skalberg@14115
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(* Title: HOL/Tools/specification_package.ML
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skalberg@14115
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ID: $Id$
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skalberg@14115
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Author: Sebastian Skalberg, TU Muenchen
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skalberg@14115
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skalberg@14115
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Package for defining constants by specification.
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skalberg@14115
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*)
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skalberg@14115
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skalberg@14115
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signature SPECIFICATION_PACKAGE =
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skalberg@14115
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sig
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wenzelm@18729
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val add_specification: string option -> (bstring * xstring * bool) list ->
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wenzelm@18729
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theory * thm -> theory * thm
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skalberg@14115
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end
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skalberg@14115
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wenzelm@17895
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structure SpecificationPackage: SPECIFICATION_PACKAGE =
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skalberg@14115
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struct
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skalberg@14115
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wenzelm@26478
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(* actual code *)
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skalberg@14115
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skalberg@14222
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local
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skalberg@14222
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fun mk_definitional [] arg = arg
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skalberg@14222
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| mk_definitional ((thname,cname,covld)::cos) (thy,thm) =
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wenzelm@17336
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case HOLogic.dest_Trueprop (concl_of thm) of
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wenzelm@17336
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Const("Ex",_) $ P =>
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wenzelm@17336
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let
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wenzelm@17336
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val ctype = domain_type (type_of P)
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wenzelm@22578
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val cname_full = Sign.intern_const thy cname
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wenzelm@17336
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val cdefname = if thname = ""
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wenzelm@17336
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then Thm.def_name (Sign.base_name cname)
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wenzelm@17336
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else thname
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wenzelm@17336
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val def_eq = Logic.mk_equals (Const(cname_full,ctype),
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wenzelm@17336
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HOLogic.choice_const ctype $ P)
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haftmann@18358
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val (thms, thy') = PureThy.add_defs_i covld [((cdefname,def_eq),[])] thy
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wenzelm@26478
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val thm' = [thm,hd thms] MRS @{thm exE_some}
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wenzelm@17336
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in
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wenzelm@17336
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mk_definitional cos (thy',thm')
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wenzelm@17336
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end
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wenzelm@17336
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| _ => raise THM ("Internal error: Bad specification theorem",0,[thm])
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skalberg@14222
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skalberg@14222
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fun mk_axiomatic axname cos arg =
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wenzelm@17336
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let
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wenzelm@17336
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fun process [] (thy,tm) =
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wenzelm@17336
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let
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haftmann@18377
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val (thms, thy') = PureThy.add_axioms_i [((axname,HOLogic.mk_Trueprop tm),[])] thy
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wenzelm@17336
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in
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wenzelm@17336
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(thy',hd thms)
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wenzelm@17336
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end
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wenzelm@17336
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| process ((thname,cname,covld)::cos) (thy,tm) =
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wenzelm@17336
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case tm of
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wenzelm@17336
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Const("Ex",_) $ P =>
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let
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wenzelm@17336
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val ctype = domain_type (type_of P)
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wenzelm@22578
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val cname_full = Sign.intern_const thy cname
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wenzelm@17336
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val cdefname = if thname = ""
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wenzelm@17336
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then Thm.def_name (Sign.base_name cname)
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wenzelm@17336
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else thname
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wenzelm@17336
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val co = Const(cname_full,ctype)
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wenzelm@17336
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val thy' = Theory.add_finals_i covld [co] thy
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wenzelm@17336
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val tm' = case P of
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wenzelm@17336
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Abs(_, _, bodt) => subst_bound (co, bodt)
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wenzelm@17336
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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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wenzelm@17336
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| _ => raise TERM ("Internal error: Bad specification theorem",[tm])
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wenzelm@17336
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in
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wenzelm@17336
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process cos arg
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wenzelm@17336
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end
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skalberg@14115
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skalberg@14222
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in
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skalberg@14222
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fun proc_exprop axiomatic cos arg =
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skalberg@14222
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case axiomatic of
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wenzelm@17336
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SOME axname => mk_axiomatic axname cos (apsnd (HOLogic.dest_Trueprop o concl_of) arg)
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skalberg@15531
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| NONE => mk_definitional cos arg
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skalberg@14222
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end
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skalberg@14222
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wenzelm@18729
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fun add_specification axiomatic cos arg =
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wenzelm@19876
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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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wenzelm@18729
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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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skalberg@14115
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| collect_consts ( Abs(_,_,t),tms) = collect_consts (t,tms)
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wenzelm@18921
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| collect_consts (tm as Const _,tms) = insert (op aconv) tm tms
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skalberg@14115
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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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wenzelm@17336
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val fmap' = map Library.swap fmap
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haftmann@17377
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fun unthaw (f as (a, S)) =
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haftmann@17377
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(case AList.lookup (op =) fmap' a of
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wenzelm@17336
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NONE => TVar f
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haftmann@17377
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| SOME (b, _) => TFree (b, S))
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in
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wenzelm@20548
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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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wenzelm@17336
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fun process_spec axiomatic cos alt_props thy =
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let
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wenzelm@17336
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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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skalberg@14167
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wenzelm@17336
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fun myfoldr f [x] = x
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wenzelm@17336
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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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skalberg@14164
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wenzelm@17895
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val rew_imps = alt_props |>
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wenzelm@24707
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map (ObjectLogic.atomize o Thm.cterm_of thy o Syntax.read_prop_global thy o snd)
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wenzelm@17895
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val props' = rew_imps |>
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wenzelm@22902
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map (HOLogic.dest_Trueprop o term_of o snd o Thm.dest_equals o cprop_of)
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skalberg@14166
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wenzelm@17336
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fun proc_single prop =
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wenzelm@17336
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let
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wenzelm@17336
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val frees = Term.term_frees prop
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wenzelm@21858
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val _ = forall (fn v => Sign.of_sort thy (type_of v,HOLogic.typeS)) frees
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wenzelm@21858
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orelse error "Specificaton: Only free variables of sort 'type' allowed"
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wenzelm@17336
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val prop_closed = foldr (fn ((vname,T),prop) => HOLogic.mk_all (vname,T,prop)) prop (map dest_Free frees)
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wenzelm@17336
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in
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wenzelm@17336
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(prop_closed,frees)
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end
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skalberg@14166
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wenzelm@17336
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val props'' = map proc_single props'
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wenzelm@17336
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val frees = map snd props''
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wenzelm@17336
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val prop = myfoldr HOLogic.mk_conj (map fst props'')
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wenzelm@17895
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val cprop = cterm_of thy (HOLogic.mk_Trueprop prop)
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skalberg@14164
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haftmann@21116
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val (vmap, prop_thawed) = Type.varify [] prop
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wenzelm@17336
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val thawed_prop_consts = collect_consts (prop_thawed,[])
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wenzelm@17336
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val (altcos,overloaded) = Library.split_list cos
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wenzelm@17336
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val (names,sconsts) = Library.split_list altcos
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wenzelm@24707
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val consts = map (Syntax.read_term_global thy) sconsts
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wenzelm@21858
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val _ = not (Library.exists (not o Term.is_Const) consts)
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wenzelm@21858
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orelse error "Specification: Non-constant found as parameter"
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skalberg@14166
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wenzelm@17336
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fun proc_const c =
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wenzelm@17336
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let
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haftmann@21116
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val (_, c') = Type.varify [] c
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wenzelm@17336
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val (cname,ctyp) = dest_Const c'
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wenzelm@17336
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in
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wenzelm@17336
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case List.filter (fn t => let val (name,typ) = dest_Const t
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wenzelm@19414
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in name = cname andalso Sign.typ_equiv thy (typ, ctyp)
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wenzelm@17336
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end) thawed_prop_consts of
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wenzelm@17895
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[] => error ("Specification: No suitable instances of constant \"" ^ (Sign.string_of_term thy c) ^ "\" found")
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wenzelm@17336
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| [cf] => unvarify cf vmap
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wenzelm@17895
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| _ => error ("Specification: Several variations of \"" ^ (Sign.string_of_term thy c) ^ "\" found (try applying explicit type constraints)")
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wenzelm@17336
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end
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wenzelm@17336
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val proc_consts = map proc_const consts
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wenzelm@17336
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fun mk_exist (c,prop) =
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wenzelm@17336
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let
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wenzelm@17336
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val T = type_of c
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wenzelm@17336
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val cname = Sign.base_name (fst (dest_Const c))
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wenzelm@17336
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val vname = if Syntax.is_identifier cname
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wenzelm@17336
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then cname
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wenzelm@17336
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else "x"
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wenzelm@17336
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in
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wenzelm@17336
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HOLogic.exists_const T $ Abs(vname,T,Term.abstract_over (c,prop))
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wenzelm@17336
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end
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wenzelm@17336
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val ex_prop = foldr mk_exist prop proc_consts
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wenzelm@17336
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val cnames = map (fst o dest_Const) proc_consts
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wenzelm@17336
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fun post_process (arg as (thy,thm)) =
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wenzelm@17336
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let
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wenzelm@17895
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fun inst_all thy (thm,v) =
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wenzelm@17336
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let
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wenzelm@17895
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val cv = cterm_of thy v
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wenzelm@17336
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val cT = ctyp_of_term cv
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wenzelm@17336
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val spec' = instantiate' [SOME cT] [NONE,SOME cv] spec
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wenzelm@17336
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in
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wenzelm@17336
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thm RS spec'
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wenzelm@17336
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end
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wenzelm@22578
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fun remove_alls frees thm =
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wenzelm@22578
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Library.foldl (inst_all (Thm.theory_of_thm thm)) (thm,frees)
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wenzelm@17336
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fun process_single ((name,atts),rew_imp,frees) args =
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wenzelm@17336
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let
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wenzelm@17336
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fun undo_imps thm =
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wenzelm@17336
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equal_elim (symmetric rew_imp) thm
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skalberg@14164
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haftmann@18358
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fun add_final (arg as (thy, thm)) =
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wenzelm@17336
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if name = ""
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haftmann@18358
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then arg |> Library.swap
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wenzelm@17336
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else (writeln (" " ^ name ^ ": " ^ (string_of_thm thm));
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haftmann@18358
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PureThy.store_thm ((name, thm), []) thy)
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wenzelm@17336
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in
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wenzelm@17336
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args |> apsnd (remove_alls frees)
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wenzelm@17336
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|> apsnd undo_imps
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wenzelm@17336
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|> apsnd standard
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wenzelm@18729
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|> Thm.theory_attributes (map (Attrib.attribute thy) atts)
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wenzelm@17336
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|> add_final
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haftmann@18358
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|> Library.swap
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wenzelm@17336
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end
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skalberg@14164
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wenzelm@17336
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fun process_all [proc_arg] args =
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wenzelm@17336
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process_single proc_arg args
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wenzelm@17336
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| process_all (proc_arg::rest) (thy,thm) =
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wenzelm@17336
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let
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wenzelm@17336
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val single_th = thm RS conjunct1
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wenzelm@17336
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val rest_th = thm RS conjunct2
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wenzelm@17336
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val (thy',_) = process_single proc_arg (thy,single_th)
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wenzelm@17336
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in
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wenzelm@17336
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process_all rest (thy',rest_th)
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wenzelm@17336
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end
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wenzelm@17336
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| process_all [] _ = error "SpecificationPackage.process_spec internal error"
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wenzelm@17336
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val alt_names = map fst alt_props
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wenzelm@17336
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val _ = if exists (fn(name,_) => not (name = "")) alt_names
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wenzelm@17336
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then writeln "specification"
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wenzelm@17336
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else ()
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wenzelm@17336
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in
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wenzelm@19876
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arg |> apsnd Thm.freezeT
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wenzelm@17336
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|> process_all (zip3 alt_names rew_imps frees)
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wenzelm@17336
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end
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wenzelm@20903
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wenzelm@20903
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fun after_qed [[thm]] = ProofContext.theory (fn thy =>
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wenzelm@20903
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#1 (post_process (add_specification axiomatic (zip3 names cnames overloaded) (thy, thm))));
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skalberg@14115
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in
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wenzelm@20903
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thy
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wenzelm@20903
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|> ProofContext.init
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wenzelm@21434
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|> Proof.theorem_i NONE after_qed [[(HOLogic.mk_Trueprop ex_prop, [])]]
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wenzelm@20903
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end;
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skalberg@14115
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wenzelm@17336
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skalberg@14115
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(* outer syntax *)
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skalberg@14115
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wenzelm@17057
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local structure P = OuterParse and K = OuterKeyword in
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skalberg@14115
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skalberg@14116
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val opt_name = Scan.optional (P.name --| P.$$$ ":") ""
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wenzelm@17336
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val opt_overloaded = P.opt_keyword "overloaded";
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skalberg@14116
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skalberg@14115
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val specification_decl =
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wenzelm@17336
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P.$$$ "(" |-- Scan.repeat1 (opt_name -- P.term -- opt_overloaded) --| P.$$$ ")" --
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wenzelm@22101
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Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop)
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skalberg@14115
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wenzelm@24867
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val _ =
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skalberg@14115
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OuterSyntax.command "specification" "define constants by specification" K.thy_goal
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skalberg@14164
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(specification_decl >> (fn (cos,alt_props) =>
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wenzelm@17336
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Toplevel.print o (Toplevel.theory_to_proof
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wenzelm@17336
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(process_spec NONE cos alt_props))))
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skalberg@14115
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skalberg@14222
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val ax_specification_decl =
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skalberg@14222
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P.name --
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skalberg@14222
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(P.$$$ "(" |-- Scan.repeat1 (opt_name -- P.term -- opt_overloaded) --| P.$$$ ")" --
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wenzelm@22101
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Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop))
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skalberg@14222
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wenzelm@24867
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val _ =
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skalberg@14222
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OuterSyntax.command "ax_specification" "define constants by specification" K.thy_goal
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skalberg@14222
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(ax_specification_decl >> (fn (axname,(cos,alt_props)) =>
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wenzelm@17336
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Toplevel.print o (Toplevel.theory_to_proof
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wenzelm@17336
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(process_spec (SOME axname) cos alt_props))))
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skalberg@14222
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wenzelm@24867
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end
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wenzelm@24867
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skalberg@14115
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skalberg@14115
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end
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