(* Title: HOLCF/Tools/domain/domain_axioms.ML Author: David von Oheimb Syntax generator for domain command. *) 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 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 = 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 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) = List.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 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,_) = (mat_name con ^"_def",%%:(mat_name con) == list_ccomb(%%:(dname^"_when"),map (fn (con',args) => (List.foldr /\# (if con'=con then mk_return (mk_ctuple (map (bound_arg args) args)) else mk_fail) 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 [] => 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 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 (mk_fix (%%:(comp_dname^"_copy"))) eqs n `%x_name === %:x_name)); val take_def = ("take_def",%%:(dname^"_take") == mk_lam("n",cproj (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 FixrecPackage.add_matchers ms thy end; in (* local *) 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))); 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 = 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)))); in foldr1 mk_conj (mapn one_comp 0 eqs)end )); fun add_one (thy,(dnam,axs,dfs)) = thy |> Sign.add_path dnam |> add_defs_infer dfs |> add_axioms_infer axs |> Sign.parent_path; val thy = Library.foldl add_one (thy', mapn (calc_axioms comp_dname eqs) 0 eqs); 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; (* local *) end; (* struct *)