.empty ten (Ex.singleton "x+y<=10") in aux sim x_y; aux sim (Sim.Core.P.from_list ["y", Rat.one]); aux sim (Sim.Core.P.from_list ["y", Rat.m_one]); ocplib-simplex-0.3/tests/var.ml000066400000000000000000000010061301061175500165630ustar00rootroot00000000000000(******************************************************************************) (* ocp-fun-sim *) (* *) (* Copyright (C) --- OCamlPro --- See README.md for information and licensing *) (******************************************************************************) type t = string let print fmt s = Format.fprintf fmt "%s" s let compare = String.compare let is_int _ = true