(*  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

	type solver  (* PropLogic.prop_formula -> (int -> bool) option option *)

	(* 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 -> (int -> bool) option

	val make_external_solver  : string -> (PropLogic.prop_formula -> unit) -> (unit -> (int -> bool) option)

			-> PropLogic.prop_formula -> (int -> bool) option

	(* 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;

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

(* Type of SAT solvers: given a propositional formula, a satisfying          *)

(*      assignment may be returned                                           *)

(*      - 'Some None' means that no satisfying assignment was found          *)

(*      - 'None' means that the solver was not configured/installed properly *)

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

	type solver = prop_formula -> (int -> bool) option option;

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

(* 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' is converted into (definitional) 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 True =

			error "formula is not in CNF"

		  | cnf_string False =

			error "formula is not in CNF"

		  | cnf_string (BoolVar i) =

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

			string_of_int i)

		  | cnf_string (Not fm) =

			"-" ^ (cnf_string fm)

		  | cnf_string (Or (fm1,fm2)) =

			(cnf_string fm1) ^ " " ^ (cnf_string fm2)

		  | cnf_string (And (fm1,fm2)) =

			(cnf_string fm1) ^ " 0\n" ^ (cnf_string fm2)

	in

		File.write path

			(let

				val cnf               = (cnf_True_False_elim o defcnf) fm  (* conversion into def. CNF *)

				val number_of_vars    = maxidx cnf

				val number_of_clauses = cnf_number_of_clauses cnf

			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 cnf) ^ "\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 True =

			"*()"

		  | sat_string False =

			"+()"

		  | sat_string (BoolVar i) =

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

			string_of_int i)

		  | sat_string (Not fm) =

			"-(" ^ (sat_string fm) ^ ")"

		  | sat_string (Or (fm1,fm2)) =

			"+(" ^ (sat_string fm1) ^ " " ^ (sat_string fm2) ^ ")"

		  | sat_string (And (fm1,fm2)) =

			"*(" ^ (sat_string fm1) ^ " " ^ (sat_string fm2) ^ ")"

	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 'None' if the SAT   *)

(*      solver did not find one.  The file format must be as follows:        *)

(*      ,-----                                                               *)

(*      | 0 or more lines not containing 'success'                           *)

(*      | A line containing 'success' as a substring                         *)

(*      | A line ASSIGNMENT containing integers, separated by " "            *)

(*      | 0 or more lines                                                    *)

(*      `-----                                                               *)

(*      If variable i is contained in ASSIGNMENT, then i is interpreted as   *)

(*      'true'.  If ~i is contained in ASSIGNMENT, then i is interpreted as  *)

(*      'false'.                                                             *)

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

	(* Path.T -> string -> (int -> bool) option *)

	fun parse_std_result_file path success =

	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 -> int -> bool *)

		fun assignment_from_list [] i =

			false  (* could be 'true' just as well; the SAT solver didn't provide a value for this variable *)

		  | assignment_from_list (x::xs) i =

			if x=i then true

			else if x=(~i) then false

			else assignment_from_list xs i

		(* 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 -> int list option *)

		fun parse_lines [] =

			None

		  | parse_lines (line::lines) =

			if is_substring success line then

				(* the next line must be a list of integers *)

				(Some o assignment_from_list o int_list_from_string o hd) lines

			else

				parse_lines lines

	in

		(parse_lines o split_lines o File.read) path

	end;

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

(* make_external_solver: call 'writefn', execute 'cmd', call 'readfn'        *)

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

	(* string -> (prop_formula -> unit) -> (unit -> (int -> bool) option) -> prop_formula -> (int -> bool) option *)

	fun make_external_solver cmd writefn readfn fm =

		(writefn fm;

		assert ((system cmd)=0) ("system command " ^ quote cmd ^ " failed (make sure the SAT solver is installed)");

		readfn ());

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

(* 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 -> (int -> bool) option *)

		fun solver_loop xs =

			if PropLogic.eval (assignment_from_list xs) fm then

				Some (assignment_from_list xs)

			else

				(case next_list xs indices of

				  Some xs' => solver_loop xs'

				| None     => None)

	in

		(* start with the "first" assignment (all variables are interpreted as 'False') *)

		solver_loop []

	end

in

	SatSolver.add_solver ("enumerate", Some o 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 '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 -> int -> bool *)

			fun assignment_from_list [] i =

				false  (* could be 'true' just as well; the DPLL procedure didn't provide a value for this variable *)

			  | assignment_from_list (x::xs) i =

				if x=i then true

				else if x=(~i) then false

				else assignment_from_list xs i

		in

			(* initially, no variable is interpreted yet *)

			apsome assignment_from_list (dpll [] fm')

		end

	end  (* local *)

in

	SatSolver.add_solver ("dpll", Some o dpll_solver)

end;

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

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

(* the first installed solver (other than "auto" itself)                     *)

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

let

	fun auto_solver fm =

		get_first (fn (name,solver) =>

			if name="auto" then

				None

			else

				((if name="dpll" then

					warning ("Using SAT solver \"dpll\"; for better performance, consider using an external solver.")

				else

					());

				solver fm)) (rev (!SatSolver.solvers))

in

	SatSolver.add_solver ("auto", auto_solver)

end;

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

(* ZChaff, Version 2003.12.04                                                *)

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

let

	fun zchaff fm =

	let

		val inname     = "isabelle.cnf"

		val outname    = "result"

		val inpath     = File.tmp_path (Path.unpack inname)

		val outpath    = File.tmp_path (Path.unpack outname)

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

		fun writefn fm = SatSolver.write_dimacs_cnf_file inpath fm

		fun readfn ()  = SatSolver.parse_std_result_file outpath "Verify Solution successful. Instance satisfiable"

		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 assignment = SatSolver.make_external_solver cmd writefn readfn fm

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

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

	in

		assignment

	end

in

		SatSolver.add_solver ("zchaff", (fn fm => if getenv "ZCHAFF_HOME" <> "" then Some (zchaff fm) else None))

end;

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

(* Add code for other SAT solvers below.                                     *)

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

(*

let

	fun mysolver fm = ...

in

	SatSolver.add_solver ("myname", (fn fm => if mysolver_is_installed then Some (mysolver fm) else None));  -- register the solver

end;

-- the solver is now available as SatSolver.invoke_solver "myname"

*)