author  haftmann 
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permissions  rwrr 
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(* title: HOL/Nominal/nominal_atoms.ML 
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ID: $Id$ 
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Author: Christian Urban and Stefan Berghofer, TU Muenchen 

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Declaration of atom types to be used in nominal datatypes. 

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*) 

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signature NOMINAL_ATOMS = 

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sig 

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val create_nom_typedecls : string list > theory > theory 

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type atom_info 
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val get_atom_infos : theory > atom_info Symtab.table 
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val get_atom_info : theory > string > atom_info option 
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val the_atom_info : theory > string > atom_info 
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val fs_class_of : theory > string > string 
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val pt_class_of : theory > string > string 
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val cp_class_of : theory > string > string > string 
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val at_inst_of : theory > string > thm 
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val pt_inst_of : theory > string > thm 
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val cp_inst_of : theory > string > string > thm 
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val dj_thm_of : theory > string > string > thm 
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val atoms_of : theory > string list 
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val mk_permT : typ > typ 

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end 

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structure NominalAtoms : NOMINAL_ATOMS = 

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struct 

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val finite_emptyI = @{thm "finite.emptyI"}; 
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val Collect_const = @{thm "Collect_const"}; 
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val inductive_forall_def = @{thm "induct_forall_def"}; 
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(* theory data *) 
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type atom_info = 
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{pt_class : string, 
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fs_class : string, 
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cp_classes : string Symtab.table, 
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at_inst : thm, 
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pt_inst : thm, 

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cp_inst : thm Symtab.table, 
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dj_thms : thm Symtab.table}; 
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structure NominalData = TheoryDataFun 
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( 

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type T = atom_info Symtab.table; 
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val empty = Symtab.empty; 
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val copy = I; 

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val extend = I; 

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fun merge _ x = Symtab.merge (K true) x; 

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); 
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fun make_atom_info ((((((pt_class, fs_class), cp_classes), at_inst), pt_inst), cp_inst), dj_thms) = 
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{pt_class = pt_class, 
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fs_class = fs_class, 
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cp_classes = cp_classes, 
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at_inst = at_inst, 

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pt_inst = pt_inst, 

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cp_inst = cp_inst, 
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dj_thms = dj_thms}; 
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val get_atom_infos = NominalData.get; 
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val get_atom_info = Symtab.lookup o NominalData.get; 
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fun gen_lookup lookup name = case lookup name of 
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SOME info => info 
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 NONE => error ("Unknown atom type " ^ quote name); 
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fun the_atom_info thy = gen_lookup (get_atom_info thy); 
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fun gen_lookup' f thy = the_atom_info thy #> f; 
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fun gen_lookup'' f thy = 
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gen_lookup' (f #> Symtab.lookup #> gen_lookup) thy; 
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val fs_class_of = gen_lookup' #fs_class; 
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val pt_class_of = gen_lookup' #pt_class; 
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val at_inst_of = gen_lookup' #at_inst; 
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val pt_inst_of = gen_lookup' #pt_inst; 
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val cp_class_of = gen_lookup'' #cp_classes; 
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val cp_inst_of = gen_lookup'' #cp_inst; 
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val dj_thm_of = gen_lookup'' #dj_thms; 
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fun atoms_of thy = map fst (Symtab.dest (NominalData.get thy)); 
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fun mk_permT T = HOLogic.listT (HOLogic.mk_prodT (T, T)); 
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fun mk_Cons x xs = 

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let val T = fastype_of x 

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in Const ("List.list.Cons", T > HOLogic.listT T > HOLogic.listT T) $ x $ xs end; 
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fun add_thms_string args = PureThy.add_thms ((map o apfst o apfst) Binding.name args); 
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fun add_thmss_string args = PureThy.add_thmss ((map o apfst o apfst) Binding.name args); 

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(* this function sets up all matters related to atom *) 
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(* kinds; the user specifies a list of atomkind names *) 

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(* atom_decl <ak1> ... <akn> *) 

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fun create_nom_typedecls ak_names thy = 

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let 

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val (_,thy1) = 
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fold_map (fn ak => fn thy => 
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let val dt = ([],ak,NoSyn,[(ak,[@{typ nat}],NoSyn)]) 
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val ({inject,case_thms,...},thy1) = DatatypePackage.add_datatype true false [ak] [dt] thy 
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val inject_flat = Library.flat inject 
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val ak_type = Type (Sign.intern_type thy1 ak,[]) 
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val ak_sign = Sign.intern_const thy1 ak 
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val inj_type = @{typ nat}>ak_type 
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val inj_on_type = inj_type>(@{typ "nat set"})>@{typ bool} 
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(* first statement *) 
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val stmnt1 = HOLogic.mk_Trueprop 
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(Const (@{const_name "inj_on"},inj_on_type) $ 
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Const (ak_sign,inj_type) $ HOLogic.mk_UNIV @{typ nat}) 
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val simp1 = @{thm inj_on_def}::inject_flat 
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val proof1 = fn _ => EVERY [simp_tac (HOL_basic_ss addsimps simp1) 1, 
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rtac @{thm ballI} 1, 
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rtac @{thm ballI} 1, 
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rtac @{thm impI} 1, 
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atac 1] 
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val (inj_thm,thy2) = 
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add_thms_string [((ak^"_inj",Goal.prove_global thy1 [] [] stmnt1 proof1), [])] thy1 
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(* second statement *) 
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val y = Free ("y",ak_type) 
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val stmnt2 = HOLogic.mk_Trueprop 
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(HOLogic.mk_exists ("x",@{typ nat},HOLogic.mk_eq (y,Const (ak_sign,inj_type) $ Bound 0))) 
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val proof2 = fn {prems, context} => 
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InductTacs.case_tac context "y" 1 THEN 
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asm_simp_tac (HOL_basic_ss addsimps simp1) 1 THEN 
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rtac @{thm exI} 1 THEN 
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rtac @{thm refl} 1 
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(* third statement *) 
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val (inject_thm,thy3) = 
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add_thms_string [((ak^"_injection",Goal.prove_global thy2 [] [] stmnt2 proof2), [])] thy2 
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val stmnt3 = HOLogic.mk_Trueprop 
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(HOLogic.mk_not 
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(Const ("Finite_Set.finite", HOLogic.mk_setT ak_type > HOLogic.boolT) $ 
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HOLogic.mk_UNIV ak_type)) 
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val simp2 = [@{thm image_def},@{thm bex_UNIV}]@inject_thm 
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val simp3 = [@{thm UNIV_def}] 
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val proof3 = fn _ => EVERY [cut_facts_tac inj_thm 1, 
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dtac @{thm range_inj_infinite} 1, 
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asm_full_simp_tac (HOL_basic_ss addsimps simp2) 1, 
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simp_tac (HOL_basic_ss addsimps simp3) 1] 
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val (inf_thm,thy4) = 
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add_thms_string [((ak^"_infinite",Goal.prove_global thy3 [] [] stmnt3 proof3), [])] thy3 
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in 
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((inj_thm,inject_thm,inf_thm),thy4) 
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end) ak_names thy 
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(* produces a list consisting of pairs: *) 
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(* fst component is the atomkind name *) 

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(* snd component is its type *) 

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val full_ak_names = map (Sign.intern_type thy1) ak_names; 
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val ak_names_types = ak_names ~~ map (Type o rpair []) full_ak_names; 
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(* declares a swapping function for every atomkind, it is *) 

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(* const swap_<ak> :: <akT> * <akT> => <akT> => <akT> *) 

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(* swap_<ak> (a,b) c = (if a=c then b (else if b=c then a else c)) *) 

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(* overloades then the general swapfunction *) 

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val (swap_eqs, thy3) = fold_map (fn (ak_name, T) => fn thy => 
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let 
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val swapT = HOLogic.mk_prodT (T, T) > T > T; 

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val swap_name = Sign.full_bname thy ("swap_" ^ ak_name); 
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val a = Free ("a", T); 
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val b = Free ("b", T); 

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val c = Free ("c", T); 

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val ab = Free ("ab", HOLogic.mk_prodT (T, T)) 

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val cif = Const ("HOL.If", HOLogic.boolT > T > T > T); 

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val cswap_akname = Const (swap_name, swapT); 

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val cswap = Const ("Nominal.swap", swapT) 
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val name = "swap_"^ak_name^"_def"; 

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val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq 

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(cswap_akname $ HOLogic.mk_prod (a,b) $ c, 
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cif $ HOLogic.mk_eq (a,c) $ b $ (cif $ HOLogic.mk_eq (b,c) $ a $ c))) 
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val def2 = Logic.mk_equals (cswap $ ab $ c, cswap_akname $ ab $ c) 

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in 

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thy > Sign.add_consts_i [("swap_" ^ ak_name, swapT, NoSyn)] 
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> PureThy.add_defs_unchecked true [((Binding.name name, def2),[])] 
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> snd 
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> OldPrimrecPackage.add_primrec_unchecked_i "" [(("", def1),[])] 
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195 
end) ak_names_types thy1; 
18068  196 

197 
(* declares a permutation function for every atomkind acting *) 

198 
(* on such atoms *) 

199 
(* const <ak>_prm_<ak> :: (<akT> * <akT>)list => akT => akT *) 

200 
(* <ak>_prm_<ak> [] a = a *) 

201 
(* <ak>_prm_<ak> (x#xs) a = swap_<ak> x (perm xs a) *) 

20179  202 
val (prm_eqs, thy4) = fold_map (fn (ak_name, T) => fn thy => 
18068  203 
let 
204 
val swapT = HOLogic.mk_prodT (T, T) > T > T; 

28965  205 
val swap_name = Sign.full_bname thy ("swap_" ^ ak_name) 
18068  206 
val prmT = mk_permT T > T > T; 
207 
val prm_name = ak_name ^ "_prm_" ^ ak_name; 

28965  208 
val qu_prm_name = Sign.full_bname thy prm_name; 
18068  209 
val x = Free ("x", HOLogic.mk_prodT (T, T)); 
210 
val xs = Free ("xs", mk_permT T); 

211 
val a = Free ("a", T) ; 

212 

213 
val cnil = Const ("List.list.Nil", mk_permT T); 

214 

215 
val def1 = HOLogic.mk_Trueprop (HOLogic.mk_eq (Const (qu_prm_name, prmT) $ cnil $ a, a)); 

216 

217 
val def2 = HOLogic.mk_Trueprop (HOLogic.mk_eq 

218 
(Const (qu_prm_name, prmT) $ mk_Cons x xs $ a, 

219 
Const (swap_name, swapT) $ x $ (Const (qu_prm_name, prmT) $ xs $ a))); 

220 
in 

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221 
thy > Sign.add_consts_i [(prm_name, mk_permT T > T > T, NoSyn)] 
25557  222 
> OldPrimrecPackage.add_primrec_unchecked_i "" [(("", def1), []),(("", def2), [])] 
20179  223 
end) ak_names_types thy3; 
18068  224 

225 
(* defines permutation functions for all combinations of atomkinds; *) 

226 
(* there are a trivial cases and nontrivial cases *) 

227 
(* nontrivial case: *) 

228 
(* <ak>_prm_<ak>_def: perm pi a == <ak>_prm_<ak> pi a *) 

229 
(* trivial case with <ak> != <ak'> *) 

230 
(* <ak>_prm<ak'>_def[simp]: perm pi a == a *) 

231 
(* *) 

232 
(* the trivial cases are added to the simplifier, while the non *) 

233 
(* have their own rules proved below *) 

18366  234 
val (perm_defs, thy5) = fold_map (fn (ak_name, T) => fn thy => 
235 
fold_map (fn (ak_name', T') => fn thy' => 

18068  236 
let 
237 
val perm_def_name = ak_name ^ "_prm_" ^ ak_name'; 

238 
val pi = Free ("pi", mk_permT T); 

239 
val a = Free ("a", T'); 

19494  240 
val cperm = Const ("Nominal.perm", mk_permT T > T' > T'); 
28965  241 
val cperm_def = Const (Sign.full_bname thy' perm_def_name, mk_permT T > T' > T'); 
18068  242 

243 
val name = ak_name ^ "_prm_" ^ ak_name' ^ "_def"; 

244 
val def = Logic.mk_equals 

245 
(cperm $ pi $ a, if ak_name = ak_name' then cperm_def $ pi $ a else a) 

246 
in 

29585  247 
PureThy.add_defs_unchecked true [((Binding.name name, def),[])] thy' 
18366  248 
end) ak_names_types thy) ak_names_types thy4; 
18068  249 

250 
(* proves that every atomkind is an instance of at *) 

251 
(* lemma at_<ak>_inst: *) 

252 
(* at TYPE(<ak>) *) 

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253 
val (prm_cons_thms,thy6) = 
29585  254 
thy5 > add_thms_string (map (fn (ak_name, T) => 
18068  255 
let 
28965  256 
val ak_name_qu = Sign.full_bname thy5 (ak_name); 
18068  257 
val i_type = Type(ak_name_qu,[]); 
26337  258 
val cat = Const ("Nominal.at",(Term.itselfT i_type) > HOLogic.boolT); 
18068  259 
val at_type = Logic.mk_type i_type; 
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260 
val simp_s = HOL_ss addsimps maps (PureThy.get_thms thy5) 
26337  261 
["at_def", 
262 
ak_name ^ "_prm_" ^ ak_name ^ "_def", 

263 
ak_name ^ "_prm_" ^ ak_name ^ ".simps", 

264 
"swap_" ^ ak_name ^ "_def", 

265 
"swap_" ^ ak_name ^ ".simps", 

266 
ak_name ^ "_infinite"] 

267 

268 
val name = "at_"^ak_name^ "_inst"; 

18068  269 
val statement = HOLogic.mk_Trueprop (cat $ at_type); 
270 

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271 
val proof = fn _ => simp_tac simp_s 1 
18068  272 

273 
in 

20046  274 
((name, Goal.prove_global thy5 [] [] statement proof), []) 
18068  275 
end) ak_names_types); 
276 

277 
(* declares a permaxclass for every atomkind *) 

278 
(* axclass pt_<ak> *) 

279 
(* pt_<ak>1[simp]: perm [] x = x *) 

280 
(* pt_<ak>2: perm (pi1@pi2) x = perm pi1 (perm pi2 x) *) 

281 
(* pt_<ak>3: pi1 ~ pi2 ==> perm pi1 x = perm pi2 x *) 

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282 
val (pt_ax_classes,thy7) = fold_map (fn (ak_name, T) => fn thy => 
18068  283 
let 
26337  284 
val cl_name = "pt_"^ak_name; 
18068  285 
val ty = TFree("'a",["HOL.type"]); 
286 
val x = Free ("x", ty); 

287 
val pi1 = Free ("pi1", mk_permT T); 

288 
val pi2 = Free ("pi2", mk_permT T); 

19494  289 
val cperm = Const ("Nominal.perm", mk_permT T > ty > ty); 
18068  290 
val cnil = Const ("List.list.Nil", mk_permT T); 
23029  291 
val cappend = Const ("List.append",mk_permT T > mk_permT T > mk_permT T); 
19494  292 
val cprm_eq = Const ("Nominal.prm_eq",mk_permT T > mk_permT T > HOLogic.boolT); 
18068  293 
(* nil axiom *) 
294 
val axiom1 = HOLogic.mk_Trueprop (HOLogic.mk_eq 

295 
(cperm $ cnil $ x, x)); 

296 
(* append axiom *) 

297 
val axiom2 = HOLogic.mk_Trueprop (HOLogic.mk_eq 

298 
(cperm $ (cappend $ pi1 $ pi2) $ x, cperm $ pi1 $ (cperm $ pi2 $ x))); 

299 
(* permeq axiom *) 

300 
val axiom3 = Logic.mk_implies 

301 
(HOLogic.mk_Trueprop (cprm_eq $ pi1 $ pi2), 

302 
HOLogic.mk_Trueprop (HOLogic.mk_eq (cperm $ pi1 $ x, cperm $ pi2 $ x))); 

303 
in 

22745  304 
AxClass.define_class (cl_name, ["HOL.type"]) [] 
28965  305 
[((Binding.name (cl_name ^ "1"), [Simplifier.simp_add]), [axiom1]), 
306 
((Binding.name (cl_name ^ "2"), []), [axiom2]), 

307 
((Binding.name (cl_name ^ "3"), []), [axiom3])] thy 

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308 
end) ak_names_types thy6; 
18068  309 

310 
(* proves that every pt_<ak>type together with <ak>type *) 

311 
(* instance of pt *) 

312 
(* lemma pt_<ak>_inst: *) 

313 
(* pt TYPE('x::pt_<ak>) TYPE(<ak>) *) 

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314 
val (prm_inst_thms,thy8) = 
29585  315 
thy7 > add_thms_string (map (fn (ak_name, T) => 
18068  316 
let 
28965  317 
val ak_name_qu = Sign.full_bname thy7 ak_name; 
318 
val pt_name_qu = Sign.full_bname thy7 ("pt_"^ak_name); 

18068  319 
val i_type1 = TFree("'x",[pt_name_qu]); 
320 
val i_type2 = Type(ak_name_qu,[]); 

26337  321 
val cpt = Const ("Nominal.pt",(Term.itselfT i_type1)>(Term.itselfT i_type2)>HOLogic.boolT); 
18068  322 
val pt_type = Logic.mk_type i_type1; 
323 
val at_type = Logic.mk_type i_type2; 

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324 
val simp_s = HOL_ss addsimps maps (PureThy.get_thms thy7) 
26337  325 
["pt_def", 
326 
"pt_" ^ ak_name ^ "1", 

327 
"pt_" ^ ak_name ^ "2", 

328 
"pt_" ^ ak_name ^ "3"]; 

18068  329 

26337  330 
val name = "pt_"^ak_name^ "_inst"; 
18068  331 
val statement = HOLogic.mk_Trueprop (cpt $ pt_type $ at_type); 
332 

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changeset

333 
val proof = fn _ => simp_tac simp_s 1; 
18068  334 
in 
20046  335 
((name, Goal.prove_global thy7 [] [] statement proof), []) 
18068  336 
end) ak_names_types); 
337 

338 
(* declares an fsaxclass for every atomkind *) 

339 
(* axclass fs_<ak> *) 

340 
(* fs_<ak>1: finite ((supp x)::<ak> set) *) 

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341 
val (fs_ax_classes,thy11) = fold_map (fn (ak_name, T) => fn thy => 
18068  342 
let 
26337  343 
val cl_name = "fs_"^ak_name; 
28965  344 
val pt_name = Sign.full_bname thy ("pt_"^ak_name); 
18068  345 
val ty = TFree("'a",["HOL.type"]); 
346 
val x = Free ("x", ty); 

19494  347 
val csupp = Const ("Nominal.supp", ty > HOLogic.mk_setT T); 
22274  348 
val cfinite = Const ("Finite_Set.finite", HOLogic.mk_setT T > HOLogic.boolT) 
18068  349 

22274  350 
val axiom1 = HOLogic.mk_Trueprop (cfinite $ (csupp $ x)); 
18068  351 

352 
in 

28965  353 
AxClass.define_class (cl_name, [pt_name]) [] [((Binding.name (cl_name ^ "1"), []), [axiom1])] thy 
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changeset

354 
end) ak_names_types thy8; 
26337  355 

18068  356 
(* proves that every fs_<ak>type together with <ak>type *) 
357 
(* instance of fstype *) 

358 
(* lemma abst_<ak>_inst: *) 

359 
(* fs TYPE('x::pt_<ak>) TYPE (<ak>) *) 

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changeset

360 
val (fs_inst_thms,thy12) = 
29585  361 
thy11 > add_thms_string (map (fn (ak_name, T) => 
18068  362 
let 
28965  363 
val ak_name_qu = Sign.full_bname thy11 ak_name; 
364 
val fs_name_qu = Sign.full_bname thy11 ("fs_"^ak_name); 

18068  365 
val i_type1 = TFree("'x",[fs_name_qu]); 
366 
val i_type2 = Type(ak_name_qu,[]); 

26337  367 
val cfs = Const ("Nominal.fs", 
18068  368 
(Term.itselfT i_type1)>(Term.itselfT i_type2)>HOLogic.boolT); 
369 
val fs_type = Logic.mk_type i_type1; 

370 
val at_type = Logic.mk_type i_type2; 

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26337
diff
changeset

371 
val simp_s = HOL_ss addsimps maps (PureThy.get_thms thy11) 
26337  372 
["fs_def", 
373 
"fs_" ^ ak_name ^ "1"]; 

18068  374 

26337  375 
val name = "fs_"^ak_name^ "_inst"; 
18068  376 
val statement = HOLogic.mk_Trueprop (cfs $ fs_type $ at_type); 
377 

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urbanc
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24218
diff
changeset

378 
val proof = fn _ => simp_tac simp_s 1; 
18068  379 
in 
20046  380 
((name, Goal.prove_global thy11 [] [] statement proof), []) 
18068  381 
end) ak_names_types); 
382 

383 
(* declares for every atomkind combination an axclass *) 

384 
(* cp_<ak1>_<ak2> giving a composition property *) 

385 
(* cp_<ak1>_<ak2>1: pi1 o pi2 o x = (pi1 o pi2) o (pi1 o x) *) 

22418
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urbanc
parents:
22274
diff
changeset

386 
val (cp_ax_classes,thy12b) = fold_map (fn (ak_name, T) => fn thy => 
26337  387 
fold_map (fn (ak_name', T') => fn thy' => 
388 
let 

389 
val cl_name = "cp_"^ak_name^"_"^ak_name'; 

390 
val ty = TFree("'a",["HOL.type"]); 

18068  391 
val x = Free ("x", ty); 
392 
val pi1 = Free ("pi1", mk_permT T); 

26337  393 
val pi2 = Free ("pi2", mk_permT T'); 
394 
val cperm1 = Const ("Nominal.perm", mk_permT T > ty > ty); 

19494  395 
val cperm2 = Const ("Nominal.perm", mk_permT T' > ty > ty); 
396 
val cperm3 = Const ("Nominal.perm", mk_permT T > mk_permT T' > mk_permT T'); 

18068  397 

398 
val ax1 = HOLogic.mk_Trueprop 

26337  399 
(HOLogic.mk_eq (cperm1 $ pi1 $ (cperm2 $ pi2 $ x), 
18068  400 
cperm2 $ (cperm3 $ pi1 $ pi2) $ (cperm1 $ pi1 $ x))); 
26337  401 
in 
28083
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explicit type Name.binding for higherspecification elements;
wenzelm
parents:
28011
diff
changeset

402 
AxClass.define_class (cl_name, ["HOL.type"]) [] 
28965  403 
[((Binding.name (cl_name ^ "1"), []), [ax1])] thy' 
26337  404 
end) ak_names_types thy) ak_names_types thy12; 
18068  405 

406 
(* proves for every <ak>combination a cp_<ak1>_<ak2>_inst theorem; *) 

407 
(* lemma cp_<ak1>_<ak2>_inst: *) 

408 
(* cp TYPE('a::cp_<ak1>_<ak2>) TYPE(<ak1>) TYPE(<ak2>) *) 

18381
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urbanc
parents:
18366
diff
changeset

409 
val (cp_thms,thy12c) = fold_map (fn (ak_name, T) => fn thy => 
26337  410 
fold_map (fn (ak_name', T') => fn thy' => 
18068  411 
let 
28965  412 
val ak_name_qu = Sign.full_bname thy' (ak_name); 
413 
val ak_name_qu' = Sign.full_bname thy' (ak_name'); 

414 
val cp_name_qu = Sign.full_bname thy' ("cp_"^ak_name^"_"^ak_name'); 

18068  415 
val i_type0 = TFree("'a",[cp_name_qu]); 
416 
val i_type1 = Type(ak_name_qu,[]); 

417 
val i_type2 = Type(ak_name_qu',[]); 

26337  418 
val ccp = Const ("Nominal.cp", 
18068  419 
(Term.itselfT i_type0)>(Term.itselfT i_type1)> 
420 
(Term.itselfT i_type2)>HOLogic.boolT); 

421 
val at_type = Logic.mk_type i_type1; 

422 
val at_type' = Logic.mk_type i_type2; 

26337  423 
val cp_type = Logic.mk_type i_type0; 
26343
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wenzelm
parents:
26337
diff
changeset

424 
val simp_s = HOL_basic_ss addsimps maps (PureThy.get_thms thy') ["cp_def"]; 
0dd2eab7b296
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wenzelm
parents:
26337
diff
changeset

425 
val cp1 = PureThy.get_thm thy' ("cp_" ^ ak_name ^ "_" ^ ak_name' ^ "1"); 
18068  426 

26337  427 
val name = "cp_"^ak_name^ "_"^ak_name'^"_inst"; 
18068  428 
val statement = HOLogic.mk_Trueprop (ccp $ cp_type $ at_type $ at_type'); 
429 

24527
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urbanc
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24218
diff
changeset

430 
val proof = fn _ => EVERY [simp_tac simp_s 1, 
888d56a8d9d3
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urbanc
parents:
24218
diff
changeset

431 
rtac allI 1, rtac allI 1, rtac allI 1, 
888d56a8d9d3
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urbanc
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24218
diff
changeset

432 
rtac cp1 1]; 
26337  433 
in 
29585  434 
yield_singleton add_thms_string ((name, 
28729
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Some more functions for accessing information about atoms.
berghofe
parents:
28372
diff
changeset

435 
Goal.prove_global thy' [] [] statement proof), []) thy' 
26337  436 
end) 
18381
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urbanc
parents:
18366
diff
changeset

437 
ak_names_types thy) ak_names_types thy12b; 
18068  438 

439 
(* proves for every nontrivial <ak>combination a disjointness *) 

440 
(* theorem; i.e. <ak1> != <ak2> *) 

441 
(* lemma ds_<ak1>_<ak2>: *) 

442 
(* dj TYPE(<ak1>) TYPE(<ak2>) *) 

18381
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urbanc
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diff
changeset

443 
val (dj_thms, thy12d) = fold_map (fn (ak_name,T) => fn thy => 
26337  444 
fold_map (fn (ak_name',T') => fn thy' => 
18068  445 
(if not (ak_name = ak_name') 
446 
then 

26337  447 
let 
28965  448 
val ak_name_qu = Sign.full_bname thy' ak_name; 
449 
val ak_name_qu' = Sign.full_bname thy' ak_name'; 

18068  450 
val i_type1 = Type(ak_name_qu,[]); 
451 
val i_type2 = Type(ak_name_qu',[]); 

26337  452 
val cdj = Const ("Nominal.disjoint", 
18068  453 
(Term.itselfT i_type1)>(Term.itselfT i_type2)>HOLogic.boolT); 
454 
val at_type = Logic.mk_type i_type1; 

455 
val at_type' = Logic.mk_type i_type2; 

26343
0dd2eab7b296
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wenzelm
parents:
26337
diff
changeset

456 
val simp_s = HOL_ss addsimps maps (PureThy.get_thms thy') 
26337  457 
["disjoint_def", 
458 
ak_name ^ "_prm_" ^ ak_name' ^ "_def", 

459 
ak_name' ^ "_prm_" ^ ak_name ^ "_def"]; 

18068  460 

26337  461 
val name = "dj_"^ak_name^"_"^ak_name'; 
18068  462 
val statement = HOLogic.mk_Trueprop (cdj $ at_type $ at_type'); 
463 

24527
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urbanc
parents:
24218
diff
changeset

464 
val proof = fn _ => simp_tac simp_s 1; 
26337  465 
in 
29585  466 
add_thms_string [((name, Goal.prove_global thy' [] [] statement proof), [])] thy' 
26337  467 
end 
18068  468 
else 
18381
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urbanc
parents:
18366
diff
changeset

469 
([],thy'))) (* do nothing branch, if ak_name = ak_name' *) 
26337  470 
ak_names_types thy) ak_names_types thy12c; 
18068  471 

20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

472 
(******** pt_<ak> class instances ********) 
18068  473 
(*=========================================*) 
18279
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urbanc
parents:
18262
diff
changeset

474 
(* some abbreviations for theorems *) 
23894
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wenzelm
parents:
23158
diff
changeset

475 
val pt1 = @{thm "pt1"}; 
1a4167d761ac
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wenzelm
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23158
diff
changeset

476 
val pt2 = @{thm "pt2"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

477 
val pt3 = @{thm "pt3"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

478 
val at_pt_inst = @{thm "at_pt_inst"}; 
1a4167d761ac
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wenzelm
parents:
23158
diff
changeset

479 
val pt_unit_inst = @{thm "pt_unit_inst"}; 
1a4167d761ac
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wenzelm
parents:
23158
diff
changeset

480 
val pt_prod_inst = @{thm "pt_prod_inst"}; 
1a4167d761ac
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wenzelm
parents:
23158
diff
changeset

481 
val pt_nprod_inst = @{thm "pt_nprod_inst"}; 
1a4167d761ac
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wenzelm
parents:
23158
diff
changeset

482 
val pt_list_inst = @{thm "pt_list_inst"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

483 
val pt_optn_inst = @{thm "pt_option_inst"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

484 
val pt_noptn_inst = @{thm "pt_noption_inst"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

485 
val pt_fun_inst = @{thm "pt_fun_inst"}; 
18068  486 

18435  487 
(* for all atomkind combinations <ak>/<ak'> show that *) 
488 
(* every <ak> is an instance of pt_<ak'>; the proof for *) 

489 
(* ak!=ak' is by definition; the case ak=ak' uses at_pt_inst. *) 

18431  490 
val thy13 = fold (fn ak_name => fn thy => 
26337  491 
fold (fn ak_name' => fn thy' => 
18431  492 
let 
28965  493 
val qu_name = Sign.full_bname thy' ak_name'; 
494 
val cls_name = Sign.full_bname thy' ("pt_"^ak_name); 

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changeset

495 
val at_inst = PureThy.get_thm thy' ("at_" ^ ak_name' ^ "_inst"); 
18431  496 

24218  497 
val proof1 = EVERY [Class.intro_classes_tac [], 
18068  498 
rtac ((at_inst RS at_pt_inst) RS pt1) 1, 
499 
rtac ((at_inst RS at_pt_inst) RS pt2) 1, 

500 
rtac ((at_inst RS at_pt_inst) RS pt3) 1, 

501 
atac 1]; 

18431  502 
val simp_s = HOL_basic_ss addsimps 
26343
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changeset

503 
maps (PureThy.get_thms thy') [ak_name ^ "_prm_" ^ ak_name' ^ "_def"]; 
24218  504 
val proof2 = EVERY [Class.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)]; 
18431  505 

506 
in 

507 
thy' 

19275  508 
> AxClass.prove_arity (qu_name,[],[cls_name]) 
18431  509 
(if ak_name = ak_name' then proof1 else proof2) 
26484  510 
end) ak_names thy) ak_names thy12d; 
18068  511 

18430  512 
(* show that *) 
513 
(* fun(pt_<ak>,pt_<ak>) *) 

18579
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changed the name of the type "nOption" to "noption".
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18438
diff
changeset

514 
(* noption(pt_<ak>) *) 
18430  515 
(* option(pt_<ak>) *) 
516 
(* list(pt_<ak>) *) 

517 
(* *(pt_<ak>,pt_<ak>) *) 

18600  518 
(* nprod(pt_<ak>,pt_<ak>) *) 
18430  519 
(* unit *) 
520 
(* set(pt_<ak>) *) 

521 
(* are instances of pt_<ak> *) 

18431  522 
val thy18 = fold (fn ak_name => fn thy => 
18068  523 
let 
28965  524 
val cls_name = Sign.full_bname thy ("pt_"^ak_name); 
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changeset

525 
val at_thm = PureThy.get_thm thy ("at_"^ak_name^"_inst"); 
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changeset

526 
val pt_inst = PureThy.get_thm thy ("pt_"^ak_name^"_inst"); 
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changeset

527 

18430  528 
fun pt_proof thm = 
24218  529 
EVERY [Class.intro_classes_tac [], 
18430  530 
rtac (thm RS pt1) 1, rtac (thm RS pt2) 1, rtac (thm RS pt3) 1, atac 1]; 
531 

532 
val pt_thm_fun = at_thm RS (pt_inst RS (pt_inst RS pt_fun_inst)); 

533 
val pt_thm_noptn = pt_inst RS pt_noptn_inst; 

534 
val pt_thm_optn = pt_inst RS pt_optn_inst; 

535 
val pt_thm_list = pt_inst RS pt_list_inst; 

536 
val pt_thm_prod = pt_inst RS (pt_inst RS pt_prod_inst); 

18600  537 
val pt_thm_nprod = pt_inst RS (pt_inst RS pt_nprod_inst); 
18430  538 
val pt_thm_unit = pt_unit_inst; 
20097
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parents:
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diff
changeset

539 
in 
be2d96bbf39c
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webertj
parents:
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diff
changeset

540 
thy 
be2d96bbf39c
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parents:
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changeset

541 
> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_fun) 
19494  542 
> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (pt_proof pt_thm_noptn) 
24194  543 
> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (pt_proof pt_thm_optn) 
19275  544 
> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (pt_proof pt_thm_list) 
545 
> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (pt_proof pt_thm_prod) 

19494  546 
> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
18600  547 
(pt_proof pt_thm_nprod) 
19275  548 
> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (pt_proof pt_thm_unit) 
18430  549 
end) ak_names thy13; 
18068  550 

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changeset

551 
(******** fs_<ak> class instances ********) 
18068  552 
(*=========================================*) 
18279
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changeset

553 
(* abbreviations for some lemmas *) 
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changeset

554 
val fs1 = @{thm "fs1"}; 
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changeset

555 
val fs_at_inst = @{thm "fs_at_inst"}; 
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556 
val fs_unit_inst = @{thm "fs_unit_inst"}; 
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changeset

557 
val fs_prod_inst = @{thm "fs_prod_inst"}; 
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changeset

558 
val fs_nprod_inst = @{thm "fs_nprod_inst"}; 
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changeset

559 
val fs_list_inst = @{thm "fs_list_inst"}; 
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parents:
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changeset

560 
val fs_option_inst = @{thm "fs_option_inst"}; 
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changeset

561 
val dj_supp = @{thm "dj_supp"}; 
18068  562 

563 
(* shows that <ak> is an instance of fs_<ak> *) 

564 
(* uses the theorem at_<ak>_inst *) 

18431  565 
val thy20 = fold (fn ak_name => fn thy => 
20097
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parents:
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changeset

566 
fold (fn ak_name' => fn thy' => 
18437
ee0283e5dfe3
added proofs to show that every atomkind combination
urbanc
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18436
diff
changeset

567 
let 
28965  568 
val qu_name = Sign.full_bname thy' ak_name'; 
569 
val qu_class = Sign.full_bname thy' ("fs_"^ak_name); 

20097
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parents:
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diff
changeset

570 
val proof = 
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parents:
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changeset

571 
(if ak_name = ak_name' 
be2d96bbf39c
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webertj
parents:
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diff
changeset

572 
then 
26343
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wenzelm
parents:
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diff
changeset

573 
let val at_thm = PureThy.get_thm thy' ("at_"^ak_name^"_inst"); 
24218  574 
in EVERY [Class.intro_classes_tac [], 
18437
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urbanc
parents:
18436
diff
changeset

575 
rtac ((at_thm RS fs_at_inst) RS fs1) 1] end 
ee0283e5dfe3
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urbanc
parents:
18436
diff
changeset

576 
else 
26343
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parents:
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diff
changeset

577 
let val dj_inst = PureThy.get_thm thy' ("dj_"^ak_name'^"_"^ak_name); 
22274  578 
val simp_s = HOL_basic_ss addsimps [dj_inst RS dj_supp, finite_emptyI]; 
24218  579 
in EVERY [Class.intro_classes_tac [], asm_simp_tac simp_s 1] end) 
20097
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parents:
20046
diff
changeset

580 
in 
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

581 
AxClass.prove_arity (qu_name,[],[qu_class]) proof thy' 
18437
ee0283e5dfe3
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urbanc
parents:
18436
diff
changeset

582 
end) ak_names thy) ak_names thy18; 
18068  583 

18431  584 
(* shows that *) 
585 
(* unit *) 

586 
(* *(fs_<ak>,fs_<ak>) *) 

18600  587 
(* nprod(fs_<ak>,fs_<ak>) *) 
18431  588 
(* list(fs_<ak>) *) 
589 
(* option(fs_<ak>) *) 

590 
(* are instances of fs_<ak> *) 

18068  591 

18431  592 
val thy24 = fold (fn ak_name => fn thy => 
593 
let 

28965  594 
val cls_name = Sign.full_bname thy ("fs_"^ak_name); 
26343
0dd2eab7b296
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wenzelm
parents:
26337
diff
changeset

595 
val fs_inst = PureThy.get_thm thy ("fs_"^ak_name^"_inst"); 
24218  596 
fun fs_proof thm = EVERY [Class.intro_classes_tac [], rtac (thm RS fs1) 1]; 
18068  597 

18600  598 
val fs_thm_unit = fs_unit_inst; 
599 
val fs_thm_prod = fs_inst RS (fs_inst RS fs_prod_inst); 

600 
val fs_thm_nprod = fs_inst RS (fs_inst RS fs_nprod_inst); 

601 
val fs_thm_list = fs_inst RS fs_list_inst; 

602 
val fs_thm_optn = fs_inst RS fs_option_inst; 

18431  603 
in 
20097
be2d96bbf39c
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webertj
parents:
20046
diff
changeset

604 
thy 
19275  605 
> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (fs_proof fs_thm_unit) 
606 
> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (fs_proof fs_thm_prod) 

19494  607 
> AxClass.prove_arity ("Nominal.nprod",[[cls_name],[cls_name]],[cls_name]) 
18600  608 
(fs_proof fs_thm_nprod) 
19275  609 
> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (fs_proof fs_thm_list) 
24194  610 
> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (fs_proof fs_thm_optn) 
20097
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webertj
parents:
20046
diff
changeset

611 
end) ak_names thy20; 
18431  612 

20097
be2d96bbf39c
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webertj
parents:
20046
diff
changeset

613 
(******** cp_<ak>_<ai> class instances ********) 
18068  614 
(*==============================================*) 
18279
f7a18e2b10fc
made some of the theorem lookups static (by using
urbanc
parents:
18262
diff
changeset

615 
(* abbreviations for some lemmas *) 
23894
1a4167d761ac
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wenzelm
parents:
23158
diff
changeset

616 
val cp1 = @{thm "cp1"}; 
1a4167d761ac
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wenzelm
parents:
23158
diff
changeset

617 
val cp_unit_inst = @{thm "cp_unit_inst"}; 
1a4167d761ac
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wenzelm
parents:
23158
diff
changeset

618 
val cp_bool_inst = @{thm "cp_bool_inst"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

619 
val cp_prod_inst = @{thm "cp_prod_inst"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

620 
val cp_list_inst = @{thm "cp_list_inst"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

621 
val cp_fun_inst = @{thm "cp_fun_inst"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

622 
val cp_option_inst = @{thm "cp_option_inst"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

623 
val cp_noption_inst = @{thm "cp_noption_inst"}; 
1a4167d761ac
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wenzelm
parents:
23158
diff
changeset

624 
val pt_perm_compose = @{thm "pt_perm_compose"}; 
20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

625 

23894
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

626 
val dj_pp_forget = @{thm "dj_perm_perm_forget"}; 
18068  627 

628 
(* shows that <aj> is an instance of cp_<ak>_<ai> *) 

18432  629 
(* for every <ak>/<ai>combination *) 
20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

630 
val thy25 = fold (fn ak_name => fn thy => 
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

631 
fold (fn ak_name' => fn thy' => 
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

632 
fold (fn ak_name'' => fn thy'' => 
18068  633 
let 
28965  634 
val name = Sign.full_bname thy'' ak_name; 
635 
val cls_name = Sign.full_bname thy'' ("cp_"^ak_name'^"_"^ak_name''); 

18068  636 
val proof = 
637 
(if (ak_name'=ak_name'') then 

20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

638 
(let 
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

639 
val pt_inst = PureThy.get_thm thy'' ("pt_"^ak_name''^"_inst"); 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

640 
val at_inst = PureThy.get_thm thy'' ("at_"^ak_name''^"_inst"); 
20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

641 
in 
26337  642 
EVERY [Class.intro_classes_tac [], 
18068  643 
rtac (at_inst RS (pt_inst RS pt_perm_compose)) 1] 
644 
end) 

26337  645 
else 
646 
(let 

26343
0dd2eab7b296
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wenzelm
parents:
26337
diff
changeset

647 
val dj_inst = PureThy.get_thm thy'' ("dj_"^ak_name''^"_"^ak_name'); 
26337  648 
val simp_s = HOL_basic_ss addsimps 
18068  649 
((dj_inst RS dj_pp_forget):: 
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

650 
(maps (PureThy.get_thms thy'') 
26337  651 
[ak_name' ^"_prm_"^ak_name^"_def", 
652 
ak_name''^"_prm_"^ak_name^"_def"])); 

20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

653 
in 
24218  654 
EVERY [Class.intro_classes_tac [], simp_tac simp_s 1] 
18068  655 
end)) 
20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

656 
in 
19275  657 
AxClass.prove_arity (name,[],[cls_name]) proof thy'' 
20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

658 
end) ak_names thy') ak_names thy) ak_names thy24; 
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

659 

18432  660 
(* shows that *) 
661 
(* units *) 

662 
(* products *) 

663 
(* lists *) 

664 
(* functions *) 

665 
(* options *) 

666 
(* noptions *) 

22536
35debf264656
made the type sets instance of the "cp" typeclass
urbanc
parents:
22535
diff
changeset

667 
(* sets *) 
18432  668 
(* are instances of cp_<ak>_<ai> for every <ak>/<ai>combination *) 
669 
val thy26 = fold (fn ak_name => fn thy => 

26337  670 
fold (fn ak_name' => fn thy' => 
18432  671 
let 
28965  672 
val cls_name = Sign.full_bname thy' ("cp_"^ak_name^"_"^ak_name'); 
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

673 
val cp_inst = PureThy.get_thm thy' ("cp_"^ak_name^"_"^ak_name'^"_inst"); 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

674 
val pt_inst = PureThy.get_thm thy' ("pt_"^ak_name^"_inst"); 
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

675 
val at_inst = PureThy.get_thm thy' ("at_"^ak_name^"_inst"); 
18432  676 

24218  677 
fun cp_proof thm = EVERY [Class.intro_classes_tac [],rtac (thm RS cp1) 1]; 
26337  678 

18432  679 
val cp_thm_unit = cp_unit_inst; 
680 
val cp_thm_prod = cp_inst RS (cp_inst RS cp_prod_inst); 

681 
val cp_thm_list = cp_inst RS cp_list_inst; 

682 
val cp_thm_fun = at_inst RS (pt_inst RS (cp_inst RS (cp_inst RS cp_fun_inst))); 

683 
val cp_thm_optn = cp_inst RS cp_option_inst; 

684 
val cp_thm_noptn = cp_inst RS cp_noption_inst; 

685 
in 

686 
thy' 

19275  687 
> AxClass.prove_arity ("Product_Type.unit",[],[cls_name]) (cp_proof cp_thm_unit) 
26337  688 
> AxClass.prove_arity ("*",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_prod) 
19275  689 
> AxClass.prove_arity ("List.list",[[cls_name]],[cls_name]) (cp_proof cp_thm_list) 
690 
> AxClass.prove_arity ("fun",[[cls_name],[cls_name]],[cls_name]) (cp_proof cp_thm_fun) 

24194  691 
> AxClass.prove_arity ("Datatype.option",[[cls_name]],[cls_name]) (cp_proof cp_thm_optn) 
19494  692 
> AxClass.prove_arity ("Nominal.noption",[[cls_name]],[cls_name]) (cp_proof cp_thm_noptn) 
18432  693 
end) ak_names thy) ak_names thy25; 
20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

694 

be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

695 
(* show that discrete nominal types are permutation types, finitely *) 
18432  696 
(* supported and have the commutation property *) 
697 
(* discrete types have a permutation operation defined as pi o x = x; *) 

20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

698 
(* which renders the proofs to be simple "simp_all"proofs. *) 
18432  699 
val thy32 = 
20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

700 
let 
26337  701 
fun discrete_pt_inst discrete_ty defn = 
702 
fold (fn ak_name => fn thy => 

703 
let 

28965  704 
val qu_class = Sign.full_bname thy ("pt_"^ak_name); 
26337  705 
val simp_s = HOL_basic_ss addsimps [defn]; 
24218  706 
val proof = EVERY [Class.intro_classes_tac [], REPEAT (asm_simp_tac simp_s 1)]; 
20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

707 
in 
26337  708 
AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy 
18432  709 
end) ak_names; 
18068  710 

18432  711 
fun discrete_fs_inst discrete_ty defn = 
26337  712 
fold (fn ak_name => fn thy => 
713 
let 

28965  714 
val qu_class = Sign.full_bname thy ("fs_"^ak_name); 
26337  715 
val supp_def = @{thm "Nominal.supp_def"}; 
22274  716 
val simp_s = HOL_ss addsimps [supp_def,Collect_const,finite_emptyI,defn]; 
24218  717 
val proof = EVERY [Class.intro_classes_tac [], asm_simp_tac simp_s 1]; 
20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

718 
in 
26337  719 
AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy 
20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

720 
end) ak_names; 
18068  721 

18432  722 
fun discrete_cp_inst discrete_ty defn = 
26337  723 
fold (fn ak_name' => (fold (fn ak_name => fn thy => 
724 
let 

28965  725 
val qu_class = Sign.full_bname thy ("cp_"^ak_name^"_"^ak_name'); 
26337  726 
val supp_def = @{thm "Nominal.supp_def"}; 
18432  727 
val simp_s = HOL_ss addsimps [defn]; 
24218  728 
val proof = EVERY [Class.intro_classes_tac [], asm_simp_tac simp_s 1]; 
20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

729 
in 
26337  730 
AxClass.prove_arity (discrete_ty,[],[qu_class]) proof thy 
20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

731 
end) ak_names)) ak_names; 
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

732 

18432  733 
in 
734 
thy26 

23894
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

735 
> discrete_pt_inst "nat" @{thm "perm_nat_def"} 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

736 
> discrete_fs_inst "nat" @{thm "perm_nat_def"} 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

737 
> discrete_cp_inst "nat" @{thm "perm_nat_def"} 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

738 
> discrete_pt_inst "bool" @{thm "perm_bool"} 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

739 
> discrete_fs_inst "bool" @{thm "perm_bool"} 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

740 
> discrete_cp_inst "bool" @{thm "perm_bool"} 
25919
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25557
diff
changeset

741 
> discrete_pt_inst @{type_name "Int.int"} @{thm "perm_int_def"} 
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25557
diff
changeset

742 
> discrete_fs_inst @{type_name "Int.int"} @{thm "perm_int_def"} 
8b1c0d434824
joined theories IntDef, Numeral, IntArith to theory Int
haftmann
parents:
25557
diff
changeset

743 
> discrete_cp_inst @{type_name "Int.int"} @{thm "perm_int_def"} 
23894
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

744 
> discrete_pt_inst "List.char" @{thm "perm_char_def"} 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

745 
> discrete_fs_inst "List.char" @{thm "perm_char_def"} 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

746 
> discrete_cp_inst "List.char" @{thm "perm_char_def"} 
18432  747 
end; 
748 

20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

749 

18262  750 
(* abbreviations for some lemmas *) 
751 
(*===============================*) 

23894
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

752 
val abs_fun_pi = @{thm "Nominal.abs_fun_pi"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

753 
val abs_fun_pi_ineq = @{thm "Nominal.abs_fun_pi_ineq"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

754 
val abs_fun_eq = @{thm "Nominal.abs_fun_eq"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

755 
val abs_fun_eq' = @{thm "Nominal.abs_fun_eq'"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

756 
val abs_fun_fresh = @{thm "Nominal.abs_fun_fresh"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

757 
val abs_fun_fresh' = @{thm "Nominal.abs_fun_fresh'"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

758 
val dj_perm_forget = @{thm "Nominal.dj_perm_forget"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

759 
val dj_pp_forget = @{thm "Nominal.dj_perm_perm_forget"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

760 
val fresh_iff = @{thm "Nominal.fresh_abs_fun_iff"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

761 
val fresh_iff_ineq = @{thm "Nominal.fresh_abs_fun_iff_ineq"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

762 
val abs_fun_supp = @{thm "Nominal.abs_fun_supp"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

763 
val abs_fun_supp_ineq = @{thm "Nominal.abs_fun_supp_ineq"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

764 
val pt_swap_bij = @{thm "Nominal.pt_swap_bij"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

765 
val pt_swap_bij' = @{thm "Nominal.pt_swap_bij'"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

766 
val pt_fresh_fresh = @{thm "Nominal.pt_fresh_fresh"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

767 
val pt_bij = @{thm "Nominal.pt_bij"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

768 
val pt_perm_compose = @{thm "Nominal.pt_perm_compose"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

769 
val pt_perm_compose' = @{thm "Nominal.pt_perm_compose'"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

770 
val perm_app = @{thm "Nominal.pt_fun_app_eq"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

771 
val at_fresh = @{thm "Nominal.at_fresh"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

772 
val at_fresh_ineq = @{thm "Nominal.at_fresh_ineq"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

773 
val at_calc = @{thms "Nominal.at_calc"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

774 
val at_swap_simps = @{thms "Nominal.at_swap_simps"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

775 
val at_supp = @{thm "Nominal.at_supp"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

776 
val dj_supp = @{thm "Nominal.dj_supp"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

777 
val fresh_left_ineq = @{thm "Nominal.pt_fresh_left_ineq"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

778 
val fresh_left = @{thm "Nominal.pt_fresh_left"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

779 
val fresh_right_ineq = @{thm "Nominal.pt_fresh_right_ineq"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

780 
val fresh_right = @{thm "Nominal.pt_fresh_right"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

781 
val fresh_bij_ineq = @{thm "Nominal.pt_fresh_bij_ineq"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

782 
val fresh_bij = @{thm "Nominal.pt_fresh_bij"}; 
26773  783 
val fresh_star_bij_ineq = @{thms "Nominal.pt_fresh_star_bij_ineq"}; 
784 
val fresh_star_bij = @{thms "Nominal.pt_fresh_star_bij"}; 

23894
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

785 
val fresh_eqvt = @{thm "Nominal.pt_fresh_eqvt"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

786 
val fresh_eqvt_ineq = @{thm "Nominal.pt_fresh_eqvt_ineq"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

787 
val set_diff_eqvt = @{thm "Nominal.pt_set_diff_eqvt"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

788 
val in_eqvt = @{thm "Nominal.pt_in_eqvt"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

789 
val eq_eqvt = @{thm "Nominal.pt_eq_eqvt"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

790 
val all_eqvt = @{thm "Nominal.pt_all_eqvt"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

791 
val ex_eqvt = @{thm "Nominal.pt_ex_eqvt"}; 
28011  792 
val ex1_eqvt = @{thm "Nominal.pt_ex1_eqvt"}; 
793 
val the_eqvt = @{thm "Nominal.pt_the_eqvt"}; 

23894
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

794 
val pt_pi_rev = @{thm "Nominal.pt_pi_rev"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

795 
val pt_rev_pi = @{thm "Nominal.pt_rev_pi"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

796 
val at_exists_fresh = @{thm "Nominal.at_exists_fresh"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

797 
val at_exists_fresh' = @{thm "Nominal.at_exists_fresh'"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

798 
val fresh_perm_app_ineq = @{thm "Nominal.pt_fresh_perm_app_ineq"}; 
26337  799 
val fresh_perm_app = @{thm "Nominal.pt_fresh_perm_app"}; 
23894
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

800 
val fresh_aux = @{thm "Nominal.pt_fresh_aux"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

801 
val pt_perm_supp_ineq = @{thm "Nominal.pt_perm_supp_ineq"}; 
1a4167d761ac
tactics: avoid dynamic reference to accidental theory context (via ML_Context.the_context etc.);
wenzelm
parents:
23158
diff
changeset

802 
val pt_perm_supp = @{thm "Nominal.pt_perm_supp"}; 
26090  803 
val subseteq_eqvt = @{thm "Nominal.pt_subseteq_eqvt"}; 
29128
4c243e6a71b2
changed the names of insert_eqvt and set_eqvt so that it is clear that they have preconditions
Christian Urban <urbanc@in.tum.de>
parents:
28965
diff
changeset

804 
val insert_eqvt = @{thm "Nominal.pt_insert_eqvt"}; 
4c243e6a71b2
changed the names of insert_eqvt and set_eqvt so that it is clear that they have preconditions
Christian Urban <urbanc@in.tum.de>
parents:
28965
diff
changeset

805 
val set_eqvt = @{thm "Nominal.pt_set_eqvt"}; 
26820  806 
val perm_set_eq = @{thm "Nominal.perm_set_eq"}; 
22786  807 

18262  808 
(* Now we collect and instantiate some lemmas w.r.t. all atom *) 
809 
(* types; this allows for example to use abs_perm (which is a *) 

810 
(* collection of theorems) instead of thm abs_fun_pi with explicit *) 

811 
(* instantiations. *) 

20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

812 
val (_, thy33) = 
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

813 
let 
18651
0cb5a8f501aa
added the thmscollection "pt_id" (collection of all pt_<ak>1 lemmas)
urbanc
parents:
18626
diff
changeset

814 

18279
f7a18e2b10fc
made some of the theorem lookups static (by using
urbanc
parents:
18262
diff
changeset

815 
(* takes a theorem thm and a list of theorems [t1,..,tn] *) 
f7a18e2b10fc
made some of the theorem lookups static (by using
urbanc
parents:
18262
diff
changeset

816 
(* produces a list of theorems of the form [t1 RS thm,..,tn RS thm] *) 
18262  817 
fun instR thm thms = map (fn ti => ti RS thm) thms; 
18068  818 

26773  819 
(* takes a theorem thm and a list of theorems [(t1,m1),..,(tn,mn)] *) 
820 
(* produces a list of theorems of the form [[t1,m1] MRS thm,..,[tn,mn] MRS thm] *) 

821 
fun instRR thm thms = map (fn (ti,mi) => [ti,mi] MRS thm) thms; 

822 

18262  823 
(* takes two theorem lists (hopefully of the same length ;o) *) 
824 
(* produces a list of theorems of the form *) 

825 
(* [t1 RS m1,..,tn RS mn] where [t1,..,tn] is thms1 and [m1,..,mn] is thms2 *) 

18279
f7a18e2b10fc
made some of the theorem lookups static (by using
urbanc
parents:
18262
diff
changeset

826 
fun inst_zip thms1 thms2 = map (fn (t1,t2) => t1 RS t2) (thms1 ~~ thms2); 
18068  827 

18262  828 
(* takes a theorem list of the form [l1,...,ln] *) 
829 
(* and a list of theorem lists of the form *) 

830 
(* [[h11,...,h1m],....,[hk1,....,hkm] *) 

831 
(* produces the list of theorem lists *) 

832 
(* [[l1 RS h11,...,l1 RS h1m],...,[ln RS hk1,...,ln RS hkm]] *) 

18279
f7a18e2b10fc
made some of the theorem lookups static (by using
urbanc
parents:
18262
diff
changeset

833 
fun inst_mult thms thmss = map (fn (t,ts) => instR t ts) (thms ~~ thmss); 
f7a18e2b10fc
made some of the theorem lookups static (by using
urbanc
parents:
18262
diff
changeset

834 

f7a18e2b10fc
made some of the theorem lookups static (by using
urbanc
parents:
18262
diff
changeset

835 
(* FIXME: these lists do not need to be created dynamically again *) 
18262  836 

22418
49e2d9744ae1
major update of the nominal package; there is now an infrastructure
urbanc
parents:
22274
diff
changeset

837 

18068  838 
(* list of all at_insttheorems *) 
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

839 
val ats = map (fn ak => PureThy.get_thm thy32 ("at_"^ak^"_inst")) ak_names 
18068  840 
(* list of all pt_insttheorems *) 
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

841 
val pts = map (fn ak => PureThy.get_thm thy32 ("pt_"^ak^"_inst")) ak_names 
18262  842 
(* list of all cp_insttheorems as a collection of lists*) 
18068  843 
val cps = 
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

844 
let fun cps_fun ak1 ak2 = PureThy.get_thm thy32 ("cp_"^ak1^"_"^ak2^"_inst") 
26337  845 
in map (fn aki => (map (cps_fun aki) ak_names)) ak_names end; 
18262  846 
(* list of all cp_insttheorems that have different atom types *) 
847 
val cps' = 

26337  848 
let fun cps'_fun ak1 ak2 = 
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

849 
if ak1=ak2 then NONE else SOME (PureThy.get_thm thy32 ("cp_"^ak1^"_"^ak2^"_inst")) 
26337  850 
in map (fn aki => (List.mapPartial I (map (cps'_fun aki) ak_names))) ak_names end; 
18068  851 
(* list of all dj_insttheorems *) 
852 
val djs = 

26337  853 
let fun djs_fun ak1 ak2 = 
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

854 
if ak1=ak2 then NONE else SOME(PureThy.get_thm thy32 ("dj_"^ak2^"_"^ak1)) 
26337  855 
in map_filter I (map_product djs_fun ak_names ak_names) end; 
18262  856 
(* list of all fs_insttheorems *) 
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

857 
val fss = map (fn ak => PureThy.get_thm thy32 ("fs_"^ak^"_inst")) ak_names 
22418
49e2d9744ae1
major update of the nominal package; there is now an infrastructure
urbanc
parents:
22274
diff
changeset

858 
(* list of all at_insttheorems *) 
26343
0dd2eab7b296
simplified get_thm(s): back to plain name argument;
wenzelm
parents:
26337
diff
changeset

859 
val fs_axs = map (fn ak => PureThy.get_thm thy32 ("fs_"^ak^"1")) ak_names 
20097
be2d96bbf39c
replaced mk_listT by HOLogic.listT; trivial whitespace/comment changes
webertj
parents:
20046
diff
changeset

860 

25538  861 
fun inst_pt thms = maps (fn ti => instR ti pts) thms; 
862 
fun inst_at thms = maps (fn ti => instR ti ats) thms; 

863 
fun inst_fs thms = maps (fn ti => instR ti fss) thms; 

864 
fun inst_cp thms cps = flat (inst_mult thms cps); 

26773  865 
fun inst_pt_at thms = maps (fn ti => instRR ti (pts ~~ ats)) thms; 
25538  866 
fun inst_dj thms = maps (fn ti => instR ti djs) thms; 
26337  867 
fun inst_pt_pt_at_cp thms = inst_cp (inst_zip ats (inst_zip pts (inst_pt thms))) cps; 
18262  868 
fun inst_pt_at_fs thms = inst_zip (inst_fs [fs1]) (inst_zip ats (inst_pt thms)); 
26337  869 
fun inst_pt_pt_at_cp thms = 
870 
let val i_pt_pt_at = inst_zip ats (inst_zip pts (inst_pt thms)); 

18436
9649e24bc10e
added thms to perm_compose (so far only composition
urbanc
parents:
18435
diff
changeset

871 
val i_pt_pt_at_cp = inst_cp i_pt_pt_at cps'; 
26337  872 
in i_pt_pt_at_cp end; 
18396
b3e7da94b51f
added a fresh_left lemma that contains all instantiation
urbanc
parents:
18381
diff
changeset

873 
fun inst_pt_pt_at_cp_dj thms = inst_zip djs (inst_pt_pt_at_cp thms); 
18068  874 
in 
18262  875 
thy32 
29585  876 
> add_thmss_string [(("alpha", inst_pt_at [abs_fun_eq]),[])] 
877 
>> add_thmss_string [(("alpha'", inst_pt_at [abs_fun_eq']),[])] 

878 
>> add_thmss_string [(("alpha_fresh", inst_pt_at [abs_fun_fresh]),[])] 

879 
>> add_thmss_string [(("alpha_fresh'", inst_pt_at [abs_fun_fresh']),[])] 

880 
>> add_thmss_string [(("perm_swap", inst_pt_at [pt_swap_bij] @ inst_pt_at [pt_swap_bij']),[])] 

881 
>> add_thmss_string 

27399
1fb3d1219c12
added facts to lemma swap_simps and tuned lemma calc_atms
urbanc
parents:
27216
diff
changeset

882 
let val thms1 = inst_at at_swap_simps 
1fb3d1219c12
added facts to lemma swap_simps and tuned lemma calc_atms
urbanc
parents:
27216
diff
changeset

883 
and thms2 = inst_dj [dj_perm_forget] 
1fb3d1219c12
added facts to lemma swap_simps and tuned lemma calc_atms
urbanc
parents:
27216
diff
changeset

884 
in [(("swap_simps", thms1 @ thms2),[])] end 
29585  885 
>> add_thmss_string 
26337  886 
let val thms1 = inst_pt_at [pt_pi_rev]; 
887 
val thms2 = inst_pt_at [pt_rev_pi]; 

19139  888 
in [(("perm_pi_simp",thms1 @ thms2),[])] end 
29585  889 
>> add_thmss_string [(("perm_fresh_fresh", inst_pt_at [pt_fresh_fresh]),[])] 
890 
>> add_thmss_string [(("perm_bij", inst_pt_at [pt_bij]),[])] 

891 
>> add_thmss_string 

26337  892 
let val thms1 = inst_pt_at [pt_perm_compose]; 
893 
val thms2 = instR cp1 (Library.flat cps'); 

18436
9649e24bc10e
added thms to perm_compose (so far only composition
urbanc
parents:
18435
diff
changeset

894 
in [(("perm_compose",thms1 @ thms2),[])] end 
29585  895 
>> add_thmss_string [(("perm_compose'",inst_pt_at [pt_perm_compose']),[])] 
896 
>> add_thmss_string [(("perm_app", inst_pt_at [perm_app]),[])] 

897 
>> add_thmss_string [(("supp_atm", (inst_at [at_supp]) @ (inst_dj [dj_supp])),[])] 

898 
>> add_thmss_string [(("exists_fresh", inst_at [at_exists_fresh]),[])] 

899 
>> add_thmss_string [(("exists_fresh'", inst_at [at_exists_fresh']),[])] 

900 
>> add_thmss_string 

24569  901 
let 
902 
val thms1 = inst_pt_at [all_eqvt]; 

903 
val thms2 = map (fold_rule [inductive_forall_def]) thms1 

904 
in 

905 
[(("all_eqvt", thms1 @ thms2), [NominalThmDecls.eqvt_force_add])] 

906 
end 

29585  907 
>> add_thmss_string [(("ex_eqvt", inst_pt_at [ex_eqvt]),[NominalThmDecls.eqvt_force_add])] 
908 
>> add_thmss_string [(("ex1_eqvt", inst_pt_at [ex1_eqvt]),[NominalThmDecls.eqvt_force_add])] 

909 
>> add_thmss_string [(("the_eqvt", inst_pt_at [the_eqvt]),[NominalThmDecls.eqvt_force_add])] 

910 
>> add_thmss_string 

26337  911 
let val thms1 = inst_at [at_fresh] 
912 
val thms2 = inst_dj [at_fresh_ineq] 

913 
in [(("fresh_atm", thms1 @ thms2),[])] end 

29585  914 
>> add_thmss_string 
27399
1fb3d1219c12
added facts to lemma swap_simps and tuned lemma calc_atms
urbanc
parents:
27216
diff
changeset

915 
let val thms1 = inst_at at_calc 
1fb3d1219c12
added facts to lemma swap_simps and tuned lemma calc_atms
urbanc
parents:
27216
diff
changeset

916 
and thms2 = inst_dj [dj_perm_forget] 
1fb3d1219c12
added facts to lemma swap_simps and tuned lemma calc_atms
urbanc
parents:
27216
diff
changeset

917 
in [(("calc_atm", thms1 @ thms2),[])] end 
29585  918 
>> add_thmss_string 
26337  919 
let val thms1 = inst_pt_at [abs_fun_pi] 
920 
and thms2 = inst_pt_pt_at_cp [abs_fun_pi_ineq] 

921 
in [(("abs_perm", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end 

29585  922 
>> add_thmss_string 
26337  923 
let val thms1 = inst_dj [dj_perm_forget] 
924 
and thms2 = inst_dj [dj_pp_forget] 

18279
f7a18e2b10fc
made some of the theorem lookups static (by using
urbanc
parents:
18262
diff
changeset

925 
in [(("perm_dj", thms1 @ thms2),[])] end 
29585  926 
>> add_thmss_string 
26337  927 
let val thms1 = inst_pt_at_fs [fresh_iff] 
18626  928 
and thms2 = inst_pt_at [fresh_iff] 
26337  929 
and thms3 = inst_pt_pt_at_cp_dj [fresh_iff_ineq] 
930 
in [(("abs_fresh", thms1 @ thms2 @ thms3),[])] end 

29585  931 
>> add_thmss_string 
26337  932 
let val thms1 = inst_pt_at [abs_fun_supp] 
933 
and thms2 = inst_pt_at_fs [abs_fun_supp] 

934 
and thms3 = inst_pt_pt_at_cp_dj [abs_fun_supp_ineq] 

935 
in [(("abs_supp", thms1 @ thms2 @ thms3),[])] end 

29585  936 
>> add_thmss_string 
26337  937 
let val thms1 = inst_pt_at [fresh_left] 
938 
and thms2 = inst_pt_pt_at_cp [fresh_left_ineq] 

939 
in [(("fresh_left", thms1 @ thms2),[])] end 

29585  940 
>> add_thmss_string 
26337  941 
let val thms1 = inst_pt_at [fresh_right] 
942 
and thms2 = inst_pt_pt_at_cp [fresh_right_ineq] 

943 
in [(("fresh_right", thms1 @ thms2),[])] end 

29585  944 
>> add_thmss_string 
26337  945 
let val thms1 = inst_pt_at [fresh_bij] 
946 
and thms2 = inst_pt_pt_at_cp [fresh_bij_ineq] 

947 
in [(("fresh_bij", thms1 @ thms2),[])] end 

29585  948 
>> add_thmss_string 
26773  949 
let val thms1 = inst_pt_at fresh_star_bij 
950 
and thms2 = flat (map (fn ti => inst_pt_pt_at_cp [ti]) fresh_star_bij_ineq); 

951 
in [(("fresh_star_bij", thms1 @ thms2),[])] end 

29585  952 
>> add_thmss_string 
26337  953 
let val thms1 = inst_pt_at [fresh_eqvt] 
22535
cbee450f88a6
added extended the lemma for equivariance of freshness
urbanc
parents:
22418
diff
changeset

954 
and thms2 = inst_pt_pt_at_cp_dj [fresh_eqvt_ineq] 
26337  955 
in [(("fresh_eqvt", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end 
29585  956 
>> add_thmss_string 
26337  957 
let val thms1 = inst_pt_at [in_eqvt] 
958 
in [(("in_eqvt", thms1),[NominalThmDecls.eqvt_add])] end 

29585  959 
>> add_thmss_string 
26337  960 
let val thms1 = inst_pt_at [eq_eqvt] 
961 
in [(("eq_eqvt", thms1),[NominalThmDecls.eqvt_add])] end 

29585  962 
>> add_thmss_string 
26337  963 
let val thms1 = inst_pt_at [set_diff_eqvt] 
964 
in [(("set_diff_eqvt", thms1),[NominalThmDecls.eqvt_add])] end 

29585  965 
>> add_thmss_string 
26337  966 
let val thms1 = inst_pt_at [subseteq_eqvt] 
967 
in [(("subseteq_eqvt", thms1),[NominalThmDecls.eqvt_add])] end 

29585  968 
>> add_thmss_string [(("insert_eqvt", inst_pt_at [insert_eqvt]), [NominalThmDecls.eqvt_add])] 
969 
>> add_thmss_string [(("set_eqvt", inst_pt_at [set_eqvt]), [NominalThmDecls.eqvt_add])] 

970 
>> add_thmss_string [(("perm_set_eq", inst_pt_at [perm_set_eq]), [])] 

971 
>> add_thmss_string 

26337  972 
let val thms1 = inst_pt_at [fresh_aux] 
973 
and thms2 = inst_pt_pt_at_cp_dj [fresh_perm_app_ineq] 

974 
in [(("fresh_aux", thms1 @ thms2),[])] end 

29585  975 
>> add_thmss_string 
26337  976 
let val thms1 = inst_pt_at [fresh_perm_app] 
977 
and thms2 = inst_pt_pt_at_cp_dj [fresh_perm_app_ineq] 

978 
in [(("fresh_perm_app", thms1 @ thms2),[])] end 

29585  979 
>> add_thmss_string 
26337  980 
let val thms1 = inst_pt_at [pt_perm_supp] 
981 
and thms2 = inst_pt_pt_at_cp [pt_perm_supp_ineq] 

982 
in [(("supp_eqvt", thms1 @ thms2),[NominalThmDecls.eqvt_add])] end 

29585  983 
>> add_thmss_string [(("fin_supp",fs_axs),[])] 
26337  984 
end; 
18068  985 

22418
49e2d9744ae1
major update of the nominal package; there is now an infrastructure
urbanc
parents:
22274
diff
changeset

986 
in 
49e2d9744ae1
major update of the nominal package; there is now an infrastructure
urbanc
parents:
22274
diff
changeset

987 
NominalData.map (fold Symtab.update (full_ak_names ~~ map make_atom_info 
49e2d9744ae1
major update of the nominal package; there is now an infrastructure
urbanc
parents:
22274
diff
changeset

988 
(pt_ax_classes ~~ 
49e2d9744ae1
major update of the nominal package; there is now an infrastructure
urbanc
parents:
22274
diff
changeset

989 
fs_ax_classes ~~ 
28729
cfd169f1dae2
Some more functions for accessing information about atoms.
berghofe
parents:
28372
diff
changeset

990 
map (fn cls => Symtab.make (full_ak_names ~~ cls)) cp_ax_classes ~~ 
28372  991 
prm_cons_thms ~~ prm_inst_thms ~~ 
28729
cfd169f1dae2
Some more functions for accessing information about atoms.
berghofe
parents:
28372
diff
changeset

992 
map (fn ths => Symtab.make (full_ak_names ~~ ths)) cp_thms ~~ 
cfd169f1dae2
Some more functions for accessing information about atoms.
berghofe
parents:
28372
diff
changeset

993 
map (fn thss => Symtab.make 
cfd169f1dae2
Some more functions for accessing information about atoms.
berghofe
parents:
28372
diff
changeset

994 
(List.mapPartial (fn (s, [th]) => SOME (s, th)  _ => NONE) 
cfd169f1dae2
Some more functions for accessing information about atoms.
berghofe
parents:
28372
diff
changeset

995 
(full_ak_names ~~ thss))) dj_thms))) thy33 
18068  996 
end; 
997 

998 

999 
(* syntax und parsing *) 

1000 
structure P = OuterParse and K = OuterKeyword; 

1001 

24867  1002 
val _ = 
18068  1003 
OuterSyntax.command "atom_decl" "Declare new kinds of atoms" K.thy_decl 
1004 
(Scan.repeat1 P.name >> (Toplevel.theory o create_nom_typedecls)); 

1005 

1006 
end; 