(* Title: HOL/Tools/specification_package.ML ID: $Id: specification_package.ML,v 1.46 2007/10/06 14:50:05 wenzelm Exp $ Author: Sebastian Skalberg, TU Muenchen Package for defining constants by specification. *) signature SPECIFICATION_PACKAGE = sig val quiet_mode: bool ref val add_specification: string option -> (bstring * xstring * bool) list -> theory * thm -> theory * thm end structure SpecificationPackage: SPECIFICATION_PACKAGE = struct (* messages *) val quiet_mode = ref false fun message s = if ! quiet_mode then () else writeln s (* Actual code *) local val exE_some = thm "exE_some"; fun mk_definitional [] arg = arg | mk_definitional ((thname,cname,covld)::cos) (thy,thm) = case HOLogic.dest_Trueprop (concl_of thm) of Const("Ex",_) $ P => let val ctype = domain_type (type_of P) val cname_full = Sign.intern_const thy cname val cdefname = if thname = "" then Thm.def_name (Sign.base_name cname) else thname val def_eq = Logic.mk_equals (Const(cname_full,ctype), HOLogic.choice_const ctype $ P) val (thms, thy') = PureThy.add_defs_i covld [((cdefname,def_eq),[])] thy val thm' = [thm,hd thms] MRS exE_some in mk_definitional cos (thy',thm') end | _ => raise THM ("Internal error: Bad specification theorem",0,[thm]) fun mk_axiomatic axname cos arg = let fun process [] (thy,tm) = let val (thms, thy') = PureThy.add_axioms_i [((axname,HOLogic.mk_Trueprop tm),[])] thy in (thy',hd thms) end | process ((thname,cname,covld)::cos) (thy,tm) = case tm of Const("Ex",_) $ P => let val ctype = domain_type (type_of P) val cname_full = Sign.intern_const thy cname val cdefname = if thname = "" then Thm.def_name (Sign.base_name cname) else thname val co = Const(cname_full,ctype) val thy' = Theory.add_finals_i covld [co] thy val tm' = case P of Abs(_, _, bodt) => subst_bound (co, bodt) | _ => P $ co in process cos (thy',tm') end | _ => raise TERM ("Internal error: Bad specification theorem",[tm]) in process cos arg end in fun proc_exprop axiomatic cos arg = case axiomatic of SOME axname => mk_axiomatic axname cos (apsnd (HOLogic.dest_Trueprop o concl_of) arg) | NONE => mk_definitional cos arg end fun add_specification axiomatic cos arg = arg |> apsnd Thm.freezeT |> proc_exprop axiomatic cos |> apsnd standard (* Collect all intances of constants in term *) fun collect_consts ( t $ u,tms) = collect_consts (u,collect_consts (t,tms)) | collect_consts ( Abs(_,_,t),tms) = collect_consts (t,tms) | collect_consts (tm as Const _,tms) = insert (op aconv) tm tms | collect_consts ( _,tms) = tms (* Complementing Type.varify... *) fun unvarify t fmap = let val fmap' = map Library.swap fmap fun unthaw (f as (a, S)) = (case AList.lookup (op =) fmap' a of NONE => TVar f | SOME (b, _) => TFree (b, S)) in map_types (map_type_tvar unthaw) t end (* The syntactic meddling needed to setup add_specification for work *) fun process_spec axiomatic cos alt_props thy = let fun zip3 [] [] [] = [] | zip3 (x::xs) (y::ys) (z::zs) = (x,y,z)::zip3 xs ys zs | zip3 _ _ _ = error "SpecificationPackage.process_spec internal error" fun myfoldr f [x] = x | myfoldr f (x::xs) = f (x,myfoldr f xs) | myfoldr f [] = error "SpecificationPackage.process_spec internal error" val rew_imps = alt_props |> map (ObjectLogic.atomize o Thm.cterm_of thy o Syntax.read_prop_global thy o snd) val props' = rew_imps |> map (HOLogic.dest_Trueprop o term_of o snd o Thm.dest_equals o cprop_of) fun proc_single prop = let val frees = Term.term_frees prop val _ = forall (fn v => Sign.of_sort thy (type_of v,HOLogic.typeS)) frees orelse error "Specificaton: Only free variables of sort 'type' allowed" val prop_closed = foldr (fn ((vname,T),prop) => HOLogic.mk_all (vname,T,prop)) prop (map dest_Free frees) in (prop_closed,frees) end val props'' = map proc_single props' val frees = map snd props'' val prop = myfoldr HOLogic.mk_conj (map fst props'') val cprop = cterm_of thy (HOLogic.mk_Trueprop prop) val (vmap, prop_thawed) = Type.varify [] prop val thawed_prop_consts = collect_consts (prop_thawed,[]) val (altcos,overloaded) = Library.split_list cos val (names,sconsts) = Library.split_list altcos val consts = map (Syntax.read_term_global thy) sconsts val _ = not (Library.exists (not o Term.is_Const) consts) orelse error "Specification: Non-constant found as parameter" fun proc_const c = let val (_, c') = Type.varify [] c val (cname,ctyp) = dest_Const c' in case List.filter (fn t => let val (name,typ) = dest_Const t in name = cname andalso Sign.typ_equiv thy (typ, ctyp) end) thawed_prop_consts of [] => error ("Specification: No suitable instances of constant \"" ^ (Sign.string_of_term thy c) ^ "\" found") | [cf] => unvarify cf vmap | _ => error ("Specification: Several variations of \"" ^ (Sign.string_of_term thy c) ^ "\" found (try applying explicit type constraints)") end val proc_consts = map proc_const consts fun mk_exist (c,prop) = let val T = type_of c val cname = Sign.base_name (fst (dest_Const c)) val vname = if Syntax.is_identifier cname then cname else "x" in HOLogic.exists_const T $ Abs(vname,T,Term.abstract_over (c,prop)) end val ex_prop = foldr mk_exist prop proc_consts val cnames = map (fst o dest_Const) proc_consts fun post_process (arg as (thy,thm)) = let fun inst_all thy (thm,v) = let val cv = cterm_of thy v val cT = ctyp_of_term cv val spec' = instantiate' [SOME cT] [NONE,SOME cv] spec in thm RS spec' end fun remove_alls frees thm = Library.foldl (inst_all (Thm.theory_of_thm thm)) (thm,frees) fun process_single ((name,atts),rew_imp,frees) args = let fun undo_imps thm = equal_elim (symmetric rew_imp) thm fun add_final (arg as (thy, thm)) = if name = "" then arg |> Library.swap else (writeln (" " ^ name ^ ": " ^ (string_of_thm thm)); PureThy.store_thm ((name, thm), []) thy) in args |> apsnd (remove_alls frees) |> apsnd undo_imps |> apsnd standard |> Thm.theory_attributes (map (Attrib.attribute thy) atts) |> add_final |> Library.swap end fun process_all [proc_arg] args = process_single proc_arg args | process_all (proc_arg::rest) (thy,thm) = let val single_th = thm RS conjunct1 val rest_th = thm RS conjunct2 val (thy',_) = process_single proc_arg (thy,single_th) in process_all rest (thy',rest_th) end | process_all [] _ = error "SpecificationPackage.process_spec internal error" val alt_names = map fst alt_props val _ = if exists (fn(name,_) => not (name = "")) alt_names then writeln "specification" else () in arg |> apsnd Thm.freezeT |> process_all (zip3 alt_names rew_imps frees) end fun after_qed [[thm]] = ProofContext.theory (fn thy => #1 (post_process (add_specification axiomatic (zip3 names cnames overloaded) (thy, thm)))); in thy |> ProofContext.init |> Proof.theorem_i NONE after_qed [[(HOLogic.mk_Trueprop ex_prop, [])]] end; (* outer syntax *) local structure P = OuterParse and K = OuterKeyword in val opt_name = Scan.optional (P.name --| P.$$$ ":") "" val opt_overloaded = P.opt_keyword "overloaded"; val specification_decl = P.$$$ "(" |-- Scan.repeat1 (opt_name -- P.term -- opt_overloaded) --| P.$$$ ")" -- Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop) val _ = OuterSyntax.command "specification" "define constants by specification" K.thy_goal (specification_decl >> (fn (cos,alt_props) => Toplevel.print o (Toplevel.theory_to_proof (process_spec NONE cos alt_props)))) val ax_specification_decl = P.name -- (P.$$$ "(" |-- Scan.repeat1 (opt_name -- P.term -- opt_overloaded) --| P.$$$ ")" -- Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop)) val _ = OuterSyntax.command "ax_specification" "define constants by specification" K.thy_goal (ax_specification_decl >> (fn (axname,(cos,alt_props)) => Toplevel.print o (Toplevel.theory_to_proof (process_spec (SOME axname) cos alt_props)))) end end