(* Title: HOLCF/domain/library.ML
ID: $Id$
Author: David von Oheimb
Library for domain section.
*)
(* ----- general support ---------------------------------------------------- *)
fun Id x = x;
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,Id);
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);
(* 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 assoc(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* (* 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);
(* ----- 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);
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;
fun mk_ex (x,P) = mk_exists (x,dummyT,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 = mk_not (S === T);
infix 1 <<; fun S << T = %%:"op <<" $ S $ T;
infix 1 ~<<; fun S ~<< T = mk_not (S << T);
infix 9 ` ; fun f` x = %%:"Rep_CFun" $ 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) Id (%# 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(%%:"cfst"`S)) (fn S => K(%%:"csnd"`S)) x;
fun prj' _ _ x ( _::[]) _ = x
| prj' f1 _ x (_:: ys) 0 = f1 x (foldr' 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("cfst",mk_prodT(dummyT,t)->>dummyT)`S)
(fn S => fn t => Const("csnd",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_CFun" $ mk_lam(v,T);
fun /\# (arg,T) = /\ (vname arg) T;
infixr 9 oo; fun S oo T = %%:"cfcomp"`S`T;
val UU = %%:"UU";
fun strict f = f`UU === UU;
fun defined t = t ~= UU;
fun cpair (S,T) = %%:"cpair"`S`T;
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("Abs_CFun",TT) $ Abs(a,T,body)) =
(case cont_eta_contract body of
body' as (Const("Rep_CFun",Ta) $ f $ Bound 0) =>
if not (0 mem loose_bnos f) then incr_boundvars ~1 f
else Const("Abs_CFun",TT) $ Abs(a,T,body')
| body' => Const("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=> %%:"fup"`%%"ID"`x
else Id) (Bound(l2-m));
in cont_eta_contract (foldr''
(fn (a,t) => %%:"ssplit"`(/\# (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 => %%:"strictify"`t else Id)
(foldr' (fn (x,y)=> %%:"sscase"`x`y) (mapn one_fun 1 cons)) end;
end; (* struct *)