(* ID: $Id$ 

   Author: Jia Meng, NICTA

FOL clauses translated from HOL formulae.  Combinators are used to represent lambda terms.

*)

structure ResHolClause =

struct

val include_combS = ref false;

val include_min_comb = ref false;

(**********************************************************************)

(* convert a Term.term with lambdas into a Term.term with combinators *) 

(**********************************************************************)

fun is_free (Bound(a)) n = (a = n)

  | is_free (Abs(x,_,b)) n = (is_free b (n+1))

  | is_free (P $ Q) n = ((is_free P n) orelse (is_free Q n))

  | is_free _ _ = false;

exception LAM2COMB of term;

exception BND of term;

fun decre_bndVar (Bound n) = Bound (n-1)

  | decre_bndVar (P $ Q) = (decre_bndVar P) $ (decre_bndVar Q)

  | decre_bndVar t =

    case t of Const(_,_) => t

	    | Free(_,_) => t

	    | Var(_,_) => t

	    | Abs(_,_,_) => raise BND(t); (*should not occur*)

(*******************************************)

fun lam2comb (Abs(x,tp,Bound 0)) _ = 

    let val tpI = Type("fun",[tp,tp])

    in 

	include_min_comb:=true;

	Const("COMBI",tpI) 

    end

  | lam2comb (Abs(x,t1,Const(c,t2))) _ = 

    let val tK = Type("fun",[t2,Type("fun",[t1,t2])])

    in 

	include_min_comb:=true;

	Const("COMBK",tK) $ Const(c,t2) 

    end

  | lam2comb (Abs(x,t1,Free(v,t2))) _ =

    let val tK = Type("fun",[t2,Type("fun",[t1,t2])])

    in

	include_min_comb:=true;

	Const("COMBK",tK) $ Free(v,t2)

    end

  | lam2comb (Abs(x,t1,Var(ind,t2))) _=

    let val tK = Type("fun",[t2,Type("fun",[t1,t2])])

    in

	include_min_comb:=true;

	Const("COMBK",tK) $ Var(ind,t2)

    end

  | lam2comb (t as (Abs(x,t1,P$(Bound 0)))) Bnds =

    let val nfreeP = not(is_free P 0)

	val tr = Term.type_of1(t1::Bnds,P)

    in

	if nfreeP then (decre_bndVar P)

	else (

	      let val tI = Type("fun",[t1,t1])

		  val P' = lam2comb (Abs(x,t1,P)) Bnds

		  val tp' = Term.type_of1(Bnds,P')

		  val tS = Type("fun",[tp',Type("fun",[tI,tr])])

	      in

		  include_min_comb:=true;

		  include_combS:=true;

		  Const("COMBS",tS) $ P' $ Const("COMBI",tI)

	      end)

    end

  | lam2comb (t as (Abs(x,t1,P$Q))) Bnds =

    let val (nfreeP,nfreeQ) = (not(is_free P 0),not(is_free Q 0))

	val tpq = Term.type_of1(t1::Bnds, P$Q) 

    in

	if(nfreeP andalso nfreeQ) then (

	    let val tK = Type("fun",[tpq,Type("fun",[t1,tpq])])

		val PQ' = decre_bndVar(P $ Q)

	    in 

		include_min_comb:=true;

		Const("COMBK",tK) $ PQ'

	    end)

	else (

	      if nfreeP then (

			       let val Q' = lam2comb (Abs(x,t1,Q)) Bnds

				   val P' = decre_bndVar P

				   val tp = Term.type_of1(Bnds,P')

				   val tq' = Term.type_of1(Bnds, Q')

				   val tB = Type("fun",[tp,Type("fun",[tq',Type("fun",[t1,tpq])])])

			       in

				   include_min_comb:=true;

				   Const("COMBB",tB) $ P' $ Q' 

			       end)

	      else (

		    if nfreeQ then (

				    let val P' = lam2comb (Abs(x,t1,P)) Bnds

					val Q' = decre_bndVar Q

					val tq = Term.type_of1(Bnds,Q')

					val tp' = Term.type_of1(Bnds, P')

					val tC = Type("fun",[tp',Type("fun",[tq,Type("fun",[t1,tpq])])])

				    in

					include_min_comb:=true;

					Const("COMBC",tC) $ P' $ Q'

				    end)

		    else(

			 let val P' = lam2comb (Abs(x,t1,P)) Bnds

			     val Q' = lam2comb (Abs(x,t1,Q)) Bnds

			     val tp' = Term.type_of1(Bnds,P')

			     val tq' = Term.type_of1(Bnds,Q')

			     val tS = Type("fun",[tp',Type("fun",[tq',Type("fun",[t1,tpq])])])

			 in

			     include_min_comb:=true;

			     include_combS:=true;

			     Const("COMBS",tS) $ P' $ Q'

			 end)))

    end

  | lam2comb (t as (Abs(x,t1,_))) _ = raise LAM2COMB (t);

(*********************)

fun to_comb (Abs(x,tp,b)) Bnds =

    let val b' = to_comb b (tp::Bnds)

    in lam2comb (Abs(x,tp,b')) Bnds end

  | to_comb (P $ Q) Bnds = ((to_comb P Bnds) $ (to_comb Q Bnds))

  | to_comb t _ = t;

fun comb_of t = to_comb t [];

(* print a term containing combinators, used for debugging *)

exception TERM_COMB of term;

fun string_of_term (Const(c,t)) = c

  | string_of_term (Free(v,t)) = v

  | string_of_term (Var((x,n),t)) =

    let val xn = x ^ "_" ^ (string_of_int n)

    in xn end

  | string_of_term (P $ Q) =

    let val P' = string_of_term P

	val Q' = string_of_term Q

    in

	"(" ^ P' ^ " " ^ Q' ^ ")" end

  | string_of_term t =  raise TERM_COMB (t);

(******************************************************)

(* data types for typed combinator expressions        *)

(******************************************************)

type axiom_name = string;

datatype kind = Axiom | Conjecture;

fun name_of_kind Axiom = "axiom"

  | name_of_kind Conjecture = "conjecture";

type polarity = bool;

type indexname = Term.indexname;

type clause_id = int;

type csort = Term.sort;

type ctyp = string;

type ctyp_var = ResClause.typ_var;

type ctype_literal = ResClause.type_literal;

datatype combterm = CombConst of string * ctyp

		  | CombFree of string * ctyp

		  | CombVar of string * ctyp

		  | CombApp of combterm * combterm * ctyp

		  | Bool of combterm

		  | Equal of combterm * combterm;

datatype literal = Literal of polarity * combterm;

datatype clause = 

	 Clause of {clause_id: clause_id,

		    axiom_name: axiom_name,

		    kind: kind,

		    literals: literal list,

		    ctypes_sorts: (ctyp_var * csort) list, 

                    ctvar_type_literals: ctype_literal list, 

                    ctfree_type_literals: ctype_literal list};

fun string_of_kind (Clause cls) = name_of_kind (#kind cls);

fun get_axiomName (Clause cls) = #axiom_name cls;

fun get_clause_id (Clause cls) = #clause_id cls;

(*********************************************************************)

(* convert a clause with type Term.term to a clause with type clause *)

(*********************************************************************)

fun isFalse (Literal(pol,Bool(CombConst(c,_)))) =

    (pol andalso c = "c_False") orelse

    (not pol andalso c = "c_True")

  | isFalse _ = false;

fun isTrue (Literal (pol,Bool(CombConst(c,_)))) =

      (pol andalso c = "c_True") orelse

      (not pol andalso c = "c_False")

  | isTrue _ = false;

fun isTaut (Clause {literals,...}) = exists isTrue literals;  

fun make_clause(clause_id,axiom_name,kind,literals,ctypes_sorts,ctvar_type_literals,ctfree_type_literals) =

    if forall isFalse literals

    then error "Problem too trivial for resolution (empty clause)"

    else

	Clause {clause_id = clause_id, axiom_name = axiom_name, kind = kind,

		literals = literals, ctypes_sorts = ctypes_sorts, 

		ctvar_type_literals = ctvar_type_literals,

		ctfree_type_literals = ctfree_type_literals};

(* convert a Term.type to a string; gather sort information of type variables; also check if the type is a bool type *)

fun type_of (Type (a, [])) = ((ResClause.make_fixed_type_const a,[]),a ="bool")

  | type_of (Type (a, Ts)) = 

    let val typbs = map type_of Ts

	val (types,_) = ListPair.unzip typbs

	val (ctyps,tvarSorts) = ListPair.unzip types

	val ts = ResClause.union_all tvarSorts

	val t = ResClause.make_fixed_type_const a

    in

	(((t ^ ResClause.paren_pack ctyps),ts),false)

    end

  | type_of (tp as (TFree (a,s))) = ((ResClause.make_fixed_type_var a,[ResClause.mk_typ_var_sort tp]),false)

  | type_of (tp as (TVar (v,s))) = ((ResClause.make_schematic_type_var v,[ResClause.mk_typ_var_sort tp]),false);

(* same as above, but no gathering of sort information *)

fun simp_type_of (Type (a, [])) = (ResClause.make_fixed_type_const a,a ="bool")

  | simp_type_of (Type (a, Ts)) = 

    let val typbs = map simp_type_of Ts

	val (types,_) = ListPair.unzip typbs

	val t = ResClause.make_fixed_type_const a

    in

	((t ^ ResClause.paren_pack types),false)

    end

  | simp_type_of (TFree (a,s)) = (ResClause.make_fixed_type_var a,false)

  | simp_type_of (TVar (v,s)) = (ResClause.make_schematic_type_var v,false);

(* convert a Term.term (with combinators) into a combterm, also accummulate sort info *)

fun combterm_of (Const(c,t)) =

    let val ((tp,ts),is_bool) = type_of t

	val c' = CombConst(ResClause.make_fixed_const c,tp)

	val c'' = if is_bool then Bool(c') else c'

    in

	(c'',ts)

    end

  | combterm_of (Free(v,t)) =

    let val ((tp,ts),is_bool) = type_of t

	val v' = if ResClause.isMeta v then CombVar(ResClause.make_schematic_var(v,0),tp)

		 else CombFree(ResClause.make_fixed_var v,tp)

	val v'' = if is_bool then Bool(v') else v'

    in

	(v'',ts)

    end

  | combterm_of (Var(v,t)) =

    let val ((tp,ts),is_bool) = type_of t

	val v' = CombVar(ResClause.make_schematic_var v,tp)

	val v'' = if is_bool then Bool(v') else v'

    in

	(v'',ts)

    end

  | combterm_of (Const("op =",T) $ P $ Q) = (*FIXME: allow equal between bools?*)

    let val (P',tsP) = combterm_of P        

	val (Q',tsQ) = combterm_of Q

    in

	(Equal(P',Q'),tsP union tsQ)

    end

  | combterm_of (t as (P $ Q)) =

    let val (P',tsP) = combterm_of P

	val (Q',tsQ) = combterm_of Q

	val tp = Term.type_of t

	val (tp',is_bool) = simp_type_of tp

	val t' = CombApp(P',Q',tp')

	val t'' = if is_bool then Bool(t') else t'

    in

	(t'',tsP union tsQ)

    end;

fun predicate_of ((Const("Not",_) $ P), polarity) =

    predicate_of (P, not polarity)

  | predicate_of (term,polarity) = (combterm_of term,polarity);

fun literals_of_term1 args (Const("Trueprop",_) $ P) = literals_of_term1 args P

  | literals_of_term1 args (Const("op |",_) $ P $ Q) = 

    let val args' = literals_of_term1 args P

    in

	literals_of_term1 args' Q

    end

  | literals_of_term1 (lits,ts) P =

    let val ((pred,ts'),pol) = predicate_of (P,true)

	val lits' = Literal(pol,pred)::lits

    in

	(lits',ts union ts')

    end;

fun literals_of_term P = literals_of_term1 ([],[]) P;

(* making axiom and conjecture clauses *)

fun make_axiom_clause term (ax_name,cls_id) =

    let val term' = comb_of term

	val (lits,ctypes_sorts) = literals_of_term term'

	val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux2 ctypes_sorts

    in

	make_clause(cls_id,ax_name,Axiom,

		    lits,ctypes_sorts,ctvar_lits,ctfree_lits)

    end;

fun make_conjecture_clause n t =

    let val t' = comb_of t

	val (lits,ctypes_sorts) = literals_of_term t'

	val (ctvar_lits,ctfree_lits) = ResClause.add_typs_aux2 ctypes_sorts

    in

	make_clause(n,"conjecture",Conjecture,lits,ctypes_sorts,ctvar_lits,ctfree_lits)

    end;

fun make_conjecture_clauses_aux _ [] = []

  | make_conjecture_clauses_aux n (t::ts) =

    make_conjecture_clause n t :: make_conjecture_clauses_aux (n+1) ts;

val make_conjecture_clauses = make_conjecture_clauses_aux 0;

(**********************************************************************)

(* convert clause into ATP specific formats:                          *)

(* TPTP used by Vampire and E                                         *)

(**********************************************************************)

val keep_types = ref true;

val type_wrapper = "typeinfo";

fun put_type (c,t) = 

    if !keep_types then type_wrapper ^ (ResClause.paren_pack [c,t])

    else c;

val bool_tp = ResClause.make_fixed_type_const "bool";

val app_str = "hAPP";

val bool_str = "hBOOL";

(* convert literals of clauses into strings *)

fun string_of_combterm _ (CombConst(c,tp)) = put_type(c,tp)

  | string_of_combterm _ (CombFree(v,tp)) = put_type(v,tp)

  | string_of_combterm _ (CombVar(v,tp)) = put_type(v,tp)

  | string_of_combterm is_pred (CombApp(t1,t2,tp)) = 

    let val s1 = string_of_combterm is_pred t1

	val s2 = string_of_combterm is_pred t2

	val app = app_str ^ (ResClause.paren_pack [s1,s2])

    in

	put_type(app,tp)

    end

  | string_of_combterm is_pred (Bool(t)) = 

    let val t' = string_of_combterm false t

    in

	if is_pred then bool_str ^ (ResClause.paren_pack [t'])

	else t'

    end

  | string_of_combterm _ (Equal(t1,t2)) =

    let val s1 = string_of_combterm false t1

	val s2 = string_of_combterm false t2

    in

	"equal" ^ (ResClause.paren_pack [s1,s2]) 

    end;

fun string_of_clausename (cls_id,ax_name) = 

    ResClause.clause_prefix ^ ResClause.ascii_of ax_name ^ "_" ^ Int.toString cls_id;

fun string_of_type_clsname (cls_id,ax_name,idx) = 

    string_of_clausename (cls_id,ax_name) ^ "_tcs" ^ (Int.toString idx);

fun tptp_literal (Literal(pol,pred)) =

    let val pred_string = string_of_combterm true pred

	val pol_str = if pol then "++" else "--"

    in

	pol_str ^ pred_string

    end;

fun tptp_type_lits (Clause cls) = 

    let val lits = map tptp_literal (#literals cls)

	val ctvar_lits_strs =

	      if !keep_types 

	      then (map ResClause.tptp_of_typeLit (#ctvar_type_literals cls)) 

	      else []

	val ctfree_lits = 

	      if !keep_types

	      then (map ResClause.tptp_of_typeLit (#ctfree_type_literals cls)) 

	      else []

    in

	(ctvar_lits_strs @ lits, ctfree_lits)

    end; 

fun clause2tptp cls =

    let val (lits,ctfree_lits) = tptp_type_lits cls

	val cls_id = get_clause_id cls

	val ax_name = get_axiomName cls

	val knd = string_of_kind cls

	val lits_str = ResClause.bracket_pack lits

	val cls_str = ResClause.gen_tptp_cls(cls_id,ax_name,knd,lits_str)

    in

	(cls_str,ctfree_lits)

    end;

end