(*  Title:      HOL/Tools/sat_solver.ML

    ID:         $Id$

    Author:     Tjark Weber

    Copyright   2004

Interface to external SAT solvers, and (simple) built-in SAT solvers.

*)

signature SAT_SOLVER =

sig

	exception NOT_CONFIGURED

	type assignment = int -> bool option

	datatype result = SATISFIABLE of assignment

	                | UNSATISFIABLE

	                | 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 parse_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 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 assigment regardless of the value of variable 'i'       *)

(* ------------------------------------------------------------------------- *)

	type assignment = int -> bool option;

(* ------------------------------------------------------------------------- *)

(* return type of SAT solvers: if the result is 'SATISFIABLE', a satisfying  *)

(*      assignment must be returned as well                                  *)

(* ------------------------------------------------------------------------- *)

	datatype result = SATISFIABLE of assignment

	                | UNSATISFIABLE

	                | 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 *)

		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 =

				(assert (i>=1) "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

			concat (cnf_string_acc fm [])

		end

	in

		File.write path

			(let

				val fm'               = cnf_True_False_elim fm

				val number_of_vars    = maxidx fm'

				val number_of_clauses = cnf_number_of_clauses fm'

			in

				"c This file was generated by SatSolver.write_dimacs_cnf_file\n" ^

				"c (c) Tjark Weber\n" ^

				"p cnf " ^ string_of_int number_of_vars ^ " " ^ string_of_int number_of_clauses ^ "\n" ^

				cnf_string fm' ^ " 0\n"

			end)

	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 *)

		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 =

				(assert (i>=1) "formula contains a variable index less than 1";

				string_of_int i :: acc)

			  | sat_string_acc (Not fm) acc =

				"-(" :: sat_string_acc fm (")" :: acc)

			  | sat_string_acc (Or (fm1,fm2)) acc =

				"+(" :: sat_string_acc fm1 (" " :: sat_string_acc fm2 (")" :: acc))

			  | sat_string_acc (And (fm1,fm2)) acc =

				"*(" :: sat_string_acc fm1 (" " :: sat_string_acc fm2 (")" :: acc))

		in

			concat (sat_string_acc fm [])

		end

	in

		File.write path

			(let

				val number_of_vars = Int.max (maxidx fm, 1)

			in

				"c This file was generated by SatSolver.write_dimacs_sat_file\n" ^

				"c (c) Tjark Weber\n" ^

				"p sat " ^ string_of_int number_of_vars ^ "\n" ^

				"(" ^ sat_string fm ^ ")\n"

			end)

	end;

(* ------------------------------------------------------------------------- *)

(* parse_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 parse_std_result_file path (satisfiable, assignment_prefix, unsatisfiable) =

	let

		(* 'a option -> 'a Library.option *)

		fun option (SOME a) =

			Some a

		  | option NONE =

			None

		(* string -> int list *)

		fun int_list_from_string s =

			mapfilter (option o 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 satisfiable line then

				SATISFIABLE (parse_assignment [] lines)

			else if is_substring unsatisfiable line then

				UNSATISFIABLE

			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'        *)

(* ------------------------------------------------------------------------- *)

	(* 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 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

			end

		(* int -> PropLogic.prop_formula *)

		fun literal_from_int i =

			(assert (i<>0) "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 flat

		o (map (String.fields (fn c => c mem [#" ", #"\t", #"\n"])))

		o filter_preamble

		o (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) =

		(solvers := overwrite_warn (!solvers, (name, new_solver)) ("SAT solver " ^ quote name ^ " was defined before"));

(* ------------------------------------------------------------------------- *)

(* 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 assoc) (!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)

	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 introduces more boolean variables than we can *)

			(* handle efficiently.                                              *)

			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 _                 = raise 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 = the (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

		end

	end  (* local *)

in

	SatSolver.add_solver ("dpll", dpll_solver)

end;

(* ------------------------------------------------------------------------- *)

(* Internal SAT solver, available as 'SatSolver.invoke_solver "auto"': uses  *)

(* the first 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

					());

				(* apply 'solver' to 'fm' *)

				solver fm

					handle SatSolver.NOT_CONFIGURED => loop solvers

			)

	in

		loop (rev (!SatSolver.solvers))

	end

in

	SatSolver.add_solver ("auto", auto_solver)

end;

(* ------------------------------------------------------------------------- *)

(* ZChaff, Version 2004.05.13 (http://www.princeton.edu/~chaff/zchaff.html)  *)

(* ------------------------------------------------------------------------- *)

let

	fun zchaff fm =

	let

		val _          = if (getenv "ZCHAFF_HOME") = "" then raise SatSolver.NOT_CONFIGURED else ()

		val inpath     = File.tmp_path (Path.unpack "isabelle.cnf")

		val outpath    = File.tmp_path (Path.unpack "result")

		val cmd        = (getenv "ZCHAFF_HOME") ^ "/zchaff " ^ (Path.pack inpath) ^ " > " ^ (Path.pack outpath)

		fun writefn fm = SatSolver.write_dimacs_cnf_file inpath (PropLogic.defcnf fm)

		fun readfn ()  = SatSolver.parse_std_result_file outpath ("Instance Satisfiable", "", "Instance Unsatisfiable")

		val _          = assert (not (File.exists inpath)) ("file " ^ quote (Path.pack inpath) ^ " exists, please delete (will not overwrite)")

		val _          = assert (not (File.exists outpath)) ("file " ^ quote (Path.pack outpath) ^ " exists, please delete (will not overwrite)")

		val result     = SatSolver.make_external_solver cmd writefn readfn fm

		val _          = (File.rm inpath handle _ => ())

		val _          = (File.rm outpath handle _ => ())

	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") = "" orelse (getenv "BERKMIN_EXE") = "" then raise SatSolver.NOT_CONFIGURED else ()

		val inpath     = File.tmp_path (Path.unpack "isabelle.cnf")

		val outpath    = File.tmp_path (Path.unpack "result")

		val cmd        = (getenv "BERKMIN_HOME") ^ "/" ^ (getenv "BERKMIN_EXE") ^ " " ^ (Path.pack inpath) ^ " > " ^ (Path.pack outpath)

		fun writefn fm = SatSolver.write_dimacs_cnf_file inpath (PropLogic.defcnf fm)

		fun readfn ()  = SatSolver.parse_std_result_file outpath ("Satisfiable          !!", "solution =", "UNSATISFIABLE          !!")

		val _          = assert (not (File.exists inpath)) ("file " ^ quote (Path.pack inpath) ^ " exists, please delete (will not overwrite)")

		val _          = assert (not (File.exists outpath)) ("file " ^ quote (Path.pack outpath) ^ " exists, please delete (will not overwrite)")

		val result     = SatSolver.make_external_solver cmd writefn readfn fm

		val _          = (File.rm inpath handle _ => ())

		val _          = (File.rm outpath handle _ => ())

	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 inpath     = File.tmp_path (Path.unpack "isabelle.cnf")

		val outpath    = File.tmp_path (Path.unpack "result")

		val cmd        = (getenv "JERUSAT_HOME") ^ "/Jerusat1.3 " ^ (Path.pack inpath) ^ " > " ^ (Path.pack outpath)

		fun writefn fm = SatSolver.write_dimacs_cnf_file inpath (PropLogic.defcnf fm)

		fun readfn ()  = SatSolver.parse_std_result_file outpath ("s SATISFIABLE", "v ", "s UNSATISFIABLE")

		val _          = assert (not (File.exists inpath)) ("file " ^ quote (Path.pack inpath) ^ " exists, please delete (will not overwrite)")

		val _          = assert (not (File.exists outpath)) ("file " ^ quote (Path.pack outpath) ^ " exists, please delete (will not overwrite)")

		val result     = SatSolver.make_external_solver cmd writefn readfn fm

		val _          = (File.rm inpath handle _ => ())

		val _          = (File.rm outpath handle _ => ())

	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"

*)