src/HOL/Tools/sat_solver.ML
author wenzelm
Tue Apr 03 19:24:11 2007 +0200 (2007-04-03)
changeset 22567 1565d476a9e2
parent 22220 6dc8d0dca678
child 29872 14e208d607af
permissions -rw-r--r--
removed assert/deny (avoid clash with Alice keywords and confusion due to strict evaluation);
     1 (*  Title:      HOL/Tools/sat_solver.ML
     2     ID:         $Id$
     3     Author:     Tjark Weber
     4     Copyright   2004-2006
     5 
     6 Interface to external SAT solvers, and (simple) built-in SAT solvers.
     7 *)
     8 
     9 signature SAT_SOLVER =
    10 sig
    11   exception NOT_CONFIGURED
    12 
    13   type assignment = int -> bool option
    14   type proof      = int list Inttab.table * int
    15   datatype result = SATISFIABLE of assignment
    16                   | UNSATISFIABLE of proof option
    17                   | UNKNOWN
    18   type solver     = PropLogic.prop_formula -> result
    19 
    20   (* auxiliary functions to create external SAT solvers *)
    21   val write_dimacs_cnf_file : Path.T -> PropLogic.prop_formula -> unit
    22   val write_dimacs_sat_file : Path.T -> PropLogic.prop_formula -> unit
    23   val read_std_result_file  : Path.T -> string * string * string -> result
    24   val make_external_solver  : string -> (PropLogic.prop_formula -> unit) -> (unit -> result) -> solver
    25 
    26   val read_dimacs_cnf_file : Path.T -> PropLogic.prop_formula
    27 
    28   (* generic solver interface *)
    29   val solvers       : (string * solver) list ref
    30   val add_solver    : string * solver -> unit
    31   val invoke_solver : string -> solver  (* exception Option *)
    32 end;
    33 
    34 structure SatSolver : SAT_SOLVER =
    35 struct
    36 
    37   open PropLogic;
    38 
    39 (* ------------------------------------------------------------------------- *)
    40 (* should be raised by an external SAT solver to indicate that the solver is *)
    41 (* not configured properly                                                   *)
    42 (* ------------------------------------------------------------------------- *)
    43 
    44   exception NOT_CONFIGURED;
    45 
    46 (* ------------------------------------------------------------------------- *)
    47 (* type of partial (satisfying) assignments: 'a i = NONE' means that 'a' is  *)
    48 (*      a satisfying assignment regardless of the value of variable 'i'      *)
    49 (* ------------------------------------------------------------------------- *)
    50 
    51   type assignment = int -> bool option;
    52 
    53 (* ------------------------------------------------------------------------- *)
    54 (* a proof of unsatisfiability, to be interpreted as follows: each integer   *)
    55 (*      is a clause ID, each list 'xs' stored under the key 'x' in the table *)
    56 (*      contains the IDs of clauses that must be resolved (in the given      *)
    57 (*      order) to obtain the new clause 'x'.  Each list 'xs' must be         *)
    58 (*      non-empty, and the literal to be resolved upon must always be unique *)
    59 (*      (e.g. "A | ~B" must not be resolved with "~A | B").  Circular        *)
    60 (*      dependencies of clauses are not allowed.  (At least) one of the      *)
    61 (*      clauses in the table must be the empty clause (i.e. contain no       *)
    62 (*      literals); its ID is given by the second component of the proof.     *)
    63 (*      The clauses of the original problem passed to the SAT solver have    *)
    64 (*      consecutive IDs starting with 0.  Clause IDs must be non-negative,   *)
    65 (*      but do not need to be consecutive.                                   *)
    66 (* ------------------------------------------------------------------------- *)
    67 
    68   type proof = int list Inttab.table * int;
    69 
    70 (* ------------------------------------------------------------------------- *)
    71 (* return type of SAT solvers: if the result is 'SATISFIABLE', a satisfying  *)
    72 (*      assignment must be returned as well; if the result is                *)
    73 (*      'UNSATISFIABLE', a proof of unsatisfiability may be returned         *)
    74 (* ------------------------------------------------------------------------- *)
    75 
    76   datatype result = SATISFIABLE of assignment
    77                   | UNSATISFIABLE of proof option
    78                   | UNKNOWN;
    79 
    80 (* ------------------------------------------------------------------------- *)
    81 (* type of SAT solvers: given a propositional formula, a satisfying          *)
    82 (*      assignment may be returned                                           *)
    83 (* ------------------------------------------------------------------------- *)
    84 
    85   type solver = prop_formula -> result;
    86 
    87 (* ------------------------------------------------------------------------- *)
    88 (* write_dimacs_cnf_file: serializes a formula 'fm' of propositional logic   *)
    89 (*      to a file in DIMACS CNF format (see "Satisfiability Suggested        *)
    90 (*      Format", May 8 1993, Section 2.1)                                    *)
    91 (* Note: 'fm' must not contain a variable index less than 1.                 *)
    92 (* Note: 'fm' must be given in CNF.                                          *)
    93 (* ------------------------------------------------------------------------- *)
    94 
    95   (* Path.T -> prop_formula -> unit *)
    96 
    97   fun write_dimacs_cnf_file path fm =
    98   let
    99     (* prop_formula -> prop_formula *)
   100     fun cnf_True_False_elim True =
   101       Or (BoolVar 1, Not (BoolVar 1))
   102       | cnf_True_False_elim False =
   103       And (BoolVar 1, Not (BoolVar 1))
   104       | cnf_True_False_elim fm =
   105       fm  (* since 'fm' is in CNF, either 'fm'='True'/'False', or 'fm' does not contain 'True'/'False' at all *)
   106     (* prop_formula -> int *)
   107     fun cnf_number_of_clauses (And (fm1,fm2)) =
   108       (cnf_number_of_clauses fm1) + (cnf_number_of_clauses fm2)
   109       | cnf_number_of_clauses _ =
   110       1
   111     (* prop_formula -> string list *)
   112     fun cnf_string fm =
   113     let
   114       (* prop_formula -> string list -> string list *)
   115       fun cnf_string_acc True acc =
   116         error "formula is not in CNF"
   117         | cnf_string_acc False acc =
   118         error "formula is not in CNF"
   119         | cnf_string_acc (BoolVar i) acc =
   120         (i>=1 orelse error "formula contains a variable index less than 1";
   121         string_of_int i :: acc)
   122         | cnf_string_acc (Not (BoolVar i)) acc =
   123         "-" :: cnf_string_acc (BoolVar i) acc
   124         | cnf_string_acc (Not _) acc =
   125         error "formula is not in CNF"
   126         | cnf_string_acc (Or (fm1,fm2)) acc =
   127         cnf_string_acc fm1 (" " :: cnf_string_acc fm2 acc)
   128         | cnf_string_acc (And (fm1,fm2)) acc =
   129         cnf_string_acc fm1 (" 0\n" :: cnf_string_acc fm2 acc)
   130     in
   131       cnf_string_acc fm []
   132     end
   133     val fm'               = cnf_True_False_elim fm
   134     val number_of_vars    = maxidx fm'
   135     val number_of_clauses = cnf_number_of_clauses fm'
   136   in
   137     File.write path
   138       ("c This file was generated by SatSolver.write_dimacs_cnf_file\n" ^
   139        "p cnf " ^ string_of_int number_of_vars ^ " " ^ string_of_int number_of_clauses ^ "\n");
   140     File.append_list path
   141       (cnf_string fm');
   142     File.append path
   143       " 0\n"
   144   end;
   145 
   146 (* ------------------------------------------------------------------------- *)
   147 (* write_dimacs_sat_file: serializes a formula 'fm' of propositional logic   *)
   148 (*      to a file in DIMACS SAT format (see "Satisfiability Suggested        *)
   149 (*      Format", May 8 1993, Section 2.2)                                    *)
   150 (* Note: 'fm' must not contain a variable index less than 1.                 *)
   151 (* ------------------------------------------------------------------------- *)
   152 
   153   (* Path.T -> prop_formula -> unit *)
   154 
   155   fun write_dimacs_sat_file path fm =
   156   let
   157     (* prop_formula -> string list *)
   158     fun sat_string fm =
   159     let
   160       (* prop_formula -> string list -> string list *)
   161       fun sat_string_acc True acc =
   162         "*()" :: acc
   163         | sat_string_acc False acc =
   164         "+()" :: acc
   165         | sat_string_acc (BoolVar i) acc =
   166         (i>=1 orelse error "formula contains a variable index less than 1";
   167         string_of_int i :: acc)
   168         | sat_string_acc (Not (BoolVar i)) acc =
   169         "-" :: sat_string_acc (BoolVar i) acc
   170         | sat_string_acc (Not fm) acc =
   171         "-(" :: sat_string_acc fm (")" :: acc)
   172         | sat_string_acc (Or (fm1,fm2)) acc =
   173         "+(" :: sat_string_acc_or fm1 (" " :: sat_string_acc_or fm2 (")" :: acc))
   174         | sat_string_acc (And (fm1,fm2)) acc =
   175         "*(" :: sat_string_acc_and fm1 (" " :: sat_string_acc_and fm2 (")" :: acc))
   176       (* optimization to make use of n-ary disjunction/conjunction *)
   177       (* prop_formula -> string list -> string list *)
   178       and sat_string_acc_or (Or (fm1,fm2)) acc =
   179         sat_string_acc_or fm1 (" " :: sat_string_acc_or fm2 acc)
   180         | sat_string_acc_or fm acc =
   181         sat_string_acc fm acc
   182       (* prop_formula -> string list -> string list *)
   183       and sat_string_acc_and (And (fm1,fm2)) acc =
   184         sat_string_acc_and fm1 (" " :: sat_string_acc_and fm2 acc)
   185         | sat_string_acc_and fm acc =
   186         sat_string_acc fm acc
   187     in
   188       sat_string_acc fm []
   189     end
   190     val number_of_vars = Int.max (maxidx fm, 1)
   191   in
   192     File.write path
   193       ("c This file was generated by SatSolver.write_dimacs_sat_file\n" ^
   194        "p sat " ^ string_of_int number_of_vars ^ "\n" ^
   195        "(");
   196     File.append_list path
   197       (sat_string fm);
   198     File.append path
   199       ")\n"
   200   end;
   201 
   202 (* ------------------------------------------------------------------------- *)
   203 (* read_std_result_file: scans a SAT solver's output file for a satisfying   *)
   204 (*      variable assignment.  Returns the assignment, or 'UNSATISFIABLE' if  *)
   205 (*      the file contains 'unsatisfiable', or 'UNKNOWN' if the file contains *)
   206 (*      neither 'satisfiable' nor 'unsatisfiable'.  Empty lines are ignored. *)
   207 (*      The assignment must be given in one or more lines immediately after  *)
   208 (*      the line that contains 'satisfiable'.  These lines must begin with   *)
   209 (*      'assignment_prefix'.  Variables must be separated by " ".  Non-      *)
   210 (*      integer strings are ignored.  If variable i is contained in the      *)
   211 (*      assignment, then i is interpreted as 'true'.  If ~i is contained in  *)
   212 (*      the assignment, then i is interpreted as 'false'.  Otherwise the     *)
   213 (*      value of i is taken to be unspecified.                               *)
   214 (* ------------------------------------------------------------------------- *)
   215 
   216   (* Path.T -> string * string * string -> result *)
   217 
   218   fun read_std_result_file path (satisfiable, assignment_prefix, unsatisfiable) =
   219   let
   220     (* string -> int list *)
   221     fun int_list_from_string s =
   222       List.mapPartial Int.fromString (space_explode " " s)
   223     (* int list -> assignment *)
   224     fun assignment_from_list [] i =
   225       NONE  (* the SAT solver didn't provide a value for this variable *)
   226       | assignment_from_list (x::xs) i =
   227       if x=i then (SOME true)
   228       else if x=(~i) then (SOME false)
   229       else assignment_from_list xs i
   230     (* int list -> string list -> assignment *)
   231     fun parse_assignment xs [] =
   232       assignment_from_list xs
   233       | parse_assignment xs (line::lines) =
   234       if String.isPrefix assignment_prefix line then
   235         parse_assignment (xs @ int_list_from_string line) lines
   236       else
   237         assignment_from_list xs
   238     (* string -> string -> bool *)
   239     fun is_substring needle haystack =
   240     let
   241       val length1 = String.size needle
   242       val length2 = String.size haystack
   243     in
   244       if length2 < length1 then
   245         false
   246       else if needle = String.substring (haystack, 0, length1) then
   247         true
   248       else is_substring needle (String.substring (haystack, 1, length2-1))
   249     end
   250     (* string list -> result *)
   251     fun parse_lines [] =
   252       UNKNOWN
   253       | parse_lines (line::lines) =
   254       if is_substring unsatisfiable line then
   255         UNSATISFIABLE NONE
   256       else if is_substring satisfiable line then
   257         SATISFIABLE (parse_assignment [] lines)
   258       else
   259         parse_lines lines
   260   in
   261     (parse_lines o (List.filter (fn l => l <> "")) o split_lines o File.read) path
   262   end;
   263 
   264 (* ------------------------------------------------------------------------- *)
   265 (* make_external_solver: call 'writefn', execute 'cmd', call 'readfn'        *)
   266 (* ------------------------------------------------------------------------- *)
   267 
   268   (* string -> (PropLogic.prop_formula -> unit) -> (unit -> result) -> solver *)
   269 
   270   fun make_external_solver cmd writefn readfn fm =
   271     (writefn fm; system cmd; readfn ());
   272 
   273 (* ------------------------------------------------------------------------- *)
   274 (* read_dimacs_cnf_file: returns a propositional formula that corresponds to *)
   275 (*      a SAT problem given in DIMACS CNF format                             *)
   276 (* ------------------------------------------------------------------------- *)
   277 
   278   (* Path.T -> PropLogic.prop_formula *)
   279 
   280   fun read_dimacs_cnf_file path =
   281   let
   282     (* string list -> string list *)
   283     fun filter_preamble [] =
   284       error "problem line not found in DIMACS CNF file"
   285       | filter_preamble (line::lines) =
   286       if String.isPrefix "c " line orelse line = "c" then
   287         (* ignore comments *)
   288         filter_preamble lines
   289       else if String.isPrefix "p " line then
   290         (* ignore the problem line (which must be the last line of the preamble) *)
   291         (* Ignoring the problem line implies that if the file contains more clauses *)
   292         (* or variables than specified in its preamble, we will accept it anyway.   *)
   293         lines
   294       else
   295         error "preamble in DIMACS CNF file contains a line that does not begin with \"c \" or \"p \""
   296     (* string -> int *)
   297     fun int_from_string s =
   298       case Int.fromString s of
   299         SOME i => i
   300       | NONE   => error ("token " ^ quote s ^ "in DIMACS CNF file is not a number")
   301     (* int list -> int list list *)
   302     fun clauses xs =
   303       let
   304         val (xs1, xs2) = take_prefix (fn i => i <> 0) xs
   305       in
   306         case xs2 of
   307           []      => [xs1]
   308         | (0::[]) => [xs1]
   309         | (0::tl) => xs1 :: clauses tl
   310         | _       => sys_error "this cannot happen"
   311       end
   312     (* int -> PropLogic.prop_formula *)
   313     fun literal_from_int i =
   314       (i<>0 orelse error "variable index in DIMACS CNF file is 0";
   315       if i>0 then
   316         PropLogic.BoolVar i
   317       else
   318         PropLogic.Not (PropLogic.BoolVar (~i)))
   319     (* PropLogic.prop_formula list -> PropLogic.prop_formula *)
   320     fun disjunction [] =
   321       error "empty clause in DIMACS CNF file"
   322       | disjunction (x::xs) =
   323       (case xs of
   324         [] => x
   325       | _  => PropLogic.Or (x, disjunction xs))
   326     (* PropLogic.prop_formula list -> PropLogic.prop_formula *)
   327     fun conjunction [] =
   328       error "no clause in DIMACS CNF file"
   329       | conjunction (x::xs) =
   330       (case xs of
   331         [] => x
   332       | _  => PropLogic.And (x, conjunction xs))
   333   in
   334     (conjunction
   335     o (map disjunction)
   336     o (map (map literal_from_int))
   337     o clauses
   338     o (map int_from_string)
   339     o List.concat
   340     o (map (String.fields (fn c => c mem [#" ", #"\t", #"\n"])))
   341     o filter_preamble
   342     o (List.filter (fn l => l <> ""))
   343     o split_lines
   344     o File.read)
   345       path
   346   end;
   347 
   348 (* ------------------------------------------------------------------------- *)
   349 (* solvers: a (reference to a) table of all registered SAT solvers           *)
   350 (* ------------------------------------------------------------------------- *)
   351 
   352   val solvers = ref ([] : (string * solver) list);
   353 
   354 (* ------------------------------------------------------------------------- *)
   355 (* add_solver: updates 'solvers' by adding a new solver                      *)
   356 (* ------------------------------------------------------------------------- *)
   357 
   358   (* string * solver -> unit *)
   359 
   360     fun add_solver (name, new_solver) =
   361       let
   362         val the_solvers = !solvers;
   363         val _ = if AList.defined (op =) the_solvers name
   364           then warning ("SAT solver " ^ quote name ^ " was defined before")
   365           else ();
   366       in solvers := AList.update (op =) (name, new_solver) the_solvers end;
   367 
   368 (* ------------------------------------------------------------------------- *)
   369 (* invoke_solver: returns the solver associated with the given 'name'        *)
   370 (* Note: If no solver is associated with 'name', exception 'Option' will be  *)
   371 (*       raised.                                                             *)
   372 (* ------------------------------------------------------------------------- *)
   373 
   374   (* string -> solver *)
   375 
   376   fun invoke_solver name =
   377     (the o AList.lookup (op =) (!solvers)) name;
   378 
   379 end;  (* SatSolver *)
   380 
   381 
   382 (* ------------------------------------------------------------------------- *)
   383 (* Predefined SAT solvers                                                    *)
   384 (* ------------------------------------------------------------------------- *)
   385 
   386 (* ------------------------------------------------------------------------- *)
   387 (* Internal SAT solver, available as 'SatSolver.invoke_solver "enumerate"'   *)
   388 (* -- simply enumerates assignments until a satisfying assignment is found   *)
   389 (* ------------------------------------------------------------------------- *)
   390 
   391 let
   392   fun enum_solver fm =
   393   let
   394     (* int list *)
   395     val indices = PropLogic.indices fm
   396     (* int list -> int list -> int list option *)
   397     (* binary increment: list 'xs' of current bits, list 'ys' of all bits (lower bits first) *)
   398     fun next_list _ ([]:int list) =
   399       NONE
   400       | next_list [] (y::ys) =
   401       SOME [y]
   402       | next_list (x::xs) (y::ys) =
   403       if x=y then
   404         (* reset the bit, continue *)
   405         next_list xs ys
   406       else
   407         (* set the lowest bit that wasn't set before, keep the higher bits *)
   408         SOME (y::x::xs)
   409     (* int list -> int -> bool *)
   410     fun assignment_from_list xs i =
   411       i mem xs
   412     (* int list -> SatSolver.result *)
   413     fun solver_loop xs =
   414       if PropLogic.eval (assignment_from_list xs) fm then
   415         SatSolver.SATISFIABLE (SOME o (assignment_from_list xs))
   416       else
   417         (case next_list xs indices of
   418           SOME xs' => solver_loop xs'
   419         | NONE     => SatSolver.UNSATISFIABLE NONE)
   420   in
   421     (* start with the "first" assignment (all variables are interpreted as 'false') *)
   422     solver_loop []
   423   end
   424 in
   425   SatSolver.add_solver ("enumerate", enum_solver)
   426 end;
   427 
   428 (* ------------------------------------------------------------------------- *)
   429 (* Internal SAT solver, available as 'SatSolver.invoke_solver "dpll"' -- a   *)
   430 (* simple implementation of the DPLL algorithm (cf. L. Zhang, S. Malik: "The *)
   431 (* Quest for Efficient Boolean Satisfiability Solvers", July 2002, Fig. 1).  *)
   432 (* ------------------------------------------------------------------------- *)
   433 
   434 let
   435   local
   436     open PropLogic
   437   in
   438     fun dpll_solver fm =
   439     let
   440       (* We could use 'PropLogic.defcnf fm' instead of 'PropLogic.nnf fm' *)
   441       (* but that sometimes leads to worse performance due to the         *)
   442       (* introduction of additional variables.                            *)
   443       val fm' = PropLogic.nnf fm
   444       (* int list *)
   445       val indices = PropLogic.indices fm'
   446       (* int list -> int -> prop_formula *)
   447       fun partial_var_eval []      i = BoolVar i
   448         | partial_var_eval (x::xs) i = if x=i then True else if x=(~i) then False else partial_var_eval xs i
   449       (* int list -> prop_formula -> prop_formula *)
   450       fun partial_eval xs True             = True
   451         | partial_eval xs False            = False
   452         | partial_eval xs (BoolVar i)      = partial_var_eval xs i
   453         | partial_eval xs (Not fm)         = SNot (partial_eval xs fm)
   454         | partial_eval xs (Or (fm1, fm2))  = SOr (partial_eval xs fm1, partial_eval xs fm2)
   455         | partial_eval xs (And (fm1, fm2)) = SAnd (partial_eval xs fm1, partial_eval xs fm2)
   456       (* prop_formula -> int list *)
   457       fun forced_vars True              = []
   458         | forced_vars False             = []
   459         | forced_vars (BoolVar i)       = [i]
   460         | forced_vars (Not (BoolVar i)) = [~i]
   461         | forced_vars (Or (fm1, fm2))   = (forced_vars fm1) inter_int (forced_vars fm2)
   462         | forced_vars (And (fm1, fm2))  = (forced_vars fm1) union_int (forced_vars fm2)
   463         (* Above, i *and* ~i may be forced.  In this case the first occurrence takes   *)
   464         (* precedence, and the next partial evaluation of the formula returns 'False'. *)
   465         | forced_vars _                 = error "formula is not in negation normal form"
   466       (* int list -> prop_formula -> (int list * prop_formula) *)
   467       fun eval_and_force xs fm =
   468       let
   469         val fm' = partial_eval xs fm
   470         val xs' = forced_vars fm'
   471       in
   472         if null xs' then
   473           (xs, fm')
   474         else
   475           eval_and_force (xs@xs') fm'  (* xs and xs' should be distinct, so '@' here should have *)
   476                                        (* the same effect as 'union_int'                         *)
   477       end
   478       (* int list -> int option *)
   479       fun fresh_var xs =
   480         Library.find_first (fn i => not (i mem_int xs) andalso not ((~i) mem_int xs)) indices
   481       (* int list -> prop_formula -> int list option *)
   482       (* partial assignment 'xs' *)
   483       fun dpll xs fm =
   484       let
   485         val (xs', fm') = eval_and_force xs fm
   486       in
   487         case fm' of
   488           True  => SOME xs'
   489         | False => NONE
   490         | _     =>
   491           let
   492             val x = valOf (fresh_var xs')  (* a fresh variable must exist since 'fm' did not evaluate to 'True'/'False' *)
   493           in
   494             case dpll (x::xs') fm' of  (* passing fm' rather than fm should save some simplification work *)
   495               SOME xs'' => SOME xs''
   496             | NONE      => dpll ((~x)::xs') fm'  (* now try interpreting 'x' as 'False' *)
   497           end
   498       end
   499       (* int list -> assignment *)
   500       fun assignment_from_list [] i =
   501         NONE  (* the DPLL procedure didn't provide a value for this variable *)
   502         | assignment_from_list (x::xs) i =
   503         if x=i then (SOME true)
   504         else if x=(~i) then (SOME false)
   505         else assignment_from_list xs i
   506     in
   507       (* initially, no variable is interpreted yet *)
   508       case dpll [] fm' of
   509         SOME assignment => SatSolver.SATISFIABLE (assignment_from_list assignment)
   510       | NONE            => SatSolver.UNSATISFIABLE NONE
   511     end
   512   end  (* local *)
   513 in
   514   SatSolver.add_solver ("dpll", dpll_solver)
   515 end;
   516 
   517 (* ------------------------------------------------------------------------- *)
   518 (* Internal SAT solver, available as 'SatSolver.invoke_solver "auto"': uses  *)
   519 (* the last installed solver (other than "auto" itself) that does not raise  *)
   520 (* 'NOT_CONFIGURED'.  (However, the solver may return 'UNKNOWN'.)            *)
   521 (* ------------------------------------------------------------------------- *)
   522 
   523 let
   524   fun auto_solver fm =
   525   let
   526     fun loop [] =
   527       SatSolver.UNKNOWN
   528       | loop ((name, solver)::solvers) =
   529       if name="auto" then
   530         (* do not call solver "auto" from within "auto" *)
   531         loop solvers
   532       else (
   533         (if name="dpll" orelse name="enumerate" then
   534           warning ("Using SAT solver " ^ quote name ^ "; for better performance, consider using an external solver.")
   535         else
   536           tracing ("Using SAT solver " ^ quote name ^ "."));
   537         (* apply 'solver' to 'fm' *)
   538         solver fm
   539           handle SatSolver.NOT_CONFIGURED => loop solvers
   540       )
   541   in
   542     loop (!SatSolver.solvers)
   543   end
   544 in
   545   SatSolver.add_solver ("auto", auto_solver)
   546 end;
   547 
   548 (* ------------------------------------------------------------------------- *)
   549 (* MiniSat 1.14                                                              *)
   550 (* (http://www.cs.chalmers.se/Cs/Research/FormalMethods/MiniSat/)            *)
   551 (* ------------------------------------------------------------------------- *)
   552 
   553 (* ------------------------------------------------------------------------- *)
   554 (* "minisat_with_proofs" requires a modified version of MiniSat 1.14 by John *)
   555 (* Matthews, which can output ASCII proof traces.  Replaying binary proof    *)
   556 (* traces generated by MiniSat-p_v1.14 has _not_ been implemented.           *)
   557 (* ------------------------------------------------------------------------- *)
   558 
   559 (* add "minisat_with_proofs" _before_ "minisat" to the available solvers, so *)
   560 (* that the latter is preferred by the "auto" solver                         *)
   561 
   562 (* There is a complication that is dealt with in the code below: MiniSat     *)
   563 (* introduces IDs for original clauses in the proof trace.  It does not (in  *)
   564 (* general) follow the convention that the original clauses are numbered     *)
   565 (* from 0 to n-1 (where n is the number of clauses in the formula).          *)
   566 
   567 let
   568   exception INVALID_PROOF of string
   569   fun minisat_with_proofs fm =
   570   let
   571     val _          = if (getenv "MINISAT_HOME") = "" then raise SatSolver.NOT_CONFIGURED else ()
   572     val inpath     = File.tmp_path (Path.explode "isabelle.cnf")
   573     val outpath    = File.tmp_path (Path.explode "result")
   574     val proofpath  = File.tmp_path (Path.explode "result.prf")
   575     val cmd        = (getenv "MINISAT_HOME") ^ "/minisat " ^ (Path.implode inpath) ^ " -r " ^ (Path.implode outpath) ^ " -t " ^ (Path.implode proofpath) ^ "> /dev/null"
   576     fun writefn fm = SatSolver.write_dimacs_cnf_file inpath fm
   577     fun readfn ()  = SatSolver.read_std_result_file outpath ("SAT", "", "UNSAT")
   578     val _          = if File.exists inpath then warning ("overwriting existing file " ^ quote (Path.implode inpath)) else ()
   579     val _          = if File.exists outpath then warning ("overwriting existing file " ^ quote (Path.implode outpath)) else ()
   580     val cnf        = PropLogic.defcnf fm
   581     val result     = SatSolver.make_external_solver cmd writefn readfn cnf
   582     val _          = try File.rm inpath
   583     val _          = try File.rm outpath
   584   in  case result of
   585     SatSolver.UNSATISFIABLE NONE =>
   586     (let
   587       (* string list *)
   588       val proof_lines = (split_lines o File.read) proofpath
   589         handle IO.Io _ => raise INVALID_PROOF "Could not read file \"result.prf\""
   590       (* representation of clauses as ordered lists of literals (with duplicates removed) *)
   591       (* prop_formula -> int list *)
   592       fun clause_to_lit_list (PropLogic.Or (fm1, fm2)) =
   593         OrdList.union int_ord (clause_to_lit_list fm1) (clause_to_lit_list fm2)
   594         | clause_to_lit_list (PropLogic.BoolVar i) =
   595         [i]
   596         | clause_to_lit_list (PropLogic.Not (PropLogic.BoolVar i)) =
   597         [~i]
   598         | clause_to_lit_list _ =
   599         raise INVALID_PROOF "Error: invalid clause in CNF formula."
   600       (* prop_formula -> int *)
   601       fun cnf_number_of_clauses (PropLogic.And (fm1, fm2)) =
   602         cnf_number_of_clauses fm1 + cnf_number_of_clauses fm2
   603         | cnf_number_of_clauses _ =
   604         1
   605       val number_of_clauses = cnf_number_of_clauses cnf
   606       (* int list array *)
   607       val clauses = Array.array (number_of_clauses, [])
   608       (* initialize the 'clauses' array *)
   609       (* prop_formula * int -> int *)
   610       fun init_array (PropLogic.And (fm1, fm2), n) =
   611         init_array (fm2, init_array (fm1, n))
   612         | init_array (fm, n) =
   613         (Array.update (clauses, n, clause_to_lit_list fm); n+1)
   614       val _ = init_array (cnf, 0)
   615       (* optimization for the common case where MiniSat "R"s clauses in their *)
   616       (* original order:                                                      *)
   617       val last_ref_clause = ref (number_of_clauses - 1)
   618       (* search the 'clauses' array for the given list of literals 'lits', *)
   619       (* starting at index '!last_ref_clause + 1'                          *)
   620       (* int list -> int option *)
   621       fun original_clause_id lits =
   622       let
   623         fun original_clause_id_from index =
   624           if index = number_of_clauses then
   625             (* search from beginning again *)
   626             original_clause_id_from 0
   627           (* both 'lits' and the list of literals used in 'clauses' are sorted, so *)
   628           (* testing for equality should suffice -- barring duplicate literals     *)
   629           else if Array.sub (clauses, index) = lits then (
   630             (* success *)
   631             last_ref_clause := index;
   632             SOME index
   633           ) else if index = !last_ref_clause then
   634             (* failure *)
   635             NONE
   636           else
   637             (* continue search *)
   638             original_clause_id_from (index + 1)
   639       in
   640         original_clause_id_from (!last_ref_clause + 1)
   641       end
   642       (* string -> int *)
   643       fun int_from_string s = (
   644         case Int.fromString s of
   645           SOME i => i
   646         | NONE   => raise INVALID_PROOF ("File format error: number expected (" ^ quote s ^ " encountered).")
   647       )
   648       (* parse the proof file *)
   649       val clause_table  = ref (Inttab.empty : int list Inttab.table)
   650       val empty_id      = ref ~1
   651       (* contains a mapping from clause IDs as used by MiniSat to clause IDs in *)
   652       (* our proof format, where original clauses are numbered starting from 0  *)
   653       val clause_id_map = ref (Inttab.empty : int Inttab.table)
   654       fun sat_to_proof id = (
   655         case Inttab.lookup (!clause_id_map) id of
   656           SOME id' => id'
   657         | NONE     => raise INVALID_PROOF ("Clause ID " ^ Int.toString id ^ " used, but not defined.")
   658       )
   659       val next_id = ref (number_of_clauses - 1)
   660       (* string list -> unit *)
   661       fun process_tokens [] =
   662         ()
   663         | process_tokens (tok::toks) =
   664         if tok="R" then (
   665           case toks of
   666             id::sep::lits =>
   667             let
   668               val _        = if !empty_id = ~1 then () else raise INVALID_PROOF "File format error: \"R\" disallowed after \"X\"."
   669               val cid      = int_from_string id
   670               val _        = if sep = "<=" then () else raise INVALID_PROOF ("File format error: \"<=\" expected (" ^ quote sep ^ " encountered).")
   671               val ls       = sort int_ord (map int_from_string lits)
   672               val proof_id = case original_clause_id ls of
   673                                SOME orig_id => orig_id
   674                              | NONE         => raise INVALID_PROOF ("Original clause (new ID is " ^ id ^ ") not found.")
   675             in
   676               (* extend the mapping of clause IDs with this newly defined ID *)
   677               clause_id_map := Inttab.update_new (cid, proof_id) (!clause_id_map)
   678                 handle Inttab.DUP _ => raise INVALID_PROOF ("File format error: clause " ^ id ^ " defined more than once (in \"R\").")
   679               (* the proof itself doesn't change *)
   680             end
   681           | _ =>
   682             raise INVALID_PROOF "File format error: \"R\" followed by an insufficient number of tokens."
   683         ) else if tok="C" then (
   684           case toks of
   685             id::sep::ids =>
   686             let
   687               val _        = if !empty_id = ~1 then () else raise INVALID_PROOF "File format error: \"C\" disallowed after \"X\"."
   688               val cid      = int_from_string id
   689               val _        = if sep = "<=" then () else raise INVALID_PROOF ("File format error: \"<=\" expected (" ^ quote sep ^ " encountered).")
   690               (* ignore the pivot literals in MiniSat's trace *)
   691               fun unevens []             = raise INVALID_PROOF "File format error: \"C\" followed by an even number of IDs."
   692                 | unevens (x :: [])      = x :: []
   693                 | unevens (x :: _ :: xs) = x :: unevens xs
   694               val rs       = (map sat_to_proof o unevens o map int_from_string) ids
   695               (* extend the mapping of clause IDs with this newly defined ID *)
   696               val proof_id = inc next_id
   697               val _        = clause_id_map := Inttab.update_new (cid, proof_id) (!clause_id_map)
   698                                handle Inttab.DUP _ => raise INVALID_PROOF ("File format error: clause " ^ id ^ " defined more than once (in \"C\").")
   699             in
   700               (* update clause table *)
   701               clause_table := Inttab.update_new (proof_id, rs) (!clause_table)
   702                 handle Inttab.DUP _ => raise INVALID_PROOF ("Error: internal ID for clause " ^ id ^ " already used.")
   703             end
   704           | _ =>
   705             raise INVALID_PROOF "File format error: \"C\" followed by an insufficient number of tokens."
   706         ) else if tok="D" then (
   707           case toks of
   708             [id] =>
   709             let
   710               val _ = if !empty_id = ~1 then () else raise INVALID_PROOF "File format error: \"D\" disallowed after \"X\"."
   711               val _ = sat_to_proof (int_from_string id)
   712             in
   713               (* simply ignore "D" *)
   714               ()
   715             end
   716           | _ =>
   717             raise INVALID_PROOF "File format error: \"D\" followed by an illegal number of tokens."
   718         ) else if tok="X" then (
   719           case toks of
   720             [id1, id2] =>
   721             let
   722               val _            = if !empty_id = ~1 then () else raise INVALID_PROOF "File format error: more than one end-of-proof statement."
   723               val _            = sat_to_proof (int_from_string id1)
   724               val new_empty_id = sat_to_proof (int_from_string id2)
   725             in
   726               (* update conflict id *)
   727               empty_id := new_empty_id
   728             end
   729           | _ =>
   730             raise INVALID_PROOF "File format error: \"X\" followed by an illegal number of tokens."
   731         ) else
   732           raise INVALID_PROOF ("File format error: unknown token " ^ quote tok ^ " encountered.")
   733       (* string list -> unit *)
   734       fun process_lines [] =
   735         ()
   736         | process_lines (l::ls) = (
   737           process_tokens (String.tokens (fn c => c = #" " orelse c = #"\t") l);
   738           process_lines ls
   739         )
   740       (* proof *)
   741       val _ = process_lines proof_lines
   742       val _ = if !empty_id <> ~1 then () else raise INVALID_PROOF "File format error: no conflicting clause specified."
   743     in
   744       SatSolver.UNSATISFIABLE (SOME (!clause_table, !empty_id))
   745     end handle INVALID_PROOF reason => (warning reason; SatSolver.UNSATISFIABLE NONE))
   746   | result =>
   747     result
   748   end
   749 in
   750   SatSolver.add_solver ("minisat_with_proofs", minisat_with_proofs)
   751 end;
   752 
   753 let
   754   fun minisat fm =
   755   let
   756     val _          = if (getenv "MINISAT_HOME") = "" then raise SatSolver.NOT_CONFIGURED else ()
   757     val inpath     = File.tmp_path (Path.explode "isabelle.cnf")
   758     val outpath    = File.tmp_path (Path.explode "result")
   759     val cmd        = (getenv "MINISAT_HOME") ^ "/minisat " ^ (Path.implode inpath) ^ " -r " ^ (Path.implode outpath) ^ " > /dev/null"
   760     fun writefn fm = SatSolver.write_dimacs_cnf_file inpath (PropLogic.defcnf fm)
   761     fun readfn ()  = SatSolver.read_std_result_file outpath ("SAT", "", "UNSAT")
   762     val _          = if File.exists inpath then warning ("overwriting existing file " ^ quote (Path.implode inpath)) else ()
   763     val _          = if File.exists outpath then warning ("overwriting existing file " ^ quote (Path.implode outpath)) else ()
   764     val result     = SatSolver.make_external_solver cmd writefn readfn fm
   765     val _          = try File.rm inpath
   766     val _          = try File.rm outpath
   767   in
   768     result
   769   end
   770 in
   771   SatSolver.add_solver ("minisat", minisat)
   772 end;
   773 
   774 (* ------------------------------------------------------------------------- *)
   775 (* zChaff (http://www.princeton.edu/~chaff/zchaff.html)                      *)
   776 (* ------------------------------------------------------------------------- *)
   777 
   778 (* ------------------------------------------------------------------------- *)
   779 (* 'zchaff_with_proofs' applies the "zchaff" prover to a formula, and if     *)
   780 (* zChaff finds that the formula is unsatisfiable, a proof of this is read   *)
   781 (* from a file "resolve_trace" that was generated by zChaff.  See the code   *)
   782 (* below for the expected format of the "resolve_trace" file.  Aside from    *)
   783 (* some basic syntactic checks, no verification of the proof is performed.   *)
   784 (* ------------------------------------------------------------------------- *)
   785 
   786 (* add "zchaff_with_proofs" _before_ "zchaff" to the available solvers, so   *)
   787 (* that the latter is preferred by the "auto" solver                         *)
   788 
   789 let
   790   exception INVALID_PROOF of string
   791   fun zchaff_with_proofs fm =
   792   case SatSolver.invoke_solver "zchaff" fm of
   793     SatSolver.UNSATISFIABLE NONE =>
   794     (let
   795       (* string list *)
   796       val proof_lines = ((split_lines o File.read) (Path.explode "resolve_trace"))
   797         handle IO.Io _ => raise INVALID_PROOF "Could not read file \"resolve_trace\""
   798       (* PropLogic.prop_formula -> int *)
   799       fun cnf_number_of_clauses (PropLogic.And (fm1, fm2)) = cnf_number_of_clauses fm1 + cnf_number_of_clauses fm2
   800         | cnf_number_of_clauses _                          = 1
   801       (* string -> int *)
   802       fun int_from_string s = (
   803         case Int.fromString s of
   804           SOME i => i
   805         | NONE   => raise INVALID_PROOF ("File format error: number expected (" ^ quote s ^ " encountered).")
   806       )
   807       (* parse the "resolve_trace" file *)
   808       val clause_offset = ref ~1
   809       val clause_table  = ref (Inttab.empty : int list Inttab.table)
   810       val empty_id      = ref ~1
   811       (* string list -> unit *)
   812       fun process_tokens [] =
   813         ()
   814         | process_tokens (tok::toks) =
   815         if tok="CL:" then (
   816           case toks of
   817             id::sep::ids =>
   818             let
   819               val _   = if !clause_offset = ~1 then () else raise INVALID_PROOF ("File format error: \"CL:\" disallowed after \"VAR:\".")
   820               val _   = if !empty_id = ~1 then () else raise INVALID_PROOF ("File format error: \"CL:\" disallowed after \"CONF:\".")
   821               val cid = int_from_string id
   822               val _   = if sep = "<=" then () else raise INVALID_PROOF ("File format error: \"<=\" expected (" ^ quote sep ^ " encountered).")
   823               val rs  = map int_from_string ids
   824             in
   825               (* update clause table *)
   826               clause_table := Inttab.update_new (cid, rs) (!clause_table)
   827                 handle Inttab.DUP _ => raise INVALID_PROOF ("File format error: clause " ^ id ^ " defined more than once.")
   828             end
   829           | _ =>
   830             raise INVALID_PROOF "File format error: \"CL:\" followed by an insufficient number of tokens."
   831         ) else if tok="VAR:" then (
   832           case toks of
   833             id::levsep::levid::valsep::valid::antesep::anteid::litsep::lits =>
   834             let
   835               val _   = if !empty_id = ~1 then () else raise INVALID_PROOF ("File format error: \"VAR:\" disallowed after \"CONF:\".")
   836               (* set 'clause_offset' to the largest used clause ID *)
   837               val _   = if !clause_offset = ~1 then clause_offset :=
   838                 (case Inttab.max_key (!clause_table) of
   839                   SOME id => id
   840                 | NONE    => cnf_number_of_clauses (PropLogic.defcnf fm) - 1  (* the first clause ID is 0, not 1 *))
   841                 else
   842                   ()
   843               val vid = int_from_string id
   844               val _   = if levsep = "L:" then () else raise INVALID_PROOF ("File format error: \"L:\" expected (" ^ quote levsep ^ " encountered).")
   845               val _   = int_from_string levid
   846               val _   = if valsep = "V:" then () else raise INVALID_PROOF ("File format error: \"V:\" expected (" ^ quote valsep ^ " encountered).")
   847               val _   = int_from_string valid
   848               val _   = if antesep = "A:" then () else raise INVALID_PROOF ("File format error: \"A:\" expected (" ^ quote antesep ^ " encountered).")
   849               val aid = int_from_string anteid
   850               val _   = if litsep = "Lits:" then () else raise INVALID_PROOF ("File format error: \"Lits:\" expected (" ^ quote litsep ^ " encountered).")
   851               val ls  = map int_from_string lits
   852               (* convert the data provided by zChaff to our resolution-style proof format *)
   853               (* each "VAR:" line defines a unit clause, the resolvents are implicitly    *)
   854               (* given by the literals in the antecedent clause                           *)
   855               (* we use the sum of '!clause_offset' and the variable ID as clause ID for the unit clause *)
   856               val cid = !clause_offset + vid
   857               (* the low bit of each literal gives its sign (positive/negative), therefore  *)
   858               (* we have to divide each literal by 2 to obtain the proper variable ID; then *)
   859               (* we add '!clause_offset' to obtain the ID of the corresponding unit clause  *)
   860               val vids = filter (not_equal vid) (map (fn l => l div 2) ls)
   861               val rs   = aid :: map (fn v => !clause_offset + v) vids
   862             in
   863               (* update clause table *)
   864               clause_table := Inttab.update_new (cid, rs) (!clause_table)
   865                 handle Inttab.DUP _ => raise INVALID_PROOF ("File format error: clause " ^ string_of_int cid ^ " (derived from antecedent for variable " ^ id ^ ") already defined.")
   866             end
   867           | _ =>
   868             raise INVALID_PROOF "File format error: \"VAR:\" followed by an insufficient number of tokens."
   869         ) else if tok="CONF:" then (
   870           case toks of
   871             id::sep::ids =>
   872             let
   873               val _   = if !empty_id = ~1 then () else raise INVALID_PROOF "File format error: more than one conflicting clause specified."
   874               val cid = int_from_string id
   875               val _   = if sep = "==" then () else raise INVALID_PROOF ("File format error: \"==\" expected (" ^ quote sep ^ " encountered).")
   876               val ls  = map int_from_string ids
   877               (* the conflict clause must be resolved with the unit clauses *)
   878               (* for its literals to obtain the empty clause                *)
   879               val vids         = map (fn l => l div 2) ls
   880               val rs           = cid :: map (fn v => !clause_offset + v) vids
   881               val new_empty_id = getOpt (Inttab.max_key (!clause_table), !clause_offset) + 1
   882             in
   883               (* update clause table and conflict id *)
   884               clause_table := Inttab.update_new (new_empty_id, rs) (!clause_table)
   885                 handle Inttab.DUP _ => raise INVALID_PROOF ("File format error: clause " ^ string_of_int new_empty_id ^ " (empty clause derived from clause " ^ id ^ ") already defined.");
   886               empty_id     := new_empty_id
   887             end
   888           | _ =>
   889             raise INVALID_PROOF "File format error: \"CONF:\" followed by an insufficient number of tokens."
   890         ) else
   891           raise INVALID_PROOF ("File format error: unknown token " ^ quote tok ^ " encountered.")
   892       (* string list -> unit *)
   893       fun process_lines [] =
   894         ()
   895         | process_lines (l::ls) = (
   896           process_tokens (String.tokens (fn c => c = #" " orelse c = #"\t") l);
   897           process_lines ls
   898         )
   899       (* proof *)
   900       val _ = process_lines proof_lines
   901       val _ = if !empty_id <> ~1 then () else raise INVALID_PROOF "File format error: no conflicting clause specified."
   902     in
   903       SatSolver.UNSATISFIABLE (SOME (!clause_table, !empty_id))
   904     end handle INVALID_PROOF reason => (warning reason; SatSolver.UNSATISFIABLE NONE))
   905   | result =>
   906     result
   907 in
   908   SatSolver.add_solver ("zchaff_with_proofs", zchaff_with_proofs)
   909 end;
   910 
   911 let
   912   fun zchaff fm =
   913   let
   914     val _          = if (getenv "ZCHAFF_HOME") = "" then raise SatSolver.NOT_CONFIGURED else ()
   915     val _          = if (getenv "ZCHAFF_VERSION") <> "2004.5.13" andalso
   916                         (getenv "ZCHAFF_VERSION") <> "2004.11.15" then raise SatSolver.NOT_CONFIGURED else ()
   917       (* both versions of zChaff appear to have the same interface, so we do *)
   918       (* not actually need to distinguish between them in the following code *)
   919     val inpath     = File.tmp_path (Path.explode "isabelle.cnf")
   920     val outpath    = File.tmp_path (Path.explode "result")
   921     val cmd        = (getenv "ZCHAFF_HOME") ^ "/zchaff " ^ (Path.implode inpath) ^ " > " ^ (Path.implode outpath)
   922     fun writefn fm = SatSolver.write_dimacs_cnf_file inpath (PropLogic.defcnf fm)
   923     fun readfn ()  = SatSolver.read_std_result_file outpath ("Instance Satisfiable", "", "Instance Unsatisfiable")
   924     val _          = if File.exists inpath then warning ("overwriting existing file " ^ quote (Path.implode inpath)) else ()
   925     val _          = if File.exists outpath then warning ("overwriting existing file " ^ quote (Path.implode outpath)) else ()
   926     val result     = SatSolver.make_external_solver cmd writefn readfn fm
   927     val _          = try File.rm inpath
   928     val _          = try File.rm outpath
   929   in
   930     result
   931   end
   932 in
   933   SatSolver.add_solver ("zchaff", zchaff)
   934 end;
   935 
   936 (* ------------------------------------------------------------------------- *)
   937 (* BerkMin 561 (http://eigold.tripod.com/BerkMin.html)                       *)
   938 (* ------------------------------------------------------------------------- *)
   939 
   940 let
   941   fun berkmin fm =
   942   let
   943     val _          = if (getenv "BERKMIN_HOME") = "" orelse (getenv "BERKMIN_EXE") = "" then raise SatSolver.NOT_CONFIGURED else ()
   944     val inpath     = File.tmp_path (Path.explode "isabelle.cnf")
   945     val outpath    = File.tmp_path (Path.explode "result")
   946     val cmd        = (getenv "BERKMIN_HOME") ^ "/" ^ (getenv "BERKMIN_EXE") ^ " " ^ (Path.implode inpath) ^ " > " ^ (Path.implode outpath)
   947     fun writefn fm = SatSolver.write_dimacs_cnf_file inpath (PropLogic.defcnf fm)
   948     fun readfn ()  = SatSolver.read_std_result_file outpath ("Satisfiable          !!", "solution =", "UNSATISFIABLE          !!")
   949     val _          = if File.exists inpath then warning ("overwriting existing file " ^ quote (Path.implode inpath)) else ()
   950     val _          = if File.exists outpath then warning ("overwriting existing file " ^ quote (Path.implode outpath)) else ()
   951     val result     = SatSolver.make_external_solver cmd writefn readfn fm
   952     val _          = try File.rm inpath
   953     val _          = try File.rm outpath
   954   in
   955     result
   956   end
   957 in
   958   SatSolver.add_solver ("berkmin", berkmin)
   959 end;
   960 
   961 (* ------------------------------------------------------------------------- *)
   962 (* Jerusat 1.3 (http://www.cs.tau.ac.il/~ale1/)                              *)
   963 (* ------------------------------------------------------------------------- *)
   964 
   965 let
   966   fun jerusat fm =
   967   let
   968     val _          = if (getenv "JERUSAT_HOME") = "" then raise SatSolver.NOT_CONFIGURED else ()
   969     val inpath     = File.tmp_path (Path.explode "isabelle.cnf")
   970     val outpath    = File.tmp_path (Path.explode "result")
   971     val cmd        = (getenv "JERUSAT_HOME") ^ "/Jerusat1.3 " ^ (Path.implode inpath) ^ " > " ^ (Path.implode outpath)
   972     fun writefn fm = SatSolver.write_dimacs_cnf_file inpath (PropLogic.defcnf fm)
   973     fun readfn ()  = SatSolver.read_std_result_file outpath ("s SATISFIABLE", "v ", "s UNSATISFIABLE")
   974     val _          = if File.exists inpath then warning ("overwriting existing file " ^ quote (Path.implode inpath)) else ()
   975     val _          = if File.exists outpath then warning ("overwriting existing file " ^ quote (Path.implode outpath)) else ()
   976     val result     = SatSolver.make_external_solver cmd writefn readfn fm
   977     val _          = try File.rm inpath
   978     val _          = try File.rm outpath
   979   in
   980     result
   981   end
   982 in
   983   SatSolver.add_solver ("jerusat", jerusat)
   984 end;
   985 
   986 (* ------------------------------------------------------------------------- *)
   987 (* Add code for other SAT solvers below.                                     *)
   988 (* ------------------------------------------------------------------------- *)
   989 
   990 (*
   991 let
   992   fun mysolver fm = ...
   993 in
   994   SatSolver.add_solver ("myname", (fn fm => if mysolver_is_configured then mysolver fm else raise SatSolver.NOT_CONFIGURED));  -- register the solver
   995 end;
   996 
   997 -- the solver is now available as SatSolver.invoke_solver "myname"
   998 *)