(* Title: HOLCF/Tools/Domain/domain_axioms.ML
Author: David von Oheimb
Syntax generator for domain command.
*)
signature DOMAIN_AXIOMS =
sig
val copy_of_dtyp :
string Symtab.table -> (int -> term) -> Datatype.dtyp -> term
val calc_axioms :
bool -> string Symtab.table ->
string -> Domain_Library.eq list -> int -> Domain_Library.eq ->
string * (string * term) list * (string * term) list
val add_axioms :
bool ->
((string * typ list) *
(binding * (bool * binding option * typ) list * mixfix) list) list ->
bstring -> Domain_Library.eq list -> theory -> theory
end;
structure Domain_Axioms : DOMAIN_AXIOMS =
struct
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;
(* FIXME: use theory data for this *)
val copy_tab : string Symtab.table =
Symtab.make [(@{type_name "->"}, @{const_name "cfun_map"}),
(@{type_name "++"}, @{const_name "ssum_map"}),
(@{type_name "**"}, @{const_name "sprod_map"}),
(@{type_name "*"}, @{const_name "cprod_map"}),
(@{type_name "u"}, @{const_name "u_map"})];
fun copy_of_dtyp tab r dt =
if Datatype_Aux.is_rec_type dt then copy tab r dt else ID
and copy tab r (Datatype_Aux.DtRec i) = r i
| copy tab r (Datatype_Aux.DtTFree a) = ID
| copy tab r (Datatype_Aux.DtType (c, ds)) =
case Symtab.lookup tab c of
SOME f => list_ccomb (%%:f, map (copy_of_dtyp tab r) ds)
| NONE => (warning ("copy_of_dtyp: unknown type constructor " ^ c); ID);
fun calc_axioms
(definitional : bool)
(map_tab : string Symtab.table)
(comp_dname : string)
(eqs : eq list)
(n : int)
(eqn as ((dname,_),cons) : eq)
: string * (string * term) list * (string * term) list =
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 = Long_Name.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'));
(* ----- axiom and definitions concerning induction ------------------------- *)
val finite_def =
("finite_def",
%%:(dname^"_finite") ==
mk_lam(x_name,
mk_ex("n",(%%:(dname^"_take") $ Bound 0)`Bound 1 === Bound 1)));
in (dnam,
(if definitional then [] else [abs_iso_ax, rep_iso_ax]),
[finite_def])
end; (* let (calc_axioms) *)
(* legacy type inference *)
fun legacy_infer_term thy t =
singleton (Syntax.check_terms (ProofContext.init thy)) (Sign.intern_term thy t);
fun legacy_infer_prop thy t = legacy_infer_term thy (TypeInfer.constrain propT t);
fun infer_props thy = map (apsnd (legacy_infer_prop thy));
fun add_axioms_i x = snd o PureThy.add_axioms (map (Thm.no_attributes o apfst Binding.name) x);
fun add_axioms_infer axms thy = add_axioms_i (infer_props thy axms) thy;
fun add_defs_i x = snd o (PureThy.add_defs false) (map (Thm.no_attributes o apfst Binding.name) x);
fun add_defs_infer defs thy = add_defs_i (infer_props thy defs) thy;
fun add_axioms definitional eqs' comp_dnam (eqs : eq list) thy' =
let
val comp_dname = Sign.full_bname thy' comp_dnam;
val dnames = map (fst o fst) eqs;
val x_name = idx_name dnames "x";
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 =
List.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
List.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))));
(* TEMPORARILY DISABLED
val bisim_def =
("bisim_def", %%:(comp_dname^"_bisim") ==
mk_lam("R", foldr1 mk_conj (mapn one_comp 0 eqs)));
TEMPORARILY DISABLED *)
fun add_one (dnam, axs, dfs) =
Sign.add_path dnam
#> add_axioms_infer axs
#> Sign.parent_path;
val map_tab = Domain_Isomorphism.get_map_tab thy';
val axs = mapn (calc_axioms definitional map_tab comp_dname eqs) 0 eqs;
val thy = thy' |> fold add_one axs;
fun get_iso_info ((dname, tyvars), cons') =
let
fun opt_lazy (lazy,_,t) = if lazy then mk_uT t else t
fun prod (_,args,_) =
case args of [] => oneT
| _ => foldr1 mk_sprodT (map opt_lazy args);
val ax_abs_iso = PureThy.get_thm thy (dname ^ ".abs_iso");
val ax_rep_iso = PureThy.get_thm thy (dname ^ ".rep_iso");
val lhsT = Type(dname,tyvars);
val rhsT = foldr1 mk_ssumT (map prod cons');
val rep_const = Const(dname^"_rep", lhsT ->> rhsT);
val abs_const = Const(dname^"_abs", rhsT ->> lhsT);
in
{
absT = lhsT,
repT = rhsT,
abs_const = abs_const,
rep_const = rep_const,
abs_inverse = ax_abs_iso,
rep_inverse = ax_rep_iso
}
end;
val dom_binds = map (Binding.name o Long_Name.base_name) dnames;
val thy =
if definitional then thy
else snd (Domain_Isomorphism.define_take_functions
(dom_binds ~~ map get_iso_info eqs') thy);
fun add_one' (dnam, axs, dfs) =
Sign.add_path dnam
#> add_defs_infer dfs
#> Sign.parent_path;
val thy = fold add_one' axs thy;
(* declare lub_take axioms *)
local
fun ax_lub_take dname =
let
val dnam : string = Long_Name.base_name dname;
val take_const = %%:(dname^"_take");
val lub = %%: @{const_name lub};
val image = %%: @{const_name image};
val UNIV = %%: @{const_name UNIV};
val lhs = lub $ (image $ take_const $ UNIV);
val ax = mk_trp (lhs === ID);
in
add_one (dnam, [("lub_take", ax)], [])
end
in
val thy =
if definitional then thy
else fold ax_lub_take dnames thy
end;
in
thy
|> Sign.add_path comp_dnam
(*
|> add_defs_infer [bisim_def]
*)
|> Sign.parent_path
end; (* let (add_axioms) *)
end; (* struct *)