(* Title: HOL/Tools/sat_solver.ML
ID: $Id$
Author: Tjark Weber
Copyright 2004-2006
Interface to external SAT solvers, and (simple) built-in SAT solvers.
*)
signature SAT_SOLVER =
sig
exception NOT_CONFIGURED
type assignment = int -> bool option
type proof = int list Inttab.table * int
datatype result = SATISFIABLE of assignment
| UNSATISFIABLE of proof option
| UNKNOWN
type solver = PropLogic.prop_formula -> result
(* auxiliary functions to create external SAT solvers *)
val write_dimacs_cnf_file : Path.T -> PropLogic.prop_formula -> unit
val write_dimacs_sat_file : Path.T -> PropLogic.prop_formula -> unit
val read_std_result_file : Path.T -> string * string * string -> result
val make_external_solver : string -> (PropLogic.prop_formula -> unit) -> (unit -> result) -> solver
val read_dimacs_cnf_file : Path.T -> PropLogic.prop_formula
(* generic solver interface *)
val solvers : (string * solver) list ref
val add_solver : string * solver -> unit
val invoke_solver : string -> solver (* exception Option *)
end;
structure SatSolver : SAT_SOLVER =
struct
open PropLogic;
(* ------------------------------------------------------------------------- *)
(* should be raised by an external SAT solver to indicate that the solver is *)
(* not configured properly *)
(* ------------------------------------------------------------------------- *)
exception NOT_CONFIGURED;
(* ------------------------------------------------------------------------- *)
(* type of partial (satisfying) assignments: 'a i = NONE' means that 'a' is *)
(* a satisfying assignment regardless of the value of variable 'i' *)
(* ------------------------------------------------------------------------- *)
type assignment = int -> bool option;
(* ------------------------------------------------------------------------- *)
(* a proof of unsatisfiability, to be interpreted as follows: each integer *)
(* is a clause ID, each list 'xs' stored under the key 'x' in the table *)
(* contains the IDs of clauses that must be resolved (in the given *)
(* order) to obtain the new clause 'x'. Each list 'xs' must be *)
(* non-empty, and the literal to be resolved upon must always be unique *)
(* (e.g. "A | ~B" must not be resolved with "~A | B"). Circular *)
(* dependencies of clauses are not allowed. (At least) one of the *)
(* clauses in the table must be the empty clause (i.e. contain no *)
(* literals); its ID is given by the second component of the proof. *)
(* The clauses of the original problem passed to the SAT solver have *)
(* consecutive IDs starting with 0. Clause IDs must be non-negative, *)
(* but do not need to be consecutive. *)
(* ------------------------------------------------------------------------- *)
type proof = int list Inttab.table * int;
(* ------------------------------------------------------------------------- *)
(* return type of SAT solvers: if the result is 'SATISFIABLE', a satisfying *)
(* assignment must be returned as well; if the result is *)
(* 'UNSATISFIABLE', a proof of unsatisfiability may be returned *)
(* ------------------------------------------------------------------------- *)
datatype result = SATISFIABLE of assignment
| UNSATISFIABLE of proof option
| UNKNOWN;
(* ------------------------------------------------------------------------- *)
(* type of SAT solvers: given a propositional formula, a satisfying *)
(* assignment may be returned *)
(* ------------------------------------------------------------------------- *)
type solver = prop_formula -> result;
(* ------------------------------------------------------------------------- *)
(* write_dimacs_cnf_file: serializes a formula 'fm' of propositional logic *)
(* to a file in DIMACS CNF format (see "Satisfiability Suggested *)
(* Format", May 8 1993, Section 2.1) *)
(* Note: 'fm' must not contain a variable index less than 1. *)
(* Note: 'fm' must be given in CNF. *)
(* ------------------------------------------------------------------------- *)
(* Path.T -> prop_formula -> unit *)
fun write_dimacs_cnf_file path fm =
let
(* prop_formula -> prop_formula *)
fun cnf_True_False_elim True =
Or (BoolVar 1, Not (BoolVar 1))
| cnf_True_False_elim False =
And (BoolVar 1, Not (BoolVar 1))
| cnf_True_False_elim fm =
fm (* since 'fm' is in CNF, either 'fm'='True'/'False', or 'fm' does not contain 'True'/'False' at all *)
(* prop_formula -> int *)
fun cnf_number_of_clauses (And (fm1,fm2)) =
(cnf_number_of_clauses fm1) + (cnf_number_of_clauses fm2)
| cnf_number_of_clauses _ =
1
(* prop_formula -> string list *)
fun cnf_string fm =
let
(* prop_formula -> string list -> string list *)
fun cnf_string_acc True acc =
error "formula is not in CNF"
| cnf_string_acc False acc =
error "formula is not in CNF"
| cnf_string_acc (BoolVar i) acc =
(i>=1 orelse error "formula contains a variable index less than 1";
string_of_int i :: acc)
| cnf_string_acc (Not (BoolVar i)) acc =
"-" :: cnf_string_acc (BoolVar i) acc
| cnf_string_acc (Not _) acc =
error "formula is not in CNF"
| cnf_string_acc (Or (fm1,fm2)) acc =
cnf_string_acc fm1 (" " :: cnf_string_acc fm2 acc)
| cnf_string_acc (And (fm1,fm2)) acc =
cnf_string_acc fm1 (" 0\n" :: cnf_string_acc fm2 acc)
in
cnf_string_acc fm []
end
val fm' = cnf_True_False_elim fm
val number_of_vars = maxidx fm'
val number_of_clauses = cnf_number_of_clauses fm'
in
File.write path
("c This file was generated by SatSolver.write_dimacs_cnf_file\n" ^
"p cnf " ^ string_of_int number_of_vars ^ " " ^ string_of_int number_of_clauses ^ "\n");
File.append_list path
(cnf_string fm');
File.append path
" 0\n"
end;
(* ------------------------------------------------------------------------- *)
(* write_dimacs_sat_file: serializes a formula 'fm' of propositional logic *)
(* to a file in DIMACS SAT format (see "Satisfiability Suggested *)
(* Format", May 8 1993, Section 2.2) *)
(* Note: 'fm' must not contain a variable index less than 1. *)
(* ------------------------------------------------------------------------- *)
(* Path.T -> prop_formula -> unit *)
fun write_dimacs_sat_file path fm =
let
(* prop_formula -> string list *)
fun sat_string fm =
let
(* prop_formula -> string list -> string list *)
fun sat_string_acc True acc =
"*()" :: acc
| sat_string_acc False acc =
"+()" :: acc
| sat_string_acc (BoolVar i) acc =
(i>=1 orelse error "formula contains a variable index less than 1";
string_of_int i :: acc)
| sat_string_acc (Not (BoolVar i)) acc =
"-" :: sat_string_acc (BoolVar i) acc
| sat_string_acc (Not fm) acc =
"-(" :: sat_string_acc fm (")" :: acc)
| sat_string_acc (Or (fm1,fm2)) acc =
"+(" :: sat_string_acc_or fm1 (" " :: sat_string_acc_or fm2 (")" :: acc))
| sat_string_acc (And (fm1,fm2)) acc =
"*(" :: sat_string_acc_and fm1 (" " :: sat_string_acc_and fm2 (")" :: acc))
(* optimization to make use of n-ary disjunction/conjunction *)
(* prop_formula -> string list -> string list *)
and sat_string_acc_or (Or (fm1,fm2)) acc =
sat_string_acc_or fm1 (" " :: sat_string_acc_or fm2 acc)
| sat_string_acc_or fm acc =
sat_string_acc fm acc
(* prop_formula -> string list -> string list *)
and sat_string_acc_and (And (fm1,fm2)) acc =
sat_string_acc_and fm1 (" " :: sat_string_acc_and fm2 acc)
| sat_string_acc_and fm acc =
sat_string_acc fm acc
in
sat_string_acc fm []
end
val number_of_vars = Int.max (maxidx fm, 1)
in
File.write path
("c This file was generated by SatSolver.write_dimacs_sat_file\n" ^
"p sat " ^ string_of_int number_of_vars ^ "\n" ^
"(");
File.append_list path
(sat_string fm);
File.append path
")\n"
end;
(* ------------------------------------------------------------------------- *)
(* read_std_result_file: scans a SAT solver's output file for a satisfying *)
(* variable assignment. Returns the assignment, or 'UNSATISFIABLE' if *)
(* the file contains 'unsatisfiable', or 'UNKNOWN' if the file contains *)
(* neither 'satisfiable' nor 'unsatisfiable'. Empty lines are ignored. *)
(* The assignment must be given in one or more lines immediately after *)
(* the line that contains 'satisfiable'. These lines must begin with *)
(* 'assignment_prefix'. Variables must be separated by " ". Non- *)
(* integer strings are ignored. If variable i is contained in the *)
(* assignment, then i is interpreted as 'true'. If ~i is contained in *)
(* the assignment, then i is interpreted as 'false'. Otherwise the *)
(* value of i is taken to be unspecified. *)
(* ------------------------------------------------------------------------- *)
(* Path.T -> string * string * string -> result *)
fun read_std_result_file path (satisfiable, assignment_prefix, unsatisfiable) =
let
(* string -> int list *)
fun int_list_from_string s =
List.mapPartial Int.fromString (space_explode " " s)
(* int list -> assignment *)
fun assignment_from_list [] i =
NONE (* the SAT solver didn't provide a value for this variable *)
| assignment_from_list (x::xs) i =
if x=i then (SOME true)
else if x=(~i) then (SOME false)
else assignment_from_list xs i
(* int list -> string list -> assignment *)
fun parse_assignment xs [] =
assignment_from_list xs
| parse_assignment xs (line::lines) =
if String.isPrefix assignment_prefix line then
parse_assignment (xs @ int_list_from_string line) lines
else
assignment_from_list xs
(* string -> string -> bool *)
fun is_substring needle haystack =
let
val length1 = String.size needle
val length2 = String.size haystack
in
if length2 < length1 then
false
else if needle = String.substring (haystack, 0, length1) then
true
else is_substring needle (String.substring (haystack, 1, length2-1))
end
(* string list -> result *)
fun parse_lines [] =
UNKNOWN
| parse_lines (line::lines) =
if is_substring unsatisfiable line then
UNSATISFIABLE NONE
else if is_substring satisfiable line then
SATISFIABLE (parse_assignment [] lines)
else
parse_lines lines
in
(parse_lines o (List.filter (fn l => l <> "")) o split_lines o File.read) path
end;
(* ------------------------------------------------------------------------- *)
(* make_external_solver: call 'writefn', execute 'cmd', call 'readfn' *)
(* ------------------------------------------------------------------------- *)
(* string -> (PropLogic.prop_formula -> unit) -> (unit -> result) -> solver *)
fun make_external_solver cmd writefn readfn fm =
(writefn fm; system cmd; readfn ());
(* ------------------------------------------------------------------------- *)
(* read_dimacs_cnf_file: returns a propositional formula that corresponds to *)
(* a SAT problem given in DIMACS CNF format *)
(* ------------------------------------------------------------------------- *)
(* Path.T -> PropLogic.prop_formula *)
fun read_dimacs_cnf_file path =
let
(* string list -> string list *)
fun filter_preamble [] =
error "problem line not found in DIMACS CNF file"
| filter_preamble (line::lines) =
if String.isPrefix "c " line orelse line = "c" then
(* ignore comments *)
filter_preamble lines
else if String.isPrefix "p " line then
(* ignore the problem line (which must be the last line of the preamble) *)
(* Ignoring the problem line implies that if the file contains more clauses *)
(* or variables than specified in its preamble, we will accept it anyway. *)
lines
else
error "preamble in DIMACS CNF file contains a line that does not begin with \"c \" or \"p \""
(* string -> int *)
fun int_from_string s =
case Int.fromString s of
SOME i => i
| NONE => error ("token " ^ quote s ^ "in DIMACS CNF file is not a number")
(* int list -> int list list *)
fun clauses xs =
let
val (xs1, xs2) = take_prefix (fn i => i <> 0) xs
in
case xs2 of
[] => [xs1]
| (0::[]) => [xs1]
| (0::tl) => xs1 :: clauses tl
| _ => sys_error "this cannot happen"
end
(* int -> PropLogic.prop_formula *)
fun literal_from_int i =
(i<>0 orelse error "variable index in DIMACS CNF file is 0";
if i>0 then
PropLogic.BoolVar i
else
PropLogic.Not (PropLogic.BoolVar (~i)))
(* PropLogic.prop_formula list -> PropLogic.prop_formula *)
fun disjunction [] =
error "empty clause in DIMACS CNF file"
| disjunction (x::xs) =
(case xs of
[] => x
| _ => PropLogic.Or (x, disjunction xs))
(* PropLogic.prop_formula list -> PropLogic.prop_formula *)
fun conjunction [] =
error "no clause in DIMACS CNF file"
| conjunction (x::xs) =
(case xs of
[] => x
| _ => PropLogic.And (x, conjunction xs))
in
(conjunction
o (map disjunction)
o (map (map literal_from_int))
o clauses
o (map int_from_string)
o List.concat
o (map (String.fields (fn c => c mem [#" ", #"\t", #"\n"])))
o filter_preamble
o (List.filter (fn l => l <> ""))
o split_lines
o File.read)
path
end;
(* ------------------------------------------------------------------------- *)
(* solvers: a (reference to a) table of all registered SAT solvers *)
(* ------------------------------------------------------------------------- *)
val solvers = ref ([] : (string * solver) list);
(* ------------------------------------------------------------------------- *)
(* add_solver: updates 'solvers' by adding a new solver *)
(* ------------------------------------------------------------------------- *)
(* string * solver -> unit *)
fun add_solver (name, new_solver) =
let
val the_solvers = !solvers;
val _ = if AList.defined (op =) the_solvers name
then warning ("SAT solver " ^ quote name ^ " was defined before")
else ();
in solvers := AList.update (op =) (name, new_solver) the_solvers end;
(* ------------------------------------------------------------------------- *)
(* invoke_solver: returns the solver associated with the given 'name' *)
(* Note: If no solver is associated with 'name', exception 'Option' will be *)
(* raised. *)
(* ------------------------------------------------------------------------- *)
(* string -> solver *)
fun invoke_solver name =
(the o AList.lookup (op =) (!solvers)) name;
end; (* SatSolver *)
(* ------------------------------------------------------------------------- *)
(* Predefined SAT solvers *)
(* ------------------------------------------------------------------------- *)
(* ------------------------------------------------------------------------- *)
(* Internal SAT solver, available as 'SatSolver.invoke_solver "enumerate"' *)
(* -- simply enumerates assignments until a satisfying assignment is found *)
(* ------------------------------------------------------------------------- *)
let
fun enum_solver fm =
let
(* int list *)
val indices = PropLogic.indices fm
(* int list -> int list -> int list option *)
(* binary increment: list 'xs' of current bits, list 'ys' of all bits (lower bits first) *)
fun next_list _ ([]:int list) =
NONE
| next_list [] (y::ys) =
SOME [y]
| next_list (x::xs) (y::ys) =
if x=y then
(* reset the bit, continue *)
next_list xs ys
else
(* set the lowest bit that wasn't set before, keep the higher bits *)
SOME (y::x::xs)
(* int list -> int -> bool *)
fun assignment_from_list xs i =
i mem xs
(* int list -> SatSolver.result *)
fun solver_loop xs =
if PropLogic.eval (assignment_from_list xs) fm then
SatSolver.SATISFIABLE (SOME o (assignment_from_list xs))
else
(case next_list xs indices of
SOME xs' => solver_loop xs'
| NONE => SatSolver.UNSATISFIABLE NONE)
in
(* start with the "first" assignment (all variables are interpreted as 'false') *)
solver_loop []
end
in
SatSolver.add_solver ("enumerate", enum_solver)
end;
(* ------------------------------------------------------------------------- *)
(* Internal SAT solver, available as 'SatSolver.invoke_solver "dpll"' -- a *)
(* simple implementation of the DPLL algorithm (cf. L. Zhang, S. Malik: "The *)
(* Quest for Efficient Boolean Satisfiability Solvers", July 2002, Fig. 1). *)
(* ------------------------------------------------------------------------- *)
let
local
open PropLogic
in
fun dpll_solver fm =
let
(* We could use 'PropLogic.defcnf fm' instead of 'PropLogic.nnf fm' *)
(* but that sometimes leads to worse performance due to the *)
(* introduction of additional variables. *)
val fm' = PropLogic.nnf fm
(* int list *)
val indices = PropLogic.indices fm'
(* int list -> int -> prop_formula *)
fun partial_var_eval [] i = BoolVar i
| partial_var_eval (x::xs) i = if x=i then True else if x=(~i) then False else partial_var_eval xs i
(* int list -> prop_formula -> prop_formula *)
fun partial_eval xs True = True
| partial_eval xs False = False
| partial_eval xs (BoolVar i) = partial_var_eval xs i
| partial_eval xs (Not fm) = SNot (partial_eval xs fm)
| partial_eval xs (Or (fm1, fm2)) = SOr (partial_eval xs fm1, partial_eval xs fm2)
| partial_eval xs (And (fm1, fm2)) = SAnd (partial_eval xs fm1, partial_eval xs fm2)
(* prop_formula -> int list *)
fun forced_vars True = []
| forced_vars False = []
| forced_vars (BoolVar i) = [i]
| forced_vars (Not (BoolVar i)) = [~i]
| forced_vars (Or (fm1, fm2)) = (forced_vars fm1) inter_int (forced_vars fm2)
| forced_vars (And (fm1, fm2)) = (forced_vars fm1) union_int (forced_vars fm2)
(* Above, i *and* ~i may be forced. In this case the first occurrence takes *)
(* precedence, and the next partial evaluation of the formula returns 'False'. *)
| forced_vars _ = error "formula is not in negation normal form"
(* int list -> prop_formula -> (int list * prop_formula) *)
fun eval_and_force xs fm =
let
val fm' = partial_eval xs fm
val xs' = forced_vars fm'
in
if null xs' then
(xs, fm')
else
eval_and_force (xs@xs') fm' (* xs and xs' should be distinct, so '@' here should have *)
(* the same effect as 'union_int' *)
end
(* int list -> int option *)
fun fresh_var xs =
Library.find_first (fn i => not (i mem_int xs) andalso not ((~i) mem_int xs)) indices
(* int list -> prop_formula -> int list option *)
(* partial assignment 'xs' *)
fun dpll xs fm =
let
val (xs', fm') = eval_and_force xs fm
in
case fm' of
True => SOME xs'
| False => NONE
| _ =>
let
val x = valOf (fresh_var xs') (* a fresh variable must exist since 'fm' did not evaluate to 'True'/'False' *)
in
case dpll (x::xs') fm' of (* passing fm' rather than fm should save some simplification work *)
SOME xs'' => SOME xs''
| NONE => dpll ((~x)::xs') fm' (* now try interpreting 'x' as 'False' *)
end
end
(* int list -> assignment *)
fun assignment_from_list [] i =
NONE (* the DPLL procedure didn't provide a value for this variable *)
| assignment_from_list (x::xs) i =
if x=i then (SOME true)
else if x=(~i) then (SOME false)
else assignment_from_list xs i
in
(* initially, no variable is interpreted yet *)
case dpll [] fm' of
SOME assignment => SatSolver.SATISFIABLE (assignment_from_list assignment)
| NONE => SatSolver.UNSATISFIABLE NONE
end
end (* local *)
in
SatSolver.add_solver ("dpll", dpll_solver)
end;
(* ------------------------------------------------------------------------- *)
(* Internal SAT solver, available as 'SatSolver.invoke_solver "auto"': uses *)
(* the last installed solver (other than "auto" itself) that does not raise *)
(* 'NOT_CONFIGURED'. (However, the solver may return 'UNKNOWN'.) *)
(* ------------------------------------------------------------------------- *)
let
fun auto_solver fm =
let
fun loop [] =
SatSolver.UNKNOWN
| loop ((name, solver)::solvers) =
if name="auto" then
(* do not call solver "auto" from within "auto" *)
loop solvers
else (
(if name="dpll" orelse name="enumerate" then
warning ("Using SAT solver " ^ quote name ^ "; for better performance, consider using an external solver.")
else
tracing ("Using SAT solver " ^ quote name ^ "."));
(* apply 'solver' to 'fm' *)
solver fm
handle SatSolver.NOT_CONFIGURED => loop solvers
)
in
loop (!SatSolver.solvers)
end
in
SatSolver.add_solver ("auto", auto_solver)
end;
(* ------------------------------------------------------------------------- *)
(* MiniSat 1.14 *)
(* (http://www.cs.chalmers.se/Cs/Research/FormalMethods/MiniSat/) *)
(* ------------------------------------------------------------------------- *)
(* ------------------------------------------------------------------------- *)
(* "minisat_with_proofs" requires a modified version of MiniSat 1.14 by John *)
(* Matthews, which can output ASCII proof traces. Replaying binary proof *)
(* traces generated by MiniSat-p_v1.14 has _not_ been implemented. *)
(* ------------------------------------------------------------------------- *)
(* add "minisat_with_proofs" _before_ "minisat" to the available solvers, so *)
(* that the latter is preferred by the "auto" solver *)
(* There is a complication that is dealt with in the code below: MiniSat *)
(* introduces IDs for original clauses in the proof trace. It does not (in *)
(* general) follow the convention that the original clauses are numbered *)
(* from 0 to n-1 (where n is the number of clauses in the formula). *)
let
exception INVALID_PROOF of string
fun minisat_with_proofs fm =
let
val _ = if (getenv "MINISAT_HOME") = "" then raise SatSolver.NOT_CONFIGURED else ()
val serial_str = serial_string ()
val inpath = File.tmp_path (Path.explode ("isabelle" ^ serial_str ^ ".cnf"))
val outpath = File.tmp_path (Path.explode ("result" ^ serial_str))
val proofpath = File.tmp_path (Path.explode ("result" ^ serial_str ^ ".prf"))
val cmd = (getenv "MINISAT_HOME") ^ "/minisat " ^ (Path.implode inpath) ^ " -r " ^ (Path.implode outpath) ^ " -t " ^ (Path.implode proofpath) ^ "> /dev/null"
fun writefn fm = SatSolver.write_dimacs_cnf_file inpath fm
fun readfn () = SatSolver.read_std_result_file outpath ("SAT", "", "UNSAT")
val _ = if File.exists inpath then warning ("overwriting existing file " ^ quote (Path.implode inpath)) else ()
val _ = if File.exists outpath then warning ("overwriting existing file " ^ quote (Path.implode outpath)) else ()
val cnf = PropLogic.defcnf fm
val result = SatSolver.make_external_solver cmd writefn readfn cnf
val _ = try File.rm inpath
val _ = try File.rm outpath
in case result of
SatSolver.UNSATISFIABLE NONE =>
(let
(* string list *)
val proof_lines = (split_lines o File.read) proofpath
handle IO.Io _ => raise INVALID_PROOF "Could not read file \"result.prf\""
(* representation of clauses as ordered lists of literals (with duplicates removed) *)
(* prop_formula -> int list *)
fun clause_to_lit_list (PropLogic.Or (fm1, fm2)) =
OrdList.union int_ord (clause_to_lit_list fm1) (clause_to_lit_list fm2)
| clause_to_lit_list (PropLogic.BoolVar i) =
[i]
| clause_to_lit_list (PropLogic.Not (PropLogic.BoolVar i)) =
[~i]
| clause_to_lit_list _ =
raise INVALID_PROOF "Error: invalid clause in CNF formula."
(* prop_formula -> int *)
fun cnf_number_of_clauses (PropLogic.And (fm1, fm2)) =
cnf_number_of_clauses fm1 + cnf_number_of_clauses fm2
| cnf_number_of_clauses _ =
1
val number_of_clauses = cnf_number_of_clauses cnf
(* int list array *)
val clauses = Array.array (number_of_clauses, [])
(* initialize the 'clauses' array *)
(* prop_formula * int -> int *)
fun init_array (PropLogic.And (fm1, fm2), n) =
init_array (fm2, init_array (fm1, n))
| init_array (fm, n) =
(Array.update (clauses, n, clause_to_lit_list fm); n+1)
val _ = init_array (cnf, 0)
(* optimization for the common case where MiniSat "R"s clauses in their *)
(* original order: *)
val last_ref_clause = ref (number_of_clauses - 1)
(* search the 'clauses' array for the given list of literals 'lits', *)
(* starting at index '!last_ref_clause + 1' *)
(* int list -> int option *)
fun original_clause_id lits =
let
fun original_clause_id_from index =
if index = number_of_clauses then
(* search from beginning again *)
original_clause_id_from 0
(* both 'lits' and the list of literals used in 'clauses' are sorted, so *)
(* testing for equality should suffice -- barring duplicate literals *)
else if Array.sub (clauses, index) = lits then (
(* success *)
last_ref_clause := index;
SOME index
) else if index = !last_ref_clause then
(* failure *)
NONE
else
(* continue search *)
original_clause_id_from (index + 1)
in
original_clause_id_from (!last_ref_clause + 1)
end
(* string -> int *)
fun int_from_string s = (
case Int.fromString s of
SOME i => i
| NONE => raise INVALID_PROOF ("File format error: number expected (" ^ quote s ^ " encountered).")
)
(* parse the proof file *)
val clause_table = ref (Inttab.empty : int list Inttab.table)
val empty_id = ref ~1
(* contains a mapping from clause IDs as used by MiniSat to clause IDs in *)
(* our proof format, where original clauses are numbered starting from 0 *)
val clause_id_map = ref (Inttab.empty : int Inttab.table)
fun sat_to_proof id = (
case Inttab.lookup (!clause_id_map) id of
SOME id' => id'
| NONE => raise INVALID_PROOF ("Clause ID " ^ Int.toString id ^ " used, but not defined.")
)
val next_id = ref (number_of_clauses - 1)
(* string list -> unit *)
fun process_tokens [] =
()
| process_tokens (tok::toks) =
if tok="R" then (
case toks of
id::sep::lits =>
let
val _ = if !empty_id = ~1 then () else raise INVALID_PROOF "File format error: \"R\" disallowed after \"X\"."
val cid = int_from_string id
val _ = if sep = "<=" then () else raise INVALID_PROOF ("File format error: \"<=\" expected (" ^ quote sep ^ " encountered).")
val ls = sort int_ord (map int_from_string lits)
val proof_id = case original_clause_id ls of
SOME orig_id => orig_id
| NONE => raise INVALID_PROOF ("Original clause (new ID is " ^ id ^ ") not found.")
in
(* extend the mapping of clause IDs with this newly defined ID *)
clause_id_map := Inttab.update_new (cid, proof_id) (!clause_id_map)
handle Inttab.DUP _ => raise INVALID_PROOF ("File format error: clause " ^ id ^ " defined more than once (in \"R\").")
(* the proof itself doesn't change *)
end
| _ =>
raise INVALID_PROOF "File format error: \"R\" followed by an insufficient number of tokens."
) else if tok="C" then (
case toks of
id::sep::ids =>
let
val _ = if !empty_id = ~1 then () else raise INVALID_PROOF "File format error: \"C\" disallowed after \"X\"."
val cid = int_from_string id
val _ = if sep = "<=" then () else raise INVALID_PROOF ("File format error: \"<=\" expected (" ^ quote sep ^ " encountered).")
(* ignore the pivot literals in MiniSat's trace *)
fun unevens [] = raise INVALID_PROOF "File format error: \"C\" followed by an even number of IDs."
| unevens (x :: []) = x :: []
| unevens (x :: _ :: xs) = x :: unevens xs
val rs = (map sat_to_proof o unevens o map int_from_string) ids
(* extend the mapping of clause IDs with this newly defined ID *)
val proof_id = inc next_id
val _ = clause_id_map := Inttab.update_new (cid, proof_id) (!clause_id_map)
handle Inttab.DUP _ => raise INVALID_PROOF ("File format error: clause " ^ id ^ " defined more than once (in \"C\").")
in
(* update clause table *)
clause_table := Inttab.update_new (proof_id, rs) (!clause_table)
handle Inttab.DUP _ => raise INVALID_PROOF ("Error: internal ID for clause " ^ id ^ " already used.")
end
| _ =>
raise INVALID_PROOF "File format error: \"C\" followed by an insufficient number of tokens."
) else if tok="D" then (
case toks of
[id] =>
let
val _ = if !empty_id = ~1 then () else raise INVALID_PROOF "File format error: \"D\" disallowed after \"X\"."
val _ = sat_to_proof (int_from_string id)
in
(* simply ignore "D" *)
()
end
| _ =>
raise INVALID_PROOF "File format error: \"D\" followed by an illegal number of tokens."
) else if tok="X" then (
case toks of
[id1, id2] =>
let
val _ = if !empty_id = ~1 then () else raise INVALID_PROOF "File format error: more than one end-of-proof statement."
val _ = sat_to_proof (int_from_string id1)
val new_empty_id = sat_to_proof (int_from_string id2)
in
(* update conflict id *)
empty_id := new_empty_id
end
| _ =>
raise INVALID_PROOF "File format error: \"X\" followed by an illegal number of tokens."
) else
raise INVALID_PROOF ("File format error: unknown token " ^ quote tok ^ " encountered.")
(* string list -> unit *)
fun process_lines [] =
()
| process_lines (l::ls) = (
process_tokens (String.tokens (fn c => c = #" " orelse c = #"\t") l);
process_lines ls
)
(* proof *)
val _ = process_lines proof_lines
val _ = if !empty_id <> ~1 then () else raise INVALID_PROOF "File format error: no conflicting clause specified."
in
SatSolver.UNSATISFIABLE (SOME (!clause_table, !empty_id))
end handle INVALID_PROOF reason => (warning reason; SatSolver.UNSATISFIABLE NONE))
| result =>
result
end
in
SatSolver.add_solver ("minisat_with_proofs", minisat_with_proofs)
end;
let
fun minisat fm =
let
val _ = if (getenv "MINISAT_HOME") = "" then raise SatSolver.NOT_CONFIGURED else ()
val serial_str = serial_string ()
val inpath = File.tmp_path (Path.explode ("isabelle" ^ serial_str ^ ".cnf"))
val outpath = File.tmp_path (Path.explode ("result" ^ serial_str))
val cmd = (getenv "MINISAT_HOME") ^ "/minisat " ^ (Path.implode inpath) ^ " -r " ^ (Path.implode outpath) ^ " > /dev/null"
fun writefn fm = SatSolver.write_dimacs_cnf_file inpath (PropLogic.defcnf fm)
fun readfn () = SatSolver.read_std_result_file outpath ("SAT", "", "UNSAT")
val _ = if File.exists inpath then warning ("overwriting existing file " ^ quote (Path.implode inpath)) else ()
val _ = if File.exists outpath then warning ("overwriting existing file " ^ quote (Path.implode outpath)) else ()
val result = SatSolver.make_external_solver cmd writefn readfn fm
val _ = try File.rm inpath
val _ = try File.rm outpath
in
result
end
in
SatSolver.add_solver ("minisat", minisat)
end;
(* ------------------------------------------------------------------------- *)
(* zChaff (http://www.princeton.edu/~chaff/zchaff.html) *)
(* ------------------------------------------------------------------------- *)
(* ------------------------------------------------------------------------- *)
(* 'zchaff_with_proofs' applies the "zchaff" prover to a formula, and if *)
(* zChaff finds that the formula is unsatisfiable, a proof of this is read *)
(* from a file "resolve_trace" that was generated by zChaff. See the code *)
(* below for the expected format of the "resolve_trace" file. Aside from *)
(* some basic syntactic checks, no verification of the proof is performed. *)
(* ------------------------------------------------------------------------- *)
(* add "zchaff_with_proofs" _before_ "zchaff" to the available solvers, so *)
(* that the latter is preferred by the "auto" solver *)
let
exception INVALID_PROOF of string
fun zchaff_with_proofs fm =
case SatSolver.invoke_solver "zchaff" fm of
SatSolver.UNSATISFIABLE NONE =>
(let
(* string list *)
val proof_lines = ((split_lines o File.read) (Path.explode "resolve_trace"))
handle IO.Io _ => raise INVALID_PROOF "Could not read file \"resolve_trace\""
(* PropLogic.prop_formula -> int *)
fun cnf_number_of_clauses (PropLogic.And (fm1, fm2)) = cnf_number_of_clauses fm1 + cnf_number_of_clauses fm2
| cnf_number_of_clauses _ = 1
(* string -> int *)
fun int_from_string s = (
case Int.fromString s of
SOME i => i
| NONE => raise INVALID_PROOF ("File format error: number expected (" ^ quote s ^ " encountered).")
)
(* parse the "resolve_trace" file *)
val clause_offset = ref ~1
val clause_table = ref (Inttab.empty : int list Inttab.table)
val empty_id = ref ~1
(* string list -> unit *)
fun process_tokens [] =
()
| process_tokens (tok::toks) =
if tok="CL:" then (
case toks of
id::sep::ids =>
let
val _ = if !clause_offset = ~1 then () else raise INVALID_PROOF ("File format error: \"CL:\" disallowed after \"VAR:\".")
val _ = if !empty_id = ~1 then () else raise INVALID_PROOF ("File format error: \"CL:\" disallowed after \"CONF:\".")
val cid = int_from_string id
val _ = if sep = "<=" then () else raise INVALID_PROOF ("File format error: \"<=\" expected (" ^ quote sep ^ " encountered).")
val rs = map int_from_string ids
in
(* update clause table *)
clause_table := Inttab.update_new (cid, rs) (!clause_table)
handle Inttab.DUP _ => raise INVALID_PROOF ("File format error: clause " ^ id ^ " defined more than once.")
end
| _ =>
raise INVALID_PROOF "File format error: \"CL:\" followed by an insufficient number of tokens."
) else if tok="VAR:" then (
case toks of
id::levsep::levid::valsep::valid::antesep::anteid::litsep::lits =>
let
val _ = if !empty_id = ~1 then () else raise INVALID_PROOF ("File format error: \"VAR:\" disallowed after \"CONF:\".")
(* set 'clause_offset' to the largest used clause ID *)
val _ = if !clause_offset = ~1 then clause_offset :=
(case Inttab.max_key (!clause_table) of
SOME id => id
| NONE => cnf_number_of_clauses (PropLogic.defcnf fm) - 1 (* the first clause ID is 0, not 1 *))
else
()
val vid = int_from_string id
val _ = if levsep = "L:" then () else raise INVALID_PROOF ("File format error: \"L:\" expected (" ^ quote levsep ^ " encountered).")
val _ = int_from_string levid
val _ = if valsep = "V:" then () else raise INVALID_PROOF ("File format error: \"V:\" expected (" ^ quote valsep ^ " encountered).")
val _ = int_from_string valid
val _ = if antesep = "A:" then () else raise INVALID_PROOF ("File format error: \"A:\" expected (" ^ quote antesep ^ " encountered).")
val aid = int_from_string anteid
val _ = if litsep = "Lits:" then () else raise INVALID_PROOF ("File format error: \"Lits:\" expected (" ^ quote litsep ^ " encountered).")
val ls = map int_from_string lits
(* convert the data provided by zChaff to our resolution-style proof format *)
(* each "VAR:" line defines a unit clause, the resolvents are implicitly *)
(* given by the literals in the antecedent clause *)
(* we use the sum of '!clause_offset' and the variable ID as clause ID for the unit clause *)
val cid = !clause_offset + vid
(* the low bit of each literal gives its sign (positive/negative), therefore *)
(* we have to divide each literal by 2 to obtain the proper variable ID; then *)
(* we add '!clause_offset' to obtain the ID of the corresponding unit clause *)
val vids = filter (not_equal vid) (map (fn l => l div 2) ls)
val rs = aid :: map (fn v => !clause_offset + v) vids
in
(* update clause table *)
clause_table := Inttab.update_new (cid, rs) (!clause_table)
handle Inttab.DUP _ => raise INVALID_PROOF ("File format error: clause " ^ string_of_int cid ^ " (derived from antecedent for variable " ^ id ^ ") already defined.")
end
| _ =>
raise INVALID_PROOF "File format error: \"VAR:\" followed by an insufficient number of tokens."
) else if tok="CONF:" then (
case toks of
id::sep::ids =>
let
val _ = if !empty_id = ~1 then () else raise INVALID_PROOF "File format error: more than one conflicting clause specified."
val cid = int_from_string id
val _ = if sep = "==" then () else raise INVALID_PROOF ("File format error: \"==\" expected (" ^ quote sep ^ " encountered).")
val ls = map int_from_string ids
(* the conflict clause must be resolved with the unit clauses *)
(* for its literals to obtain the empty clause *)
val vids = map (fn l => l div 2) ls
val rs = cid :: map (fn v => !clause_offset + v) vids
val new_empty_id = getOpt (Inttab.max_key (!clause_table), !clause_offset) + 1
in
(* update clause table and conflict id *)
clause_table := Inttab.update_new (new_empty_id, rs) (!clause_table)
handle Inttab.DUP _ => raise INVALID_PROOF ("File format error: clause " ^ string_of_int new_empty_id ^ " (empty clause derived from clause " ^ id ^ ") already defined.");
empty_id := new_empty_id
end
| _ =>
raise INVALID_PROOF "File format error: \"CONF:\" followed by an insufficient number of tokens."
) else
raise INVALID_PROOF ("File format error: unknown token " ^ quote tok ^ " encountered.")
(* string list -> unit *)
fun process_lines [] =
()
| process_lines (l::ls) = (
process_tokens (String.tokens (fn c => c = #" " orelse c = #"\t") l);
process_lines ls
)
(* proof *)
val _ = process_lines proof_lines
val _ = if !empty_id <> ~1 then () else raise INVALID_PROOF "File format error: no conflicting clause specified."
in
SatSolver.UNSATISFIABLE (SOME (!clause_table, !empty_id))
end handle INVALID_PROOF reason => (warning reason; SatSolver.UNSATISFIABLE NONE))
| result =>
result
in
SatSolver.add_solver ("zchaff_with_proofs", zchaff_with_proofs)
end;
let
fun zchaff fm =
let
val _ = if (getenv "ZCHAFF_HOME") = "" then raise SatSolver.NOT_CONFIGURED else ()
val serial_str = serial_string ()
val inpath = File.tmp_path (Path.explode ("isabelle" ^ serial_str ^ ".cnf"))
val outpath = File.tmp_path (Path.explode ("result" ^ serial_str))
val cmd = (getenv "ZCHAFF_HOME") ^ "/zchaff " ^ (Path.implode inpath) ^ " > " ^ (Path.implode outpath)
fun writefn fm = SatSolver.write_dimacs_cnf_file inpath (PropLogic.defcnf fm)
fun readfn () = SatSolver.read_std_result_file outpath ("Instance Satisfiable", "", "Instance Unsatisfiable")
val _ = if File.exists inpath then warning ("overwriting existing file " ^ quote (Path.implode inpath)) else ()
val _ = if File.exists outpath then warning ("overwriting existing file " ^ quote (Path.implode outpath)) else ()
val result = SatSolver.make_external_solver cmd writefn readfn fm
val _ = try File.rm inpath
val _ = try File.rm outpath
in
result
end
in
SatSolver.add_solver ("zchaff", zchaff)
end;
(* ------------------------------------------------------------------------- *)
(* BerkMin 561 (http://eigold.tripod.com/BerkMin.html) *)
(* ------------------------------------------------------------------------- *)
let
fun berkmin fm =
let
val _ = if (getenv "BERKMIN_HOME") = "" then raise SatSolver.NOT_CONFIGURED else ()
val serial_str = serial_string ()
val inpath = File.tmp_path (Path.explode ("isabelle" ^ serial_str ^ ".cnf"))
val outpath = File.tmp_path (Path.explode ("result" ^ serial_str))
val exec = getenv "BERKMIN_EXE"
val cmd = (getenv "BERKMIN_HOME") ^ "/" ^ (if exec = "" then "BerkMin561" else exec) ^ " " ^ (Path.implode inpath) ^ " > " ^ (Path.implode outpath)
fun writefn fm = SatSolver.write_dimacs_cnf_file inpath (PropLogic.defcnf fm)
fun readfn () = SatSolver.read_std_result_file outpath ("Satisfiable !!", "solution =", "UNSATISFIABLE !!")
val _ = if File.exists inpath then warning ("overwriting existing file " ^ quote (Path.implode inpath)) else ()
val _ = if File.exists outpath then warning ("overwriting existing file " ^ quote (Path.implode outpath)) else ()
val result = SatSolver.make_external_solver cmd writefn readfn fm
val _ = try File.rm inpath
val _ = try File.rm outpath
in
result
end
in
SatSolver.add_solver ("berkmin", berkmin)
end;
(* ------------------------------------------------------------------------- *)
(* Jerusat 1.3 (http://www.cs.tau.ac.il/~ale1/) *)
(* ------------------------------------------------------------------------- *)
let
fun jerusat fm =
let
val _ = if (getenv "JERUSAT_HOME") = "" then raise SatSolver.NOT_CONFIGURED else ()
val serial_str = serial_string ()
val inpath = File.tmp_path (Path.explode ("isabelle" ^ serial_str ^ ".cnf"))
val outpath = File.tmp_path (Path.explode ("result" ^ serial_str))
val cmd = (getenv "JERUSAT_HOME") ^ "/Jerusat1.3 " ^ (Path.implode inpath) ^ " > " ^ (Path.implode outpath)
fun writefn fm = SatSolver.write_dimacs_cnf_file inpath (PropLogic.defcnf fm)
fun readfn () = SatSolver.read_std_result_file outpath ("s SATISFIABLE", "v ", "s UNSATISFIABLE")
val _ = if File.exists inpath then warning ("overwriting existing file " ^ quote (Path.implode inpath)) else ()
val _ = if File.exists outpath then warning ("overwriting existing file " ^ quote (Path.implode outpath)) else ()
val result = SatSolver.make_external_solver cmd writefn readfn fm
val _ = try File.rm inpath
val _ = try File.rm outpath
in
result
end
in
SatSolver.add_solver ("jerusat", jerusat)
end;
(* ------------------------------------------------------------------------- *)
(* Add code for other SAT solvers below. *)
(* ------------------------------------------------------------------------- *)
(*
let
fun mysolver fm = ...
in
SatSolver.add_solver ("myname", (fn fm => if mysolver_is_configured then mysolver fm else raise SatSolver.NOT_CONFIGURED)); -- register the solver
end;
-- the solver is now available as SatSolver.invoke_solver "myname"
*)