author | huffman |
Mon, 01 Mar 2010 09:55:32 -0800 | |
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parent 35468 | 09bc6a2e2296 |
child 35494 | 45c9a8278faf |
permissions | -rw-r--r-- |
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(* Title: HOLCF/Tools/Domain/domain_axioms.ML |
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Author: David von Oheimb |
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Syntax generator for domain command. |
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*) |
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signature DOMAIN_AXIOMS = |
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sig |
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val copy_of_dtyp : |
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string Symtab.table -> (int -> term) -> Datatype.dtyp -> term |
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val calc_axioms : |
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bool -> string Symtab.table -> |
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string -> Domain_Library.eq list -> int -> Domain_Library.eq -> |
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string * (string * term) list * (string * term) list |
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val add_axioms : |
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bool -> |
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bstring -> Domain_Library.eq list -> theory -> theory |
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end; |
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structure Domain_Axioms : DOMAIN_AXIOMS = |
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struct |
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open Domain_Library; |
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infixr 0 ===>;infixr 0 ==>;infix 0 == ; |
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infix 1 ===; infix 1 ~= ; infix 1 <<; infix 1 ~<<; |
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infix 9 ` ; infix 9 `% ; infix 9 `%%; infixr 9 oo; |
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(* FIXME: use theory data for this *) |
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val copy_tab : string Symtab.table = |
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Symtab.make [(@{type_name "->"}, @{const_name "cfun_map"}), |
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(@{type_name "++"}, @{const_name "ssum_map"}), |
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(@{type_name "**"}, @{const_name "sprod_map"}), |
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(@{type_name "*"}, @{const_name "cprod_map"}), |
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(@{type_name "u"}, @{const_name "u_map"})]; |
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fun copy_of_dtyp tab r dt = |
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if Datatype_Aux.is_rec_type dt then copy tab r dt else ID |
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and copy tab r (Datatype_Aux.DtRec i) = r i |
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| copy tab r (Datatype_Aux.DtTFree a) = ID |
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| copy tab r (Datatype_Aux.DtType (c, ds)) = |
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case Symtab.lookup tab c of |
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SOME f => list_ccomb (%%:f, map (copy_of_dtyp tab r) ds) |
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| NONE => (warning ("copy_of_dtyp: unknown type constructor " ^ c); ID); |
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fun calc_axioms |
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(definitional : bool) |
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(map_tab : string Symtab.table) |
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(comp_dname : string) |
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(eqs : eq list) |
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(n : int) |
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(eqn as ((dname,_),cons) : eq) |
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: string * (string * term) list * (string * term) list = |
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let |
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(* ----- axioms and definitions concerning the isomorphism ------------------ *) |
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val dc_abs = %%:(dname^"_abs"); |
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val dc_rep = %%:(dname^"_rep"); |
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val x_name'= "x"; |
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val x_name = idx_name eqs x_name' (n+1); |
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val dnam = Long_Name.base_name dname; |
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val abs_iso_ax = ("abs_iso", mk_trp(dc_rep`(dc_abs`%x_name') === %:x_name')); |
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val rep_iso_ax = ("rep_iso", mk_trp(dc_abs`(dc_rep`%x_name') === %:x_name')); |
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val copy_def = |
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let fun r i = proj (Bound 0) eqs i; |
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in |
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("copy_def", %%:(dname^"_copy") == /\ "f" |
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(dc_abs oo (copy_of_dtyp map_tab r (dtyp_of_eq eqn)) oo dc_rep)) |
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end; |
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(* ----- axiom and definitions concerning induction ------------------------- *) |
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val reach_ax = ("reach", mk_trp(proj (mk_fix (%%:(comp_dname^"_copy"))) eqs n |
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`%x_name === %:x_name)); |
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val take_def = |
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("take_def", |
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%%:(dname^"_take") == |
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mk_lam("n",proj |
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(mk_iterate (Bound 0, %%:(comp_dname^"_copy"), UU)) eqs n)); |
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val finite_def = |
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("finite_def", |
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%%:(dname^"_finite") == |
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mk_lam(x_name, |
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mk_ex("n",(%%:(dname^"_take") $ Bound 0)`Bound 1 === Bound 1))); |
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in (dnam, |
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(if definitional then [] else [abs_iso_ax, rep_iso_ax, reach_ax]), |
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(if definitional then [] else [copy_def]) @ |
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[take_def, finite_def]) |
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end; (* let (calc_axioms) *) |
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(* legacy type inference *) |
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fun legacy_infer_term thy t = |
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singleton (Syntax.check_terms (ProofContext.init thy)) (Sign.intern_term thy t); |
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fun legacy_infer_prop thy t = legacy_infer_term thy (TypeInfer.constrain propT t); |
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fun infer_props thy = map (apsnd (legacy_infer_prop thy)); |
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fun add_axioms_i x = snd o PureThy.add_axioms (map (Thm.no_attributes o apfst Binding.name) x); |
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fun add_axioms_infer axms thy = add_axioms_i (infer_props thy axms) thy; |
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fun add_defs_i x = snd o (PureThy.add_defs false) (map (Thm.no_attributes o apfst Binding.name) x); |
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fun add_defs_infer defs thy = add_defs_i (infer_props thy defs) thy; |
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fun add_axioms definitional comp_dnam (eqs : eq list) thy' = |
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let |
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val comp_dname = Sign.full_bname thy' comp_dnam; |
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val dnames = map (fst o fst) eqs; |
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val x_name = idx_name dnames "x"; |
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fun copy_app dname = %%:(dname^"_copy")`Bound 0; |
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val copy_def = ("copy_def" , %%:(comp_dname^"_copy") == |
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/\ "f"(mk_ctuple (map copy_app dnames))); |
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fun one_con (con, _, args) = |
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let |
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val nonrec_args = filter_out is_rec args; |
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val rec_args = filter is_rec args; |
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val recs_cnt = length rec_args; |
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val allargs = nonrec_args @ rec_args |
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@ map (upd_vname (fn s=> s^"'")) rec_args; |
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val allvns = map vname allargs; |
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fun vname_arg s arg = if is_rec arg then vname arg^s else vname arg; |
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val vns1 = map (vname_arg "" ) args; |
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val vns2 = map (vname_arg "'") args; |
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val allargs_cnt = length nonrec_args + 2*recs_cnt; |
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val rec_idxs = (recs_cnt-1) downto 0; |
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val nonlazy_idxs = map snd (filter_out (fn (arg,_) => is_lazy arg) |
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(allargs~~((allargs_cnt-1) downto 0))); |
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fun rel_app i ra = proj (Bound(allargs_cnt+2)) eqs (rec_of ra) $ |
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Bound (2*recs_cnt-i) $ Bound (recs_cnt-i); |
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val capps = |
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List.foldr |
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mk_conj |
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(mk_conj( |
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Bound(allargs_cnt+1)===list_ccomb(%%:con,map (bound_arg allvns) vns1), |
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Bound(allargs_cnt+0)===list_ccomb(%%:con,map (bound_arg allvns) vns2))) |
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(mapn rel_app 1 rec_args); |
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in |
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List.foldr |
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mk_ex |
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(Library.foldr mk_conj |
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(map (defined o Bound) nonlazy_idxs,capps)) allvns |
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end; |
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fun one_comp n (_,cons) = |
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mk_all (x_name(n+1), |
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mk_all (x_name(n+1)^"'", |
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mk_imp (proj (Bound 2) eqs n $ Bound 1 $ Bound 0, |
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foldr1 mk_disj (mk_conj(Bound 1 === UU,Bound 0 === UU) |
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::map one_con cons)))); |
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(* TEMPORARILY DISABLED |
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val bisim_def = |
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("bisim_def", %%:(comp_dname^"_bisim") == |
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mk_lam("R", foldr1 mk_conj (mapn one_comp 0 eqs))); |
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TEMPORARILY DISABLED *) |
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fun add_one (dnam, axs, dfs) = |
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Sign.add_path dnam |
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#> add_defs_infer dfs |
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#> add_axioms_infer axs |
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#> Sign.parent_path; |
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val map_tab = Domain_Isomorphism.get_map_tab thy'; |
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val thy = thy' |
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|> fold add_one (mapn (calc_axioms definitional map_tab comp_dname eqs) 0 eqs); |
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domain_isomorphism package defines combined copy function
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val use_copy_def = length eqs>1 andalso not definitional; |
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in |
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thy |
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|> Sign.add_path comp_dnam |
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|> add_defs_infer ((*bisim_def::*)(if use_copy_def then [copy_def] else [])) |
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|> Sign.parent_path |
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end; (* let (add_axioms) *) |
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end; (* struct *) |