src/HOL/Tools/specification_package.ML
author skalberg
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Allowed for splitting the specification over several lemmas.
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(*  Title:      HOL/Tools/specification_package.ML
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    ID:         $Id$
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    Author:     Sebastian Skalberg, TU Muenchen
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    License:    GPL (GNU GENERAL PUBLIC LICENSE)
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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 quiet_mode: bool ref
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    val add_specification_i: (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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(* messages *)
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val quiet_mode = ref false
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fun message s = if ! quiet_mode then () else writeln s
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local
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    val _ = Goal "[| Ex P ; c == Eps P |] ==> P c"
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    val _ = by (Asm_simp_tac 1)
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    val _ = by (rtac (thm "someI_ex") 1)
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    val _ = ba 1
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in
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val helper = Goals.result()
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end
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(* Akin to HOLogic.exists_const *)
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fun choice_const T = Const("Hilbert_Choice.Eps",(T-->HOLogic.boolT)-->T)
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(* Actual code *)
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fun proc_exprop [] arg = arg
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  | proc_exprop ((thname,cname,covld)::cos) (thy,thm) =
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    case concl_of thm of
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	Const("Trueprop",_) $ (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 (sign_of 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),choice_const ctype $  P)
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	    val (thy',thms) = PureThy.add_defs_i covld [((cdefname,def_eq),[])] thy
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	    val thm' = [thm,hd thms] MRS helper
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	in
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	    proc_exprop 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 add_specification_i cos arg =
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    arg |> apsnd freezeT
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	|> proc_exprop 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) = gen_ins (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 assoc (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_term_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 cos alt_props int thy =
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    let
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	fun myfoldr f [] = error "SpecificationPackage.process_spec internal error"
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	  | myfoldr f [x] = x
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	  | myfoldr f (x::xs) = f (x,myfoldr f xs)
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	val sg = sign_of thy
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	fun typ_equiv t u =
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	    let
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		val tsig = Sign.tsig_of sg
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	    in
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		Type.typ_instance(tsig,t,u) andalso
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		Type.typ_instance(tsig,u,t)
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	    end
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	val cprops = map (Thm.read_cterm sg o rpair Term.propT o snd) alt_props
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	val ss = empty_ss setmksimps single addsimps [thm "HOL.atomize_imp",thm "HOL.atomize_all"]
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	val rew_imps = map (Simplifier.full_rewrite ss) cprops
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	val props' = map (HOLogic.dest_Trueprop o term_of o snd o dest_equals o cprop_of) rew_imps
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	val prop  = myfoldr HOLogic.mk_conj props'
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	val cprop = cterm_of sg (HOLogic.mk_Trueprop prop)
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	val (prop_thawed,vmap) = 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 (term_of o Thm.read_cterm sg o rpair TypeInfer.logicT) sconsts
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	val _ = assert (not (Library.exists (not o Term.is_Const) consts))
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		       "Non-constant found as parameter"
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	fun proc_const c =
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	    let
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		val c' = fst (Type.varify (c,[]))
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		val (cname,ctyp) = dest_Const c'
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	    in
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		case filter (fn t => let val (name,typ) = dest_Const t
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				     in name = cname andalso typ_equiv typ ctyp
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				     end) thawed_prop_consts of
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		    [] => error ("Constant \"" ^ (Sign.string_of_term sg c) ^ "\" not found in specification")
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		  | [cf] => unvarify cf vmap
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		  | _ => error ("Several variations of \"" ^ (Sign.string_of_term sg c) ^ "\" found in specification")
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	    end
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	val frees = Term.term_frees prop
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	val tsig = Sign.tsig_of (sign_of thy)
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	val _ = assert (forall (fn v => Type.of_sort tsig (type_of v,HOLogic.typeS)) frees)
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		"Only free variables of sort 'type' allowed in specifications"
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	val prop_closed = foldr (fn ((vname,T),prop) => HOLogic.mk_all (vname,T,prop)) (map dest_Free frees,prop)
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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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	    in
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		HOLogic.exists_const T $ Abs("x",T,Term.abstract_over (c,prop))
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	    end
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	val ex_prop = foldr mk_exist (proc_consts,prop_closed)
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	val cnames = map (fst o dest_Const) proc_consts
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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 "Internal error: Bad specification syntax"
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	fun post_process (arg as (thy,thm)) =
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	    let
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		fun inst_all sg (thm,v) =
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		    let
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			val cv = cterm_of sg 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 = foldl (inst_all (sign_of_thm thm)) (thm,frees)
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		fun process_single (name,atts) rew_imp 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 apply_atts arg = Thm.apply_attributes (arg,map (Attrib.global_attribute thy) atts)
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			fun add_final (arg as (thy,thm)) =
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			    if name = ""
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			    then arg
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			    else (writeln ("  " ^ name ^ ": " ^ (string_of_thm thm));
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				  PureThy.store_thm((name,thm),[]) thy)
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		    in
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			args |> apsnd (undo_imps)
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			     |> apsnd standard
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			     |> apply_atts
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			     |> add_final
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		    end
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		fun process_all [alt_name] [rew_imp] args =
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		    process_single alt_name rew_imp args
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		  | process_all (alt_name::rest_alt) (rew_imp::rest_imp) (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 alt_name rew_imp (thy,single_th)
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		    in
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			process_all rest_alt rest_imp (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 freezeT
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		    |> apsnd (remove_alls frees)
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		    |> process_all alt_names rew_imps
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	    end
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    in
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	IsarThy.theorem_i Drule.internalK
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	    (("",[add_specification_i (zip3 (names:string list) (cnames:string list) (overloaded:bool list)),post_process]),
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	     (HOLogic.mk_Trueprop ex_prop,([],[]))) int thy
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    end
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(* outer syntax *)
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local structure P = OuterParse and K = OuterSyntax.Keyword in
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(* taken from ~~/Pure/Isar/isar_syn.ML *)
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val opt_overloaded =
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  Scan.optional (P.$$$ "(" |-- P.!!! ((P.$$$ "overloaded" >> K true) --| P.$$$ ")")) false
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val opt_name = Scan.optional (P.name --| P.$$$ ":") ""
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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 (P.opt_thm_name ":" -- P.prop)
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val specificationP =
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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 (process_spec cos alt_props))))
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val _ = OuterSyntax.add_parsers [specificationP]
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end
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end