(* Title: HOLCF/domain/axioms.ML
ID: $Id$
Author : David von Oheimb
Copyright 1995, 1996 TU Muenchen
syntax generator for domain section
*)
structure Domain_Axioms = struct
local
open Domain_Library;
infixr 0 ===>;infixr 0 ==>;infix 0 == ;
infix 1 ===; infix 1 ~= ; infix 1 <<; infix 1 ~<<;
infix 9 ` ; infix 9 `% ; infix 9 `%%; infixr 9 oo;
fun infer_types thy' = map (inferT_axm (sign_of thy'));
fun calc_axioms comp_dname (eqs : eq list) n (((dname,_),cons) : eq)=
let
(* ----- axioms and definitions concerning the isomorphism ------------------ *)
val dc_abs = %%(dname^"_abs");
val dc_rep = %%(dname^"_rep");
val x_name'= "x";
val x_name = idx_name eqs x_name' (n+1);
val dnam = Sign.base_name dname;
val abs_iso_ax = ("abs_iso" ,mk_trp(dc_rep`(dc_abs`%x_name')=== %x_name'));
val rep_iso_ax = ("rep_iso" ,mk_trp(dc_abs`(dc_rep`%x_name')=== %x_name'));
val when_def = ("when_def",%%(dname^"_when") ==
foldr (uncurry /\ ) (when_funs cons, /\x_name'((when_body cons (fn (x,y) =>
Bound(1+length cons+x-y)))`(dc_rep`Bound 0))));
fun con_def outer recu m n (_,args) = let
fun idxs z x arg = (if is_lazy arg then fn t => %%"up"`t else Id)
(if recu andalso is_rec arg then (cproj (Bound z) eqs
(rec_of arg))`Bound(z-x) else Bound(z-x));
fun parms [] = %%"ONE"
| parms vs = foldr'(fn(x,t)=> %%"spair"`x`t)(mapn (idxs(length vs))1 vs);
fun inj y 1 _ = y
| inj y _ 0 = %%"sinl"`y
| inj y i j = %%"sinr"`(inj y (i-1) (j-1));
in foldr /\# (args, outer (inj (parms args) m n)) end;
val copy_def = ("copy_def", %%(dname^"_copy") == /\"f" (dc_abs oo
foldl (op `) (%%(dname^"_when") ,
mapn (con_def Id true (length cons)) 0 cons)));
(* -- definitions concerning the constructors, discriminators and selectors - *)
val con_defs = mapn (fn n => fn (con,args) => (extern_name con ^"_def",
%%con == con_def (fn t => dc_abs`t) false (length cons) n (con,args))) 0 cons;
val dis_defs = let
fun ddef (con,_) = (dis_name con ^"_def",%%(dis_name con) ==
mk_cRep_CFun(%%(dname^"_when"),map
(fn (con',args) => (foldr /\#
(args,if con'=con then %%"TT" else %%"FF"))) cons))
in map ddef cons end;
val sel_defs = let
fun sdef con n arg = (sel_of arg^"_def",%%(sel_of arg) ==
mk_cRep_CFun(%%(dname^"_when"),map
(fn (con',args) => if con'<>con then %%"UU" else
foldr /\# (args,Bound (length args - n))) cons));
in flat(map (fn (con,args) => mapn (sdef con) 1 args) cons) end;
(* ----- axiom and definitions concerning induction ------------------------- *)
val reach_ax = ("reach", mk_trp(cproj (%%"fix"`%%(comp_dname^"_copy")) eqs n
`%x_name === %x_name));
val take_def = ("take_def",%%(dname^"_take") == mk_lam("n",cproj'
(%%"iterate" $ Bound 0 $ %%(comp_dname^"_copy") $ %%"UU") eqs n));
val finite_def = ("finite_def",%%(dname^"_finite") == mk_lam(x_name,
mk_ex("n",(%%(dname^"_take") $ Bound 0)`Bound 1 === Bound 1)));
in (dnam,
[abs_iso_ax, rep_iso_ax, reach_ax],
[when_def, copy_def] @
con_defs @ dis_defs @ sel_defs @
[take_def, finite_def])
end; (* let *)
fun add_axioms_i x = #1 o PureThy.add_axioms_i (map Thm.no_attributes x);
in (* local *)
fun add_axioms (comp_dnam, eqs : eq list) thy' = let
val comp_dname = Sign.full_name (sign_of thy') comp_dnam;
val dnames = map (fst o fst) eqs;
val x_name = idx_name dnames "x";
fun copy_app dname = %%(dname^"_copy")`Bound 0;
val copy_def = ("copy_def" , %%(comp_dname^"_copy") ==
/\"f"(foldr' cpair (map copy_app dnames)));
val bisim_def = ("bisim_def",%%(comp_dname^"_bisim")==mk_lam("R",
let
fun one_con (con,args) = let
val nonrec_args = filter_out is_rec args;
val rec_args = filter is_rec args;
val recs_cnt = length rec_args;
val allargs = nonrec_args @ rec_args
@ map (upd_vname (fn s=> s^"'")) rec_args;
val allvns = map vname allargs;
fun vname_arg s arg = if is_rec arg then vname arg^s else vname arg;
val vns1 = map (vname_arg "" ) args;
val vns2 = map (vname_arg "'") args;
val allargs_cnt = length nonrec_args + 2*recs_cnt;
val rec_idxs = (recs_cnt-1) downto 0;
val nonlazy_idxs = map snd (filter_out (fn (arg,_) => is_lazy arg)
(allargs~~((allargs_cnt-1) downto 0)));
fun rel_app i ra = proj (Bound(allargs_cnt+2)) eqs (rec_of ra) $
Bound (2*recs_cnt-i) $ Bound (recs_cnt-i);
val capps = foldr mk_conj (mapn rel_app 1 rec_args, mk_conj(
Bound(allargs_cnt+1)===mk_cRep_CFun(%%con,map (bound_arg allvns) vns1),
Bound(allargs_cnt+0)===mk_cRep_CFun(%%con,map (bound_arg allvns) vns2)));
in foldr mk_ex (allvns, foldr mk_conj
(map (defined o Bound) nonlazy_idxs,capps)) end;
fun one_comp n (_,cons) =mk_all(x_name(n+1),mk_all(x_name(n+1)^"'",mk_imp(
proj (Bound 2) eqs n $ Bound 1 $ Bound 0,
foldr' mk_disj (mk_conj(Bound 1 === UU,Bound 0 === UU)
::map one_con cons))));
in foldr' mk_conj (mapn one_comp 0 eqs)end ));
fun add_one (thy,(dnam,axs,dfs)) = thy
|> Theory.add_path dnam
|> add_axioms_i (infer_types thy' dfs)(*add_defs_i*)
|> add_axioms_i (infer_types thy' axs)
|> Theory.parent_path;
val thy = foldl add_one (thy', mapn (calc_axioms comp_dname eqs) 0 eqs);
in thy |> Theory.add_path comp_dnam
|> add_axioms_i (infer_types thy'
(bisim_def::(if length eqs>1 then [copy_def] else [])))
|> Theory.parent_path
end;
end; (* local *)
end; (* struct *)