author | webertj |
Wed, 26 May 2004 17:42:46 +0200 | |
changeset 14805 | eff7b9df27e9 |
parent 14753 | f40b45db8cf0 |
child 14965 | 7155b319eafa |
permissions | -rw-r--r-- |
14453 | 1 |
(* Title: HOL/Tools/sat_solver.ML |
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ID: $Id$ |
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Author: Tjark Weber |
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Copyright 2004 |
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Interface to external SAT solvers, and (simple) built-in SAT solvers. |
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*) |
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signature SAT_SOLVER = |
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sig |
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type solver (* PropLogic.prop_formula -> (int -> bool) option option *) |
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(* external SAT solvers *) |
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val write_dimacs_cnf_file : Path.T -> PropLogic.prop_formula -> unit |
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val write_dimacs_sat_file : Path.T -> PropLogic.prop_formula -> unit |
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val parse_std_result_file : Path.T -> string -> (int -> bool) option |
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val make_external_solver : string -> (PropLogic.prop_formula -> unit) -> (unit -> (int -> bool) option) |
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-> PropLogic.prop_formula -> (int -> bool) option |
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(* generic interface *) |
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val solvers : (string * solver) list ref |
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val add_solver : string * solver -> unit |
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val invoke_solver : string -> solver (* exception OPTION *) |
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end; |
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structure SatSolver : SAT_SOLVER = |
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struct |
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open PropLogic; |
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(* ------------------------------------------------------------------------- *) |
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(* Type of SAT solvers: given a propositional formula, a satisfying *) |
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(* assignment may be returned *) |
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(* - 'Some None' means that no satisfying assignment was found *) |
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(* - 'None' means that the solver was not configured/installed properly *) |
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(* ------------------------------------------------------------------------- *) |
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type solver = prop_formula -> (int -> bool) option option; |
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(* ------------------------------------------------------------------------- *) |
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(* write_dimacs_cnf_file: serializes a formula 'fm' of propositional logic *) |
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(* to a file in DIMACS CNF format (see "Satisfiability Suggested *) |
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(* Format", May 8 1993, Section 2.1) *) |
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(* Note: 'fm' must not contain a variable index less than 1. *) |
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(* Note: 'fm' is converted into (definitional) CNF. *) |
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(* ------------------------------------------------------------------------- *) |
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(* Path.T -> prop_formula -> unit *) |
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fun write_dimacs_cnf_file path fm = |
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let |
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(* prop_formula -> prop_formula *) |
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fun cnf_True_False_elim True = |
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Or (BoolVar 1, Not (BoolVar 1)) |
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| cnf_True_False_elim False = |
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And (BoolVar 1, Not (BoolVar 1)) |
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| cnf_True_False_elim fm = |
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fm (* since 'fm' is in CNF, either 'fm'='True'/'False', or 'fm' does not contain 'True'/'False' at all *) |
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(* prop_formula -> int *) |
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fun cnf_number_of_clauses (And (fm1,fm2)) = |
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(cnf_number_of_clauses fm1) + (cnf_number_of_clauses fm2) |
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| cnf_number_of_clauses _ = |
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1 |
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(* prop_formula -> string *) |
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fun cnf_string True = |
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error "formula is not in CNF" |
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| cnf_string False = |
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error "formula is not in CNF" |
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| cnf_string (BoolVar i) = |
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(assert (i>=1) "formula contains a variable index less than 1"; |
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string_of_int i) |
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| cnf_string (Not fm) = |
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"-" ^ (cnf_string fm) |
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| cnf_string (Or (fm1,fm2)) = |
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(cnf_string fm1) ^ " " ^ (cnf_string fm2) |
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| cnf_string (And (fm1,fm2)) = |
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(cnf_string fm1) ^ " 0\n" ^ (cnf_string fm2) |
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in |
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File.write path |
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(let |
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val cnf = (cnf_True_False_elim o defcnf) fm (* conversion into def. CNF *) |
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val number_of_vars = maxidx cnf |
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val number_of_clauses = cnf_number_of_clauses cnf |
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in |
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"c This file was generated by SatSolver.write_dimacs_cnf_file\n" ^ |
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"c (c) Tjark Weber\n" ^ |
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"p cnf " ^ (string_of_int number_of_vars) ^ " " ^ (string_of_int number_of_clauses) ^ "\n" ^ |
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(cnf_string cnf) ^ "\n" |
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end) |
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end; |
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(* ------------------------------------------------------------------------- *) |
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(* write_dimacs_sat_file: serializes a formula 'fm' of propositional logic *) |
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(* to a file in DIMACS SAT format (see "Satisfiability Suggested *) |
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(* Format", May 8 1993, Section 2.2) *) |
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(* Note: 'fm' must not contain a variable index less than 1. *) |
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(* ------------------------------------------------------------------------- *) |
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(* Path.T -> prop_formula -> unit *) |
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fun write_dimacs_sat_file path fm = |
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let |
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(* prop_formula -> string *) |
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fun sat_string True = |
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"*()" |
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| sat_string False = |
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"+()" |
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| sat_string (BoolVar i) = |
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(assert (i>=1) "formula contains a variable index less than 1"; |
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string_of_int i) |
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| sat_string (Not fm) = |
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"-(" ^ (sat_string fm) ^ ")" |
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| sat_string (Or (fm1,fm2)) = |
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"+(" ^ (sat_string fm1) ^ " " ^ (sat_string fm2) ^ ")" |
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| sat_string (And (fm1,fm2)) = |
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"*(" ^ (sat_string fm1) ^ " " ^ (sat_string fm2) ^ ")" |
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in |
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File.write path |
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(let |
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val number_of_vars = Int.max (maxidx fm, 1) |
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in |
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"c This file was generated by SatSolver.write_dimacs_sat_file\n" ^ |
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"c (c) Tjark Weber\n" ^ |
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"p sat " ^ (string_of_int number_of_vars) ^ "\n" ^ |
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"(" ^ (sat_string fm) ^ ")\n" |
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end) |
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end; |
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(* ------------------------------------------------------------------------- *) |
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(* parse_std_result_file: scans a SAT solver's output file for a satisfying *) |
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(* variable assignment. Returns the assignment, or 'None' if the SAT *) |
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(* solver did not find one. The file format must be as follows: *) |
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(* ,----- *) |
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(* | 0 or more lines not containing 'success' *) |
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(* | A line containing 'success' as a substring *) |
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(* | A line ASSIGNMENT containing integers, separated by " " *) |
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(* | 0 or more lines *) |
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(* `----- *) |
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(* If variable i is contained in ASSIGNMENT, then i is interpreted as *) |
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(* 'true'. If ~i is contained in ASSIGNMENT, then i is interpreted as *) |
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(* 'false'. *) |
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(* ------------------------------------------------------------------------- *) |
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(* Path.T -> string -> (int -> bool) option *) |
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fun parse_std_result_file path success = |
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let |
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(* 'a option -> 'a Library.option *) |
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fun option (SOME a) = |
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Some a |
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| option NONE = |
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None |
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(* string -> int list *) |
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fun int_list_from_string s = |
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mapfilter (option o Int.fromString) (space_explode " " s) |
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(* int list -> int -> bool *) |
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fun assignment_from_list [] i = |
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false (* could be 'true' just as well; the SAT solver didn't provide a value for this variable *) |
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| assignment_from_list (x::xs) i = |
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if x=i then true |
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else if x=(~i) then false |
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else assignment_from_list xs i |
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(* string -> string -> bool *) |
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fun is_substring needle haystack = |
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let |
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val length1 = String.size needle |
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val length2 = String.size haystack |
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in |
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if length2 < length1 then |
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false |
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else if needle = String.substring (haystack, 0, length1) then |
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true |
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else is_substring needle (String.substring (haystack, 1, length2-1)) |
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end |
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(* string list -> int list option *) |
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fun parse_lines [] = |
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None |
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| parse_lines (line::lines) = |
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if is_substring success line then |
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(* the next line must be a list of integers *) |
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(Some o assignment_from_list o int_list_from_string o hd) lines |
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else |
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parse_lines lines |
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in |
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(parse_lines o split_lines o File.read) path |
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end; |
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(* ------------------------------------------------------------------------- *) |
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(* make_external_solver: call 'writefn', execute 'cmd', call 'readfn' *) |
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(* ------------------------------------------------------------------------- *) |
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(* string -> (prop_formula -> unit) -> (unit -> (int -> bool) option) -> prop_formula -> (int -> bool) option *) |
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fun make_external_solver cmd writefn readfn fm = |
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(writefn fm; |
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assert ((system cmd)=0) ("system command " ^ quote cmd ^ " failed (make sure the SAT solver is installed)"); |
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readfn ()); |
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(* ------------------------------------------------------------------------- *) |
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(* solvers: a (reference to a) table of all registered SAT solvers *) |
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(* ------------------------------------------------------------------------- *) |
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val solvers = ref ([] : (string * solver) list); |
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(* ------------------------------------------------------------------------- *) |
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(* add_solver: updates 'solvers' by adding a new solver *) |
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(* ------------------------------------------------------------------------- *) |
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(* string * solver -> unit *) |
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fun add_solver (name, new_solver) = |
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(solvers := overwrite_warn (!solvers, (name, new_solver)) ("SAT solver " ^ quote name ^ " was defined before")); |
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(* ------------------------------------------------------------------------- *) |
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(* invoke_solver: returns the solver associated with the given 'name' *) |
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(* Note: If no solver is associated with 'name', exception 'OPTION' will be *) |
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(* raised. *) |
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(* ------------------------------------------------------------------------- *) |
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(* string -> solver *) |
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fun invoke_solver name = |
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(the o assoc) (!solvers, name); |
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end; (* SatSolver *) |
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(* ------------------------------------------------------------------------- *) |
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(* Predefined SAT solvers *) |
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(* ------------------------------------------------------------------------- *) |
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(* ------------------------------------------------------------------------- *) |
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(* Internal SAT solver, available as 'SatSolver.invoke_solver "enumerate"' *) |
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(* -- simply enumerates assignments until a satisfying assignment is found *) |
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(* ------------------------------------------------------------------------- *) |
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let |
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fun enum_solver fm = |
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let |
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(* int list *) |
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val indices = PropLogic.indices fm |
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(* int list -> int list -> int list option *) |
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(* binary increment: list 'xs' of current bits, list 'ys' of all bits (lower bits first) *) |
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fun next_list _ ([]:int list) = |
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None |
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| next_list [] (y::ys) = |
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Some [y] |
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| next_list (x::xs) (y::ys) = |
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if x=y then |
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(* reset the bit, continue *) |
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next_list xs ys |
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else |
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(* set the lowest bit that wasn't set before, keep the higher bits *) |
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Some (y::x::xs) |
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(* int list -> int -> bool *) |
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fun assignment_from_list xs i = |
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i mem xs |
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(* int list -> (int -> bool) option *) |
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fun solver_loop xs = |
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if PropLogic.eval (assignment_from_list xs) fm then |
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Some (assignment_from_list xs) |
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else |
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(case next_list xs indices of |
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Some xs' => solver_loop xs' |
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| None => None) |
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in |
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(* start with the "first" assignment (all variables are interpreted as 'False') *) |
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solver_loop [] |
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end |
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in |
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SatSolver.add_solver ("enumerate", Some o enum_solver) |
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end; |
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(* ------------------------------------------------------------------------- *) |
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(* Internal SAT solver, available as 'SatSolver.invoke_solver "dpll"' -- a *) |
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(* simple implementation of the DPLL algorithm (cf. L. Zhang, S. Malik: "The *) |
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(* Quest for Efficient Boolean Satisfiability Solvers", July 2002, Fig. 1). *) |
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(* ------------------------------------------------------------------------- *) |
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let |
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local |
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open PropLogic |
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in |
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fun dpll_solver fm = |
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let |
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(* We could use 'PropLogic.defcnf fm' instead of 'nnf fm', but that *) |
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(* sometimes introduces more boolean variables than we can handle *) |
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(* efficiently. *) |
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val fm' = PropLogic.nnf fm |
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(* int list *) |
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val indices = PropLogic.indices fm' |
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(* int list -> int -> prop_formula *) |
293 |
fun partial_var_eval [] i = BoolVar i |
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| partial_var_eval (x::xs) i = if x=i then True else if x=(~i) then False else partial_var_eval xs i |
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(* int list -> prop_formula -> prop_formula *) |
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fun partial_eval xs True = True |
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| partial_eval xs False = False |
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| partial_eval xs (BoolVar i) = partial_var_eval xs i |
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| partial_eval xs (Not fm) = SNot (partial_eval xs fm) |
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| partial_eval xs (Or (fm1, fm2)) = SOr (partial_eval xs fm1, partial_eval xs fm2) |
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| partial_eval xs (And (fm1, fm2)) = SAnd (partial_eval xs fm1, partial_eval xs fm2) |
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(* prop_formula -> int list *) |
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fun forced_vars True = [] |
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| forced_vars False = [] |
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| forced_vars (BoolVar i) = [i] |
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| forced_vars (Not (BoolVar i)) = [~i] |
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| forced_vars (Or (fm1, fm2)) = (forced_vars fm1) inter_int (forced_vars fm2) |
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| forced_vars (And (fm1, fm2)) = (forced_vars fm1) union_int (forced_vars fm2) |
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(* Above, i *and* ~i may be forced. In this case the first occurrence takes *) |
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(* precedence, and the next partial evaluation of the formula returns 'False'. *) |
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| forced_vars _ = raise ERROR (* formula is not in negation normal form *) |
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312 |
(* int list -> prop_formula -> (int list * prop_formula) *) |
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fun eval_and_force xs fm = |
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314 |
let |
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315 |
val fm' = partial_eval xs fm |
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val xs' = forced_vars fm' |
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317 |
in |
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318 |
if null xs' then |
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(xs, fm') |
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else |
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eval_and_force (xs@xs') fm' (* xs and xs' should be distinct, so '@' here should have *) |
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(* the same effect as 'union_int' *) |
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323 |
end |
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(* int list -> int option *) |
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325 |
fun fresh_var xs = |
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326 |
Library.find_first (fn i => not (i mem_int xs) andalso not ((~i) mem_int xs)) indices |
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327 |
(* int list -> prop_formula -> int list option *) |
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328 |
(* partial assignment 'xs' *) |
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329 |
fun dpll xs fm = |
|
330 |
let |
|
331 |
val (xs', fm') = eval_and_force xs fm |
|
332 |
in |
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333 |
case fm' of |
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334 |
True => Some xs' |
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335 |
| False => None |
|
336 |
| _ => |
|
337 |
let |
|
338 |
val x = the (fresh_var xs') (* a fresh variable must exist since 'fm' did not evaluate to 'True'/'False' *) |
|
339 |
in |
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340 |
case dpll (x::xs') fm' of (* passing fm' rather than fm should save some simplification work *) |
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Some xs'' => Some xs'' |
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342 |
| None => dpll ((~x)::xs') fm' (* now try interpreting 'x' as 'False' *) |
|
343 |
end |
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344 |
end |
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345 |
(* int list -> int -> bool *) |
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346 |
fun assignment_from_list [] i = |
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347 |
false (* could be 'true' just as well; the DPLL procedure didn't provide a value for this variable *) |
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348 |
| assignment_from_list (x::xs) i = |
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349 |
if x=i then true |
|
350 |
else if x=(~i) then false |
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351 |
else assignment_from_list xs i |
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352 |
in |
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353 |
(* initially, no variable is interpreted yet *) |
|
14514 | 354 |
apsome assignment_from_list (dpll [] fm') |
14453 | 355 |
end |
356 |
end (* local *) |
|
357 |
in |
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SatSolver.add_solver ("dpll", Some o dpll_solver) |
14453 | 359 |
end; |
360 |
||
361 |
(* ------------------------------------------------------------------------- *) |
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14753 | 362 |
(* Internal SAT solver, available as 'SatSolver.invoke_solver "auto"': uses *) |
363 |
(* the first installed solver (other than "auto" itself) *) |
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14453 | 364 |
(* ------------------------------------------------------------------------- *) |
365 |
||
366 |
let |
|
367 |
fun auto_solver fm = |
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get_first (fn (name,solver) => |
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if name="auto" then |
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None |
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else |
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((if name="dpll" orelse name="enumerate" then |
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warning ("Using SAT solver " ^ quote name ^ "; for better performance, consider using an external solver.") |
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else |
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375 |
()); |
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376 |
solver fm)) (rev (!SatSolver.solvers)) |
14453 | 377 |
in |
378 |
SatSolver.add_solver ("auto", auto_solver) |
|
379 |
end; |
|
380 |
||
381 |
(* ------------------------------------------------------------------------- *) |
|
382 |
(* ZChaff, Version 2003.12.04 *) |
|
383 |
(* ------------------------------------------------------------------------- *) |
|
384 |
||
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385 |
let |
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parents:
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changeset
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386 |
fun zchaff fm = |
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let |
388 |
val inname = "isabelle.cnf" |
|
389 |
val outname = "result" |
|
390 |
val inpath = File.tmp_path (Path.unpack inname) |
|
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val outpath = File.tmp_path (Path.unpack outname) |
|
392 |
val cmd = (getenv "ZCHAFF_HOME") ^ "/zchaff " ^ (Path.pack inpath) ^ " > " ^ (Path.pack outpath) |
|
393 |
fun writefn fm = SatSolver.write_dimacs_cnf_file inpath fm |
|
394 |
fun readfn () = SatSolver.parse_std_result_file outpath "Verify Solution successful. Instance satisfiable" |
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395 |
val _ = assert (not (File.exists inpath)) ("file " ^ quote (Path.pack inpath) ^ " exists, please delete (will not overwrite)") |
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changeset
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396 |
val _ = assert (not (File.exists outpath)) ("file " ^ quote (Path.pack outpath) ^ " exists, please delete (will not overwrite)") |
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parents:
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changeset
|
397 |
val assignment = SatSolver.make_external_solver cmd writefn readfn fm |
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changeset
|
398 |
val _ = (File.rm inpath handle _ => ()) |
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parents:
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changeset
|
399 |
val _ = (File.rm outpath handle _ => ()) |
14453 | 400 |
in |
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changeset
|
401 |
assignment |
14453 | 402 |
end |
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changeset
|
403 |
in |
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parents:
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changeset
|
404 |
SatSolver.add_solver ("zchaff", (fn fm => if getenv "ZCHAFF_HOME" <> "" then Some (zchaff fm) else None)) |
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parents:
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diff
changeset
|
405 |
end; |
14453 | 406 |
|
407 |
(* ------------------------------------------------------------------------- *) |
|
408 |
(* Add code for other SAT solvers below. *) |
|
409 |
(* ------------------------------------------------------------------------- *) |
|
410 |
||
411 |
(* |
|
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changeset
|
412 |
let |
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parents:
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diff
changeset
|
413 |
fun mysolver fm = ... |
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parents:
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diff
changeset
|
414 |
in |
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Installed solvers now determined at call time (as opposed to compile time)
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parents:
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diff
changeset
|
415 |
SatSolver.add_solver ("myname", (fn fm => if mysolver_is_installed then Some (mysolver fm) else None)); -- register the solver |
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parents:
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diff
changeset
|
416 |
end; |
14453 | 417 |
|
418 |
-- the solver is now available as SatSolver.invoke_solver "myname" |
|
419 |
*) |