(* Title: HOLCF/Tools/Domain/domain_axioms.ML
Author: David von Oheimb
Syntax generator for domain command.
*)
signature DOMAIN_AXIOMS =
sig
val copy_of_dtyp : (int -> term) -> Datatype.dtyp -> term
val calc_axioms :
string -> Domain_Library.eq list -> int -> Domain_Library.eq ->
string * (string * term) list * (string * term) list
val add_axioms :
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 r dt = if DatatypeAux.is_rec_type dt then copy r dt else ID
and copy r (DatatypeAux.DtRec i) = r i
| copy r (DatatypeAux.DtTFree a) = ID
| copy r (DatatypeAux.DtType (c, ds)) =
case Symtab.lookup copy_tab c of
SOME f => list_ccomb (%%:f, map (copy_of_dtyp r) ds)
| NONE => (warning ("copy_of_dtyp: unknown type constructor " ^ c); ID);
fun calc_axioms
(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'));
val when_def = ("when_def",%%:(dname^"_when") ==
List.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 r i = proj (Bound 0) eqs i;
in ("copy_def", %%:(dname^"_copy") ==
/\ "f" (dc_abs oo (copy_of_dtyp r (dtyp_of_eq eqn)) oo dc_rep)) 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 mk_up else I) (Bound(z-x));
fun parms vs = mk_stuple (mapn (idxs(length vs)) 1 vs);
fun inj y 1 _ = y
| inj y _ 0 = mk_sinl y
| inj y i j = mk_sinr (inj y (i-1) (j-1));
in List.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) => (List.foldr /\#
(if con'=con then TT else FF) args)) cons))
in map ddef cons end;
val mat_defs =
let
fun mdef (con,_) =
let
val k = Bound 0
val x = Bound 1
fun one_con (con', args') =
if con'=con then k else List.foldr /\# mk_fail args'
val w = list_ccomb(%%:(dname^"_when"), map one_con cons)
val rhs = /\ "x" (/\ "k" (w ` x))
in (mat_name con ^"_def", %%:(mat_name con) == rhs) end
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 [] => mk_return HOLogic.unit
| _ => mk_ctuple_pat ps ` mk_ctuple xs;
fun one_con (con',args') = List.foldr /\# (if con'=con then rhs else mk_fail) 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
List.foldr /\# (Bound (length args - n)) args) cons))) (sel_of arg);
in map_filter I (maps (fn (con,args) => mapn (sdef con) 1 args) cons) end;
(* ----- axiom and definitions concerning induction ------------------------- *)
val reach_ax = ("reach", mk_trp(proj (mk_fix (%%:(comp_dname^"_copy"))) eqs n
`%x_name === %:x_name));
val take_def =
("take_def",
%%:(dname^"_take") ==
mk_lam("n",proj
(mk_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 @ mat_defs @ pat_defs @ sel_defs @
[take_def, 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_matchers (((dname,_),cons) : eq) thy =
let
val con_names = map fst cons;
val mat_names = map mat_name con_names;
fun qualify n = Sign.full_name thy (Binding.name n);
val ms = map qualify con_names ~~ map qualify mat_names;
in Fixrec.add_matchers ms thy end;
fun add_axioms 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 copy_app dname = %%:(dname^"_copy")`Bound 0;
val copy_def = ("copy_def" , %%:(comp_dname^"_copy") ==
/\ "f"(mk_ctuple (map copy_app dnames)));
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))));
val bisim_def =
("bisim_def",
%%:(comp_dname^"_bisim")==mk_lam("R", foldr1 mk_conj (mapn one_comp 0 eqs)));
fun add_one (dnam, axs, dfs) =
Sign.add_path dnam
#> add_defs_infer dfs
#> add_axioms_infer axs
#> Sign.parent_path;
val thy = fold add_one (mapn (calc_axioms comp_dname eqs) 0 eqs) thy';
in thy |> Sign.add_path comp_dnam
|> add_defs_infer (bisim_def::(if length eqs>1 then [copy_def] else []))
|> Sign.parent_path
|> fold add_matchers eqs
end; (* let (add_axioms) *)
end; (* struct *)