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The Parma Polyhedra Library OCaml Language

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2. PPL The Parma Polyhedra Library OCaml Language Interface User s Manual version 1 1 Roberto Bagnara Patricia M Hill Enea Zaffanella Abramo Bagnara October 28 2013 This work has been partly supported by University of Parma s FIL scientific research project ex 60 Pure and Applied Math ematics MURST project Automatic Program Certification by Abstract Interpretation MURST project Abstract Interpretation Type Systems and Control Flow Analysis MURST project Automatic Aggregate and Number Reasoning for Computing from Decision Algorithms to Constraint Programming with Multisets Sets and Maps MURST project Constraint Based Verification of Reactive Systems MURST project Abstract Interpretation Design and Applications EPSRC project Numerical Domains for Software Analysis EPSRC project Geometric Abstractions for Scalable Program Analyzers TbagnaraGcs unipr it Department of Mathematics University of Parma Italy and BUGSENG srl t patricia hill bugseng com BUGSENG srl 87affanella Gcs unipr it Department of Mathematics University of Parma Italy and BUGSENG srl labramo bagnara bugseng com BUGSENG srl Copyright 2001 2010 Roberto Bagnara bagnara cs unipr it Copyright O 2010 2013 BUGSENG srl http bugseng com This document describes the Parma Polyhedra Library PPL Permission is granted to copy distribute and or modify this document under the terms of the GNU Free Documenta
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7. 2 constraint system c unsigned 1 It is assumed that the polyhedron PP referenced by handle_1 contains the polyhedron P2 referenced by handle 2 let P denote the H79 extrapolation of P with P2 improved by enforcing those constraints in constraint system together with all constraints of the form x lt r and x lt r that are satisfied by every point in P4 Assuming that the quantity t given by c unsigned 1 is the number of tokens available this function will return the number of tokens tz remaining at the end of the operation ppl Polyhedron topological closure assign handle Assigns to the polyhedron referenced by hanale its topological closure ppl Polyhedron add space dimensions and embed handle space dimension Embeds the polyhedron referenced by handle in a space that is enlarged by space dimension dimen sions ppl Polyhedron concatenate assign handle 1 handle 2 Updates the polyhedron P referenced by handle by first embedding P in a new space enlarged by the space dimensions of the polyhedron P2 referenced by handle 2 and then adds to its system of constraints a renamed apart version of the constraints of Pa ppl Polyhedron add space dimensions and project handle space dimension Projects the polyhedron referenced by handle onto a space that is enlarged by space dimension dimensions ppl Polyhedron remove space dimensions handle Int List Removes the space dimensions given by the identifiers of the PPL variables i
8. PIP Node true child 20 _se l reset deterministic timeout 19 l reset timeout 19 l restore pre PPL rounding 18 t deterministic timeout 19 irrational precision 18 l se l se ty un l version l l version beta 18 l version major l8 rounding for PPL l18 t timeout 19 L timeout exception l6 L unexpected error l6 known standard exception l6 8 l version minor l18 l version revision l18 lation symbol 17 lation with congruence 17 36
9. PPL user manual Domain Independent Functions First we describe some domain independent functions included with all instantiations of the OCaml inter faces ppl version major Returns the major number of the PPL version ppl version minor Returns the minor number of the PPL version ppl version revision Returns the revision number of the PPL version ppl version beta Returns the beta number of the PPL version ppl version Returns the PPL version ppl banner Returns information about the PPL version the licensing the lack of any warranty whatsoever the C compiler used to build the library where to report bugs and where to look for further information pp1_max_space dimension Returns the maximum space dimension the C interface can handle ppl Coefficient bits Returns the number of bits used in the C interface for PPL coefficients O if unbounded ppl Coefficient is bounded Returns true if and only if the coefficients in the C interface are bounded ppl Coefficient max If the coefficients are bounded returns the maximum coefficient the C interface can handle ppl Coefficient min If the coefficients are bounded returns the minimum coefficient the C interface can handle ppl io wrap string source string indent depth preferred first line length preferred line length Utility function for the wrapping of lines of text The function wraps the lines of text stored in its first string a
10. Polyhedron from C Polyhedron ppl new C Polyhedron from constraints ppl new C Polyhedron from generators These functions will return a new handle for referencing a PPL polyhedron For a PPL object with space dimension k the identifiers used for the PPL variables must lie between 0 and k 1 and correspond to the indices of the associated Cartesian axes For example when using the functions that combine PPL polyhedra or add constraints or generators to a representation of a PPL polyhedron the polyhedra referenced and any constraints or generators in the call should follow all the space dimension compatibility rules stated in Section Representations of Convex Polyhedra of the main PPL user manual As explained above a polyhedron has a fixed topology C or NNC that is determined at the time of its initialization All subsequent operations on the polyhedron must respect all the topological compatibility rules stated in Section Representations of Convex Polyhedra of the main PPL user manual Any application using the PPL should make sure that only the intended version s of the library are ever used Functions ppl version major ppl version minor ppl version revision ppl_version_beta ppl version ppl_banner allow run time checking of information about the version being used Function Descriptions Below is a short description of many of the interface functions For full definitions of terminology used here see the main
11. Problem clear handle Resets the PIP problem referenced by handle to be the trivial problem with space dimension 0 ppl PIP Problem add space dimensions and embed handle dimension O0 dimension 1 Embeds the PIP problem referenced by handle in a space that is enlarged by dimension 0 non parameter dimensions and dimension_1 parameter dimensions ppl PIP Problem add to parameter space dimensions handle vars list Sets the space dimensions whose indexes are in vars list to be parameter space dimensions ppl PIP Problem add constraint handle constraint Updates the PIP Problem referenced by handle so that the feasible region is represented by the original constraint system together with the constraint const raint ppl PIP Problem add constraints handle constraint system Updates the PIP Problem referenced by handle so that the feasible region is represented by the original constraint system together with all the constraints in constraint system ppl PIP Problem set big parameter dimension handle dimension Sets the dimension for the big parameter to dimension ppl PIP Problem get big parameter dimension handle Returns the dimension for the big parameter Exception is thrown if no big parameter dimension has been set ppl PIP Problem has big parameter dimension handle Returns true if and only if the dimension for the big parameter has been set ppl PIP Problem is satisfiable handle Returns true if the PIP Problem referenced by handle i
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13. expression Node is decision pip tree node gt bool Node true child pip tree node gt pip tree node ppl PIP Tr ppl PIP Tree ppl PIP Tr Node false child pip tree node gt pip tree node 20 Compilation and Installation When the Parma Polyhedra Library is configured it tests for the existence of the OCaml system If OCaml is correctly installed in a standard location things are arranged so that the OCaml interface is built and installed 3 GNU General Public License Version 3 29 June 2007 Copyright C 2007 Free Software Foundation Inc http fsf org Everyone is permitted to copy and distribute verbatim copies of this license document but changing it 1s not allowed Preamble The GNU General Public License is a free copyleft license for software and other kinds of works The licenses for most software and other practical works are designed to take away your freedom to share and change the works By contrast the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program to make sure it remains free software for all its users We the Free Software Foundation use the GNU General Public License for most of our software it applies also to any other work released this way by its authors You can apply it to your programs too When we speak of free software we are referring to freedom not price Our General Publi
14. mip problem int list P Problem constraints mip problem gt constraint system P Problem add space dimensions and embed lem int gt unit val ppl MIP Problem add constraint mip problem linear constraint gt unit val ppl MIP mip problem gt constraint system gt unit E I I b I b I I b val ppl MI mip problem linear expression gt unit I I I I JE I I T b g Problem add constraints P Problem set objective function val ppl MIP Problem is satisfiable mip problem bool val ppl val ppl val ppl val ppl val ppl val ppl val ppl MIP Problem evaluate objective function mip problem gt linear generator gt Gmp Z t Gmp Z t P Problem solve mip problem mip problem status P Problem optimization mode mip problem gt optimization mode P Problem feasible point mip problem gt linear generator P Problem optimizing point mip problem gt linear generator P Problem objective function mip problem gt linear expression P Problem optimal value mip problem Gmp Z t Gmp Z t val ppl MIP Problem OK mip problem gt bool val ppl MI val ppl MI mip prob I b P Problem clear mip problem unit P Problem set optimization mode lem optimization mode gt unit val ppl MIP Problem set control parameter mip problem gt control parame
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16. the internal representation of the Pip tree node referenced by handle Useful for debugging purposes ppl PIP Tree Node constraints handle Returns a list of the parameter constraints in the PIP tree node referenced by handle ppl PIP Tree Node artificials handle Returns a list of the artificial parameters in the PIP tree node referenced by handle ppl PIP Tree Node is bottom handle Returns true if and only if handle represents bottom pp1_PIP_Tree Node is decision handle Returns true if and only if handle represents a decision node ppl PIP Tree Node is solution handle Returns true if and only if handle represents a solution node ppl PIP Tree Node parametric values handle var Returns a linear expression representing the values of problem variable var in the solution node repre sented by handle The returned linear expression may involve problem parameters as well as artificial parameters ppl PIP Tree Node true child handle var Returns a handle to the child on the true branch of the PIP tree node represented by handle ppl PIP Tree Node false child handle var Returns a handle to the child on the false branch of the PIP tree node represented by handle C Polyhedron Functions Here we describe the main functions available for PPL objects defining convex and closed polyhedra Pp new C Polyhedron from space dimension space dimension universe or empty Returns a handle to a C polyhedron P with space_dimension dimensio
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19. Coefficient max 18 20 ppl Coefficient min 18 ppl PIP Problem add to parameter space dimension PPL internal error l6 20 ppl io wrap string l8 ppl PIP Problem ascii dump 20 ppl irrational precision 18 ppl PLIP Problem clear 20 ppl Linear Expression all homogeneougp efns amp rebiemoconstraints 20 18 ppl PIP Problem get big parameter dimension ppl Linear Expression is zero l18 20 ppl max space dimension 18 ppl PIP Problem get control parameter ppl MIP Problem add constraint 19 20 35 PP ppl l PIP Prob l PIP Prob PP PP Pp PP ppl ppl l PIP Probl l PIP Prob PP PP ppl ppl ppl ppl ppl ppl ppl ppl ppl ppl ppl PP Pp PP Pp PP PP PP PP PP PP PP PP PP PP ES re l PIP Prob l PIP Prob l se ppl l PIP Probl 20 PIP Prob lem has big parameter dimension em is satisfiable 20 20 20 20 PIP Prob 20 PIP Probl lem OK 20 lem optimizing solution lem parameter space dimensions lem set big parameter dimension lem set control parameter em solution 20 em solve 20 PIP Prob PIP lree lem space dimension 20 lem swap 20 Node artificials 20 PIP Tree Node ascii dump 20 PIP Node constraints 20 PIR false child 20 PIR is_bottom 20 PIR is_decision 20 PIP is_solution 20 PIP OK 20 PIP parametric_values 20
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22. Polyhedron equals Polyhedron handle_1 handle_2 Returns true if the polyhedron referenced by handle _1 is equal to the polyhedron referenced by handle 2 and false otherwise ppl Polyhedron OK handle Returns true if the polyhedron referenced by handle is well formed i e if it satisfies all its implementa tion invariants and false otherwise Useful for debugging purposes ppl Polyhedron add constraint handle constraint Updates the polyhedron referenced by handle to one obtained by adding constraint to its constraint system ppl Polyhedron add generator handle generator Updates the polyhedron referenced by handle to one obtained by adding generator to its generator system ppl Polyhedron add constraints handle constraint system Updates the polyhedron referenced by handle to one obtained by adding to its constraint system the constraints in constraint system ppl C Polyhedron add generators handle generator system Updates the polyhedron referenced by handle to one obtained by adding to its generator system the generators in generator system ppl Polyhedron intersection assign handle 1 handle 2 Assigns to the polyhedron referenced by handle_1 its intersection with the polyhedron referenced by handle 2 ppl Polyhedron poly hull assign handle 1 handle 2 Assigns to the polyhedron referenced by handle_1 its poly hull with the polyhedron referenced by handle 2 ppl Polyhedron poly difference assign handle 1 handle 2 A
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31. ent CPU operating system compiler etc The weight mechanism is under beta testing client applications should be ready to reconsider the tuning of these weight thresholds when upgrading to newer version of the PPL ppl reset deterministic timeout Resets the timeout time so that the computation is not interrupted An exception is thrown if the PPL Watchdog library is not enabled ppl_set_rounding_for_PPL Sets the FPU rounding mode so that the PPL abstractions based on floating point numbers work correctly This is performed automatically at initialization time Calling this function is needed only if restore_ pre_PPL_rounding has previously been called ppl restore pre PPL rounding Sets the FPU rounding mode as it was before initialization of the PPL After calling this function it is ab solutely necessary to call set_rounding_for_PPL before using any PPL abstractions based on floating point numbers This is performed automatically at finalization time ppl irrational precision Returns the precision parameter for irrational calculations ppl set irrational precision Sets the precision parameter p for irrational calculations In the following irrational calculations returning an unbounded rational e g when computing a square root the lesser between numerator and denominator will be limited to 2 p MIP Functions Here we describe some functions available for PPL objects defining mixed integer linear programming proble
32. ere N is one of the numeric types short signed char int long long long mpz class mpq class boxes which consist of Int8 Box Int16 Box Int32 Box Int64 Box Uint8 Box Uint16 Box Uint32 Box Uint64 Box Double Box Long Double Box Z Box Rational Box Float Box and the Grid domain The powerset domains are Pointset_Powerset_S where S is a simple domain The product domains consist of Direct Product S T Smash Product S T and Constraints_ Product S T where S and T are simple domains n the following any of the above numerical abstract domains is called a PPL domain and any element of a PPL domain is called a PPL object The OCaml interface files are all installed in the directory pre ix lib ppl Since this includes shared and dynamically loaded libraries you must make your dynamic linker loader aware of this fact If you use a GNU Linux system try the commands man 1d so and man ldconfig for more information A PPL object such as a polyhedron can only be accessed by means of a OCaml term called a handle Note however that the data structure of a handle is implementation dependent system dependent and version dependent and for this reason deliberately left unspecified What we do guarantee is that the handle requires very little memory An OCaml program can obtain a valid handle for a PPL object by using functions such as ppl new C Polyhedron from space dimension ppl new C
33. ersion filling the role of the Document thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it In addition you must do these things in the Modified Version A Use in the Title Page and on the covers if any a title distinct from that of the Document and from those of previous versions which should if there were any be listed in the History section of the Document You may use the same title as a previous version if the original publisher of that version gives permission B List on the Title Page as authors one or more persons or entities responsible for authorship of the modifications in the Modified Version together with at least five of the principal authors of the Document all of its principal authors if it has fewer than five unless they release you from this requirement C State on the Title page the name of the publisher of the Modified Version as the publisher D Preserve all the copyright notices of the Document E Add an appropriate copyright notice for your modifications adjacent to the other copyright notices F Include immediately after the copyright notices a license notice giving the public permission to use the Modified Version under the terms of this License in the form shown in the Addendum below G Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document s license notice 31 H
34. handle_1 contains the polyhedron P2 referenced by handle 2 then handle 1 will refer to the BHRZ03 widening of P with P2 ppl Polyhedron BHRZ03 widening assign with tokens handle 1 handle 2 c unsigned 1 It is assumed that the polyhedron P referenced by handle_1 contains the polyhedron D referenced by handle_2 let P denote the BHRZ03 widening of P with P2 Assuming that the quantity t given by c unsigned l is the number of tokens available Then this function will return the number of tokens remaining at the end of the operation ppl Polyhedron limited BHRZ03 extrapolation assign handle 1 handle 2 constraint system If the polyhedron 7 referenced by handle_1 contains the polyhedron P2 referenced by handle 2 then handle 1 will refer to the BHRZO3 extrapolation of P with P improved by enforcing the constraints in constraint system ppl Polyhedron limited BHRZ03 extrapolation assign with tokens handle 1 handle 2 constraint system c unsigned 1 It is assumed that the polyhedron PP referenced by handle_1 contains the polyhedron P2 referenced by handle 2 let P denote the BHRZ03 extrapolation of P with 75 improved by enforcing those con straints in constraint system Assuming that the quantity t given by c unsigned 1 is the number of tokens available then this function will return the number of tokens t2 remaining at the end of the operation 13 ppl Polyhedron bounded BHRZ03 extrapolation assign handle_1 handle_2 const
35. herein The Document below refers to any such manual or work Any member of the public is a licensee and is addressed as you You accept the license if you copy modify or distribute the work in a way requiring permission under copyright law A Modified Version of the Document means any work containing the Document or a portion of it either copied verbatim or with modifications and or translated into another language A Secondary Section is a named appendix or a front matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document s overall subject or to related matters and contains nothing that could fall directly within that overall subject Thus if the Document is in part a textbook of mathematics a Secondary Section may not explain any mathematics The relationship could be a matter of historical connection with the subject or with related matters or of legal commercial philosophical ethical or political position regarding them The Invariant Sections are certain Secondary Sections whose titles are designated as being those of Invariant Sections in the notice that says that the Document is released under this License If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant The Document may contain zero Invariant Sections If the Document does not identify any Invariant Sections then there are n
36. ht C year name of author This program comes with ABSOLUTELY NO WARRANTY for details type show w This is free software and you are welcome to redistribute it under certain conditions type show c for details The hypothetical commands show w and show c should show the appropriate parts of the General Public License Of course your program s commands might be different for a GUI interface you would use an about box You should also get your employer if you work as a programmer or school if any to sign a copyright disclaimer for the program if necessary For more information on this and how to apply and follow the GNU GPL see http www gnu org licenses The GNU General Public License does not permit incorporating your program into proprietary pro grams If your program is a subroutine library you may consider it more useful to permit linking proprietary applications with the library If this is what you want to do use the GNU Lesser General Public License in stead of this License But first please read http www gnu org philosophy why not lgpl html 4 GNU Free Documentation License Version 1 2 November 2002 Copyright C 2000 2001 2002 Free Software Foundation Inc 51 Franklin St 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 0 PREAMBLE The purpose of this License
37. inimized list of the constraints in the constraints system representing the polyhedron referenced by handle ppl Polyhedron get generators handle Returns a list of the generators in the generators system representing the polyhedron referenced by handle ppl Polyhedron get minimized generators handle Returns a minimized list of the generators in the generators system representing the polyhedron referenced by handle ppl Polyhedron relation with constraint handle constraint Returns the list of relations the polyhedron referenced by handle has with constraint The possible relations and their meaning is given in Section Relation With Operators of the main PPL user manual ppl Polyhedron relation with generator handle generator Returns the list of relations the polyhedron referenced by handle has with generator The possible relations and their meaning is given in Section Relation With Operators of the main PPL user manual ppl Polyhedron is empty handle Returns true if the polyhedron referenced by handle is empty and false otherwise ppl Polyhedron is universe handle Returns true if the polyhedron referenced by handle is the universe and false otherwise ppl Polyhedron is bounded handle Returns true if the polyhedron referenced by handle is bounded and false otherwise ppl Polyhedron contains integer point handle Returns true if the polyhedron referenced by handle contains at least one integer point and false other wise ppl Pol
38. ion mode handle Returns the optimization mode for the MIP Problem referenced by handle ppl MIP Problem clear handle Resets the MIP problem referenced by handle to be the trivial problem with the feasible region the 0 dimensional universe objective function 0 and optimization mode Maximization ppl MIP Problem add space dimensions and embed handle dimension Embeds the MIP problem referenced by handle in a space that is enlarged by dimension dimensions ppl MIP Problem add to integer space dimensions handle vars list Updates the MIP Problem referenced by handle so that the variables in vars_list are added to the set of integer space dimensions ppl MIP Problem add constraint handle constraint Updates the MIP Problem referenced by handle so that the feasible region is represented by the original constraint system together with the constraint const raint ppl MIP Problem add constraints handle constraint system Updates the MIP Problem referenced by handle so that the feasible region is represented by the original constraint system together with all the constraints in constraint system ppl MIP Problem set objective function handle lin expr Updates the MIP Problem referenced by handle so that the objective function is changed to 1in expr ppl MIP Problem set optimization mode handle optimization mode Updates the MIP Problem referenced by handle so that the optimization mode is changed to optimization mode ppl MIP Problem is sati
39. ipt of the notice Termination of your rights under this section does not terminate the licenses of parties who have re ceived copies or rights from you under this License If your rights have been terminated and not perma nently reinstated you do not qualify to receive new licenses for the same material under section 10 9 Acceptance Not Required for Having Copies You are not required to accept this License in order to receive or run a copy of the Program Ancillary propagation of a covered work occurring solely as a consequence of using peer to peer transmission to receive a copy likewise does not require acceptance However nothing other than this License grants you permission to propagate or modify any covered work These actions infringe copyright if you do not accept this License Therefore by modifying or propagating a covered work you indicate your acceptance of this License to do so 10 Automatic Licensing of Downstream Recipients Each time you convey a covered work the recipient automatically receives a license from the original licensors to run modify and propagate that work subject to this License You are not responsible for enforcing compliance by third parties with this License An entity transaction is a transaction transferring control of an organization or substantially all assets of one or subdividing an organization or merging organizations If propagation of a covered work results from an entity transaction e
40. is included in the section entitled GNU Free Documentation License If you have Invariant Sections Front Cover Texts and Back Cover Texts replace the with Texts line with this with the Invariant Sections being LIST THEIR TITLES with the Front Cover Texts being LIST and with the Back Cover Texts being LIST If you have Invariant Sections without Cover Texts or some other combination of the three merge those two alternatives to suit the situation If your document contains nontrivial examples of program code we recommend releasing these exam ples in parallel under your choice of free software license such as the GNU General Public License to permit their use in free software 5 Module Index 5 1 Modules Here is a list of all modules OCaml Language Interface 34 6 Module Documentation 6 1 OCaml Language Interface The Parma Polyhedra Library comes equipped with an interface for the OCaml language 34 Index artificial_parameter 20 ppl_MIP_Problem_add_constraints 19 pp1_MIP_Problem_add_space_dimensions_and_embed bounded_integer_type_overflow 17 19 bounded integer type representation pp MIP Problem add to integer space dimensions 17 19 bounded integer type width l7 ppl MIP Problem ascii dump 19 ppl MIP Problem clear l19 complexity class 18 ppl MIP Problem constraints 19 congruencS system 17 ppl MIP Prob
41. is to make a manual textbook or other functional and useful document free in the sense of freedom to assure everyone the effective freedom to copy and redistribute it with or without modifying it either commercially or noncommercially Secondarily this License preserves for the author and publisher a way to get credit for their work while not being considered responsible for modifications made by others This License is a kind of copyleft which means that derivative works of the document must them selves be free in the same sense It complements the GNU General Public License which is a copyleft license designed for free software We have designed this License in order to use it for manuals for free software because free software needs free documentation a free program should come with manuals providing the same freedoms that 29 the software does But this License is not limited to software manuals it can be used for any textual work regardless of subject matter or whether it is published as a printed book We recommend this License principally for works whose purpose is instruction or reference 1 APPLICABILITY AND DEFINITIONS This License applies to any manual or other work in any medium that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License Such a notice grants a world wide royalty free license unlimited in duration to use that work under the conditions stated
42. l parameter value ppl version major unit gt int ppl version minor unit gt int ppl version revision unit gt int ppl version beta unit gt int ppl version unit gt string ppl banner unit gt string ppl io wrap string string gt int int gt int gt string ppl max space dimension unit gt int ppl Coefficient bits unit gt int ppl Coefficient is bounded unit gt bool ppl Coefficient max unit gt Gmp Z t ppl Coefficient min unit Gmp Z t ppl Linear Expression is zero linear expression gt bool ppl Linear Expression all homogeneous terms are zero linear expression gt bool ppl set rounding for PPL unit unit ppl restore pre PPL rounding unit gt unit ppl irrational precision unit gt int ppl set irrational precision int unit 18 val ppl set timeout int gt unit val ppl reset timeout unit gt unit val ppl set deterministic timeout int gt int gt unit val ppl reset deterministic timeout unit gt unit type mip problem val ppl new MIP Problem from space dimension int gt mip problem val ppl new MIP Problem int gt constraint system gt linear expression gt optimization mode mip problem val ppl MIP Problem space dimension mip problem gt int val ppl val ppl val ppl mip pro val ppl MIP Problem add to integer space dimensions mip problem int list gt unit P Problem integer space dimensions
43. lem evaluate objective function constraint system 17 19 control parameter name i3 ppl MIP Problem feasible point 19 control paraheter value ME ppl MIP Problem get control parameter degenerate element 16 19 ppl MIP Problem integer space dimensions generator system 17 19 grid generator avat em 17 ppl MIP Problem is satisfiable 19 ppl MIP Problem objective function l9 linear congruence 17 ppl MIP Problem OK 19 linear constraint 17 ppl MIP Problem optimal value 19 linear expression l6 ppl MIP Problem optimization mode 19 linear generator l7 ppl MIP Problem optimizing point 19 linear grid generator l7 ppl MIP Problem set control parameter 19 mip_problen 19 ppl MIP Problem set objective function mip problem status 18 19 OCanii par metas we ppl MIP Problem set optimization mode optimization mode 18 ELS M cuu 19 pip problem 19 ppl_MIP_Problem_space_dimension 19 pip_problem_control_parameter_name 18 P IP_Problem_ Swap 19 pip problem control parameter value ppl new MIP Problem 19 18 ppl new MIP Problem from space dimension pip problem status 18 19 pip tree node 20 ppl new PIP Problem 20 poly con relation 17 ppl new PIP Problem from space dimension poly gen relation l7 20 PPL arithmetic overflow l16 Ppl ocaml globals 16 ppl banner 18 ppl PIP Problem add constraint 20 ppl Coefficient bits 18 ppl PIP Problem add constraints 20 ppl Coefficient is bounded 18 ppl PIP Problem add space dimensions and embed ppl
44. list type generator_system linear_generator list type grid generator system linear grid generator list type congruence system linear congruence list type type relation symbol Less Than RS Less Or Equal RS Equal RS Greater Than RS Greater Or Equal RS bounded integer type overflow Overflow Wraps Overflow Undefined Overflow Impossible type bounded integer type representation Unsigned Signed 2 Complement type bounded integer type width Bits 8 Bits 16 Bits 32 Bits 64 Bits 128 17 type complexity_class type optimization_mode type mip problem status type control parame type control parame val val val val val val val val val val val val val val val val val val type pip problem con type pip problem con Polynomial Complexity Simplex Complexity Any Complexity Minimization Maximization Unfeasible Mip Problem Unbounded Mip Problem Optimized Mip Problem Ler Name Pricing ter_value Edge_Float Pricing Steepest Pricing Steepest Edge Exact Pricing Textbook type pip problem status Unfeasible Pip Problem Optimized Pip Problem Cutting Strategy Pivot Row Strategy Cutting Strategy First Cutting Strategy Deepest Cutting Strategy All Pivot Row Strategy First Pivot Row Strategy Max Column trol parameter name tro
45. ly These Terms to Your New Programs If you develop a new program and you want it to be of the greatest possible use to the public the best way to achieve this is to make it free software which everyone can redistribute and change under these terms To do so attach the following notices to the program It is safest to attach them to the start of each source file to most effectively state the exclusion of warranty and each file should have at least the copyright line and a pointer to where the full notice is found 28 one line to give the program s name and a brief idea of what it does Copyright C year name of author This program is free software you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 3 of the License or at your option any later version This program 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 General Public License for more details You should have received a copy of the GNU General Public License along with this program If not see http www gnu org licenses Also add information on how to contact you by electronic and paper mail If the program does terminal interaction make it output a short notice like this when it starts in an interactive mode program Copyrig
46. m provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice keep intact all notices stating that this License and any non permissive terms added in accord with section 7 apply to the code keep intact all notices of the absence of any warranty and give all recipients a copy of this License along with the Program You may charge any price or no price for each copy that you convey and you may offer support or warranty protection for a fee 5 Conveying Modified Source Versions You may convey a work based on the Program or the modifications to produce it from the Program in the form of source code under the terms of section 4 provided that you also meet all of these conditions a The work must carry prominent notices stating that you modified it and giving a relevant date b The work must carry prominent notices stating that it is released under this License and any conditions added under section 7 This requirement modifies the requirement in section 4 to keep intact all notices c You must license the entire work as a whole under this License to anyone who comes into pos session of a copy This License will therefore apply along with any applicable section 7 additional terms to the whole of the work and all its parts regardless of how they are packaged This License gives no permission to license the work in any other way but it does not invalidate such permission if you hav
47. ms ppl new MIP Problem from space dimension dimension Return a handle to an MIP Problem MIP with the feasible region the vector space of dimension dimension objective function 0 and optimization mode max ppl new MIP Problem dimension constraint system lin expr optimization mode Return a handle to an MIP Problem MIP having space dimension dimension a feasible region repre sented by const raint system objective function 1in expr and optimization mode optimization mode ppl MIP Problem get control parameter handle param name Returns the value of the control parameter named param name ppl MIP Problem set control parameter handle param value Sets control parameter value param value ppl MIP Problem swap handle 1 handle 2 Swaps the MIP Problem referenced by handle 1 with the one referenced by handle 2 ppl MIP Problem space dimension handle Returns the dimension of the vector space in which the MIP Problem referenced by handle is embedded pp1_MIP_ Problem integer space dimensions handle Returns a list of variables representing representing the integer space dimensions of the MIP Problem referenced by handle ppPl MIP Problem constraints handle Returns a list of the constraints in the constraints system representing the feasible region for the MIP Problem referenced by handle ppl MIP Problem objective function handle Returns the objective function for the MIP Problem referenced by handle ppl MIP Problem optimizat
48. n list Int List from the polyhedron referenced by handle The identifiers for the remaining PPL variables are renumbered so that they are consecutive and the maximum index is less than the number of dimensions ppl Polyhedron remove higher space dimensions handle space dimension Projects the polyhedron referenced to by handle onto the first space dimension dimensions ppl Polyhedron expand space dimension handle var space dimension space_dimension copies of the space dimension referenced by variable var are added to the polyhe dron referenced to by handle ppl Polyhedron fold space dimensions handle list of vars var The space dimensions referenced by the PPL variables in list 11st of vars are folded into the dimension referenced by var and removed The result is undefined if 1ist of vars does not have the properties described in Section Folding Multiple Dimensions of the Vector Space into One Dimension of the main PPL user manual 15 ppl Polyhedron map space dimensions handle p func Maps the space dimensions of the polyhedron referenced by handle using the partial function defined by a list of pairs of integers p_func The result is undefined if p unc does not encode a partial function with the properties described in Section Mapping the Dimensions of the Vector Space of the main PPL user manual ppl Polyhedron wrap assign handle list of vars width representation overflow constraint system complexity threshold wrap indicator Tran
49. ndividuals or organizations To modify a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission other than the making of an exact copy The resulting work is called a modified version of the earlier work or a work based on the earlier work A covered work means either the unmodified Program or a work based on the Program To propagate a work means to do anything with it that without permission would make you directly or secondarily liable for infringement under applicable copyright law except executing it on a computer or modifying a private copy Propagation includes copying distribution with or without modification making available to the public and in some countries other activities as well To convey a work means any kind of propagation that enables other parties to make or receive copies Mere interaction with a user through a computer network with no transfer of a copy is not conveying An interactive user interface displays Appropriate Legal Notices to the extent that it includes a con venient and prominently visible feature that 1 displays an appropriate copyright notice and 2 tells the user that there is no warranty for the work except to the extent that warranties are provided that licensees may convey the work under this License and how to view a copy of this License If the interface presents a list of user commands or options such as a men
50. ns it is empty or the universe polyhedron depending on whether universe or empty is empty or universe respectively ppl new C Polyhedron from C Polyhedron handle If handle refers to a C polyhedron P then the expression will returns a handle to a copy P2 of P1 ppl new C Polyhedron from NNC Polyhedron handle If handle refers to an NNC polyhedron P then the expression returns a handle to a copy Pa of P1 When using ppl new C Polyhedron from NNC Polyhedron 2 care must be taken that the source polyhedron referenced by handle is topologically closed pplonew C Polyhedron from constraints constraint system Returns a handle to a C polyhedron P represented by const raint system pplonew C Polyhedron from generators generator system Returns a handle to a C polyhedron P represented by generator system ppl Polyhedron swap handle 1 handle 2 Swaps the polyhedron P referenced by handle_1 with the polyhedron Q referenced by handle 2 The polyhedra P and Q must have the same topology ppl Polyhedron space dimension handle Returns the dimension of the vector space in which the polyhedron referenced by handle is embedded ppl Polyhedron affine dimension handle Returns the actual dimension of the polyhedron referenced by handle ppl Polyhedron get constraints handle Return a list of the constraints in the constraints system representing the polyhedron referenced by handle ppl Polyhedron get minimized constraints handle Returns a m
51. one The Cover Texts are certain short passages of text that are listed as Front Cover Texts or Back Cover Texts in the notice that says that the Document is released under this License A Front Cover Text may be at most 5 words and a Back Cover Text may be at most 25 words A Transparent copy of the Document means a machine readable copy represented in a format whose specification is available to the general public that is suitable for revising the document straightforwardly with generic text editors or for images composed of pixels generic paint programs or for drawings some widely available drawing editor and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters A copy made in an otherwise Transparent file format whose markup or absence of markup has been arranged to thwart or discourage subsequent modification by readers is not Transparent An image format is not Transparent if used for any substantial amount of text A copy that is not Transparent is called Opaque Examples of suitable formats for Transparent copies include plain ASCII without markup Texinfo in put format LaTeX input format SGML or XML using a publicly available DTD and standard conforming simple HTML PostScript or PDF designed for human modification Examples of transparent image for mats include PNG XCF and JPG Opaque formats include proprietary formats that can be read and
52. ose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work For example Corresponding Source includes interface definition files associated with source files for the work and the source code for shared libraries and dynamically linked subprograms that the work is specifically designed to require such as by intimate data communication or control flow between those subprograms and other parts of the work The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source The Corresponding Source for a work in source code form is that same work 2 Basic Permissions All rights granted under this License are granted for the term of copyright on the Program and are irrevo cable provided the stated conditions are met This License explicitly affirms your unlimited permission to run the unmodified Program The output from running a covered work is covered by this License only if the output given its content constitutes a covered work This License acknowledges your rights of fair use or other equivalent as provided by copyright law 22 You may make run and propagate covered works that you do not convey without conditions so long as your license otherwise remains in force You may convey covered works to others for the sole purpose of having them make modifications exclusively for you or provide yo
53. out_exception exception PPL_internal_error of string exception PPL unknown standard exception of string exception PPL unexpected error of string type degenerate element Universe Empty type linear expression Variable of int Coefficient of Gmp Z t Unary Plus of linear expression Unary Minus of linear expression Plus of linear expression x linear expression Minus of linear expression x linear expression Times of Gmp Z t linear expression type linear constraint 16 Less_Than of linear_expression linear_expression Less_Or_Equal of linear_expression linear_expression Equal of linear expression x linear expression Greater Than of linear expression linear expression Greater Or Equal of linear expression linear expression typ type type type type linear_generator Line of linear_expression Ray of linear_expression Point of linear expression Gmp Z t Closure Point of linear expression Gmp Z t linear grid generator Grid Line of linear expression Grid Parameter of linear expression Gmp Z t Grid Point of linear expression Gmp Z t poly gen relation Subsumes poly con relation Is Disjoint Strictly Intersects Is Included Saturates relation with congruence Is Disjoint Strictly Intersects Is Included type linear congruence linear expression linear expression Gmp Z t type constraint_system linear_constraint
54. raint system If the polyhedron P referenced by handle_1 contains the polyhedron P3 referenced by handle 2 then handle 1 will refer to the BHRZO3 extrapolation of P with P5 improved by enforcing the constraints in constraint system together with all constraints of the form x lt r and x lt r that are satisfied by every point in 74 ppl Polyhedron bounded BHRZ03 extrapolation assign with tokens handle 1l handle 2 constraint system c unsigned 1 It is assumed that the polyhedron P referenced by handle_1 contains the polyhedron Pa referenced by handle 2 let P denote the BHRZ03 extrapolation of P with P2 improved by enforcing those constraints in constraint system together with all constraints of the form x lt r and x lt r that are satisfied by every point in 74 Assuming that the quantity t given by c_unsigned_1 is the number of tokens available this function will return the number of tokens ta remaining at the end of the operation ppl Polyhedron H79 widening assign handle 1 handle 2 If the polyhedron P referenced by handle_1 contains the polyhedron P2 referenced by handle 2 then handle 1 will refer to the H79 widening of P with P2 ppl_Polyhedron_H79 widening assign with tokens handle 1 handle 2 c unsigned 1 It is assumed that the polyhedron P referenced by handle_1 contains the polyhedron P3 referenced by handle 2 let P denote the H79 widening of P with P2 Assuming that the quantity t given b
55. raint system lem add space dimensions and embed int int gt unit lem add to parameter space dimensions int list gt unit lem add constraint pip problem gt linear constraint gt unit lem add constraints constraint system unit em is satisfiable pip problem gt bool em solve pip problem gt pip problem status em solution pip problem gt pip tree node lem optimizing solution pip problem gt pip tree node lem get big parameter dimension pip problem int lem set big parameter dimension pip problem int gt unit lem has big parameter dimension pip problem gt bool lem OK pip problem gt bool lem clear pip problem gt unit lem set control parameter ntrol parameter value gt unit lem get control parameter ntrol parameter name gt ntrol parameter value lem swap pip problem gt pip problem unit lem ascii dump pip problem gt string Node constraints pip tree node gt constraint system ppl PIP Tree Node artificials pip tree node artificial par gt ameter list ppl PIP Tree ppl PIP Tree Node ascii dump pip tree node gt string Node OK pip tree node gt bool ppl PIP Tree Node is bottom pip tree node gt bool ppl PIP Tree Node is solution pip tree node gt bool ppl PIP Tree Node parametric values pip tree node int linear
56. rgument according to the next three integer arguments which are interpreted as the indentation depth the preferred length for the first line and the preferred length for all the other lines respecively it returns a string containing the wrapped text ppl set timeout csecs Computations taking exponential time will be interrupted some time after csecs centiseconds after that call If the computation is interrupted that way a timeout exception will be thrown An exception is immediately thrown if csecs is not strictly greater than zero or if the PPL Watchdog library is not enabled ppl reset timeout Resets the timeout time so that the computation is not interrupted An exception is thrown if the PPL Watchdog library is not enabled ppl set deterministic timeout unscaled weight scale Computations taking exponential time will be interrupted some time after reaching the complexity thresh old weight unscaled weight 2 If the computation is interrupted that way a timeout exception will be thrown unscaled_weight must be strictly greater than zero scale must be non negative an exception is thrown if the computed weight threshold exceeds the maximum allowed value NOTE This timeout checking functionality is said to be deterministic because it is not based on actual elapsed time Its behavior will only depend on some of the computations performed in the PPL library and it will be otherwise independent from the computation environm
57. rvive such relicensing or conveying If you add terms to a covered work in accord with this section you must place in the relevant source files a statement of the additional terms that apply to those files or a notice indicating where to find the applicable terms Additional terms permissive or non permissive may be stated in the form of a separately written license or stated as exceptions the above requirements apply either way 25 8 Termination You may not propagate or modify a covered work except as expressly provided under this License Any attempt otherwise to propagate or modify it is void and will automatically terminate your rights under this License including any patent licenses granted under the third paragraph of section 11 However if you cease all violation of this License then your license from a particular copyright holder is reinstated a provisionally unless and until the copyright holder explicitly and finally terminates your license and b permanently if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation Moreover your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means this is the first time you have received notice of violation of this License for any work from that copyright holder and you cure the violation prior to 30 days after your rece
58. s Manual version 1 1 See http bugseng com for more information 1 OCaml Language Interface The Parma Polyhedra Library comes equipped with an interface for the OCaml language The main features of the library are described in Section OCaml Interface Features Section OCamldoc Documentation lists all the functions available to the default generated domains in the OCaml interface Section Compilation and Installation explains how the OCaml interface is compiled and installed In the sequel prefix is the prefix under which you have installed the library typically usr or usr local OCaml Interface Features The OCaml interface provides access to the numerical abstractions convex polyhedra BD shapes octag onal shapes etc implemented by the PPL library A general introduction to the numerical abstractions their representation in the PPL and the operations provided by the PPL is given in the main PPL user manual Here we just describe those aspects that are specific to the OCaml interface Overview First here is a list of notes with general information and advice on the use of the OCaml interface The numerical abstract domains available to the OCaml user consist of the simple domains powersets of a simple domain and products of simple domains The simple domains are convex polyhedra which consist of C Polyhedron and NNC_Polyhedron weakly relational which consist of BD Shape N and Octagonal Shape N wh
59. s satisfiable and false otherwise ppl PIP Problem solve handle Solves the PIP problem referenced by handle and returns a status flag indicating the outcome of the optimization attempt Optimized Pip Problem ifthe optimization attempt succeeds Unfeasible Pip Problenm otherwise ppl PIP Problem solution handle Solves the PIP problem referenced by handle and returns a handle to a PIP Tree representing a feasible solution if it exists and bottom otherwise ppl PIP Problem optimizing solution handle Solves the PIP problem referenced by handle and returns a handle to a PIP Tree representing an optimizing solution if it exists and bottom otherwise ppl PIP Problem OK handle Returns true if the PIP Problem referenced by handle is well formed i e if it satisfies all its implemen tation invariants and false otherwise Useful for debugging purposes ppl PIP Problem ascii dump handle Returns a string containing an ASCII dump of the internal representation of the PIP Problem referenced by handle Useful for debugging purposes ppl PIP Tree Node swap handle 1 handle 2 Swaps the PIP tree node referenced by handle 1 with the one referenced by handle_2 ppl PIP Tree Node OK handle Returns true if the PIP tree node referenced by handle is well formed i e if it satisfies all its implemen tation invariants and false otherwise Useful for debugging purposes ppl PIP Tree Node ascii dump handle Returns a string containing an ASCII dump of
60. sfiable handle Returns true if the MIP Problem referenced by handle is satisfiable and false otherwise ppl MIP Problem solve handle Solves the MIP problem referenced by handle and returns 0 if the MIP problem is not satisfiable 1 if the MIP problem is satisfiable but there is no finite bound to the value of the objective function 2 if the MIP problem admits an optimal solution ppl MIP Problem feasible point handle Returns a feasible point for the MIP problem referenced by handle ppl MIP Problem optimizing point handle Returns an optimizing point for the MIP problem referenced by handle ppl MIP Problem optimal value handle Returns a pair of numbers the first being the numerator and the second the denominator for the optimal value for the MIP problem referenced by handle ppl MIP Problem evaluate objective function handle generator Evaluates the objective function of the MIP problem referenced by handle at point generator Returns a pair of numbers the first being the numerator and the second the denominator for the objective function value for the MIP problem referenced by handle ppl MIP Problem OK handle Returns true if the MIP Problem referenced by handle is well formed i e if it satisfies all its implemen tation invariants and false otherwise Useful for debugging purposes ppl MIP Problem ascii dump handle Returns a string containing an ASCII dump of the internal representation of the MIP Problem referenced b
61. sforms the polyhedron referenced by handle by wrapping the dimensions given by list of vars while respecting the specified width representation and overflow behavior of all these variables The parameter constraint system represents the conditional or looping construct guard with respect to which wrapping is performed The non negative integer complexity threshold and Boolean wrap_indicator allow control of the complexity precision ratio higher values for complexity threshold will lead to possibly greater precision while a true value for wrap indicator indicates that the space dimensions should be wrapped individually See Section Wrapping Operator for a more detailed description of this operator ppl Polyhedron ascii dump handle Returns a string containing an ASCII dump of the internal representation of the polyhedron referenced by handle Useful for debugging purposes OCamldoc Documentation NOTE the complete documentation for module Pp1 ocaml including all the types and functions that were enabled at configuration time is only available in the configuration dependent OCamldoc documen tation The configuration independent OCamldoc documentation only contains those types and functions that are always enabled which are grouped into module Ppl_ocaml_globals Also note that module Ppl ocaml automatically includes module Ppl_ocaml_globals 2 Module Ppl_ocaml_globals exception PPL_arithmetic_overflow of string exception PPL_time
62. sions of a covered work in that User Product from a modified version of its Corresponding Source The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made If you convey an object code work under this section in or with or specifically for use in a User Product and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term regardless of how the 24 transaction is characterized the Corresponding Source conveyed under this section must be accompanied by the Installation Information But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product for example the work has been installed in ROM The requirement to provide Installation Information does not include a requirement to continue to provide support service warranty or updates for a work that has been modified or installed by the recipient or for the User Product in which it has been modified or installed Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network Corresponding Source conveyed and Installation Information provided in a
63. ssigns to the polyhedron referenced by handle 1 its poly difference with the polyhedron referenced by handle 2 ppl Polyhedron affine image handle var lin expr coefficient Transforms the polyhedron referenced by handle assigning the affine expression 1in expr coefficient to var ppl Polyhedron affine preimage handle var lin expr coefficient This is the inverse transformation to that for ppl affine image 12 ppl Polyhedron bounded affine image handle var lin expr 1 lin expr 2 coefficient Transforms the polyhedron referenced by handle assigning the image with respect to the transfer relation lin expr l coefficient lt var lt lin expr 2 coefficient ppl Polyhedron generalized affine image handle var Relation Symbol lin expr coefficient Transforms the polyhedron referenced by handle assigning the generalized affine image with respect to the transfer function var Relation Symbol lin expr coefficient ppl Polyhedron generalized affine image lhs rhs handle lin expr 1l Relation Symbol lin expr 2 Transforms the polyhedron referenced by handle assigning the generalized affine image with respect to the transfer function 1in expr 1 Relation Symbol lin expr 2 ppl Polyhedron time elapse assign handle 1l handle 2 Assigns to the polyhedron P referenced by handle_1 the time elapse P Q with the polyhedron Q referenced by handle 2 ppl Polyhedron BHRZ03 widening assign handle 1 handle 2 If the polyhedron P referenced by
64. ter value gt unit val ppl MIP Problem get control parameter mip problem gt control parameter name gt control parameter value val ppl MIP Problem swap mip problem gt mip problem gt unit val ppl MIP Problem ascii dump mip problem gt string type pip problem 19 type pip tree node type artificial parameter linear expression Gmp Z t val ppl new PIP Problem from space dimension int gt pip problem val ppl new PIP Problem int gt val val val val Va va val va val val val val val val val val val va va val val val val val val val val va val val constraint_sys int list gt pi ppl PIP Prob ppl PIP Prob ppl PIP Prob ppl PIP Prob pip problem gt l ppl PIP Prob pip problem gt ppl PIP Prob ppl PIP Prob pip problem gt ppl PIP Prob ppl PIP Prob ppl PIP Prob ppl PIP Prob ppl PIP Prob ppl PIP Prob ppl PIP Prob ppl PIP Prob ppl PIP Prob ppl PIP Prob pip problem gt pip problem co ppl PIP Prob pip problem gt pip problem co pip problem co ppl PIP Prob ppl PIP Prob ppl PIP Tree tem gt p problem lem space dimension pip problem gt int lem parameter space dimensions pip problem int list lem constraints pip problem const
65. tion License Version 1 2 or any later version published by the Free Software Foundation with no Invariant Sections no Front Cover Texts and no Back Cover Texts A copy of the license is included in the section entitled GNU Free Documentation License The PPL is free software you can redistribute it and or modify it under the terms of the GNU General Public License as published by the Free Software Foundation either version 3 of the License or at your option any later version A copy of the license is included in the section entitled GNU GENERAL PUBLIC LICENSE The PPL 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 General Public License for more details If you have not received a copy of one or both the above mentioned licenses along with the PPL write to the Free Software Foundation Inc 51 Franklin Street Fifth Floor Boston MA 02111 1307 USA For the most up to date information see the Parma Polyhedra Library site http bugseng com products ppl bug ceng Contents 1 OCaml Language Interface 2 Module Ppl ocaml globals 3 GNU General Public License 4 GNU Free Documentation License 5 Module Index 5 1 MOES MP 6 Module Documentation 6 1 OCaml Langues Interface uoo zo sa SRDS EEE SS Index 16 21 29 34 34 34 34 35 The PPL OCaml Language Interface User
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71. w in P and false otherwise coefficient 1 is the numerator of the infinum value and coefficient_2 the denominator of the infinum value If the infinum is also the minimum boo1_2 is true and false otherwise ppl Polyhedron minimize with point handle lin expr Returns a record bool 1 coefficient 1 coefficient_2 bool_2 bool 1 is true if the polyhedron P referenced by handle is not empty and lin_expr is bounded from below in P and false otherwise coefficient 1 is the numerator of the infinum value and coefficient_2 the denominator of the infinum value If the infinum is also the minimum boo1_2 is true and false otherwise Point is the point or closure point where 1in_expr reaches the infinum ppl Polyhedron is topologically closed handle Returns true if the polyhedron referenced by handle is topologically closed and false otherwise ppl Polyhedron contains Polyhedron handle 1 handle 2 Returns true if the polyhedron referenced by handle 2 is included in or equal to the polyhedron refer enced by handle 1 and false otherwise ppl Polyhedron strictly contains Polyhedron handle 1 handle 2 Returns true if the polyhedron referenced by handle 2 is included in but not equal to the polyhedron referenced by handle_1 and false otherwise ppl Polyhedron is disjoint from Polyhedron handle 1 handle 2 Returns true if the polyhedron referenced by handle 1 is disjoint from the polyhedron referenced by handle 2 and false otherwise 11 ppl
72. y c unsigned l is the number of tokens available Then this function will return the number of tokens remaining at the end of the operation ppl Polyhedron limited H79 extrapolation assign handle 1 handle 2 constraint system If the polyhedron P referenced by handle_1 contains the polyhedron P3 referenced by handle 2 then handle 1 will refer to the H79 extrapolation of P with P2 improved by enforcing the constraints in constraint system ppl Polyhedron limited H79 extrapolation assign with tokens handle 1 handle 2 constraint system c unsigned 1 It is assumed that the polyhedron P referenced by handle_1 contains the polyhedron Pa referenced by handle 2 let P denote the H79 extrapolation of P with P2 improved by enforcing those constraints in constraint system Assuming that the quantity t given by c unsigned 1 is the number of tokens available then this function will return the number of tokens t2 remaining at the end of the operation ppl Polyhedron bounded H79 extrapolation assign handle 1 handle 2 constraint system If the polyhedron 7 referenced by handle_1 contains the polyhedron D referenced by handle 2 then handle 1 will refer to the H79 extrapolation of P with P2 improved by enforcing the constraints in constraint system together with all constraints of the form x lt r and x lt r that are satisfied by every point in 7 14 ppl Polyhedron bounded H79 extrapolation assign with tokens handle 1 handle
73. y handle Useful for debugging purposes PIP Functions Here we describe some functions available for PPL objects defining parametric integer programming prob lems ppl new PIP Problem from space dimension dimension Return a handle to a PIP Problem PIP with the feasible region the vector space of dimension dimension empty constraint system and empty set of parametric variables ppl new PIP Problem dimension constraint system vars list Return a handle to a PIP Problem PIP having space dimension dimension a feasible region represented by constraint system and parametric variables represented by vars list ppl PIP Problem get control parameter handle param name Returns the value of the control parameter named param name ppl PIP Problem set control parameter handle param value Sets control parameter value param value ppl PIP Problem swap handle 1 handle_2 Swaps the PIP Problem referenced by handle_1 with the one referenced by handle 2 ppl PIP Problem space dimension handle Returns the dimension of the vector space in which the PIP Problem referenced by handle is embedded ppl PIP Problem parameter space dimensions handle Returns a list of variables representing representing the parameter space dimensions of the PIP Problem referenced by handle ppl PIP Problem constraints handle Returns a list of the constraints in the constraints system representing the feasible region for the PIP Prob lem referenced by hanale ppl PIP
74. yhedron bounds from above handle lin expr Returns true if the polyhedron referenced by handle is bounded from above by 1in expr and false otherwise 10 ppl Polyhedron bounds from below handle lin expr Returns true if the polyhedron referenced by handle is bounded from below by 1in expr and false otherwise ppl Polyhedron maximize handle lin expr Returns a record bool 1 coefficient_1 coefficient_2 bool_2 where bool 1 is true if the polyhedron P referenced by handle is not empty and 1in expr is bounded from above in P and false otherwise coe ficient l is the numerator of the supremum value and coe ficient 2 the denominator of the supremum value If the supremum is also the maximum boo1 2 is true and false otherwise ppl Polyhedron maximize with point handle lin expr Returns a record bool 1 coefficient 1 coefficient 2 bool 2 Point bool_1 is true if the polyhedron P referenced by handle is not empty and 1in expr is bounded from above in P and false otherwise coe ficient 1 is the numerator of the supremum value and coefficient_2 the denominator of the supremum value If the supremum is also the maximum boo1 2 is true and false otherwise Point is the point or closure point where 1in_expr reaches the supremum ppl Polyhedron minimize handle lin expr Returns a record bool 1 coefficient 1 coefficient 2 bool_2 bool 1 is true if the polyhedron P referenced by handle is not empty and lin_expr is bounded from belo

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