(*  Title:      HOLCF/Tools/domain/domain_library.ML

     ID:         $Id$

     Author:     David von Oheimb

 Library for domain command.

 *)

 (* ----- 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 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);

 fun pat_name  con = (extern_name con) ^ "_pat";

 fun pat_name_ con = (strip_esc   con) ^ "_pat";

 (* 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 pcpo_type sg t = Sign.of_sort sg (Sign.certify_typ sg t, pcpoS);

 fun string_of_typ sg = Syntax.string_of_typ_global sg o Sign.certify_typ sg;

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

 type cons = (string *				(* operator name of constr *)

 	    ((bool*int*DatatypeAux.dtyp)*	(*  (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  = second (first arg);

 fun is_lazy arg = first (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);

 (* ----- 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);

 val mk_constrain = uncurry TypeInfer.constrain;

 fun mk_constrainall (x,typ,P) = %%:"All" $ (TypeInfer.constrain (typ --> boolT) (mk_lam(x,P)));

 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 = %%:@{const_name Porder.sq_le} $ S $ T;

 infix 1 ~<<;    fun S ~<< T = HOLogic.mk_not (S << T);

 infix 9 `  ; fun f ` x = %%:@{const_name Rep_CFun} $ f $ x;

 infix 9 `% ; fun f`% s = f` %: s;

 infix 9 `%%; fun f`%%s = f` %%:s;

 fun mk_adm t = %%:@{const_name adm} $ t;

 fun mk_compact t = %%:@{const_name compact} $ t;

 val ID = %%:@{const_name ID};

 fun mk_strictify t = %%:@{const_name strictify}`t;

 fun mk_cfst t = %%:@{const_name cfst}`t;

 fun mk_csnd t = %%:@{const_name csnd}`t;

 (*val csplitN    = "Cprod.csplit";*)

 (*val sfstN      = "Sprod.sfst";*)

 (*val ssndN      = "Sprod.ssnd";*)

 fun mk_ssplit t = %%:@{const_name ssplit}`t;

 fun mk_sinl t = %%:@{const_name sinl}`t;

 fun mk_sinr t = %%:@{const_name sinr}`t;

 fun mk_sscase (x, y) = %%:@{const_name sscase}`x`y;

 fun mk_up t = %%:@{const_name up}`t;

 fun mk_fup (t,u) = %%:@{const_name fup} ` t ` u;

 val ONE = @{term ONE};

 val TT = @{term TT};

 val FF = @{term FF};

 fun mk_iterate (n,f,z) = %%:@{const_name iterate} $ n ` f ` z;

 fun mk_fix t = %%:@{const_name fix}`t;

 fun mk_return t = %%:@{const_name Fixrec.return}`t;

 val mk_fail = %%:@{const_name Fixrec.fail};

 fun mk_branch t = %%:@{const_name Fixrec.branch} $ t;

 val pcpoS = @{sort pcpo};

 val list_ccomb = Library.foldl (op `); (* continuous version of list_comb *)

 fun con_app2 con f args = list_ccomb(%%: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  proj x      = prj (fn S => K(%%:"fst" $S)) (fn S => K(%%:"snd" $S)) x;

 fun cproj x      = prj (fn S => K(mk_cfst S)) (fn S => K(mk_csnd S)) x;

 fun lift tfn = Library.foldr (fn (x,t)=> (mk_trp(tfn x) ===> t));

 fun /\ v T = %%:@{const_name Abs_CFun} $ mk_lam(v,T);

 fun /\# (arg,T) = /\ (vname arg) T;

 infixr 9 oo; fun S oo T = %%:@{const_name cfcomp}`S`T;

 val UU = %%:@{const_name UU};

 fun strict f = f`UU === UU;

 fun defined t = t ~= UU;

 fun cpair (t,u) = %%:@{const_name cpair}`t`u;

 fun spair (t,u) = %%:@{const_name spair}`t`u;

 fun mk_ctuple [] = HOLogic.unit (* used in match_defs *)

 |   mk_ctuple ts = foldr1 cpair ts;

 fun mk_stuple [] = ONE

 |   mk_stuple ts = foldr1 spair ts;

 fun mk_ctupleT [] = HOLogic.unitT   (* used in match_defs *)

 |   mk_ctupleT Ts = foldr1 HOLogic.mk_prodT Ts;

 fun mk_maybeT T = Type ("Fixrec.maybe",[T]);

 fun cpair_pat (p1,p2) = %%:@{const_name cpair_pat} $ p1 $ p2;

 val mk_ctuple_pat = foldr1 cpair_pat;

 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 t => mk_fup (ID, t))

 					         else I) (Bound(l2-m));

 		in cont_eta_contract (foldr'' 

 			(fn (a,t) => mk_ssplit (/\# (a,t)))

 			(args,

 			fn a=> /\#(a,(list_ccomb(funarg(l2,n),mapn idxs 1 args))))

 			) end;

 in (if length cons = 1 andalso length(snd(hd cons)) <= 1

     then mk_strictify else I)

      (foldr1 mk_sscase (mapn one_fun 1 cons)) end;

 end; (* struct *)