author  skalberg 
Wed, 08 Oct 2003 16:02:54 +0200  
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child 14223  0ee05eef881b 
permissions  rwrr 
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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: 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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(* 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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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 (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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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 (thy',thms) = PureThy.add_axioms_i [((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 (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 co = Const(cname_full,ctype) 
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val def = Logic.mk_implies(HOLogic.mk_Trueprop HOLogic.false_const, 
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Logic.mk_equals (co,choice_const ctype $ P)) 
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val (thy',_) = PureThy.add_defs_i covld [((cdefname,def),[])] 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_i axiomatic cos arg = 
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arg > apsnd 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) = 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 axiomatic cos alt_props int 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 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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fun proc_single prop = 

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let 

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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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"Specificaton: Only free variables of sort 'type' allowed" 
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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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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 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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"Specification: Nonconstant 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 ("Specification: No suitable instances of constant \"" ^ (Sign.string_of_term sg c) ^ "\" found") 
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 [cf] => unvarify cf vmap 
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 _ => error ("Specification: Several variations of \"" ^ (Sign.string_of_term sg c) ^ "\" found (try applying explicit type constraints)") 
14115  182 
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" 

14115  191 
in 
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HOLogic.exists_const T $ Abs(vname,T,Term.abstract_over (c,prop)) 
14115  193 
end 
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val ex_prop = foldr mk_exist (proc_consts,prop) 
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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 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,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 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 (remove_alls frees) 
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> 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 [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 freezeT 
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> process_all (zip3 alt_names rew_imps frees) 
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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 axiomatic (zip3 names cnames overloaded),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 
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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 (P.opt_thm_name ":"  P.prop)) 
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val ax_specificationP = 
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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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val _ = OuterSyntax.add_parsers [specificationP,ax_specificationP] 
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end 

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end 