(* Title: HOL/Tools/sat_solver.ML
Author: Tjark Weber
Copyright 2004-2009
Interface to external SAT solvers, and (simple) built-in SAT solvers.
Relevant Isabelle environment settings:
# MiniSat 1.14
#MINISAT_HOME=/usr/local/bin
# zChaff
#ZCHAFF_HOME=/usr/local/bin
# BerkMin561
#BERKMIN_HOME=/usr/local/bin
#BERKMIN_EXE=BerkMin561-linux
#BERKMIN_EXE=BerkMin561-solaris
# Jerusat 1.3
#JERUSAT_HOME=/usr/local/bin
*)
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 = Prop_Logic.prop_formula -> result
(* auxiliary functions to create external SAT solvers *)
val write_dimacs_cnf_file : Path.T -> Prop_Logic.prop_formula -> unit
val write_dimacs_sat_file : Path.T -> Prop_Logic.prop_formula -> unit
val read_std_result_file : Path.T -> string * string * string -> result
val make_external_solver : string -> (Prop_Logic.prop_formula -> unit) ->
(unit -> result) -> solver
val read_dimacs_cnf_file : Path.T -> Prop_Logic.prop_formula
(* generic solver interface *)
val get_solvers : unit -> (string * solver) list
val add_solver : string * solver -> unit
val invoke_solver : string -> solver (* exception Option *)
end;
structure SAT_Solver : SAT_SOLVER =
struct
open Prop_Logic;
(* ------------------------------------------------------------------------- *)
(* 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. *)
(* ------------------------------------------------------------------------- *)
fun write_dimacs_cnf_file path fm =
let
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 *)
fun cnf_number_of_clauses (And (fm1, fm2)) =
(cnf_number_of_clauses fm1) + (cnf_number_of_clauses fm2)
| cnf_number_of_clauses _ =
1
fun write_cnf_file out =
let
fun write_formula True =
error "formula is not in CNF"
| write_formula False =
error "formula is not in CNF"
| write_formula (BoolVar i) =
(i>=1 orelse error "formula contains a variable index less than 1";
File.output out (string_of_int i))
| write_formula (Not (BoolVar i)) =
(File.output out "-";
write_formula (BoolVar i))
| write_formula (Not _) =
error "formula is not in CNF"
| write_formula (Or (fm1, fm2)) =
(write_formula fm1;
File.output out " ";
write_formula fm2)
| write_formula (And (fm1, fm2)) =
(write_formula fm1;
File.output out " 0\n";
write_formula fm2)
val fm' = cnf_True_False_elim fm
val number_of_vars = maxidx fm'
val number_of_clauses = cnf_number_of_clauses fm'
in
File.output out "c This file was generated by SAT_Solver.write_dimacs_cnf_file\n";
File.output out ("p cnf " ^ string_of_int number_of_vars ^ " " ^
string_of_int number_of_clauses ^ "\n");
write_formula fm';
File.output out " 0\n"
end
in
File.open_output write_cnf_file path
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. *)
(* ------------------------------------------------------------------------- *)
fun write_dimacs_sat_file path fm =
let
fun write_sat_file out =
let
fun write_formula True =
File.output out "*()"
| write_formula False =
File.output out "+()"
| write_formula (BoolVar i) =
(i>=1 orelse error "formula contains a variable index less than 1";
File.output out (string_of_int i))
| write_formula (Not (BoolVar i)) =
(File.output out "-";
write_formula (BoolVar i))
| write_formula (Not fm) =
(File.output out "-(";
write_formula fm;
File.output out ")")
| write_formula (Or (fm1, fm2)) =
(File.output out "+(";
write_formula_or fm1;
File.output out " ";
write_formula_or fm2;
File.output out ")")
| write_formula (And (fm1, fm2)) =
(File.output out "*(";
write_formula_and fm1;
File.output out " ";
write_formula_and fm2;
File.output out ")")
(* optimization to make use of n-ary disjunction/conjunction *)
and write_formula_or (Or (fm1, fm2)) =
(write_formula_or fm1;
File.output out " ";
write_formula_or fm2)
| write_formula_or fm =
write_formula fm
and write_formula_and (And (fm1, fm2)) =
(write_formula_and fm1;
File.output out " ";
write_formula_and fm2)
| write_formula_and fm =
write_formula fm
val number_of_vars = Int.max (maxidx fm, 1)
in
File.output out "c This file was generated by SAT_Solver.write_dimacs_sat_file\n";
File.output out ("p sat " ^ string_of_int number_of_vars ^ "\n");
File.output out "(";
write_formula fm;
File.output out ")\n"
end
in
File.open_output write_sat_file path
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. *)
(* ------------------------------------------------------------------------- *)
fun read_std_result_file path (satisfiable, assignment_prefix, unsatisfiable) =
let
fun int_list_from_string s =
map_filter Int.fromString (space_explode " " s)
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
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
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
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 filter (fn l => l <> "") o split_lines o File.read) path
end;
(* ------------------------------------------------------------------------- *)
(* make_external_solver: call 'writefn', execute 'cmd', call 'readfn' *)
(* ------------------------------------------------------------------------- *)
fun make_external_solver cmd writefn readfn fm =
(writefn fm; Isabelle_System.bash cmd; readfn ());
(* ------------------------------------------------------------------------- *)
(* read_dimacs_cnf_file: returns a propositional formula that corresponds to *)
(* a SAT problem given in DIMACS CNF format *)
(* ------------------------------------------------------------------------- *)
fun read_dimacs_cnf_file path =
let
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 \""
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")
fun clauses xs =
let
val (xs1, xs2) = chop_prefix (fn i => i <> 0) xs
in
case xs2 of
[] => [xs1]
| (0::[]) => [xs1]
| (0::tl) => xs1 :: clauses tl
| _ => raise Fail "SAT_Solver.clauses"
end
fun literal_from_int i =
(i<>0 orelse error "variable index in DIMACS CNF file is 0";
if i>0 then
Prop_Logic.BoolVar i
else
Prop_Logic.Not (Prop_Logic.BoolVar (~i)))
fun disjunction [] =
error "empty clause in DIMACS CNF file"
| disjunction (x::xs) =
(case xs of
[] => x
| _ => Prop_Logic.Or (x, disjunction xs))
fun conjunction [] =
error "no clause in DIMACS CNF file"
| conjunction (x::xs) =
(case xs of
[] => x
| _ => Prop_Logic.And (x, conjunction xs))
in
(conjunction
o (map disjunction)
o (map (map literal_from_int))
o clauses
o (map int_from_string)
o (maps (String.tokens (member (op =) [#" ", #"\t", #"\n"])))
o filter_preamble
o filter (fn l => l <> "")
o split_lines
o File.read)
path
end;
(* ------------------------------------------------------------------------- *)
(* solvers: a table of all registered SAT solvers *)
(* ------------------------------------------------------------------------- *)
val solvers = Synchronized.var "solvers" ([] : (string * solver) list);
fun get_solvers () = Synchronized.value solvers;
(* ------------------------------------------------------------------------- *)
(* add_solver: updates 'solvers' by adding a new solver *)
(* ------------------------------------------------------------------------- *)
fun add_solver (name, new_solver) =
Synchronized.change solvers (fn the_solvers =>
let
val _ = if AList.defined (op =) the_solvers name
then warning ("SAT solver " ^ quote name ^ " was defined before")
else ();
in 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. *)
(* ------------------------------------------------------------------------- *)
fun invoke_solver name =
the (AList.lookup (op =) (get_solvers ()) name);
end; (* SAT_Solver *)
(* ------------------------------------------------------------------------- *)
(* Predefined SAT solvers *)
(* ------------------------------------------------------------------------- *)
(* ------------------------------------------------------------------------- *)
(* Internal SAT solver, available as 'SAT_Solver.invoke_solver "cdclite"' -- *)
(* a simplified implementation of the conflict-driven clause-learning *)
(* algorithm (cf. L. Zhang, S. Malik: "The Quest for Efficient Boolean *)
(* Satisfiability Solvers", July 2002, Fig. 2). This solver produces models *)
(* and proof traces. *)
(* ------------------------------------------------------------------------- *)
let
type clause = int list * int
type value = bool option
datatype reason = Decided | Implied of clause | Level0 of int
type variable = bool option * reason * int * int
type proofs = int * int list Inttab.table
type state =
int * int list * variable Inttab.table * clause list Inttab.table * proofs
exception CONFLICT of clause * state
exception UNSAT of clause * state
fun neg i = ~i
fun lit_value lit value = if lit > 0 then value else Option.map not value
fun var_of vars lit: variable = the (Inttab.lookup vars (abs lit))
fun value_of vars lit = lit_value lit (#1 (var_of vars lit))
fun reason_of vars lit = #2 (var_of vars lit)
fun level_of vars lit = #3 (var_of vars lit)
fun is_true vars lit = (value_of vars lit = SOME true)
fun is_false vars lit = (value_of vars lit = SOME false)
fun is_unassigned vars lit = (value_of vars lit = NONE)
fun assignment_of vars lit = the_default NONE (try (value_of vars) lit)
fun put_var value reason level (_, _, _, rank) = (value, reason, level, rank)
fun incr_rank (value, reason, level, rank) = (value, reason, level, rank + 1)
fun update_var lit f = Inttab.map_entry (abs lit) f
fun add_var lit = Inttab.update (abs lit, (NONE, Decided, ~1, 0))
fun assign lit r l = update_var lit (put_var (SOME (lit > 0)) r l)
fun unassign lit = update_var lit (put_var NONE Decided ~1)
fun add_proof [] (idx, ptab) = (idx, (idx + 1, ptab))
| add_proof ps (idx, ptab) = (idx, (idx + 1, Inttab.update (idx, ps) ptab))
fun level0_proof_of (Level0 idx) = SOME idx
| level0_proof_of _ = NONE
fun level0_proofs_of vars = map_filter (level0_proof_of o reason_of vars)
fun prems_of vars (lits, p) = p :: level0_proofs_of vars lits
fun mk_proof vars cls proofs = add_proof (prems_of vars cls) proofs
fun push lit cls (level, trail, vars, clss, proofs) =
let
val (reason, proofs) =
if level = 0 then apfst Level0 (mk_proof vars cls proofs)
else (Implied cls, proofs)
in (level, lit :: trail, assign lit reason level vars, clss, proofs) end
fun push_decided lit (level, trail, vars, clss, proofs) =
let val vars' = assign lit Decided (level + 1) vars
in (level + 1, lit :: 0 :: trail, vars', clss, proofs) end
fun prop (cls as (lits, _)) (cx as (units, state as (level, _, vars, _, _))) =
if exists (is_true vars) lits then cx
else if forall (is_false vars) lits then
if level = 0 then raise UNSAT (cls, state)
else raise CONFLICT (cls, state)
else
(case filter (is_unassigned vars) lits of
[lit] => (lit :: units, push lit cls state)
| _ => cx)
fun propagate units (state as (_, _, _, clss, _)) =
(case fold (fold prop o Inttab.lookup_list clss) units ([], state) of
([], state') => (NONE, state')
| (units', state') => propagate units' state')
handle CONFLICT (cls, state') => (SOME cls, state')
fun max_unassigned (v, (NONE, _, _, rank)) (x as (_, r)) =
if rank > r then (SOME v, rank) else x
| max_unassigned _ x = x
fun decide (state as (_, _, vars, _, _)) =
(case Inttab.fold max_unassigned vars (NONE, 0) of
(SOME lit, _) => SOME (lit, push_decided lit state)
| (NONE, _) => NONE)
fun mark lit = Inttab.update (abs lit, true)
fun marked ms lit = the_default false (Inttab.lookup ms (abs lit))
fun ignore l ms lit = ((lit = l) orelse marked ms lit)
fun first_lit _ [] = raise Empty
| first_lit _ (0 :: _) = raise Empty
| first_lit pred (lit :: lits) =
if pred lit then (lit, lits) else first_lit pred lits
fun reason_cls_of vars lit =
(case reason_of vars lit of
Implied cls => cls
| _ => raise Option)
fun analyze conflicting_cls (level, trail, vars, _, _) =
let
fun back i lit (lits, p) trail ms ls ps =
let
val (lits0, lits') = List.partition (equal 0 o level_of vars) lits
val lits1 = filter_out (ignore lit ms) lits'
val lits2 = filter_out (equal level o level_of vars) lits1
val i' = length lits1 - length lits2 + i
val ms' = fold mark lits1 ms
val ls' = lits2 @ ls
val ps' = level0_proofs_of vars lits0 @ (p :: ps)
val (lit', trail') = first_lit (marked ms') trail
in
if i' = 1 then (neg lit', ls', rev ps')
else back (i' - 1) lit' (reason_cls_of vars lit') trail' ms' ls' ps'
end
in back 0 0 conflicting_cls trail Inttab.empty [] [] end
fun keep_clause (cls as (lits, _)) (level, trail, vars, clss, proofs) =
let
val vars' = fold (fn lit => update_var lit incr_rank) lits vars
val clss' = fold (fn lit => Inttab.cons_list (neg lit, cls)) lits clss
in (level, trail, vars', clss', proofs) end
fun learn (cls as (lits, _)) = (length lits <= 2) ? keep_clause cls
fun backjump _ (state as (_, [], _, _, _)) = state
| backjump i (level, 0 :: trail, vars, clss, proofs) =
(level - 1, trail, vars, clss, proofs) |> (i > 1) ? backjump (i - 1)
| backjump i (level, lit :: trail, vars, clss, proofs) =
backjump i (level, trail, unassign lit vars, clss, proofs)
fun search units state =
(case propagate units state of
(NONE, state' as (_, _, vars, _, _)) =>
(case decide state' of
NONE => SAT_Solver.SATISFIABLE (assignment_of vars)
| SOME (lit, state'') => search [lit] state'')
| (SOME conflicting_cls, state' as (level, trail, vars, clss, proofs)) =>
let
val (lit, lits, ps) = analyze conflicting_cls state'
val (idx, proofs') = add_proof ps proofs
val cls = (lit :: lits, idx)
in
(level, trail, vars, clss, proofs')
|> backjump (level - fold (Integer.max o level_of vars) lits 0)
|> learn cls
|> push lit cls
|> search [lit]
end)
fun has_opposing_lits [] = false
| has_opposing_lits (lit :: lits) =
member (op =) lits (neg lit) orelse has_opposing_lits lits
fun add_clause (cls as ([_], _)) (units, state) =
let val (units', state') = prop cls (units, state)
in (units', state') end
| add_clause (cls as (lits, _)) (cx as (units, state)) =
if has_opposing_lits lits then cx
else (units, keep_clause cls state)
fun mk_clause lits proofs =
apfst (pair (distinct (op =) lits)) (add_proof [] proofs)
fun solve litss =
let
val (clss, proofs) = fold_map mk_clause litss (0, Inttab.empty)
val vars = fold (fold add_var) litss Inttab.empty
val state = (0, [], vars, Inttab.empty, proofs)
in uncurry search (fold add_clause clss ([], state)) end
handle UNSAT (conflicting_cls, (_, _, vars, _, proofs)) =>
let val (idx, (_, ptab)) = mk_proof vars conflicting_cls proofs
in SAT_Solver.UNSATISFIABLE (SOME (ptab, idx)) end
fun variable_of (Prop_Logic.BoolVar 0) = error "bad propositional variable"
| variable_of (Prop_Logic.BoolVar i) = i
| variable_of _ = error "expected formula in CNF"
fun literal_of (Prop_Logic.Not fm) = neg (variable_of fm)
| literal_of fm = variable_of fm
fun clause_of (Prop_Logic.Or (fm1, fm2)) = clause_of fm1 @ clause_of fm2
| clause_of fm = [literal_of fm]
fun clauses_of (Prop_Logic.And (fm1, fm2)) = clauses_of fm1 @ clauses_of fm2
| clauses_of Prop_Logic.True = [[1, ~1]]
| clauses_of Prop_Logic.False = [[1], [~1]]
| clauses_of fm = [clause_of fm]
fun dpll_solver fm =
let val fm' = if Prop_Logic.is_cnf fm then fm else Prop_Logic.defcnf fm
in solve (clauses_of fm') end
in
SAT_Solver.add_solver ("cdclite", dpll_solver)
end;
(* ------------------------------------------------------------------------- *)
(* Internal SAT solver, available as 'SAT_Solver.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 [] =
SAT_Solver.UNKNOWN
| loop ((name, solver)::solvers) =
if name="auto" then
(* do not call solver "auto" from within "auto" *)
loop solvers
else (
(* apply 'solver' to 'fm' *)
solver fm
handle SAT_Solver.NOT_CONFIGURED => loop solvers
)
in
loop (SAT_Solver.get_solvers ())
end
in
SAT_Solver.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 SAT_Solver.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 = "\"$MINISAT_HOME/minisat\" " ^ File.bash_path inpath ^ " -r " ^ File.bash_path outpath ^ " -t " ^ File.bash_path proofpath ^ "> /dev/null"
fun writefn fm = SAT_Solver.write_dimacs_cnf_file inpath fm
fun readfn () = SAT_Solver.read_std_result_file outpath ("SAT", "", "UNSAT")
val _ = if File.exists inpath then warning ("overwriting existing file " ^ Path.print inpath) else ()
val _ = if File.exists outpath then warning ("overwriting existing file " ^ Path.print outpath) else ()
val cnf = Prop_Logic.defcnf fm
val result = SAT_Solver.make_external_solver cmd writefn readfn cnf
val _ = try File.rm inpath
val _ = try File.rm outpath
in case result of
SAT_Solver.UNSATISFIABLE NONE =>
(let
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) *)
fun clause_to_lit_list (Prop_Logic.Or (fm1, fm2)) =
Ord_List.union int_ord (clause_to_lit_list fm1) (clause_to_lit_list fm2)
| clause_to_lit_list (Prop_Logic.BoolVar i) =
[i]
| clause_to_lit_list (Prop_Logic.Not (Prop_Logic.BoolVar i)) =
[~i]
| clause_to_lit_list _ =
raise INVALID_PROOF "Error: invalid clause in CNF formula."
fun cnf_number_of_clauses (Prop_Logic.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 *)
fun init_array (Prop_Logic.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 = Unsynchronized.ref (number_of_clauses - 1)
(* search the 'clauses' array for the given list of literals 'lits', *)
(* starting at index '!last_ref_clause + 1' *)
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
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 = Unsynchronized.ref (Inttab.empty : int list Inttab.table)
val empty_id = Unsynchronized.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 = Unsynchronized.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 " ^ string_of_int id ^ " used, but not defined.")
)
val next_id = Unsynchronized.ref (number_of_clauses - 1)
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 = Unsynchronized.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.")
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
SAT_Solver.UNSATISFIABLE (SOME (!clause_table, !empty_id))
end handle INVALID_PROOF reason => (warning reason; SAT_Solver.UNSATISFIABLE NONE))
| result =>
result
end
in
SAT_Solver.add_solver ("minisat_with_proofs", minisat_with_proofs)
end;
let
fun minisat fm =
let
val _ = if getenv "MINISAT_HOME" = "" then raise SAT_Solver.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 = "\"$MINISAT_HOME/minisat\" " ^ File.bash_path inpath ^ " -r " ^ File.bash_path outpath ^ " > /dev/null"
fun writefn fm = SAT_Solver.write_dimacs_cnf_file inpath (Prop_Logic.defcnf fm)
fun readfn () = SAT_Solver.read_std_result_file outpath ("SAT", "", "UNSAT")
val _ = if File.exists inpath then warning ("overwriting existing file " ^ Path.print inpath) else ()
val _ = if File.exists outpath then warning ("overwriting existing file " ^ Path.print outpath) else ()
val result = SAT_Solver.make_external_solver cmd writefn readfn fm
val _ = try File.rm inpath
val _ = try File.rm outpath
in
result
end
in
SAT_Solver.add_solver ("minisat", minisat)
end;
(* ------------------------------------------------------------------------- *)
(* zChaff (https://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 SAT_Solver.invoke_solver "zchaff" fm of
SAT_Solver.UNSATISFIABLE NONE =>
(let
(* FIXME File.tmp_path (!?) *)
val proof_lines = ((split_lines o File.read) (Path.explode "resolve_trace"))
handle IO.Io _ => raise INVALID_PROOF "Could not read file \"resolve_trace\""
fun cnf_number_of_clauses (Prop_Logic.And (fm1, fm2)) =
cnf_number_of_clauses fm1 + cnf_number_of_clauses fm2
| cnf_number_of_clauses _ = 1
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 = Unsynchronized.ref ~1
val clause_table = Unsynchronized.ref (Inttab.empty : int list Inttab.table)
val empty_id = Unsynchronized.ref ~1
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 (!clause_table) of
SOME (id, _) => id
| NONE => cnf_number_of_clauses (Prop_Logic.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 = the_default (!clause_offset) (Option.map fst (Inttab.max (!clause_table))) + 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.")
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
SAT_Solver.UNSATISFIABLE (SOME (!clause_table, !empty_id))
end handle INVALID_PROOF reason => (warning reason; SAT_Solver.UNSATISFIABLE NONE))
| result =>
result
in
SAT_Solver.add_solver ("zchaff_with_proofs", zchaff_with_proofs)
end;
let
fun zchaff fm =
let
val _ = if getenv "ZCHAFF_HOME" = "" then raise SAT_Solver.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 = "\"$ZCHAFF_HOME/zchaff\" " ^ File.bash_path inpath ^ " > " ^ File.bash_path outpath
fun writefn fm = SAT_Solver.write_dimacs_cnf_file inpath (Prop_Logic.defcnf fm)
fun readfn () = SAT_Solver.read_std_result_file outpath ("Instance Satisfiable", "", "Instance Unsatisfiable")
val _ = if File.exists inpath then warning ("overwriting existing file " ^ Path.print inpath) else ()
val _ = if File.exists outpath then warning ("overwriting existing file " ^ Path.print outpath) else ()
val result = SAT_Solver.make_external_solver cmd writefn readfn fm
val _ = try File.rm inpath
val _ = try File.rm outpath
in
result
end
in
SAT_Solver.add_solver ("zchaff", zchaff)
end;
(* ------------------------------------------------------------------------- *)
(* BerkMin 561 (http://eigold.tripod.com/BerkMin.html) *)
(* ------------------------------------------------------------------------- *)
let
fun berkmin fm =
let
val _ = if (getenv "BERKMIN_HOME") = "" then raise SAT_Solver.NOT_CONFIGURED else ()
val serial_str = serial_string ()
val inpath = File.tmp_path (Path.explode ("isabelle" ^ serial_str ^ ".cnf"))
val outpath = File.tmp_path (Path.explode ("result" ^ serial_str))
val cmd = "\"$BERKMIN_HOME/${BERKMIN_EXE:-BerkMin561}\" " ^ File.bash_path inpath ^ " > " ^ File.bash_path outpath
fun writefn fm = SAT_Solver.write_dimacs_cnf_file inpath (Prop_Logic.defcnf fm)
fun readfn () = SAT_Solver.read_std_result_file outpath ("Satisfiable !!", "solution =", "UNSATISFIABLE !!")
val _ = if File.exists inpath then warning ("overwriting existing file " ^ Path.print inpath) else ()
val _ = if File.exists outpath then warning ("overwriting existing file " ^ Path.print outpath) else ()
val result = SAT_Solver.make_external_solver cmd writefn readfn fm
val _ = try File.rm inpath
val _ = try File.rm outpath
in
result
end
in
SAT_Solver.add_solver ("berkmin", berkmin)
end;
(* ------------------------------------------------------------------------- *)
(* Jerusat 1.3 (http://www.cs.tau.ac.il/~ale1/) *)
(* ------------------------------------------------------------------------- *)
let
fun jerusat fm =
let
val _ = if (getenv "JERUSAT_HOME") = "" then raise SAT_Solver.NOT_CONFIGURED else ()
val serial_str = serial_string ()
val inpath = File.tmp_path (Path.explode ("isabelle" ^ serial_str ^ ".cnf"))
val outpath = File.tmp_path (Path.explode ("result" ^ serial_str))
val cmd = "\"$JERUSAT_HOME/Jerusat1.3\" " ^ File.bash_path inpath ^ " > " ^ File.bash_path outpath
fun writefn fm = SAT_Solver.write_dimacs_cnf_file inpath (Prop_Logic.defcnf fm)
fun readfn () = SAT_Solver.read_std_result_file outpath ("s SATISFIABLE", "v ", "s UNSATISFIABLE")
val _ = if File.exists inpath then warning ("overwriting existing file " ^ Path.print inpath) else ()
val _ = if File.exists outpath then warning ("overwriting existing file " ^ Path.print outpath) else ()
val result = SAT_Solver.make_external_solver cmd writefn readfn fm
val _ = try File.rm inpath
val _ = try File.rm outpath
in
result
end
in
SAT_Solver.add_solver ("jerusat", jerusat)
end;
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