(* Title: HOLCF/domain/axioms.ML
ID: $Id$
Author: David von Oheimb
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 (Theory.inferT_axm 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 /\ ) (/\x_name'((when_body cons (fn (x,y) =>
Bound(1+length cons+x-y)))`(dc_rep`Bound 0))) (when_funs cons));
val copy_def = let
fun idxs z x arg = if is_rec arg
then (cproj (Bound z) eqs (rec_of arg))`Bound(z-x)
else Bound(z-x);
fun one_con (con,args) =
foldr /\# (list_ccomb (%%:con, mapn (idxs (length args)) 1 args)) args;
in ("copy_def", %%:(dname^"_copy") ==
/\"f" (list_ccomb (%%:(dname^"_when"), map one_con cons))) end;
(* -- definitions concerning the constructors, discriminators and selectors - *)
fun con_def m n (_,args) = let
fun idxs z x arg = (if is_lazy arg then fn t => %%:upN`t else I) (Bound(z-x));
fun parms vs = mk_stuple (mapn (idxs(length vs)) 1 vs);
fun inj y 1 _ = y
| inj y _ 0 = %%:sinlN`y
| inj y i j = %%:sinrN`(inj y (i-1) (j-1));
in foldr /\# (dc_abs`(inj (parms args) m n)) args end;
val con_defs = mapn (fn n => fn (con,args) =>
(extern_name con ^"_def", %%:con == con_def (length cons) n (con,args))) 0 cons;
val dis_defs = let
fun ddef (con,_) = (dis_name con ^"_def",%%:(dis_name con) ==
list_ccomb(%%:(dname^"_when"),map
(fn (con',args) => (foldr /\#
(if con'=con then %%:TT_N else %%:FF_N) args)) cons))
in map ddef cons end;
val mat_defs = let
fun mdef (con,_) = (mat_name con ^"_def",%%:(mat_name con) ==
list_ccomb(%%:(dname^"_when"),map
(fn (con',args) => (foldr /\#
(if con'=con
then %%:returnN`(mk_ctuple (map (bound_arg args) args))
else %%:failN) args)) cons))
in map mdef cons end;
val pat_defs =
let
fun pdef (con,args) =
let
val ps = mapn (fn n => fn _ => %:("pat" ^ string_of_int n)) 1 args;
val xs = map (bound_arg args) args;
val r = Bound (length args);
val rhs = case args of [] => %%:returnN ` HOLogic.unit
| _ => foldr1 cpair_pat ps ` mk_ctuple xs;
fun one_con (con',args') = foldr /\# (if con'=con then rhs else %%:failN) args';
in (pat_name con ^"_def", list_comb (%%:(pat_name con), ps) ==
list_ccomb(%%:(dname^"_when"), map one_con cons))
end
in map pdef cons end;
val sel_defs = let
fun sdef con n arg = Option.map (fn sel => (sel^"_def",%%:sel ==
list_ccomb(%%:(dname^"_when"),map
(fn (con',args) => if con'<>con then UU else
foldr /\# (Bound (length args - n)) args) cons))) (sel_of arg);
in List.mapPartial I (List.concat(map (fn (con,args) => mapn (sdef con) 1 args) cons)) end;
(* ----- axiom and definitions concerning induction ------------------------- *)
val reach_ax = ("reach", mk_trp(cproj (%%:fixN`%%(comp_dname^"_copy")) eqs n
`%x_name === %:x_name));
val take_def = ("take_def",%%:(dname^"_take") == mk_lam("n",cproj
(%%:iterateN $ 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 @ mat_defs @ pat_defs @ sel_defs @
[take_def, finite_def])
end; (* let *)
fun add_axioms_i x = snd o PureThy.add_axioms_i (map Thm.no_attributes x);
fun add_axioms_infer axms thy = add_axioms_i (infer_types thy axms) thy;
fun add_defs_i x = snd o (PureThy.add_defs_i false) (map Thm.no_attributes x);
fun add_defs_infer defs thy = add_defs_i (infer_types thy defs) thy;
in (* local *)
fun add_axioms (comp_dnam, eqs : eq list) thy' = let
val comp_dname = Sign.full_name 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"(foldr1 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 = List.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 (mk_conj(
Bound(allargs_cnt+1)===list_ccomb(%%:con,map (bound_arg allvns) vns1),
Bound(allargs_cnt+0)===list_ccomb(%%:con,map (bound_arg allvns) vns2)))
(mapn rel_app 1 rec_args);
in foldr mk_ex (Library.foldr mk_conj
(map (defined o Bound) nonlazy_idxs,capps)) allvns 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,
foldr1 mk_disj (mk_conj(Bound 1 === UU,Bound 0 === UU)
::map one_con cons))));
in foldr1 mk_conj (mapn one_comp 0 eqs)end ));
fun add_one (thy,(dnam,axs,dfs)) = thy
|> Theory.add_path dnam
|> add_defs_infer dfs
|> add_axioms_infer axs
|> Theory.parent_path;
val thy = Library.foldl add_one (thy', mapn (calc_axioms comp_dname eqs) 0 eqs);
in thy |> Theory.add_path comp_dnam
|> add_defs_infer (bisim_def::(if length eqs>1 then [copy_def] else []))
|> Theory.parent_path
end;
end; (* local *)
end; (* struct *)