(* Title: HOLCF/Tools/domain/domain_library.ML ID: $Id: domain_library.ML,v 1.3 2007/09/23 20:23:27 wenzelm Exp $ 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 = Sign.string_of_typ 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); (* ----- qualified names of HOLCF constants ----- *) val lessN = @{const_name Porder.sq_le}; val UU_N = "Pcpo.UU"; val admN = "Adm.adm"; val compactN = "Adm.compact"; 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 cpair_patN = "Fixrec.cpair_pat"; val branchN = "Fixrec.branch"; 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); 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 = %%: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; 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(%%:cfstN`S)) (fn S => K(%%:csndN`S)) x; 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 (t,u) = %%:cpairN`t`u; fun spair (t,u) = %%:spairN`t`u; fun mk_ctuple [] = HOLogic.unit (* used in match_defs *) | mk_ctuple ts = foldr1 cpair ts; fun mk_stuple [] = %%:ONE_N | 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) = %%:cpair_patN $ p1 $ p2; 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,(list_ccomb(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) (foldr1 (fn (x,y)=> %%:sscaseN`x`y) (mapn one_fun 1 cons)) end; end; (* struct *)