(* library.ML
ID: $Id$
Author: David von Oheimb
Created: 18-Jul-95 extracted from syntax.ML, axioms.ML, extender.ML, interface.ML
Updated: 30-Aug-95
Copyright 1995 TU Muenchen
*)
(* ----- 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 LIST "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)) (xs,([],start));
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);
(* fn : ('a -> 'a) -> ('a -> 'a) -> 'a -> 'b list -> int -> 'a *)
fun bin_branchr f1 f2 y is j = let
fun bb y 1 _ = y
| bb y _ 0 = f1 y
| bb y i j = if i=2 then (f2 y) else bb (f2 y) (i-1) (j-1)
in bb y (length is) j end;
fun atomize thm = case concl_of thm of
_ $ (Const("op &",_) $ _ $ _) => atomize (thm RS conjunct1) @
atomize (thm RS conjunct2)
| _ $ (Const("All" ,_) $ Abs (s,_,_)) => atomize (thm RS
(read_instantiate [("x","?"^s)] spec))
| _ => [thm];
(* ----- specific support for domain ---------------------------------------------- *)
structure Domain_Library = struct
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 explode end;
fun extern_name con = case 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", "x..","f..","P.." as names *)
(*a number string is added if necessary *)
fun mk_var_names types : string list = let
fun typid (Type (id,_) ) = hd (explode id)
| typid (TFree (id,_) ) = hd (tl (explode id))
| typid (TVar ((id,_),_)) = hd (tl (explode id));
fun nonreserved id = let val cs = explode id in
if not(hd cs mem ["x","f","P"]) then id
else implode(chr(1+ord (hd cs))::tl cs) end;
fun index_vnames(vn::vns,tab) =
(case assoc(tab,vn) of
None => if vn mem vns
then (vn^"1") :: index_vnames(vns,(vn,2)::tab)
else vn :: index_vnames(vns, tab)
| Some(i) => (vn^(string_of_int i)) :: index_vnames(vns,(vn,i+1)::tab))
| index_vnames([],tab) = [];
in index_vnames(map (nonreserved o typid) types,[("o",1)]) end;
fun type_name_vars (Type(name,typevars)) = (name,typevars)
| type_name_vars _ = Imposs "library:type_name_vars";
(* ----- support for type and mixfix expressions ----- *)
fun mk_tvar s = TFree("'"^s,["pcpo"]);
fun mk_typ t (S,T) = Type(t,[S,T]);
infixr 5 -->;
infixr 6 ~>; val op ~> = mk_typ "->";
val NoSyn' = ThyOps.Mixfix NoSyn;
(* ----- 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 *)
val rec_of = snd o first;
val is_lazy = fst o first;
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 is_one_con_one_arg p cons = length cons = 1 andalso let val args = snd(hd cons) in
length args = 1 andalso p (hd args) end;
(* ----- 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 tf (Type (s,args)) = foldl (op $) (%s,map tf args)
| tf (TFree(s,_ )) = %s
| tf _ = Imposs "mk_constrainall";
in
fun mk_constrain (typ,T) = %%"_constrain" $ T $ tf typ;
fun mk_constrainall (x,typ,P) = %%"All" $ (%%"_constrainAbs"$Abs(x,dummyT,P)$tf typ);
end;
fun mk_ex (x,P) = mk_exists (x,dummyT,P);
fun mk_not P = Const("not" ,boolT --> boolT) $ P;
end;
fun mk_All (x,P) = %%"all" $ mk_lam(x,P); (* meta universal quantification *)
infixr 0 ===>;fun S ===> T = Const("==>", dummyT) $ S $ T;
infixr 0 ==>;fun S ==> T = mk_trp S ===> mk_trp T;
infix 0 ==; fun S == T = Const("==", dummyT) $ S $ T;
infix 1 ===; fun S === T = Const("op =", dummyT) $ S $ T;
infix 1 ~=; fun S ~= T = mk_not (S === T);
infix 1 <<; fun S << T = Const("op <<", dummyT) $ S $ T;
infix 1 ~<<; fun S ~<< T = mk_not (S << T);
infix 9 ` ; fun f` x = %%"fapp" $ f $ x;
infix 9 `% ; fun f`% s = f` % s;
infix 9 `%%; fun f`%%s = f` %%s;
fun mk_cfapp (F,As) = foldl (op `) (F,As);
fun con_app2 con f args = mk_cfapp(%%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);
val cproj = bin_branchr (fn S => %%"cfst"`S) (fn S => %%"csnd"`S);
val proj = bin_branchr (fn S => %%"fst" $S) (fn S => %%"snd" $S);
fun lift tfn = foldr (fn (x,t)=> (mk_trp(tfn x) ===> t));
fun /\ v T = %%"fabs" $ 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(v,vns)-1);
fun cont_eta_contract (Const("fabs",TT) $ Abs(a,T,body)) =
(case cont_eta_contract body of
body' as (Const("fapp",Ta) $ f $ Bound 0) =>
if not (0 mem loose_bnos f) then incr_boundvars ~1 f
else Const("fabs",TT) $ Abs(a,T,body')
| body' => Const("fabs",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=> %%"lift"`%%"ID"`x
else Id) (Bound(l2-m));
in cont_eta_contract (foldr''
(fn (a,t) => %%"ssplit"`(/\# (a,t)))
(args,
fn a => /\# (a,(mk_cfapp(funarg (l2,n),mapn idxs 1 args))))
) end;
in foldr' (fn (x,y)=> %%"sswhen"`x`y) (mapn one_fun 1 cons) end;
end; (* struct *)