# File library.ML

    (*  Title:      HOLCF/domain/library.ML
        ID:         $Id: library.ML,v 1.38 2005/09/12 16:21:39 haftmann Exp $
        Author:     David von Oheimb

    Library for domain section.
    *)

    (* ----- general support ---------------------------------------------------- *)

    fun mapn f n []      = []
    |   mapn f n (x::xs) = (f n x) :: mapn f (n+1) xs;

    fun foldr'' f (l,f2) = let fun itr []  = raise Fail "foldr''"
    			     | itr [a] = f2 a
    			     | itr (a::l) = f(a, itr l)
    in  itr l  end;
    fun foldr' f l = foldr'' f (l,I);
    fun map_cumulr f start xs = foldr (fn (x,(ys,res))=>case f(x,res) of (y,res2) =>
    						  (y::ys,res2)) ([],start) xs;

    fun first  (x,_,_) = x; fun second (_,x,_) = x; fun third  (_,_,x) = x;
    fun upd_first  f (x,y,z) = (f x,   y,   z);
    fun upd_second f (x,y,z) = (  x, f y,   z);
    fun upd_third  f (x,y,z) = (  x,   y, f z);

    fun atomize thm = let val r_inst = read_instantiate;
        fun at  thm = case concl_of thm of
          _$(Const("op &",_)$_$_)       => at(thm RS conjunct1)@at(thm RS conjunct2)
        | _$(Const("All" ,_)$Abs(s,_,_))=> at(thm RS (r_inst [("x","?"^s)] spec))
        | _				    => [thm];
    in map zero_var_indexes (at thm) end;

    (* ----- specific support for domain ---------------------------------------- *)

    structure Domain_Library = struct

    open HOLCFLogic;

    exception Impossible of string;
    fun Imposs msg = raise Impossible ("Domain:"^msg);

    (* ----- name handling ----- *)

    val strip_esc = let fun strip ("'" :: c :: cs) = c :: strip cs
    		    |   strip ["'"] = []
    		    |   strip (c :: cs) = c :: strip cs
    		    |   strip [] = [];
    in implode o strip o Symbol.explode end;

    fun extern_name con = case Symbol.explode con of
    		   ("o"::"p"::" "::rest) => implode rest
    		   | _ => con;
    fun dis_name  con = "is_"^ (extern_name con);
    fun dis_name_ con = "is_"^ (strip_esc   con);
    fun mat_name  con = "match_"^ (extern_name con);
    fun mat_name_ con = "match_"^ (strip_esc   con);

    (* make distinct names out of the type list,
       forbidding "o","n..","x..","f..","P.." as names *)
    (* a number string is added if necessary *)
    fun mk_var_names ids : string list = let
        fun nonreserved s = if s mem ["n","x","f","P"] then s^"'" else s;
        fun index_vnames(vn::vns,occupied) =
              (case AList.lookup (op =) occupied vn of
                 NONE => if vn mem vns
                         then (vn^"1") :: index_vnames(vns,(vn,1)  ::occupied)
                         else  vn      :: index_vnames(vns,          occupied)
               | SOME(i) => (vn^(string_of_int (i+1)))
    				   :: index_vnames(vns,(vn,i+1)::occupied))
          | index_vnames([],occupied) = [];
    in index_vnames(map nonreserved ids, [("O",0),("o",0)]) end;

    fun rep_Type  (Type  x) = x | rep_Type  _ = Imposs "library:rep_Type";
    fun rep_TFree (TFree x) = x | rep_TFree _ = Imposs "library:rep_TFree";

    fun pcpo_type sg t = Sign.of_sort sg (Sign.certify_typ sg t, pcpoS);
    fun string_of_typ sg = Sign.string_of_typ sg o Sign.certify_typ sg;
    fun str2typ sg = typ_of o read_ctyp sg;

    (* ----- constructor list handling ----- *)

    type cons = (string *			(* operator name of constr *)
    	    ((bool*int)*		(*  (lazy,recursive element or ~1) *)
    	      string option*		(*   selector name    *)
    	      string)			(*   argument name    *)
    	    list);			(* argument list      *)
    type eq = (string *		(* name      of abstracted type *)
    	   typ list) *		(* arguments of abstracted type *)
    	  cons list;		(* represented type, as a constructor list *)

    fun rec_of arg  = snd (first arg);
    fun is_lazy arg = fst (first arg);
    val sel_of    =       second;
    val     vname =       third;
    val upd_vname =   upd_third;
    fun is_rec         arg = rec_of arg >=0;
    fun is_nonlazy_rec arg = is_rec arg andalso not (is_lazy arg);
    fun nonlazy     args   = map vname (filter_out is_lazy    args);
    fun nonlazy_rec args   = map vname (List.filter is_nonlazy_rec args);

    (* ----- qualified names of HOLCF constants ----- *)

    val lessN      = "Porder.op <<"
    val UU_N       = "Pcpo.UU";
    val admN       = "Adm.adm";
    val Rep_CFunN  = "Cfun.Rep_CFun";
    val Abs_CFunN  = "Cfun.Abs_CFun";
    val ID_N       = "Cfun.ID";
    val cfcompN    = "Cfun.cfcomp";
    val strictifyN = "Cfun.strictify";
    val cpairN     = "Cprod.cpair";
    val cfstN      = "Cprod.cfst";
    val csndN      = "Cprod.csnd";
    val csplitN    = "Cprod.csplit";
    val spairN     = "Sprod.spair";
    val sfstN      = "Sprod.sfst";
    val ssndN      = "Sprod.ssnd";
    val ssplitN    = "Sprod.ssplit";
    val sinlN      = "Ssum.sinl";
    val sinrN      = "Ssum.sinr";
    val sscaseN    = "Ssum.sscase";
    val upN        = "Up.up";
    val fupN       = "Up.fup";
    val ONE_N      = "One.ONE";
    val TT_N       = "Tr.TT";
    val FF_N       = "Tr.FF";
    val iterateN   = "Fix.iterate";
    val fixN       = "Fix.fix";
    val returnN    = "Fixrec.return";
    val failN      = "Fixrec.fail";

    val pcpoN      = "Pcpo.pcpo"
    val pcpoS      = [pcpoN];

    (* ----- support for type and mixfix expressions ----- *)

    infixr 5 -->;

    (* ----- support for term expressions ----- *)

    fun %: s = Free(s,dummyT);
    fun %# arg = %:(vname arg);
    fun %%: s = Const(s,dummyT);

    local open HOLogic in
    val mk_trp = mk_Trueprop;
    fun mk_conj (S,T) = conj $ S $ T;
    fun mk_disj (S,T) = disj $ S $ T;
    fun mk_imp  (S,T) = imp  $ S $ T;
    fun mk_lam  (x,T) = Abs(x,dummyT,T);
    fun mk_all  (x,P) = HOLogic.mk_all (x,dummyT,P);
    fun mk_ex   (x,P) = mk_exists (x,dummyT,P);
    local
    		    fun sg [s]     = %:s
    		    |   sg (s::ss) = %%:"_classes" $ %:s $ sg ss
    	 	    |   sg _       = Imposs "library:sg";
    		    fun sf [] = %%:"_emptysort"
    		    |   sf s  = %%:"_sort" $ sg s
    		    fun tf (Type (s,args)) = Library.foldl (op $) (%:s,map tf args)
    		    |   tf (TFree(s,sort)) = %%:"_ofsort" $ %:s $ sf sort
    		    |   tf _               = Imposs "library:tf";
    in
    fun mk_constrain      (typ,T) = %%:"_constrain" $ T $ tf typ;
    fun mk_constrainall (x,typ,P) = %%:"All" $ (%%:"_constrainAbs" $ mk_lam(x,P) $ tf typ);
    end;
    end;

    fun mk_All  (x,P) = %%:"all" $ mk_lam(x,P); (* meta universal quantification *)

    infixr 0 ===>;  fun S ===> T = %%:"==>" $ S $ T;
    infixr 0 ==>;   fun S ==> T = mk_trp S ===> mk_trp T;
    infix 0 ==;     fun S ==  T = %%:"==" $ S $ T;
    infix 1 ===;    fun S === T = %%:"op =" $ S $ T;
    infix 1 ~=;     fun S ~=  T = HOLogic.mk_not (S === T);
    infix 1 <<;     fun S <<  T = %%:lessN $ S $ T;
    infix 1 ~<<;    fun S ~<< T = HOLogic.mk_not (S << T);

    infix 9 `  ; fun f`  x = %%:Rep_CFunN $ f $ x;
    infix 9 `% ; fun f`% s = f` %: s;
    infix 9 `%%; fun f`%%s = f` %%:s;
    fun mk_cRep_CFun (F,As) = Library.foldl (op `) (F,As);
    fun con_app2 con f args = mk_cRep_CFun(%%:con,map f args);
    fun con_app con = con_app2 con %#;
    fun if_rec  arg f y   = if is_rec arg then f (rec_of arg) else y;
    fun app_rec_arg p arg = if_rec arg (fn n => fn x => (p n)`x) I (%# arg);
    fun prj _  _  x (   _::[]) _ = x
    |   prj f1 _  x (_::y::ys) 0 = f1 x y
    |   prj f1 f2 x (y::   ys) j = prj f1 f2 (f2 x y) ys (j-1);
    fun fix_tp (tn, args) = (tn, map (K oneT) args); (* instantiate type to
    						    avoid type varaibles *)
    fun  proj x      = prj (fn S => K(%%:"fst" $S)) (fn S => K(%%:"snd" $S)) x;
    fun cproj x      = prj (fn S => K(%%:cfstN`S)) (fn S => K(%%:csndN`S)) x;
    fun prj' _  _  x (   _::[]) _ = x
    |   prj' f1 _  x (_::   ys) 0 = f1 x (foldr' HOLogic.mk_prodT ys)
    |   prj' f1 f2 x (y::   ys) j = prj' f1 f2 (f2 x y) ys (j-1);
    fun cproj' T eqs = prj'
    	(fn S => fn t => Const(cfstN, HOLogic.mk_prodT(dummyT,t)->>dummyT)`S)
    	(fn S => fn t => Const(csndN, HOLogic.mk_prodT(t,dummyT)->>dummyT)`S)
    		       T (map ((fn tp => tp ->> tp) o Type o fix_tp o fst) eqs);
    fun lift tfn = Library.foldr (fn (x,t)=> (mk_trp(tfn x) ===> t));

    fun /\ v T = %%:Abs_CFunN $ mk_lam(v,T);
    fun /\# (arg,T) = /\ (vname arg) T;
    infixr 9 oo; fun S oo T = %%:cfcompN`S`T;
    val UU = %%:UU_N;
    fun strict f = f`UU === UU;
    fun defined t = t ~= UU;
    fun cpair (S,T) = %%:cpairN`S`T;
    fun mk_ctuple [] = HOLogic.unit (* used in match_defs *)
    |   mk_ctuple (t::[]) = t
    |   mk_ctuple (t::ts) = cpair (t, mk_ctuple ts);
    fun mk_ctupleT [] = HOLogic.unitT   (* used in match_defs *)
    |   mk_ctupleT (T::[]) = T
    |   mk_ctupleT (T::Ts) = HOLogic.mk_prodT(T, mk_ctupleT Ts);
    fun lift_defined f = lift (fn x => defined (f x));
    fun bound_arg vns v = Bound(length vns -find_index_eq v vns -1);

    fun cont_eta_contract (Const("Cfun.Abs_CFun",TT) $ Abs(a,T,body)) =
          (case cont_eta_contract body  of
            body' as (Const("Cfun.Rep_CFun",Ta) $ f $ Bound 0) =>
    	  if not (0 mem loose_bnos f) then incr_boundvars ~1 f
    	  else   Const("Cfun.Abs_CFun",TT) $ Abs(a,T,body')
          | body' => Const("Cfun.Abs_CFun",TT) $ Abs(a,T,body'))
    |   cont_eta_contract(f$t) = cont_eta_contract f $ cont_eta_contract t
    |   cont_eta_contract t    = t;

    fun idx_name dnames s n = s^(if length dnames = 1 then "" else string_of_int n);
    fun when_funs cons = if length cons = 1 then ["f"]
                         else mapn (fn n => K("f"^(string_of_int n))) 1 cons;
    fun when_body cons funarg = let
    	fun one_fun n (_,[]  ) = /\ "dummy" (funarg(1,n))
    	|   one_fun n (_,args) = let
    		val l2 = length args;
    		fun idxs m arg = (if is_lazy arg then fn x=> %%:fupN` %%:ID_N`x
    					         else I) (Bound(l2-m));
    		in cont_eta_contract (foldr''
    			(fn (a,t) => %%:ssplitN`(/\# (a,t)))
    			(args,
    			fn a=> /\#(a,(mk_cRep_CFun(funarg(l2,n),mapn idxs 1 args))))
    			) end;
    in (if length cons = 1 andalso length(snd(hd cons)) <= 1
        then fn t => %%:strictifyN`t else I)
         (foldr' (fn (x,y)=> %%:sscaseN`x`y) (mapn one_fun 1 cons)) end;
    end; (* struct *)