author  wenzelm 
Sun, 01 Mar 2009 23:36:12 +0100  
changeset 30190  479806475f3c 
parent 29579  cb520b766e00 
child 30223  24d975352879 
permissions  rwrr 
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(* Title: HOL/Tools/specification_package.ML 
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Author: Sebastian Skalberg, TU Muenchen 

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Package for defining constants by specification. 

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*) 

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signature SPECIFICATION_PACKAGE = 

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sig 

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val add_specification: string option > (bstring * xstring * bool) list > 
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theory * thm > theory * thm 

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end 
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structure SpecificationPackage: SPECIFICATION_PACKAGE = 
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struct 
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(* actual code *) 
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local 
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fun mk_definitional [] arg = arg 
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 mk_definitional ((thname,cname,covld)::cos) (thy,thm) = 
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case HOLogic.dest_Trueprop (concl_of thm) of 
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Const("Ex",_) $ P => 

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let 

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val ctype = domain_type (type_of P) 

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val cname_full = Sign.intern_const thy cname 
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val cdefname = if thname = "" 
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then Thm.def_name (Sign.base_name cname) 

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else thname 

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val def_eq = Logic.mk_equals (Const(cname_full,ctype), 

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HOLogic.choice_const ctype $ P) 

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val (thms, thy') = PureThy.add_defs covld [((Binding.name cdefname, def_eq),[])] thy 
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val thm' = [thm,hd thms] MRS @{thm exE_some} 
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in 
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mk_definitional cos (thy',thm') 

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end 

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 _ => raise THM ("Internal error: Bad specification theorem",0,[thm]) 

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fun mk_axiomatic axname cos arg = 
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let 
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fun process [] (thy,tm) = 

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let 

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val (thms, thy') = PureThy.add_axioms [((Binding.name axname, HOLogic.mk_Trueprop tm),[])] thy 
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in 
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(thy',hd thms) 

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end 

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 process ((thname,cname,covld)::cos) (thy,tm) = 

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case tm of 

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Const("Ex",_) $ P => 

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let 

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val ctype = domain_type (type_of P) 

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val cname_full = Sign.intern_const thy cname 
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val cdefname = if thname = "" 
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then Thm.def_name (Sign.base_name cname) 

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else thname 

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val co = Const(cname_full,ctype) 

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val thy' = Theory.add_finals_i covld [co] thy 

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val tm' = case P of 

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Abs(_, _, bodt) => subst_bound (co, bodt) 

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 _ => P $ co 

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in 

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process cos (thy',tm') 

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end 

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 _ => raise TERM ("Internal error: Bad specification theorem",[tm]) 

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in 

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process cos arg 

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end 

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in 
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fun proc_exprop axiomatic cos arg = 
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case axiomatic of 
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SOME axname => mk_axiomatic axname cos (apsnd (HOLogic.dest_Trueprop o concl_of) arg) 
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 NONE => mk_definitional cos arg 
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end 
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fun add_specification axiomatic cos arg = 
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arg > apsnd Thm.freezeT 
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> proc_exprop axiomatic cos 
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> apsnd standard 

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(* Collect all intances of constants in term *) 
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fun collect_consts ( t $ u,tms) = collect_consts (u,collect_consts (t,tms)) 

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 collect_consts ( Abs(_,_,t),tms) = collect_consts (t,tms) 

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 collect_consts (tm as Const _,tms) = insert (op aconv) tm tms 
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 collect_consts ( _,tms) = tms 
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(* Complementing Type.varify... *) 

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fun unvarify t fmap = 

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let 

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val fmap' = map Library.swap fmap 
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fun unthaw (f as (a, S)) = 
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(case AList.lookup (op =) fmap' a of 

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NONE => TVar f 
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 SOME (b, _) => TFree (b, S)) 
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in 
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map_types (map_type_tvar unthaw) t 
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end 
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(* The syntactic meddling needed to setup add_specification for work *) 

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fun process_spec axiomatic cos alt_props thy = 
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let 
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fun zip3 [] [] [] = [] 
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 zip3 (x::xs) (y::ys) (z::zs) = (x,y,z)::zip3 xs ys zs 

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 zip3 _ _ _ = error "SpecificationPackage.process_spec internal error" 

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fun myfoldr f [x] = x 
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 myfoldr f (x::xs) = f (x,myfoldr f xs) 

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 myfoldr f [] = error "SpecificationPackage.process_spec internal error" 

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val rew_imps = alt_props > 
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map (ObjectLogic.atomize o Thm.cterm_of thy o Syntax.read_prop_global thy o snd) 
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val props' = rew_imps > 
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map (HOLogic.dest_Trueprop o term_of o snd o Thm.dest_equals o cprop_of) 
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fun proc_single prop = 
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let 

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val frees = OldTerm.term_frees prop 
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val _ = forall (fn v => Sign.of_sort thy (type_of v,HOLogic.typeS)) frees 
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orelse error "Specificaton: Only free variables of sort 'type' allowed" 
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val prop_closed = List.foldr (fn ((vname,T),prop) => HOLogic.mk_all (vname,T,prop)) prop (map dest_Free frees) 
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in 
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(prop_closed,frees) 

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end 

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val props'' = map proc_single props' 
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val frees = map snd props'' 

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val prop = myfoldr HOLogic.mk_conj (map fst props'') 

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val cprop = cterm_of thy (HOLogic.mk_Trueprop prop) 
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val (vmap, prop_thawed) = Type.varify [] prop 
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val thawed_prop_consts = collect_consts (prop_thawed,[]) 
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val (altcos,overloaded) = Library.split_list cos 

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val (names,sconsts) = Library.split_list altcos 

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val consts = map (Syntax.read_term_global thy) sconsts 
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val _ = not (Library.exists (not o Term.is_Const) consts) 
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orelse error "Specification: Nonconstant found as parameter" 
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fun proc_const c = 
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let 

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val (_, c') = Type.varify [] c 
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val (cname,ctyp) = dest_Const c' 
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in 

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case List.filter (fn t => let val (name,typ) = dest_Const t 

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in name = cname andalso Sign.typ_equiv thy (typ, ctyp) 
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end) thawed_prop_consts of 
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[] => error ("Specification: No suitable instances of constant \"" ^ Syntax.string_of_term_global thy c ^ "\" found") 
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 [cf] => unvarify cf vmap 
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 _ => error ("Specification: Several variations of \"" ^ Syntax.string_of_term_global thy c ^ "\" found (try applying explicit type constraints)") 
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end 
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val proc_consts = map proc_const consts 

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fun mk_exist (c,prop) = 

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let 

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val T = type_of c 

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val cname = Sign.base_name (fst (dest_Const c)) 

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val vname = if Syntax.is_identifier cname 

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then cname 

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else "x" 

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in 

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HOLogic.exists_const T $ Abs(vname,T,Term.abstract_over (c,prop)) 

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end 

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val ex_prop = List.foldr mk_exist prop proc_consts 
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val cnames = map (fst o dest_Const) proc_consts 
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fun post_process (arg as (thy,thm)) = 

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let 

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fun inst_all thy (thm,v) = 
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let 
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val cv = cterm_of thy v 
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val cT = ctyp_of_term cv 
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val spec' = instantiate' [SOME cT] [NONE,SOME cv] spec 

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in 

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thm RS spec' 

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end 

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fun remove_alls frees thm = 
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Library.foldl (inst_all (Thm.theory_of_thm thm)) (thm,frees) 

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fun process_single ((name,atts),rew_imp,frees) args = 
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let 

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fun undo_imps thm = 

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equal_elim (symmetric rew_imp) thm 

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fun add_final (arg as (thy, thm)) = 
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if name = "" 
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then arg > Library.swap 
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else (writeln (" " ^ name ^ ": " ^ (Display.string_of_thm thm)); 
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PureThy.store_thm (Binding.name name, thm) thy) 
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in 
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args > apsnd (remove_alls frees) 

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> apsnd undo_imps 

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> apsnd standard 

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> Thm.theory_attributes (map (Attrib.attribute thy) atts) 
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> add_final 
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> Library.swap 
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end 
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fun process_all [proc_arg] args = 
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process_single proc_arg args 

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 process_all (proc_arg::rest) (thy,thm) = 

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let 

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val single_th = thm RS conjunct1 

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val rest_th = thm RS conjunct2 

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val (thy',_) = process_single proc_arg (thy,single_th) 

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in 

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process_all rest (thy',rest_th) 

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end 

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 process_all [] _ = error "SpecificationPackage.process_spec internal error" 

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val alt_names = map fst alt_props 

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val _ = if exists (fn(name,_) => not (name = "")) alt_names 

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then writeln "specification" 

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else () 

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in 

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arg > apsnd Thm.freezeT 
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> process_all (zip3 alt_names rew_imps frees) 
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end 

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fun after_qed [[thm]] = ProofContext.theory (fn thy => 

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#1 (post_process (add_specification axiomatic (zip3 names cnames overloaded) (thy, thm)))); 

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in 
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thy 
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> ProofContext.init 

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> Proof.theorem_i NONE after_qed [[(HOLogic.mk_Trueprop ex_prop, [])]] 
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end; 
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(* outer syntax *) 
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local structure P = OuterParse and K = OuterKeyword in 
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val opt_name = Scan.optional (P.name  P.$$$ ":") "" 
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val opt_overloaded = P.opt_keyword "overloaded"; 
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val specification_decl = 
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P.$$$ "("  Scan.repeat1 (opt_name  P.term  opt_overloaded)  P.$$$ ")"  
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Scan.repeat1 ((SpecParse.opt_thm_name ":" >> apfst Binding.base_name)  P.prop) 
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val _ = 
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OuterSyntax.command "specification" "define constants by specification" K.thy_goal 
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(specification_decl >> (fn (cos,alt_props) => 
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Toplevel.print o (Toplevel.theory_to_proof 
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(process_spec NONE cos alt_props)))) 

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val ax_specification_decl = 
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P.name  
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(P.$$$ "("  Scan.repeat1 (opt_name  P.term  opt_overloaded)  P.$$$ ")"  
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Scan.repeat1 ((SpecParse.opt_thm_name ":" >> apfst Binding.base_name)  P.prop)) 
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val _ = 
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OuterSyntax.command "ax_specification" "define constants by specification" K.thy_goal 
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(ax_specification_decl >> (fn (axname,(cos,alt_props)) => 
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Toplevel.print o (Toplevel.theory_to_proof 
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(process_spec (SOME axname) cos alt_props)))) 

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end 
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end 