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(* Title: HOLCF/Tools/domain/domain_library.ML
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ID: $Id$
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Author: David von Oheimb
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Library for domain command.
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*)
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(* ----- general support ---------------------------------------------------- *)
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fun mapn f n [] = []
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| mapn f n (x::xs) = (f n x) :: mapn f (n+1) xs;
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fun foldr'' f (l,f2) = let fun itr [] = raise Fail "foldr''"
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| itr [a] = f2 a
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| itr (a::l) = f(a, itr l)
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in itr l end;
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fun map_cumulr f start xs = foldr (fn (x,(ys,res))=>case f(x,res) of (y,res2) =>
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(y::ys,res2)) ([],start) xs;
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fun first (x,_,_) = x; fun second (_,x,_) = x; fun third (_,_,x) = x;
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fun upd_first f (x,y,z) = (f x, y, z);
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fun upd_second f (x,y,z) = ( x, f y, z);
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fun upd_third f (x,y,z) = ( x, y, f z);
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fun atomize thm = let val r_inst = read_instantiate;
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fun at thm = case concl_of thm of
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_$(Const("op &",_)$_$_) => at(thm RS conjunct1)@at(thm RS conjunct2)
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| _$(Const("All" ,_)$Abs(s,_,_))=> at(thm RS (r_inst [("x","?"^s)] spec))
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| _ => [thm];
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in map zero_var_indexes (at thm) end;
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(* ----- specific support for domain ---------------------------------------- *)
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structure Domain_Library = struct
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open HOLCFLogic;
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exception Impossible of string;
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fun Imposs msg = raise Impossible ("Domain:"^msg);
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(* ----- name handling ----- *)
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val strip_esc = let fun strip ("'" :: c :: cs) = c :: strip cs
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| strip ["'"] = []
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| strip (c :: cs) = c :: strip cs
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| strip [] = [];
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in implode o strip o Symbol.explode end;
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fun extern_name con = case Symbol.explode con of
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("o"::"p"::" "::rest) => implode rest
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| _ => con;
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fun dis_name con = "is_"^ (extern_name con);
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fun dis_name_ con = "is_"^ (strip_esc con);
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fun mat_name con = "match_"^ (extern_name con);
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fun mat_name_ con = "match_"^ (strip_esc con);
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fun pat_name con = (extern_name con) ^ "_pat";
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fun pat_name_ con = (strip_esc con) ^ "_pat";
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(* make distinct names out of the type list,
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forbidding "o","n..","x..","f..","P.." as names *)
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(* a number string is added if necessary *)
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fun mk_var_names ids : string list = let
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fun nonreserved s = if s mem ["n","x","f","P"] then s^"'" else s;
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fun index_vnames(vn::vns,occupied) =
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(case AList.lookup (op =) occupied vn of
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NONE => if vn mem vns
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then (vn^"1") :: index_vnames(vns,(vn,1) ::occupied)
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else vn :: index_vnames(vns, occupied)
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| SOME(i) => (vn^(string_of_int (i+1)))
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:: index_vnames(vns,(vn,i+1)::occupied))
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| index_vnames([],occupied) = [];
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in index_vnames(map nonreserved ids, [("O",0),("o",0)]) end;
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fun pcpo_type sg t = Sign.of_sort sg (Sign.certify_typ sg t, pcpoS);
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fun string_of_typ sg = Sign.string_of_typ sg o Sign.certify_typ sg;
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(* ----- constructor list handling ----- *)
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type cons = (string * (* operator name of constr *)
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((bool*int*DatatypeAux.dtyp)* (* (lazy,recursive element or ~1) *)
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string option* (* selector name *)
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string) (* argument name *)
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list); (* argument list *)
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type eq = (string * (* name of abstracted type *)
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typ list) * (* arguments of abstracted type *)
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cons list; (* represented type, as a constructor list *)
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fun rec_of arg = second (first arg);
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fun is_lazy arg = first (first arg);
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val sel_of = second;
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val vname = third;
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val upd_vname = upd_third;
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fun is_rec arg = rec_of arg >=0;
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fun is_nonlazy_rec arg = is_rec arg andalso not (is_lazy arg);
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fun nonlazy args = map vname (filter_out is_lazy args);
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fun nonlazy_rec args = map vname (List.filter is_nonlazy_rec args);
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(* ----- qualified names of HOLCF constants ----- *)
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val lessN = "Porder.<<"
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val UU_N = "Pcpo.UU";
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val admN = "Adm.adm";
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val compactN = "Adm.compact";
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val Rep_CFunN = "Cfun.Rep_CFun";
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val Abs_CFunN = "Cfun.Abs_CFun";
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val ID_N = "Cfun.ID";
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val cfcompN = "Cfun.cfcomp";
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val strictifyN = "Cfun.strictify";
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val cpairN = "Cprod.cpair";
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val cfstN = "Cprod.cfst";
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val csndN = "Cprod.csnd";
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val csplitN = "Cprod.csplit";
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val spairN = "Sprod.spair";
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val sfstN = "Sprod.sfst";
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val ssndN = "Sprod.ssnd";
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val ssplitN = "Sprod.ssplit";
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val sinlN = "Ssum.sinl";
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val sinrN = "Ssum.sinr";
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val sscaseN = "Ssum.sscase";
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val upN = "Up.up";
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val fupN = "Up.fup";
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val ONE_N = "One.ONE";
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val TT_N = "Tr.TT";
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val FF_N = "Tr.FF";
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val iterateN = "Fix.iterate";
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val fixN = "Fix.fix";
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val returnN = "Fixrec.return";
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val failN = "Fixrec.fail";
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val cpair_patN = "Fixrec.cpair_pat";
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val branchN = "Fixrec.branch";
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val pcpoN = "Pcpo.pcpo"
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val pcpoS = [pcpoN];
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(* ----- support for type and mixfix expressions ----- *)
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infixr 5 -->;
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(* ----- support for term expressions ----- *)
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fun %: s = Free(s,dummyT);
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fun %# arg = %:(vname arg);
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fun %%: s = Const(s,dummyT);
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local open HOLogic in
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val mk_trp = mk_Trueprop;
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fun mk_conj (S,T) = conj $ S $ T;
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fun mk_disj (S,T) = disj $ S $ T;
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fun mk_imp (S,T) = imp $ S $ T;
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fun mk_lam (x,T) = Abs(x,dummyT,T);
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fun mk_all (x,P) = HOLogic.mk_all (x,dummyT,P);
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fun mk_ex (x,P) = mk_exists (x,dummyT,P);
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fun mk_constrain (typ,T) = TypeInfer.constrain T typ;
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fun mk_constrainall (x,typ,P) = %%:"All" $ (TypeInfer.constrain (mk_lam(x,P)) (typ --> boolT));
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end
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fun mk_All (x,P) = %%:"all" $ mk_lam(x,P); (* meta universal quantification *)
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infixr 0 ===>; fun S ===> T = %%:"==>" $ S $ T;
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infixr 0 ==>; fun S ==> T = mk_trp S ===> mk_trp T;
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infix 0 ==; fun S == T = %%:"==" $ S $ T;
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infix 1 ===; fun S === T = %%:"op =" $ S $ T;
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infix 1 ~=; fun S ~= T = HOLogic.mk_not (S === T);
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infix 1 <<; fun S << T = %%:lessN $ S $ T;
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infix 1 ~<<; fun S ~<< T = HOLogic.mk_not (S << T);
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infix 9 ` ; fun f` x = %%:Rep_CFunN $ f $ x;
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infix 9 `% ; fun f`% s = f` %: s;
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infix 9 `%%; fun f`%%s = f` %%:s;
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val list_ccomb = Library.foldl (op `); (* continuous version of list_comb *)
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fun con_app2 con f args = list_ccomb(%%:con,map f args);
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fun con_app con = con_app2 con %#;
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fun if_rec arg f y = if is_rec arg then f (rec_of arg) else y;
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fun app_rec_arg p arg = if_rec arg (fn n => fn x => (p n)`x) I (%# arg);
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fun prj _ _ x ( _::[]) _ = x
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| prj f1 _ x (_::y::ys) 0 = f1 x y
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| prj f1 f2 x (y:: ys) j = prj f1 f2 (f2 x y) ys (j-1);
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fun proj x = prj (fn S => K(%%:"fst" $S)) (fn S => K(%%:"snd" $S)) x;
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fun cproj x = prj (fn S => K(%%:cfstN`S)) (fn S => K(%%:csndN`S)) x;
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fun lift tfn = Library.foldr (fn (x,t)=> (mk_trp(tfn x) ===> t));
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fun /\ v T = %%:Abs_CFunN $ mk_lam(v,T);
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fun /\# (arg,T) = /\ (vname arg) T;
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infixr 9 oo; fun S oo T = %%:cfcompN`S`T;
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val UU = %%:UU_N;
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fun strict f = f`UU === UU;
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fun defined t = t ~= UU;
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fun cpair (t,u) = %%:cpairN`t`u;
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fun spair (t,u) = %%:spairN`t`u;
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fun mk_ctuple [] = HOLogic.unit (* used in match_defs *)
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| mk_ctuple ts = foldr1 cpair ts;
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fun mk_stuple [] = %%:ONE_N
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| mk_stuple ts = foldr1 spair ts;
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fun mk_ctupleT [] = HOLogic.unitT (* used in match_defs *)
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| mk_ctupleT Ts = foldr1 HOLogic.mk_prodT Ts;
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fun mk_maybeT T = Type ("Fixrec.maybe",[T]);
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fun cpair_pat (p1,p2) = %%:cpair_patN $ p1 $ p2;
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fun lift_defined f = lift (fn x => defined (f x));
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fun bound_arg vns v = Bound(length vns -find_index_eq v vns -1);
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fun cont_eta_contract (Const("Cfun.Abs_CFun",TT) $ Abs(a,T,body)) =
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(case cont_eta_contract body of
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body' as (Const("Cfun.Rep_CFun",Ta) $ f $ Bound 0) =>
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if not (0 mem loose_bnos f) then incr_boundvars ~1 f
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else Const("Cfun.Abs_CFun",TT) $ Abs(a,T,body')
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| body' => Const("Cfun.Abs_CFun",TT) $ Abs(a,T,body'))
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| cont_eta_contract(f$t) = cont_eta_contract f $ cont_eta_contract t
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| cont_eta_contract t = t;
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fun idx_name dnames s n = s^(if length dnames = 1 then "" else string_of_int n);
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fun when_funs cons = if length cons = 1 then ["f"]
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else mapn (fn n => K("f"^(string_of_int n))) 1 cons;
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fun when_body cons funarg = let
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fun one_fun n (_,[] ) = /\ "dummy" (funarg(1,n))
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| one_fun n (_,args) = let
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val l2 = length args;
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fun idxs m arg = (if is_lazy arg then fn x=> %%:fupN` %%:ID_N`x
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else I) (Bound(l2-m));
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in cont_eta_contract (foldr''
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(fn (a,t) => %%:ssplitN`(/\# (a,t)))
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(args,
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fn a=> /\#(a,(list_ccomb(funarg(l2,n),mapn idxs 1 args))))
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) end;
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in (if length cons = 1 andalso length(snd(hd cons)) <= 1
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then fn t => %%:strictifyN`t else I)
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(foldr1 (fn (x,y)=> %%:sscaseN`x`y) (mapn one_fun 1 cons)) end;
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end; (* struct *)
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