author | wenzelm |
Sat, 14 Jan 2012 17:45:04 +0100 | |
changeset 46215 | 0da9433f959e |
parent 46161 | 4ed94d92ae19 |
child 46218 | ecf6375e2abb |
permissions | -rw-r--r-- |
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(* Title: HOL/Nominal/nominal_datatype.ML |
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Author: Stefan Berghofer and Christian Urban, TU Muenchen |
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Nominal datatype package for Isabelle/HOL. |
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*) |
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signature NOMINAL_DATATYPE = |
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sig |
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val nominal_datatype : Datatype.config -> Datatype.spec list -> theory -> theory |
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val nominal_datatype_cmd : Datatype.config -> Datatype.spec_cmd list -> theory -> theory |
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type descr |
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type nominal_datatype_info |
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val get_nominal_datatypes : theory -> nominal_datatype_info Symtab.table |
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val get_nominal_datatype : theory -> string -> nominal_datatype_info option |
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val mk_perm: typ list -> term -> term -> term |
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val perm_of_pair: term * term -> term |
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val mk_not_sym: thm list -> thm list |
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val perm_simproc: simproc |
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val fresh_const: typ -> typ -> term |
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val fresh_star_const: typ -> typ -> term |
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end |
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||
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structure NominalDatatype : NOMINAL_DATATYPE = |
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struct |
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||
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val finite_emptyI = @{thm finite.emptyI}; |
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val finite_Diff = @{thm finite_Diff}; |
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val finite_Un = @{thm finite_Un}; |
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val Un_iff = @{thm Un_iff}; |
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val In0_eq = @{thm In0_eq}; |
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val In1_eq = @{thm In1_eq}; |
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val In0_not_In1 = @{thm In0_not_In1}; |
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val In1_not_In0 = @{thm In1_not_In0}; |
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val Un_assoc = @{thm Un_assoc}; |
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val Collect_disj_eq = @{thm Collect_disj_eq}; |
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val Collect_False_empty = @{thm empty_def [THEN sym, THEN eq_reflection]}; |
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val empty_iff = @{thm empty_iff}; |
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open NominalAtoms; |
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(* theory data *) |
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type descr = |
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(int * (string * Datatype.dtyp list * |
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(string * (Datatype.dtyp list * Datatype.dtyp) list) list)) list; |
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type nominal_datatype_info = |
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{index : int, |
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descr : descr, |
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rec_names : string list, |
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rec_rewrites : thm list, |
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induction : thm, |
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distinct : thm list, |
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inject : thm list}; |
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structure NominalDatatypesData = Theory_Data |
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( |
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type T = nominal_datatype_info Symtab.table; |
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val empty = Symtab.empty; |
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val extend = I; |
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fun merge data = Symtab.merge (K true) data; |
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); |
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val get_nominal_datatypes = NominalDatatypesData.get; |
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val put_nominal_datatypes = NominalDatatypesData.put; |
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val map_nominal_datatypes = NominalDatatypesData.map; |
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val get_nominal_datatype = Symtab.lookup o get_nominal_datatypes; |
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(**** make datatype info ****) |
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fun make_dt_info descr induct reccomb_names rec_thms |
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(i, (((_, (tname, _, _)), distinct), inject)) = |
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(tname, |
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{index = i, |
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descr = descr, |
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rec_names = reccomb_names, |
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rec_rewrites = rec_thms, |
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induction = induct, |
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distinct = distinct, |
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inject = inject}); |
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(*******************************) |
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val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (prems_of Datatype.distinct_lemma); |
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(** simplification procedure for sorting permutations **) |
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val dj_cp = @{thm dj_cp}; |
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fun dest_permT (Type ("fun", [Type ("List.list", [Type (@{type_name Product_Type.prod}, [T, _])]), |
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Type ("fun", [_, U])])) = (T, U); |
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fun permTs_of (Const ("Nominal.perm", T) $ t $ u) = fst (dest_permT T) :: permTs_of u |
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| permTs_of _ = []; |
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fun perm_simproc' thy ss (Const ("Nominal.perm", T) $ t $ (u as Const ("Nominal.perm", U) $ r $ s)) = |
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let |
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val (aT as Type (a, []), S) = dest_permT T; |
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val (bT as Type (b, []), _) = dest_permT U |
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in if member (op =) (permTs_of u) aT andalso aT <> bT then |
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let |
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val cp = cp_inst_of thy a b; |
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val dj = dj_thm_of thy b a; |
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val dj_cp' = [cp, dj] MRS dj_cp; |
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val cert = SOME o cterm_of thy |
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in |
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SOME (mk_meta_eq (Drule.instantiate' [SOME (ctyp_of thy S)] |
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[cert t, cert r, cert s] dj_cp')) |
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end |
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else NONE |
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end |
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| perm_simproc' thy ss _ = NONE; |
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val perm_simproc = |
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Simplifier.simproc_global @{theory} "perm_simp" ["pi1 \<bullet> (pi2 \<bullet> x)"] perm_simproc'; |
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fun projections rule = |
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Project_Rule.projections (Proof_Context.init_global (Thm.theory_of_thm rule)) rule |
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|> map (Drule.export_without_context #> Rule_Cases.save rule); |
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val supp_prod = @{thm supp_prod}; |
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val fresh_prod = @{thm fresh_prod}; |
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val supports_fresh = @{thm supports_fresh}; |
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val supports_def = Simpdata.mk_eq @{thm Nominal.supports_def}; |
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val fresh_def = Simpdata.mk_eq @{thm fresh_def}; |
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val supp_def = Simpdata.mk_eq @{thm supp_def}; |
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val rev_simps = @{thms rev.simps}; |
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val app_simps = @{thms append.simps}; |
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val at_fin_set_supp = @{thm at_fin_set_supp}; |
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val at_fin_set_fresh = @{thm at_fin_set_fresh}; |
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val abs_fun_eq1 = @{thm abs_fun_eq1}; |
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val collect_simp = rewrite_rule [mk_meta_eq mem_Collect_eq]; |
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fun mk_perm Ts t u = |
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let |
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val T = fastype_of1 (Ts, t); |
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val U = fastype_of1 (Ts, u) |
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in Const ("Nominal.perm", T --> U --> U) $ t $ u end; |
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fun perm_of_pair (x, y) = |
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let |
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val T = fastype_of x; |
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val pT = mk_permT T |
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in Const ("List.list.Cons", HOLogic.mk_prodT (T, T) --> pT --> pT) $ |
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HOLogic.mk_prod (x, y) $ Const ("List.list.Nil", pT) |
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end; |
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fun mk_not_sym ths = maps (fn th => case prop_of th of |
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_ $ (Const (@{const_name Not}, _) $ (Const (@{const_name HOL.eq}, _) $ _ $ _)) => [th, th RS not_sym] |
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| _ => [th]) ths; |
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fun fresh_const T U = Const ("Nominal.fresh", T --> U --> HOLogic.boolT); |
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fun fresh_star_const T U = |
158 |
Const ("Nominal.fresh_star", HOLogic.mk_setT T --> U --> HOLogic.boolT); |
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fun gen_nominal_datatype prep_specs config dts thy = |
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let |
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val new_type_names = map (fn ((tname, _, _), _) => Binding.name_of tname) dts; |
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val (dts', _) = prep_specs dts thy; |
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val atoms = atoms_of thy; |
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val tyvars = map (fn ((_, tvs, _), _) => tvs) dts'; |
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val sorts = flat tyvars; |
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fun inter_sort thy S S' = Sign.inter_sort thy (S, S'); |
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fun augment_sort_typ thy S = |
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let val S = Sign.minimize_sort thy (Sign.certify_sort thy S) |
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in map_type_tfree (fn (s, S') => TFree (s, |
175 |
if member (op = o apsnd fst) sorts s then inter_sort thy S S' else S')) |
|
176 |
end; |
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fun augment_sort thy S = map_types (augment_sort_typ thy S); |
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val types_syntax = map (fn ((tname, tvs, mx), constrs) => (tname, mx)) dts'; |
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val constr_syntax = map (fn (_, constrs) => |
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map (fn (cname, cargs, mx) => (cname, mx)) constrs) dts'; |
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val ps = map (fn ((n, _, _), _) => |
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(Sign.full_name thy n, Sign.full_name thy (Binding.suffix_name "_Rep" n))) dts; |
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val rps = map Library.swap ps; |
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fun replace_types (Type ("Nominal.ABS", [T, U])) = |
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Type ("fun", [T, Type ("Nominal.noption", [replace_types U])]) |
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| replace_types (Type (s, Ts)) = |
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Type (the_default s (AList.lookup op = ps s), map replace_types Ts) |
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| replace_types T = T; |
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val dts'' = map (fn ((tname, tvs, mx), constrs) => |
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((Binding.suffix_name "_Rep" tname, tvs, NoSyn), |
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map (fn (cname, cargs, mx) => (Binding.suffix_name "_Rep" cname, |
196 |
map replace_types cargs, NoSyn)) constrs)) dts'; |
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|
198 |
val new_type_names' = map (fn n => n ^ "_Rep") new_type_names; |
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val (full_new_type_names',thy1) = Datatype.add_datatype config dts'' thy; |
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val {descr, induct, ...} = Datatype.the_info thy1 (hd full_new_type_names'); |
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fun nth_dtyp i = Datatype_Aux.typ_of_dtyp descr (Datatype.DtRec i); |
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val big_name = space_implode "_" new_type_names; |
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(**** define permutation functions ****) |
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210 |
val permT = mk_permT (TFree ("'x", HOLogic.typeS)); |
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211 |
val pi = Free ("pi", permT); |
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212 |
val perm_types = map (fn (i, _) => |
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213 |
let val T = nth_dtyp i |
|
214 |
in permT --> T --> T end) descr; |
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val perm_names' = Datatype_Prop.indexify_names (map (fn (i, _) => |
45838 | 216 |
"perm_" ^ Datatype_Aux.name_of_typ (nth_dtyp i)) descr); |
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val perm_names = replicate (length new_type_names) "Nominal.perm" @ |
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map (Sign.full_bname thy1) (List.drop (perm_names', length new_type_names)); |
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val perm_names_types = perm_names ~~ perm_types; |
26680 | 220 |
val perm_names_types' = perm_names' ~~ perm_types; |
17870 | 221 |
|
26680 | 222 |
val perm_eqs = maps (fn (i, (_, _, constrs)) => |
17870 | 223 |
let val T = nth_dtyp i |
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
224 |
in map (fn (cname, dts) => |
17870 | 225 |
let |
45838 | 226 |
val Ts = map (Datatype_Aux.typ_of_dtyp descr) dts; |
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
227 |
val names = Name.variant_list ["pi"] (Datatype_Prop.make_tnames Ts); |
17870 | 228 |
val args = map Free (names ~~ Ts); |
229 |
val c = Const (cname, Ts ---> T); |
|
230 |
fun perm_arg (dt, x) = |
|
231 |
let val T = type_of x |
|
45838 | 232 |
in if Datatype_Aux.is_rec_type dt then |
40844 | 233 |
let val Us = binder_types T |
17870 | 234 |
in list_abs (map (pair "x") Us, |
45838 | 235 |
Free (nth perm_names_types' (Datatype_Aux.body_index dt)) $ pi $ |
17870 | 236 |
list_comb (x, map (fn (i, U) => |
19494 | 237 |
Const ("Nominal.perm", permT --> U --> U) $ |
17870 | 238 |
(Const ("List.rev", permT --> permT) $ pi) $ |
239 |
Bound i) ((length Us - 1 downto 0) ~~ Us))) |
|
240 |
end |
|
19494 | 241 |
else Const ("Nominal.perm", permT --> T --> T) $ pi $ x |
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
242 |
end; |
17870 | 243 |
in |
28965 | 244 |
(Attrib.empty_binding, HOLogic.mk_Trueprop (HOLogic.mk_eq |
26680 | 245 |
(Free (nth perm_names_types' i) $ |
17870 | 246 |
Free ("pi", mk_permT (TFree ("'x", HOLogic.typeS))) $ |
247 |
list_comb (c, args), |
|
26680 | 248 |
list_comb (c, map perm_arg (dts ~~ args))))) |
17870 | 249 |
end) constrs |
26680 | 250 |
end) descr; |
17870 | 251 |
|
26689
105031879f4a
Auxiliary permutation functions are no longer declared using add_consts_i,
berghofe
parents:
26680
diff
changeset
|
252 |
val (perm_simps, thy2) = |
31723
f5cafe803b55
discontinued ancient tradition to suffix certain ML module names with "_package"
haftmann
parents:
31671
diff
changeset
|
253 |
Primrec.add_primrec_overloaded |
26689
105031879f4a
Auxiliary permutation functions are no longer declared using add_consts_i,
berghofe
parents:
26680
diff
changeset
|
254 |
(map (fn (s, sT) => (s, sT, false)) |
105031879f4a
Auxiliary permutation functions are no longer declared using add_consts_i,
berghofe
parents:
26680
diff
changeset
|
255 |
(List.take (perm_names' ~~ perm_names_types, length new_type_names))) |
28965 | 256 |
(map (fn s => (Binding.name s, NONE, NoSyn)) perm_names') perm_eqs thy1; |
17870 | 257 |
|
258 |
(**** prove that permutation functions introduced by unfolding are ****) |
|
259 |
(**** equivalent to already existing permutation functions ****) |
|
260 |
||
261 |
val _ = warning ("length descr: " ^ string_of_int (length descr)); |
|
262 |
val _ = warning ("length new_type_names: " ^ string_of_int (length new_type_names)); |
|
263 |
||
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
264 |
val perm_indnames = Datatype_Prop.make_tnames (map body_type perm_types); |
44685
f5bc7d9d0d74
assert Pure equations for theorem references; avoid dynamic reference to fact
haftmann
parents:
44241
diff
changeset
|
265 |
val perm_fun_def = Simpdata.mk_eq @{thm perm_fun_def}; |
17870 | 266 |
|
267 |
val unfolded_perm_eq_thms = |
|
268 |
if length descr = length new_type_names then [] |
|
45838 | 269 |
else map Drule.export_without_context (List.drop (Datatype_Aux.split_conj_thm |
20046 | 270 |
(Goal.prove_global thy2 [] [] |
17870 | 271 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
272 |
(map (fn (c as (s, T), x) => |
|
273 |
let val [T1, T2] = binder_types T |
|
274 |
in HOLogic.mk_eq (Const c $ pi $ Free (x, T2), |
|
19494 | 275 |
Const ("Nominal.perm", T) $ pi $ Free (x, T2)) |
17870 | 276 |
end) |
18010 | 277 |
(perm_names_types ~~ perm_indnames)))) |
45735 | 278 |
(fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1, |
17870 | 279 |
ALLGOALS (asm_full_simp_tac |
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset
|
280 |
(global_simpset_of thy2 addsimps [perm_fun_def]))])), |
17870 | 281 |
length new_type_names)); |
282 |
||
283 |
(**** prove [] \<bullet> t = t ****) |
|
284 |
||
285 |
val _ = warning "perm_empty_thms"; |
|
286 |
||
32952 | 287 |
val perm_empty_thms = maps (fn a => |
17870 | 288 |
let val permT = mk_permT (Type (a, [])) |
45838 | 289 |
in map Drule.export_without_context (List.take (Datatype_Aux.split_conj_thm |
20046 | 290 |
(Goal.prove_global thy2 [] [] |
28731 | 291 |
(augment_sort thy2 [pt_class_of thy2 a] |
292 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
|
293 |
(map (fn ((s, T), x) => HOLogic.mk_eq |
|
294 |
(Const (s, permT --> T --> T) $ |
|
295 |
Const ("List.list.Nil", permT) $ Free (x, T), |
|
296 |
Free (x, T))) |
|
297 |
(perm_names ~~ |
|
298 |
map body_type perm_types ~~ perm_indnames))))) |
|
45735 | 299 |
(fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1, |
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset
|
300 |
ALLGOALS (asm_full_simp_tac (global_simpset_of thy2))])), |
17870 | 301 |
length new_type_names)) |
302 |
end) |
|
32952 | 303 |
atoms; |
17870 | 304 |
|
305 |
(**** prove (pi1 @ pi2) \<bullet> t = pi1 \<bullet> (pi2 \<bullet> t) ****) |
|
306 |
||
307 |
val _ = warning "perm_append_thms"; |
|
308 |
||
309 |
(*FIXME: these should be looked up statically*) |
|
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
310 |
val at_pt_inst = Global_Theory.get_thm thy2 "at_pt_inst"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
311 |
val pt2 = Global_Theory.get_thm thy2 "pt2"; |
17870 | 312 |
|
32952 | 313 |
val perm_append_thms = maps (fn a => |
17870 | 314 |
let |
315 |
val permT = mk_permT (Type (a, [])); |
|
316 |
val pi1 = Free ("pi1", permT); |
|
317 |
val pi2 = Free ("pi2", permT); |
|
28731 | 318 |
val pt_inst = pt_inst_of thy2 a; |
17870 | 319 |
val pt2' = pt_inst RS pt2; |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
320 |
val pt2_ax = Global_Theory.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "2") a); |
45838 | 321 |
in List.take (map Drule.export_without_context (Datatype_Aux.split_conj_thm |
20046 | 322 |
(Goal.prove_global thy2 [] [] |
28731 | 323 |
(augment_sort thy2 [pt_class_of thy2 a] |
17870 | 324 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
325 |
(map (fn ((s, T), x) => |
|
326 |
let val perm = Const (s, permT --> T --> T) |
|
327 |
in HOLogic.mk_eq |
|
23029 | 328 |
(perm $ (Const ("List.append", permT --> permT --> permT) $ |
17870 | 329 |
pi1 $ pi2) $ Free (x, T), |
330 |
perm $ pi1 $ (perm $ pi2 $ Free (x, T))) |
|
331 |
end) |
|
332 |
(perm_names ~~ |
|
28731 | 333 |
map body_type perm_types ~~ perm_indnames))))) |
45735 | 334 |
(fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1, |
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset
|
335 |
ALLGOALS (asm_full_simp_tac (global_simpset_of thy2 addsimps [pt2', pt2_ax]))]))), |
17870 | 336 |
length new_type_names) |
32952 | 337 |
end) atoms; |
17870 | 338 |
|
339 |
(**** prove pi1 ~ pi2 ==> pi1 \<bullet> t = pi2 \<bullet> t ****) |
|
340 |
||
341 |
val _ = warning "perm_eq_thms"; |
|
342 |
||
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
343 |
val pt3 = Global_Theory.get_thm thy2 "pt3"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
344 |
val pt3_rev = Global_Theory.get_thm thy2 "pt3_rev"; |
17870 | 345 |
|
32952 | 346 |
val perm_eq_thms = maps (fn a => |
17870 | 347 |
let |
348 |
val permT = mk_permT (Type (a, [])); |
|
349 |
val pi1 = Free ("pi1", permT); |
|
350 |
val pi2 = Free ("pi2", permT); |
|
28731 | 351 |
val at_inst = at_inst_of thy2 a; |
352 |
val pt_inst = pt_inst_of thy2 a; |
|
17870 | 353 |
val pt3' = pt_inst RS pt3; |
354 |
val pt3_rev' = at_inst RS (pt_inst RS pt3_rev); |
|
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
355 |
val pt3_ax = Global_Theory.get_thm thy2 (Long_Name.map_base_name (fn s => "pt_" ^ s ^ "3") a); |
45838 | 356 |
in List.take (map Drule.export_without_context (Datatype_Aux.split_conj_thm |
28731 | 357 |
(Goal.prove_global thy2 [] [] |
358 |
(augment_sort thy2 [pt_class_of thy2 a] (Logic.mk_implies |
|
19494 | 359 |
(HOLogic.mk_Trueprop (Const ("Nominal.prm_eq", |
17870 | 360 |
permT --> permT --> HOLogic.boolT) $ pi1 $ pi2), |
361 |
HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
|
362 |
(map (fn ((s, T), x) => |
|
363 |
let val perm = Const (s, permT --> T --> T) |
|
364 |
in HOLogic.mk_eq |
|
365 |
(perm $ pi1 $ Free (x, T), |
|
366 |
perm $ pi2 $ Free (x, T)) |
|
367 |
end) |
|
368 |
(perm_names ~~ |
|
28731 | 369 |
map body_type perm_types ~~ perm_indnames)))))) |
45735 | 370 |
(fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1, |
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset
|
371 |
ALLGOALS (asm_full_simp_tac (global_simpset_of thy2 addsimps [pt3', pt3_rev', pt3_ax]))]))), |
17870 | 372 |
length new_type_names) |
32952 | 373 |
end) atoms; |
17870 | 374 |
|
375 |
(**** prove pi1 \<bullet> (pi2 \<bullet> t) = (pi1 \<bullet> pi2) \<bullet> (pi1 \<bullet> t) ****) |
|
376 |
||
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
377 |
val cp1 = Global_Theory.get_thm thy2 "cp1"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
378 |
val dj_cp = Global_Theory.get_thm thy2 "dj_cp"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
379 |
val pt_perm_compose = Global_Theory.get_thm thy2 "pt_perm_compose"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
380 |
val pt_perm_compose_rev = Global_Theory.get_thm thy2 "pt_perm_compose_rev"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
381 |
val dj_perm_perm_forget = Global_Theory.get_thm thy2 "dj_perm_perm_forget"; |
17870 | 382 |
|
383 |
fun composition_instance name1 name2 thy = |
|
384 |
let |
|
28731 | 385 |
val cp_class = cp_class_of thy name1 name2; |
386 |
val pt_class = |
|
387 |
if name1 = name2 then [pt_class_of thy name1] |
|
388 |
else []; |
|
17870 | 389 |
val permT1 = mk_permT (Type (name1, [])); |
390 |
val permT2 = mk_permT (Type (name2, [])); |
|
28731 | 391 |
val Ts = map body_type perm_types; |
392 |
val cp_inst = cp_inst_of thy name1 name2; |
|
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset
|
393 |
val simps = global_simpset_of thy addsimps (perm_fun_def :: |
17870 | 394 |
(if name1 <> name2 then |
28731 | 395 |
let val dj = dj_thm_of thy name2 name1 |
17870 | 396 |
in [dj RS (cp_inst RS dj_cp), dj RS dj_perm_perm_forget] end |
397 |
else |
|
398 |
let |
|
28731 | 399 |
val at_inst = at_inst_of thy name1; |
400 |
val pt_inst = pt_inst_of thy name1; |
|
17870 | 401 |
in |
402 |
[cp_inst RS cp1 RS sym, |
|
403 |
at_inst RS (pt_inst RS pt_perm_compose) RS sym, |
|
404 |
at_inst RS (pt_inst RS pt_perm_compose_rev) RS sym] |
|
405 |
end)) |
|
36428
874843c1e96e
really minimize sorts after certification -- looks like this is intended here;
wenzelm
parents:
35994
diff
changeset
|
406 |
val sort = Sign.minimize_sort thy (Sign.certify_sort thy (cp_class :: pt_class)); |
45838 | 407 |
val thms = Datatype_Aux.split_conj_thm (Goal.prove_global thy [] [] |
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
408 |
(augment_sort thy sort |
17870 | 409 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
410 |
(map (fn ((s, T), x) => |
|
411 |
let |
|
412 |
val pi1 = Free ("pi1", permT1); |
|
413 |
val pi2 = Free ("pi2", permT2); |
|
414 |
val perm1 = Const (s, permT1 --> T --> T); |
|
415 |
val perm2 = Const (s, permT2 --> T --> T); |
|
19494 | 416 |
val perm3 = Const ("Nominal.perm", permT1 --> permT2 --> permT2) |
17870 | 417 |
in HOLogic.mk_eq |
418 |
(perm1 $ pi1 $ (perm2 $ pi2 $ Free (x, T)), |
|
419 |
perm2 $ (perm3 $ pi1 $ pi2) $ (perm1 $ pi1 $ Free (x, T))) |
|
420 |
end) |
|
28731 | 421 |
(perm_names ~~ Ts ~~ perm_indnames))))) |
45735 | 422 |
(fn _ => EVERY [Datatype_Aux.ind_tac induct perm_indnames 1, |
20046 | 423 |
ALLGOALS (asm_full_simp_tac simps)])) |
17870 | 424 |
in |
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
425 |
fold (fn (s, tvs) => fn thy => AxClass.prove_arity |
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
426 |
(s, map (inter_sort thy sort o snd) tvs, [cp_class]) |
24218 | 427 |
(Class.intro_classes_tac [] THEN ALLGOALS (resolve_tac thms)) thy) |
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
428 |
(full_new_type_names' ~~ tyvars) thy |
17870 | 429 |
end; |
430 |
||
18381
246807ef6dfb
changed the types in accordance with Florian's changes
urbanc
parents:
18366
diff
changeset
|
431 |
val (perm_thmss,thy3) = thy2 |> |
17870 | 432 |
fold (fn name1 => fold (composition_instance name1) atoms) atoms |> |
28731 | 433 |
fold (fn atom => fn thy => |
434 |
let val pt_name = pt_class_of thy atom |
|
435 |
in |
|
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
436 |
fold (fn (s, tvs) => fn thy => AxClass.prove_arity |
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
437 |
(s, map (inter_sort thy [pt_name] o snd) tvs, [pt_name]) |
28731 | 438 |
(EVERY |
439 |
[Class.intro_classes_tac [], |
|
440 |
resolve_tac perm_empty_thms 1, |
|
441 |
resolve_tac perm_append_thms 1, |
|
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
442 |
resolve_tac perm_eq_thms 1, assume_tac 1]) thy) |
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
443 |
(full_new_type_names' ~~ tyvars) thy |
28731 | 444 |
end) atoms |> |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
445 |
Global_Theory.add_thmss |
29585 | 446 |
[((Binding.name (space_implode "_" new_type_names ^ "_unfolded_perm_eq"), |
18759 | 447 |
unfolded_perm_eq_thms), [Simplifier.simp_add]), |
29585 | 448 |
((Binding.name (space_implode "_" new_type_names ^ "_perm_empty"), |
18759 | 449 |
perm_empty_thms), [Simplifier.simp_add]), |
29585 | 450 |
((Binding.name (space_implode "_" new_type_names ^ "_perm_append"), |
18759 | 451 |
perm_append_thms), [Simplifier.simp_add]), |
29585 | 452 |
((Binding.name (space_implode "_" new_type_names ^ "_perm_eq"), |
18759 | 453 |
perm_eq_thms), [Simplifier.simp_add])]; |
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
454 |
|
17870 | 455 |
(**** Define representing sets ****) |
456 |
||
457 |
val _ = warning "representing sets"; |
|
458 |
||
45838 | 459 |
val rep_set_names = |
460 |
Datatype_Prop.indexify_names |
|
461 |
(map (fn (i, _) => Datatype_Aux.name_of_typ (nth_dtyp i) ^ "_set") descr); |
|
17870 | 462 |
val big_rep_name = |
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
463 |
space_implode "_" (Datatype_Prop.indexify_names (map_filter |
19494 | 464 |
(fn (i, ("Nominal.noption", _, _)) => NONE |
45838 | 465 |
| (i, _) => SOME (Datatype_Aux.name_of_typ (nth_dtyp i))) descr)) ^ "_set"; |
17870 | 466 |
val _ = warning ("big_rep_name: " ^ big_rep_name); |
467 |
||
45896 | 468 |
fun strip_option (dtf as Datatype.DtType ("fun", [dt, Datatype.DtRec i])) = |
17870 | 469 |
(case AList.lookup op = descr i of |
19494 | 470 |
SOME ("Nominal.noption", _, [(_, [dt']), _]) => |
17870 | 471 |
apfst (cons dt) (strip_option dt') |
472 |
| _ => ([], dtf)) |
|
45896 | 473 |
| strip_option (Datatype.DtType ("fun", |
474 |
[dt, Datatype.DtType ("Nominal.noption", [dt'])])) = |
|
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
475 |
apfst (cons dt) (strip_option dt') |
17870 | 476 |
| strip_option dt = ([], dt); |
477 |
||
45838 | 478 |
val dt_atomTs = distinct op = (map (Datatype_Aux.typ_of_dtyp descr) |
32952 | 479 |
(maps (fn (_, (_, _, cs)) => maps (maps (fst o strip_option) o snd) cs) descr)); |
28731 | 480 |
val dt_atoms = map (fst o dest_Type) dt_atomTs; |
18280
45e139675daf
Corrected atom class constraints in strong induction rule.
berghofe
parents:
18261
diff
changeset
|
481 |
|
17870 | 482 |
fun make_intr s T (cname, cargs) = |
483 |
let |
|
33338 | 484 |
fun mk_prem dt (j, j', prems, ts) = |
17870 | 485 |
let |
486 |
val (dts, dt') = strip_option dt; |
|
45838 | 487 |
val (dts', dt'') = Datatype_Aux.strip_dtyp dt'; |
488 |
val Ts = map (Datatype_Aux.typ_of_dtyp descr) dts; |
|
489 |
val Us = map (Datatype_Aux.typ_of_dtyp descr) dts'; |
|
490 |
val T = Datatype_Aux.typ_of_dtyp descr dt''; |
|
491 |
val free = Datatype_Aux.mk_Free "x" (Us ---> T) j; |
|
492 |
val free' = Datatype_Aux.app_bnds free (length Us); |
|
33338 | 493 |
fun mk_abs_fun T (i, t) = |
17870 | 494 |
let val U = fastype_of t |
19494 | 495 |
in (i + 1, Const ("Nominal.abs_fun", [T, U, T] ---> |
45838 | 496 |
Type ("Nominal.noption", [U])) $ Datatype_Aux.mk_Free "y" T i $ t) |
17870 | 497 |
end |
498 |
in (j + 1, j' + length Ts, |
|
499 |
case dt'' of |
|
45896 | 500 |
Datatype.DtRec k => list_all (map (pair "x") Us, |
42364 | 501 |
HOLogic.mk_Trueprop (Free (nth rep_set_names k, |
21021 | 502 |
T --> HOLogic.boolT) $ free')) :: prems |
17870 | 503 |
| _ => prems, |
33338 | 504 |
snd (fold_rev mk_abs_fun Ts (j', free)) :: ts) |
17870 | 505 |
end; |
506 |
||
33338 | 507 |
val (_, _, prems, ts) = fold_rev mk_prem cargs (1, 1, [], []); |
21021 | 508 |
val concl = HOLogic.mk_Trueprop (Free (s, T --> HOLogic.boolT) $ |
509 |
list_comb (Const (cname, map fastype_of ts ---> T), ts)) |
|
17870 | 510 |
in Logic.list_implies (prems, concl) |
511 |
end; |
|
512 |
||
21021 | 513 |
val (intr_ts, (rep_set_names', recTs')) = |
32952 | 514 |
apfst flat (apsnd ListPair.unzip (ListPair.unzip (map_filter |
19494 | 515 |
(fn ((_, ("Nominal.noption", _, _)), _) => NONE |
17870 | 516 |
| ((i, (_, _, constrs)), rep_set_name) => |
517 |
let val T = nth_dtyp i |
|
518 |
in SOME (map (make_intr rep_set_name T) constrs, |
|
21021 | 519 |
(rep_set_name, T)) |
17870 | 520 |
end) |
21021 | 521 |
(descr ~~ rep_set_names)))); |
28965 | 522 |
val rep_set_names'' = map (Sign.full_bname thy3) rep_set_names'; |
17870 | 523 |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
524 |
val ({raw_induct = rep_induct, intrs = rep_intrs, ...}, thy4) = |
33278 | 525 |
thy3 |
526 |
|> Sign.map_naming Name_Space.conceal |
|
33726
0878aecbf119
eliminated slightly odd name space grouping -- now managed by Isar toplevel;
wenzelm
parents:
33669
diff
changeset
|
527 |
|> Inductive.add_inductive_global |
33669 | 528 |
{quiet_mode = false, verbose = false, alt_name = Binding.name big_rep_name, |
529 |
coind = false, no_elim = true, no_ind = false, skip_mono = true, fork_mono = false} |
|
28965 | 530 |
(map (fn (s, T) => ((Binding.name s, T --> HOLogic.boolT), NoSyn)) |
26128 | 531 |
(rep_set_names' ~~ recTs')) |
33278 | 532 |
[] (map (fn x => (Attrib.empty_binding, x)) intr_ts) [] |
533 |
||> Sign.restore_naming thy3; |
|
17870 | 534 |
|
535 |
(**** Prove that representing set is closed under permutation ****) |
|
536 |
||
537 |
val _ = warning "proving closure under permutation..."; |
|
538 |
||
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
539 |
val abs_perm = Global_Theory.get_thms thy4 "abs_perm"; |
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
540 |
|
32952 | 541 |
val perm_indnames' = map_filter |
19494 | 542 |
(fn (x, (_, ("Nominal.noption", _, _))) => NONE | (x, _) => SOME x) |
17870 | 543 |
(perm_indnames ~~ descr); |
544 |
||
35021
c839a4c670c6
renamed old-style Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
wenzelm
parents:
33968
diff
changeset
|
545 |
fun mk_perm_closed name = map (fn th => Drule.export_without_context (th RS mp)) |
45838 | 546 |
(List.take (Datatype_Aux.split_conj_thm (Goal.prove_global thy4 [] [] |
28731 | 547 |
(augment_sort thy4 |
33040 | 548 |
(pt_class_of thy4 name :: map (cp_class_of thy4 name) (remove (op =) name dt_atoms)) |
28731 | 549 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map |
550 |
(fn ((s, T), x) => |
|
551 |
let |
|
552 |
val S = Const (s, T --> HOLogic.boolT); |
|
553 |
val permT = mk_permT (Type (name, [])) |
|
554 |
in HOLogic.mk_imp (S $ Free (x, T), |
|
555 |
S $ (Const ("Nominal.perm", permT --> T --> T) $ |
|
556 |
Free ("pi", permT) $ Free (x, T))) |
|
557 |
end) (rep_set_names'' ~~ recTs' ~~ perm_indnames'))))) |
|
558 |
(fn _ => EVERY |
|
45735 | 559 |
[Datatype_Aux.ind_tac rep_induct [] 1, |
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset
|
560 |
ALLGOALS (simp_tac (global_simpset_of thy4 addsimps |
36945 | 561 |
(Thm.symmetric perm_fun_def :: abs_perm))), |
28731 | 562 |
ALLGOALS (resolve_tac rep_intrs THEN_ALL_NEW assume_tac)])), |
17870 | 563 |
length new_type_names)); |
564 |
||
565 |
val perm_closed_thmss = map mk_perm_closed atoms; |
|
566 |
||
567 |
(**** typedef ****) |
|
568 |
||
569 |
val _ = warning "defining type..."; |
|
570 |
||
18366 | 571 |
val (typedefs, thy6) = |
26651 | 572 |
thy4 |
45701 | 573 |
|> fold_map (fn (((name, mx), tvs), (cname, U)) => fn thy => |
574 |
Typedef.add_typedef_global false NONE |
|
575 |
(name, map (fn (v, _) => (v, dummyS)) tvs, mx) (* FIXME keep constraints!? *) |
|
37677 | 576 |
(Const (@{const_name Collect}, (U --> HOLogic.boolT) --> HOLogic.mk_setT U) $ |
21021 | 577 |
Const (cname, U --> HOLogic.boolT)) NONE |
578 |
(rtac exI 1 THEN rtac CollectI 1 THEN |
|
17870 | 579 |
QUIET_BREADTH_FIRST (has_fewer_prems 1) |
26475
3cc1e48d0ce1
eliminated quiet_mode ref of some packages (avoid CRITICAL setmp!);
wenzelm
parents:
26359
diff
changeset
|
580 |
(resolve_tac rep_intrs 1)) thy |> (fn ((_, r), thy) => |
17870 | 581 |
let |
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
582 |
val permT = mk_permT |
43324
2b47822868e4
discontinued Name.variant to emphasize that this is old-style / indirect;
wenzelm
parents:
42388
diff
changeset
|
583 |
(TFree (singleton (Name.variant_list (map fst tvs)) "'a", HOLogic.typeS)); |
17870 | 584 |
val pi = Free ("pi", permT); |
45701 | 585 |
val T = Type (Sign.full_name thy name, map TFree tvs); |
18366 | 586 |
in apfst (pair r o hd) |
45701 | 587 |
(Global_Theory.add_defs_unchecked true |
588 |
[((Binding.map_name (fn n => "prm_" ^ n ^ "_def") name, Logic.mk_equals |
|
589 |
(Const ("Nominal.perm", permT --> T --> T) $ pi $ Free ("x", T), |
|
590 |
Const (Sign.intern_const thy ("Abs_" ^ Binding.name_of name), U --> T) $ |
|
591 |
(Const ("Nominal.perm", permT --> U --> U) $ pi $ |
|
592 |
(Const (Sign.intern_const thy ("Rep_" ^ Binding.name_of name), T --> U) $ |
|
593 |
Free ("x", T))))), [])] thy) |
|
17870 | 594 |
end)) |
45701 | 595 |
(types_syntax ~~ tyvars ~~ List.take (rep_set_names'' ~~ recTs', length new_type_names)); |
17870 | 596 |
|
597 |
val perm_defs = map snd typedefs; |
|
35994
9cc3df9a606e
Typedef.info: separate global and local part, only the latter is transformed by morphisms;
wenzelm
parents:
35845
diff
changeset
|
598 |
val Abs_inverse_thms = map (collect_simp o #Abs_inverse o snd o fst) typedefs; |
9cc3df9a606e
Typedef.info: separate global and local part, only the latter is transformed by morphisms;
wenzelm
parents:
35845
diff
changeset
|
599 |
val Rep_inverse_thms = map (#Rep_inverse o snd o fst) typedefs; |
9cc3df9a606e
Typedef.info: separate global and local part, only the latter is transformed by morphisms;
wenzelm
parents:
35845
diff
changeset
|
600 |
val Rep_thms = map (collect_simp o #Rep o snd o fst) typedefs; |
17870 | 601 |
|
18016 | 602 |
|
17870 | 603 |
(** prove that new types are in class pt_<name> **) |
604 |
||
605 |
val _ = warning "prove that new types are in class pt_<name> ..."; |
|
606 |
||
28731 | 607 |
fun pt_instance (atom, perm_closed_thms) = |
21021 | 608 |
fold (fn ((((((Abs_inverse, Rep_inverse), Rep), |
17870 | 609 |
perm_def), name), tvs), perm_closed) => fn thy => |
28731 | 610 |
let |
611 |
val pt_class = pt_class_of thy atom; |
|
36428
874843c1e96e
really minimize sorts after certification -- looks like this is intended here;
wenzelm
parents:
35994
diff
changeset
|
612 |
val sort = Sign.minimize_sort thy (Sign.certify_sort thy |
874843c1e96e
really minimize sorts after certification -- looks like this is intended here;
wenzelm
parents:
35994
diff
changeset
|
613 |
(pt_class :: map (cp_class_of thy atom) (remove (op =) atom dt_atoms))) |
28731 | 614 |
in AxClass.prove_arity |
17870 | 615 |
(Sign.intern_type thy name, |
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
616 |
map (inter_sort thy sort o snd) tvs, [pt_class]) |
24218 | 617 |
(EVERY [Class.intro_classes_tac [], |
17870 | 618 |
rewrite_goals_tac [perm_def], |
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset
|
619 |
asm_full_simp_tac (global_simpset_of thy addsimps [Rep_inverse]) 1, |
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset
|
620 |
asm_full_simp_tac (global_simpset_of thy addsimps |
17870 | 621 |
[Rep RS perm_closed RS Abs_inverse]) 1, |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
622 |
asm_full_simp_tac (HOL_basic_ss addsimps [Global_Theory.get_thm thy |
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset
|
623 |
("pt_" ^ Long_Name.base_name atom ^ "3")]) 1]) thy |
28731 | 624 |
end) |
21021 | 625 |
(Abs_inverse_thms ~~ Rep_inverse_thms ~~ Rep_thms ~~ perm_defs ~~ |
626 |
new_type_names ~~ tyvars ~~ perm_closed_thms); |
|
17870 | 627 |
|
628 |
||
629 |
(** prove that new types are in class cp_<name1>_<name2> **) |
|
630 |
||
631 |
val _ = warning "prove that new types are in class cp_<name1>_<name2> ..."; |
|
632 |
||
633 |
fun cp_instance (atom1, perm_closed_thms1) (atom2, perm_closed_thms2) thy = |
|
634 |
let |
|
28731 | 635 |
val cp_class = cp_class_of thy atom1 atom2; |
36428
874843c1e96e
really minimize sorts after certification -- looks like this is intended here;
wenzelm
parents:
35994
diff
changeset
|
636 |
val sort = Sign.minimize_sort thy (Sign.certify_sort thy |
33040 | 637 |
(pt_class_of thy atom1 :: map (cp_class_of thy atom1) (remove (op =) atom1 dt_atoms) @ |
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
638 |
(if atom1 = atom2 then [cp_class_of thy atom1 atom1] else |
36428
874843c1e96e
really minimize sorts after certification -- looks like this is intended here;
wenzelm
parents:
35994
diff
changeset
|
639 |
pt_class_of thy atom2 :: map (cp_class_of thy atom2) (remove (op =) atom2 dt_atoms)))); |
28731 | 640 |
val cp1' = cp_inst_of thy atom1 atom2 RS cp1 |
21021 | 641 |
in fold (fn ((((((Abs_inverse, Rep), |
17870 | 642 |
perm_def), name), tvs), perm_closed1), perm_closed2) => fn thy => |
19275 | 643 |
AxClass.prove_arity |
17870 | 644 |
(Sign.intern_type thy name, |
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
645 |
map (inter_sort thy sort o snd) tvs, [cp_class]) |
24218 | 646 |
(EVERY [Class.intro_classes_tac [], |
17870 | 647 |
rewrite_goals_tac [perm_def], |
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset
|
648 |
asm_full_simp_tac (global_simpset_of thy addsimps |
17870 | 649 |
((Rep RS perm_closed1 RS Abs_inverse) :: |
650 |
(if atom1 = atom2 then [] |
|
651 |
else [Rep RS perm_closed2 RS Abs_inverse]))) 1, |
|
18016 | 652 |
cong_tac 1, |
17870 | 653 |
rtac refl 1, |
654 |
rtac cp1' 1]) thy) |
|
21021 | 655 |
(Abs_inverse_thms ~~ Rep_thms ~~ perm_defs ~~ new_type_names ~~ |
656 |
tyvars ~~ perm_closed_thms1 ~~ perm_closed_thms2) thy |
|
17870 | 657 |
end; |
658 |
||
659 |
val thy7 = fold (fn x => fn thy => thy |> |
|
660 |
pt_instance x |> |
|
28731 | 661 |
fold (cp_instance x) (atoms ~~ perm_closed_thmss)) |
662 |
(atoms ~~ perm_closed_thmss) thy6; |
|
17870 | 663 |
|
664 |
(**** constructors ****) |
|
665 |
||
33338 | 666 |
fun mk_abs_fun x t = |
17870 | 667 |
let |
668 |
val T = fastype_of x; |
|
669 |
val U = fastype_of t |
|
670 |
in |
|
19494 | 671 |
Const ("Nominal.abs_fun", T --> U --> T --> |
672 |
Type ("Nominal.noption", [U])) $ x $ t |
|
17870 | 673 |
end; |
674 |
||
30190 | 675 |
val (ty_idxs, _) = List.foldl |
19494 | 676 |
(fn ((i, ("Nominal.noption", _, _)), p) => p |
18016 | 677 |
| ((i, _), (ty_idxs, j)) => (ty_idxs @ [(i, j)], j + 1)) ([], 0) descr; |
678 |
||
45896 | 679 |
fun reindex (Datatype.DtType (s, dts)) = Datatype.DtType (s, map reindex dts) |
680 |
| reindex (Datatype.DtRec i) = Datatype.DtRec (the (AList.lookup op = ty_idxs i)) |
|
18016 | 681 |
| reindex dt = dt; |
682 |
||
40627
becf5d5187cc
renamed raw "explode" function to "raw_explode" to emphasize its meaning;
wenzelm
parents:
39557
diff
changeset
|
683 |
fun strip_suffix i s = implode (List.take (raw_explode s, size s - i)); (* FIXME Symbol.explode (?) *) |
18016 | 684 |
|
685 |
(** strips the "_Rep" in type names *) |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
686 |
fun strip_nth_name i s = |
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset
|
687 |
let val xs = Long_Name.explode s; |
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset
|
688 |
in Long_Name.implode (Library.nth_map (length xs - i) (strip_suffix 4) xs) end; |
18016 | 689 |
|
31458 | 690 |
val (descr'', ndescr) = ListPair.unzip (map_filter |
19494 | 691 |
(fn (i, ("Nominal.noption", _, _)) => NONE |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
692 |
| (i, (s, dts, constrs)) => |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
693 |
let |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
694 |
val SOME index = AList.lookup op = ty_idxs i; |
31458 | 695 |
val (constrs2, constrs1) = |
696 |
map_split (fn (cname, cargs) => |
|
697 |
apsnd (pair (strip_nth_name 2 (strip_nth_name 1 cname))) |
|
698 |
(fold_map (fn dt => fn dts => |
|
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
699 |
let val (dts', dt') = strip_option dt |
31458 | 700 |
in ((length dts, length dts'), dts @ dts' @ [reindex dt']) end) |
701 |
cargs [])) constrs |
|
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
702 |
in SOME ((index, (strip_nth_name 1 s, map reindex dts, constrs1)), |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
703 |
(index, constrs2)) |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
704 |
end) descr); |
18045 | 705 |
|
19489 | 706 |
val (descr1, descr2) = chop (length new_type_names) descr''; |
18016 | 707 |
val descr' = [descr1, descr2]; |
708 |
||
19710 | 709 |
fun partition_cargs idxs xs = map (fn (i, j) => |
42364 | 710 |
(List.take (List.drop (xs, i), j), nth xs (i + j))) idxs; |
19710 | 711 |
|
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
712 |
val pdescr = map (fn ((i, (s, dts, constrs)), (_, idxss)) => (i, (s, dts, |
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
713 |
map (fn ((cname, cargs), idxs) => (cname, partition_cargs idxs cargs)) |
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
714 |
(constrs ~~ idxss)))) (descr'' ~~ ndescr); |
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
715 |
|
45896 | 716 |
fun nth_dtyp' i = Datatype_Aux.typ_of_dtyp descr'' (Datatype.DtRec i); |
17870 | 717 |
|
718 |
val rep_names = map (fn s => |
|
719 |
Sign.intern_const thy7 ("Rep_" ^ s)) new_type_names; |
|
720 |
val abs_names = map (fn s => |
|
721 |
Sign.intern_const thy7 ("Abs_" ^ s)) new_type_names; |
|
722 |
||
45838 | 723 |
val recTs = Datatype_Aux.get_rec_types descr''; |
33957 | 724 |
val newTs' = take (length new_type_names) recTs'; |
725 |
val newTs = take (length new_type_names) recTs; |
|
17870 | 726 |
|
28965 | 727 |
val full_new_type_names = map (Sign.full_bname thy) new_type_names; |
17870 | 728 |
|
33244 | 729 |
fun make_constr_def tname T T' (((cname_rep, _), (cname, cargs)), (cname', mx)) |
730 |
(thy, defs, eqns) = |
|
17870 | 731 |
let |
33338 | 732 |
fun constr_arg (dts, dt) (j, l_args, r_args) = |
17870 | 733 |
let |
45838 | 734 |
val xs = |
735 |
map (fn (dt, i) => Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) i) |
|
736 |
(dts ~~ (j upto j + length dts - 1)) |
|
737 |
val x = Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts) |
|
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
738 |
in |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
739 |
(j + length dts + 1, |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
740 |
xs @ x :: l_args, |
33338 | 741 |
fold_rev mk_abs_fun xs |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
742 |
(case dt of |
45896 | 743 |
Datatype.DtRec k => if k < length new_type_names then |
45838 | 744 |
Const (nth rep_names k, Datatype_Aux.typ_of_dtyp descr'' dt --> |
745 |
Datatype_Aux.typ_of_dtyp descr dt) $ x |
|
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
746 |
else error "nested recursion not (yet) supported" |
33338 | 747 |
| _ => x) :: r_args) |
17870 | 748 |
end |
749 |
||
33338 | 750 |
val (_, l_args, r_args) = fold_rev constr_arg cargs (1, [], []); |
22578 | 751 |
val abs_name = Sign.intern_const thy ("Abs_" ^ tname); |
752 |
val rep_name = Sign.intern_const thy ("Rep_" ^ tname); |
|
17870 | 753 |
val constrT = map fastype_of l_args ---> T; |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
754 |
val lhs = list_comb (Const (cname, constrT), l_args); |
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
755 |
val rhs = list_comb (Const (cname_rep, map fastype_of r_args ---> T'), r_args); |
17870 | 756 |
val def = Logic.mk_equals (lhs, Const (abs_name, T' --> T) $ rhs); |
757 |
val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq |
|
758 |
(Const (rep_name, T --> T') $ lhs, rhs)); |
|
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset
|
759 |
val def_name = (Long_Name.base_name cname) ^ "_def"; |
18366 | 760 |
val ([def_thm], thy') = thy |> |
45701 | 761 |
Sign.add_consts_i [(cname', constrT, mx)] |> |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
762 |
(Global_Theory.add_defs false o map Thm.no_attributes) [(Binding.name def_name, def)] |
17870 | 763 |
in (thy', defs @ [def_thm], eqns @ [eqn]) end; |
764 |
||
33244 | 765 |
fun dt_constr_defs ((((((_, (_, _, constrs)), |
766 |
(_, (_, _, constrs'))), tname), T), T'), constr_syntax) (thy, defs, eqns, dist_lemmas) = |
|
17870 | 767 |
let |
768 |
val rep_const = cterm_of thy |
|
769 |
(Const (Sign.intern_const thy ("Rep_" ^ tname), T --> T')); |
|
33244 | 770 |
val dist = |
35021
c839a4c670c6
renamed old-style Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
wenzelm
parents:
33968
diff
changeset
|
771 |
Drule.export_without_context |
45909 | 772 |
(cterm_instantiate [(cterm_of thy distinct_f, rep_const)] Datatype.distinct_lemma); |
33244 | 773 |
val (thy', defs', eqns') = fold (make_constr_def tname T T') |
774 |
(constrs ~~ constrs' ~~ constr_syntax) (Sign.add_path tname thy, defs, []) |
|
17870 | 775 |
in |
32124 | 776 |
(Sign.parent_path thy', defs', eqns @ [eqns'], dist_lemmas @ [dist]) |
17870 | 777 |
end; |
778 |
||
33244 | 779 |
val (thy8, constr_defs, constr_rep_eqns, dist_lemmas) = fold dt_constr_defs |
780 |
(List.take (descr, length new_type_names) ~~ |
|
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
781 |
List.take (pdescr, length new_type_names) ~~ |
33244 | 782 |
new_type_names ~~ newTs ~~ newTs' ~~ constr_syntax) |
783 |
(thy7, [], [], []); |
|
17870 | 784 |
|
35994
9cc3df9a606e
Typedef.info: separate global and local part, only the latter is transformed by morphisms;
wenzelm
parents:
35845
diff
changeset
|
785 |
val abs_inject_thms = map (collect_simp o #Abs_inject o snd o fst) typedefs |
9cc3df9a606e
Typedef.info: separate global and local part, only the latter is transformed by morphisms;
wenzelm
parents:
35845
diff
changeset
|
786 |
val rep_inject_thms = map (#Rep_inject o snd o fst) typedefs |
17870 | 787 |
|
788 |
(* prove theorem Rep_i (Constr_j ...) = Constr'_j ... *) |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
789 |
|
17870 | 790 |
fun prove_constr_rep_thm eqn = |
791 |
let |
|
792 |
val inj_thms = map (fn r => r RS iffD1) abs_inject_thms; |
|
21021 | 793 |
val rewrites = constr_defs @ map mk_meta_eq Rep_inverse_thms |
20046 | 794 |
in Goal.prove_global thy8 [] [] eqn (fn _ => EVERY |
17870 | 795 |
[resolve_tac inj_thms 1, |
796 |
rewrite_goals_tac rewrites, |
|
797 |
rtac refl 3, |
|
798 |
resolve_tac rep_intrs 2, |
|
21021 | 799 |
REPEAT (resolve_tac Rep_thms 1)]) |
17870 | 800 |
end; |
801 |
||
802 |
val constr_rep_thmss = map (map prove_constr_rep_thm) constr_rep_eqns; |
|
803 |
||
804 |
(* prove theorem pi \<bullet> Rep_i x = Rep_i (pi \<bullet> x) *) |
|
805 |
||
806 |
fun prove_perm_rep_perm (atom, perm_closed_thms) = map (fn th => |
|
807 |
let |
|
35845
e5980f0ad025
renamed varify/unvarify operations to varify_global/unvarify_global to emphasize that these only work in a global situation;
wenzelm
parents:
35842
diff
changeset
|
808 |
val _ $ (_ $ (Rep $ x)) = Logic.unvarify_global (prop_of th); |
17870 | 809 |
val Type ("fun", [T, U]) = fastype_of Rep; |
810 |
val permT = mk_permT (Type (atom, [])); |
|
811 |
val pi = Free ("pi", permT); |
|
812 |
in |
|
28731 | 813 |
Goal.prove_global thy8 [] [] |
814 |
(augment_sort thy8 |
|
33040 | 815 |
(pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (remove (op =) atom dt_atoms)) |
28731 | 816 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
817 |
(Const ("Nominal.perm", permT --> U --> U) $ pi $ (Rep $ x), |
|
818 |
Rep $ (Const ("Nominal.perm", permT --> T --> T) $ pi $ x))))) |
|
18010 | 819 |
(fn _ => simp_tac (HOL_basic_ss addsimps (perm_defs @ Abs_inverse_thms @ |
20046 | 820 |
perm_closed_thms @ Rep_thms)) 1) |
17870 | 821 |
end) Rep_thms; |
822 |
||
32952 | 823 |
val perm_rep_perm_thms = maps prove_perm_rep_perm (atoms ~~ perm_closed_thmss); |
17870 | 824 |
|
825 |
(* prove distinctness theorems *) |
|
826 |
||
45822 | 827 |
val distinct_props = Datatype_Prop.make_distincts descr'; |
27300
4cb3101d2bf7
DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents:
27275
diff
changeset
|
828 |
val dist_rewrites = map2 (fn rep_thms => fn dist_lemma => |
4cb3101d2bf7
DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents:
27275
diff
changeset
|
829 |
dist_lemma :: rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0]) |
4cb3101d2bf7
DatatypeProp.make_distincts: only one half of each symmetric pair is constructed
haftmann
parents:
27275
diff
changeset
|
830 |
constr_rep_thmss dist_lemmas; |
17870 | 831 |
|
45889 | 832 |
fun prove_distinct_thms _ [] = [] |
833 |
| prove_distinct_thms (p as (rep_thms, dist_lemma)) (t :: ts) = |
|
17870 | 834 |
let |
20046 | 835 |
val dist_thm = Goal.prove_global thy8 [] [] t (fn _ => |
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset
|
836 |
simp_tac (global_simpset_of thy8 addsimps (dist_lemma :: rep_thms)) 1) |
35021
c839a4c670c6
renamed old-style Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
wenzelm
parents:
33968
diff
changeset
|
837 |
in |
c839a4c670c6
renamed old-style Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
wenzelm
parents:
33968
diff
changeset
|
838 |
dist_thm :: Drule.export_without_context (dist_thm RS not_sym) :: |
45889 | 839 |
prove_distinct_thms p ts |
17870 | 840 |
end; |
841 |
||
26969
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26966
diff
changeset
|
842 |
val distinct_thms = map2 prove_distinct_thms |
cf3f998d0631
moved case distinction over number of constructors for distinctness rules from DatatypeProp to DatatypeRepProofs
haftmann
parents:
26966
diff
changeset
|
843 |
(constr_rep_thmss ~~ dist_lemmas) distinct_props; |
17870 | 844 |
|
845 |
(** prove equations for permutation functions **) |
|
846 |
||
847 |
val perm_simps' = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) => |
|
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
848 |
let val T = nth_dtyp' i |
32952 | 849 |
in maps (fn (atom, perm_closed_thms) => |
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
850 |
map (fn ((cname, dts), constr_rep_thm) => |
17870 | 851 |
let |
852 |
val cname = Sign.intern_const thy8 |
|
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset
|
853 |
(Long_Name.append tname (Long_Name.base_name cname)); |
17870 | 854 |
val permT = mk_permT (Type (atom, [])); |
855 |
val pi = Free ("pi", permT); |
|
856 |
||
857 |
fun perm t = |
|
858 |
let val T = fastype_of t |
|
19494 | 859 |
in Const ("Nominal.perm", permT --> T --> T) $ pi $ t end; |
17870 | 860 |
|
33338 | 861 |
fun constr_arg (dts, dt) (j, l_args, r_args) = |
17870 | 862 |
let |
45838 | 863 |
val Ts = map (Datatype_Aux.typ_of_dtyp descr'') dts; |
864 |
val xs = |
|
865 |
map (fn (T, i) => Datatype_Aux.mk_Free "x" T i) |
|
866 |
(Ts ~~ (j upto j + length dts - 1)); |
|
867 |
val x = |
|
868 |
Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts); |
|
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
869 |
in |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
870 |
(j + length dts + 1, |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
871 |
xs @ x :: l_args, |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
872 |
map perm (xs @ [x]) @ r_args) |
17870 | 873 |
end |
874 |
||
33338 | 875 |
val (_, l_args, r_args) = fold_rev constr_arg dts (1, [], []); |
17870 | 876 |
val c = Const (cname, map fastype_of l_args ---> T) |
877 |
in |
|
20046 | 878 |
Goal.prove_global thy8 [] [] |
28731 | 879 |
(augment_sort thy8 |
33040 | 880 |
(pt_class_of thy8 atom :: map (cp_class_of thy8 atom) (remove (op =) atom dt_atoms)) |
28731 | 881 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
882 |
(perm (list_comb (c, l_args)), list_comb (c, r_args))))) |
|
18010 | 883 |
(fn _ => EVERY |
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset
|
884 |
[simp_tac (global_simpset_of thy8 addsimps (constr_rep_thm :: perm_defs)) 1, |
17870 | 885 |
simp_tac (HOL_basic_ss addsimps (Rep_thms @ Abs_inverse_thms @ |
886 |
constr_defs @ perm_closed_thms)) 1, |
|
887 |
TRY (simp_tac (HOL_basic_ss addsimps |
|
36945 | 888 |
(Thm.symmetric perm_fun_def :: abs_perm)) 1), |
17870 | 889 |
TRY (simp_tac (HOL_basic_ss addsimps |
890 |
(perm_fun_def :: perm_defs @ Rep_thms @ Abs_inverse_thms @ |
|
20046 | 891 |
perm_closed_thms)) 1)]) |
32952 | 892 |
end) (constrs ~~ constr_rep_thms)) (atoms ~~ perm_closed_thmss) |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
893 |
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss); |
17870 | 894 |
|
895 |
(** prove injectivity of constructors **) |
|
896 |
||
897 |
val rep_inject_thms' = map (fn th => th RS sym) rep_inject_thms; |
|
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
898 |
val alpha = Global_Theory.get_thms thy8 "alpha"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
899 |
val abs_fresh = Global_Theory.get_thms thy8 "abs_fresh"; |
17870 | 900 |
|
28731 | 901 |
val pt_cp_sort = |
902 |
map (pt_class_of thy8) dt_atoms @ |
|
33040 | 903 |
maps (fn s => map (cp_class_of thy8 s) (remove (op =) s dt_atoms)) dt_atoms; |
28731 | 904 |
|
17870 | 905 |
val inject_thms = map (fn (((i, (_, _, constrs)), tname), constr_rep_thms) => |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
906 |
let val T = nth_dtyp' i |
32952 | 907 |
in map_filter (fn ((cname, dts), constr_rep_thm) => |
17870 | 908 |
if null dts then NONE else SOME |
909 |
let |
|
910 |
val cname = Sign.intern_const thy8 |
|
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset
|
911 |
(Long_Name.append tname (Long_Name.base_name cname)); |
17870 | 912 |
|
33338 | 913 |
fun make_inj (dts, dt) (j, args1, args2, eqs) = |
17870 | 914 |
let |
45838 | 915 |
val Ts_idx = |
916 |
map (Datatype_Aux.typ_of_dtyp descr'') dts ~~ (j upto j + length dts - 1); |
|
917 |
val xs = map (fn (T, i) => Datatype_Aux.mk_Free "x" T i) Ts_idx; |
|
918 |
val ys = map (fn (T, i) => Datatype_Aux.mk_Free "y" T i) Ts_idx; |
|
919 |
val x = |
|
920 |
Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts); |
|
921 |
val y = |
|
922 |
Datatype_Aux.mk_Free "y" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts); |
|
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
923 |
in |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
924 |
(j + length dts + 1, |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
925 |
xs @ (x :: args1), ys @ (y :: args2), |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
926 |
HOLogic.mk_eq |
33338 | 927 |
(fold_rev mk_abs_fun xs x, fold_rev mk_abs_fun ys y) :: eqs) |
17870 | 928 |
end; |
929 |
||
33338 | 930 |
val (_, args1, args2, eqs) = fold_rev make_inj dts (1, [], [], []); |
17870 | 931 |
val Ts = map fastype_of args1; |
932 |
val c = Const (cname, Ts ---> T) |
|
933 |
in |
|
28731 | 934 |
Goal.prove_global thy8 [] [] |
935 |
(augment_sort thy8 pt_cp_sort |
|
936 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
|
937 |
(HOLogic.mk_eq (list_comb (c, args1), list_comb (c, args2)), |
|
938 |
foldr1 HOLogic.mk_conj eqs)))) |
|
18010 | 939 |
(fn _ => EVERY |
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset
|
940 |
[asm_full_simp_tac (global_simpset_of thy8 addsimps (constr_rep_thm :: |
17870 | 941 |
rep_inject_thms')) 1, |
942 |
TRY (asm_full_simp_tac (HOL_basic_ss addsimps (fresh_def :: supp_def :: |
|
943 |
alpha @ abs_perm @ abs_fresh @ rep_inject_thms @ |
|
28731 | 944 |
perm_rep_perm_thms)) 1)]) |
17870 | 945 |
end) (constrs ~~ constr_rep_thms) |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
946 |
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ constr_rep_thmss); |
17870 | 947 |
|
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
948 |
(** equations for support and freshness **) |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
949 |
|
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
950 |
val (supp_thms, fresh_thms) = ListPair.unzip (map ListPair.unzip |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
951 |
(map (fn ((((i, (_, _, constrs)), tname), inject_thms'), perm_thms') => |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
952 |
let val T = nth_dtyp' i |
32952 | 953 |
in maps (fn (cname, dts) => map (fn atom => |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
954 |
let |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
955 |
val cname = Sign.intern_const thy8 |
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset
|
956 |
(Long_Name.append tname (Long_Name.base_name cname)); |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
957 |
val atomT = Type (atom, []); |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
958 |
|
33338 | 959 |
fun process_constr (dts, dt) (j, args1, args2) = |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
960 |
let |
45838 | 961 |
val Ts_idx = |
962 |
map (Datatype_Aux.typ_of_dtyp descr'') dts ~~ (j upto j + length dts - 1); |
|
963 |
val xs = map (fn (T, i) => Datatype_Aux.mk_Free "x" T i) Ts_idx; |
|
964 |
val x = |
|
965 |
Datatype_Aux.mk_Free "x" (Datatype_Aux.typ_of_dtyp descr'' dt) (j + length dts); |
|
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
966 |
in |
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
967 |
(j + length dts + 1, |
33338 | 968 |
xs @ (x :: args1), fold_rev mk_abs_fun xs x :: args2) |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
969 |
end; |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
970 |
|
33338 | 971 |
val (_, args1, args2) = fold_rev process_constr dts (1, [], []); |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
972 |
val Ts = map fastype_of args1; |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
973 |
val c = list_comb (Const (cname, Ts ---> T), args1); |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
974 |
fun supp t = |
19494 | 975 |
Const ("Nominal.supp", fastype_of t --> HOLogic.mk_setT atomT) $ t; |
25823 | 976 |
fun fresh t = fresh_const atomT (fastype_of t) $ Free ("a", atomT) $ t; |
20046 | 977 |
val supp_thm = Goal.prove_global thy8 [] [] |
28731 | 978 |
(augment_sort thy8 pt_cp_sort |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
979 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
980 |
(supp c, |
30450 | 981 |
if null dts then HOLogic.mk_set atomT [] |
35402 | 982 |
else foldr1 (HOLogic.mk_binop @{const_abbrev union}) (map supp args2))))) |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
983 |
(fn _ => |
18010 | 984 |
simp_tac (HOL_basic_ss addsimps (supp_def :: |
46161 | 985 |
Un_assoc :: @{thm de_Morgan_conj} :: Collect_disj_eq :: finite_Un :: |
45654 | 986 |
Collect_False_empty :: finite_emptyI :: @{thms simp_thms} @ |
20046 | 987 |
abs_perm @ abs_fresh @ inject_thms' @ perm_thms')) 1) |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
988 |
in |
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
989 |
(supp_thm, |
28731 | 990 |
Goal.prove_global thy8 [] [] (augment_sort thy8 pt_cp_sort |
991 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
|
992 |
(fresh c, |
|
45740 | 993 |
if null dts then @{term True} |
28731 | 994 |
else foldr1 HOLogic.mk_conj (map fresh args2))))) |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
995 |
(fn _ => |
24459
fd114392bca9
Got rid of large simpset in proof of characteristic equations
berghofe
parents:
24218
diff
changeset
|
996 |
simp_tac (HOL_ss addsimps [Un_iff, empty_iff, fresh_def, supp_thm]) 1)) |
32952 | 997 |
end) atoms) constrs |
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
998 |
end) (List.take (pdescr, length new_type_names) ~~ new_type_names ~~ inject_thms ~~ perm_simps'))); |
17872
f08fc98a164a
Implemented proofs for support and freshness theorems.
berghofe
parents:
17870
diff
changeset
|
999 |
|
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1000 |
(**** weak induction theorem ****) |
18016 | 1001 |
|
33244 | 1002 |
fun mk_indrule_lemma (((i, _), T), U) (prems, concls) = |
18016 | 1003 |
let |
45838 | 1004 |
val Rep_t = Const (nth rep_names i, T --> U) $ Datatype_Aux.mk_Free "x" T i; |
18016 | 1005 |
|
42364 | 1006 |
val Abs_t = Const (nth abs_names i, U --> T); |
18016 | 1007 |
|
45838 | 1008 |
in |
1009 |
(prems @ [HOLogic.imp $ |
|
42364 | 1010 |
(Const (nth rep_set_names'' i, U --> HOLogic.boolT) $ Rep_t) $ |
45838 | 1011 |
(Datatype_Aux.mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t))], |
1012 |
concls @ |
|
1013 |
[Datatype_Aux.mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ Datatype_Aux.mk_Free "x" T i]) |
|
18016 | 1014 |
end; |
1015 |
||
1016 |
val (indrule_lemma_prems, indrule_lemma_concls) = |
|
33244 | 1017 |
fold mk_indrule_lemma (descr'' ~~ recTs ~~ recTs') ([], []); |
18016 | 1018 |
|
20046 | 1019 |
val indrule_lemma = Goal.prove_global thy8 [] [] |
18016 | 1020 |
(Logic.mk_implies |
45838 | 1021 |
(HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_prems), |
1022 |
HOLogic.mk_Trueprop (Datatype_Aux.mk_conj indrule_lemma_concls))) (fn _ => EVERY |
|
18016 | 1023 |
[REPEAT (etac conjE 1), |
1024 |
REPEAT (EVERY |
|
1025 |
[TRY (rtac conjI 1), full_simp_tac (HOL_basic_ss addsimps Rep_inverse_thms) 1, |
|
20046 | 1026 |
etac mp 1, resolve_tac Rep_thms 1])]); |
18016 | 1027 |
|
1028 |
val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (concl_of indrule_lemma))); |
|
1029 |
val frees = if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] else |
|
1030 |
map (Free o apfst fst o dest_Var) Ps; |
|
1031 |
val indrule_lemma' = cterm_instantiate |
|
1032 |
(map (cterm_of thy8) Ps ~~ map (cterm_of thy8) frees) indrule_lemma; |
|
1033 |
||
19833
3a3f591c838d
- Changed naming scheme: names of "internal" constructors now have
berghofe
parents:
19710
diff
changeset
|
1034 |
val Abs_inverse_thms' = map (fn r => r RS subst) Abs_inverse_thms; |
18016 | 1035 |
|
45822 | 1036 |
val dt_induct_prop = Datatype_Prop.make_ind descr'; |
20046 | 1037 |
val dt_induct = Goal.prove_global thy8 [] |
18016 | 1038 |
(Logic.strip_imp_prems dt_induct_prop) (Logic.strip_imp_concl dt_induct_prop) |
26711 | 1039 |
(fn {prems, ...} => EVERY |
18016 | 1040 |
[rtac indrule_lemma' 1, |
45735 | 1041 |
(Datatype_Aux.ind_tac rep_induct [] THEN_ALL_NEW Object_Logic.atomize_prems_tac) 1, |
18016 | 1042 |
EVERY (map (fn (prem, r) => (EVERY |
1043 |
[REPEAT (eresolve_tac Abs_inverse_thms' 1), |
|
36945 | 1044 |
simp_tac (HOL_basic_ss addsimps [Thm.symmetric r]) 1, |
18016 | 1045 |
DEPTH_SOLVE_1 (ares_tac [prem] 1 ORELSE etac allE 1)])) |
20046 | 1046 |
(prems ~~ constr_defs))]); |
18016 | 1047 |
|
45906 | 1048 |
val case_names_induct = Datatype.mk_case_names_induct descr''; |
18016 | 1049 |
|
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1050 |
(**** prove that new datatypes have finite support ****) |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1051 |
|
18246
676d2e625d98
added fsub.thy (poplmark challenge) to the examples
urbanc
parents:
18245
diff
changeset
|
1052 |
val _ = warning "proving finite support for the new datatype"; |
676d2e625d98
added fsub.thy (poplmark challenge) to the examples
urbanc
parents:
18245
diff
changeset
|
1053 |
|
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
1054 |
val indnames = Datatype_Prop.make_tnames recTs; |
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1055 |
|
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1056 |
val abs_supp = Global_Theory.get_thms thy8 "abs_supp"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1057 |
val supp_atm = Global_Theory.get_thms thy8 "supp_atm"; |
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1058 |
|
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1059 |
val finite_supp_thms = map (fn atom => |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1060 |
let val atomT = Type (atom, []) |
35021
c839a4c670c6
renamed old-style Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
wenzelm
parents:
33968
diff
changeset
|
1061 |
in map Drule.export_without_context (List.take |
45838 | 1062 |
(Datatype_Aux.split_conj_thm (Goal.prove_global thy8 [] [] |
28731 | 1063 |
(augment_sort thy8 (fs_class_of thy8 atom :: pt_cp_sort) |
1064 |
(HOLogic.mk_Trueprop |
|
1065 |
(foldr1 HOLogic.mk_conj (map (fn (s, T) => |
|
1066 |
Const ("Finite_Set.finite", HOLogic.mk_setT atomT --> HOLogic.boolT) $ |
|
1067 |
(Const ("Nominal.supp", T --> HOLogic.mk_setT atomT) $ Free (s, T))) |
|
1068 |
(indnames ~~ recTs))))) |
|
45735 | 1069 |
(fn _ => Datatype_Aux.ind_tac dt_induct indnames 1 THEN |
32149
ef59550a55d3
renamed simpset_of to global_simpset_of, and local_simpset_of to simpset_of -- same for claset and clasimpset;
wenzelm
parents:
32134
diff
changeset
|
1070 |
ALLGOALS (asm_full_simp_tac (global_simpset_of thy8 addsimps |
18067 | 1071 |
(abs_supp @ supp_atm @ |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1072 |
Global_Theory.get_thms thy8 ("fs_" ^ Long_Name.base_name atom ^ "1") @ |
32952 | 1073 |
flat supp_thms))))), |
18066
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1074 |
length new_type_names)) |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1075 |
end) atoms; |
d1e47ee13070
Added code for proving that new datatype has finite support.
berghofe
parents:
18054
diff
changeset
|
1076 |
|
18759 | 1077 |
val simp_atts = replicate (length new_type_names) [Simplifier.simp_add]; |
18658 | 1078 |
|
32960
69916a850301
eliminated hard tabulators, guessing at each author's individual tab-width;
wenzelm
parents:
32957
diff
changeset
|
1079 |
(* Function to add both the simp and eqvt attributes *) |
22245
1b8f4ef50c48
moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents:
22231
diff
changeset
|
1080 |
(* These two attributes are duplicated on all the types in the mutual nominal datatypes *) |
1b8f4ef50c48
moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents:
22231
diff
changeset
|
1081 |
|
1b8f4ef50c48
moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents:
22231
diff
changeset
|
1082 |
val simp_eqvt_atts = replicate (length new_type_names) [Simplifier.simp_add, NominalThmDecls.eqvt_add]; |
1b8f4ef50c48
moved the infrastructure from the nominal_tags file to nominal_thmdecls
urbanc
parents:
22231
diff
changeset
|
1083 |
|
18658 | 1084 |
val (_, thy9) = thy8 |> |
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24459
diff
changeset
|
1085 |
Sign.add_path big_name |> |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1086 |
Global_Theory.add_thms [((Binding.name "induct", dt_induct), [case_names_induct])] ||>> |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1087 |
Global_Theory.add_thmss [((Binding.name "inducts", projections dt_induct), [case_names_induct])] ||> |
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24459
diff
changeset
|
1088 |
Sign.parent_path ||>> |
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
1089 |
Datatype_Aux.store_thmss_atts "distinct" new_type_names simp_atts distinct_thms ||>> |
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
1090 |
Datatype_Aux.store_thmss "constr_rep" new_type_names constr_rep_thmss ||>> |
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
1091 |
Datatype_Aux.store_thmss_atts "perm" new_type_names simp_eqvt_atts perm_simps' ||>> |
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
1092 |
Datatype_Aux.store_thmss "inject" new_type_names inject_thms ||>> |
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
1093 |
Datatype_Aux.store_thmss "supp" new_type_names supp_thms ||>> |
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
1094 |
Datatype_Aux.store_thmss_atts "fresh" new_type_names simp_atts fresh_thms ||> |
18658 | 1095 |
fold (fn (atom, ths) => fn thy => |
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
1096 |
let |
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
1097 |
val class = fs_class_of thy atom; |
36428
874843c1e96e
really minimize sorts after certification -- looks like this is intended here;
wenzelm
parents:
35994
diff
changeset
|
1098 |
val sort = Sign.minimize_sort thy (Sign.certify_sort thy (class :: pt_cp_sort)); |
28736
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
1099 |
in fold (fn Type (s, Ts) => AxClass.prove_arity |
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
1100 |
(s, map (inter_sort thy sort o snd o dest_TFree) Ts, [class]) |
b1fd60fee652
Some modifications in code for proving arities to make it work for datatype
berghofe
parents:
28731
diff
changeset
|
1101 |
(Class.intro_classes_tac [] THEN resolve_tac ths 1)) newTs thy |
18658 | 1102 |
end) (atoms ~~ finite_supp_thms); |
1103 |
||
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1104 |
(**** strong induction theorem ****) |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1105 |
|
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1106 |
val pnames = if length descr'' = 1 then ["P"] |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1107 |
else map (fn i => "P" ^ string_of_int i) (1 upto length descr''); |
18245
65e60434b3c2
Fixed problem with strong induction theorem for datatypes containing
berghofe
parents:
18142
diff
changeset
|
1108 |
val ind_sort = if null dt_atomTs then HOLogic.typeS |
36428
874843c1e96e
really minimize sorts after certification -- looks like this is intended here;
wenzelm
parents:
35994
diff
changeset
|
1109 |
else Sign.minimize_sort thy9 (Sign.certify_sort thy9 (map (fs_class_of thy9) dt_atoms)); |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1110 |
val fsT = TFree ("'n", ind_sort); |
18658 | 1111 |
val fsT' = TFree ("'n", HOLogic.typeS); |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1112 |
|
18658 | 1113 |
val fresh_fs = map (fn (s, T) => (T, Free (s, fsT' --> HOLogic.mk_setT T))) |
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
1114 |
(Datatype_Prop.indexify_names (replicate (length dt_atomTs) "f") ~~ dt_atomTs); |
18658 | 1115 |
|
42364 | 1116 |
fun make_pred fsT i T = Free (nth pnames i, fsT --> T --> HOLogic.boolT); |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1117 |
|
19851
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1118 |
fun mk_fresh1 xs [] = [] |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1119 |
| mk_fresh1 xs ((y as (_, T)) :: ys) = map (fn x => HOLogic.mk_Trueprop |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1120 |
(HOLogic.mk_not (HOLogic.mk_eq (Free y, Free x)))) |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1121 |
(filter (fn (_, U) => T = U) (rev xs)) @ |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1122 |
mk_fresh1 (y :: xs) ys; |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1123 |
|
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1124 |
fun mk_fresh2 xss [] = [] |
32952 | 1125 |
| mk_fresh2 xss ((p as (ys, _)) :: yss) = maps (fn y as (_, T) => |
19851
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1126 |
map (fn (_, x as (_, U)) => HOLogic.mk_Trueprop |
32952 | 1127 |
(fresh_const T U $ Free y $ Free x)) (rev xss @ yss)) ys @ |
19851
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1128 |
mk_fresh2 (p :: xss) yss; |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1129 |
|
18658 | 1130 |
fun make_ind_prem fsT f k T ((cname, cargs), idxs) = |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1131 |
let |
45838 | 1132 |
val recs = filter Datatype_Aux.is_rec_type cargs; |
1133 |
val Ts = map (Datatype_Aux.typ_of_dtyp descr'') cargs; |
|
1134 |
val recTs' = map (Datatype_Aux.typ_of_dtyp descr'') recs; |
|
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
1135 |
val tnames = Name.variant_list pnames (Datatype_Prop.make_tnames Ts); |
45838 | 1136 |
val rec_tnames = map fst (filter (Datatype_Aux.is_rec_type o snd) (tnames ~~ cargs)); |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1137 |
val frees = tnames ~~ Ts; |
19710 | 1138 |
val frees' = partition_cargs idxs frees; |
43324
2b47822868e4
discontinued Name.variant to emphasize that this is old-style / indirect;
wenzelm
parents:
42388
diff
changeset
|
1139 |
val z = (singleton (Name.variant_list tnames) "z", fsT); |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1140 |
|
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1141 |
fun mk_prem ((dt, s), T) = |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1142 |
let |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1143 |
val (Us, U) = strip_type T; |
45838 | 1144 |
val l = length Us; |
1145 |
in |
|
1146 |
list_all (z :: map (pair "x") Us, |
|
1147 |
HOLogic.mk_Trueprop |
|
1148 |
(make_pred fsT (Datatype_Aux.body_index dt) U $ Bound l $ |
|
1149 |
Datatype_Aux.app_bnds (Free (s, T)) l)) |
|
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1150 |
end; |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1151 |
|
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1152 |
val prems = map mk_prem (recs ~~ rec_tnames ~~ recTs'); |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1153 |
val prems' = map (fn p as (_, T) => HOLogic.mk_Trueprop |
32952 | 1154 |
(f T (Free p) (Free z))) (maps fst frees') @ |
1155 |
mk_fresh1 [] (maps fst frees') @ |
|
19710 | 1156 |
mk_fresh2 [] frees' |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1157 |
|
46215
0da9433f959e
discontinued old-style Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset
|
1158 |
in |
0da9433f959e
discontinued old-style Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset
|
1159 |
fold_rev (Logic.all o Free) (frees @ [z]) |
0da9433f959e
discontinued old-style Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset
|
1160 |
(Logic.list_implies (prems' @ prems, |
0da9433f959e
discontinued old-style Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset
|
1161 |
HOLogic.mk_Trueprop (make_pred fsT k T $ Free z $ |
0da9433f959e
discontinued old-style Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset
|
1162 |
list_comb (Const (cname, Ts ---> T), map Free frees)))) |
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1163 |
end; |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1164 |
|
32952 | 1165 |
val ind_prems = maps (fn (((i, (_, _, constrs)), (_, idxss)), T) => |
18658 | 1166 |
map (make_ind_prem fsT (fn T => fn t => fn u => |
25823 | 1167 |
fresh_const T fsT $ t $ u) i T) |
32952 | 1168 |
(constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs); |
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
1169 |
val tnames = Datatype_Prop.make_tnames recTs; |
20071
8f3e1ddb50e6
replaced Term.variant(list) by Name.variant(_list);
wenzelm
parents:
20046
diff
changeset
|
1170 |
val zs = Name.variant_list tnames (replicate (length descr'') "z"); |
38795
848be46708dc
formerly unnamed infix conjunction and disjunction now named HOL.conj and HOL.disj
haftmann
parents:
38715
diff
changeset
|
1171 |
val ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop @{const_name HOL.conj}) |
18658 | 1172 |
(map (fn ((((i, _), T), tname), z) => |
1173 |
make_pred fsT i T $ Free (z, fsT) $ Free (tname, T)) |
|
1174 |
(descr'' ~~ recTs ~~ tnames ~~ zs))); |
|
18107
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1175 |
val induct = Logic.list_implies (ind_prems, ind_concl); |
ee6b4d3af498
Added strong induction theorem (currently only axiomatized!).
berghofe
parents:
18104
diff
changeset
|
1176 |
|
18658 | 1177 |
val ind_prems' = |
46215
0da9433f959e
discontinued old-style Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset
|
1178 |
map (fn (_, f as Free (_, T)) => Logic.all (Free ("x", fsT')) |
0da9433f959e
discontinued old-style Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset
|
1179 |
(HOLogic.mk_Trueprop (Const ("Finite_Set.finite", |
44692
ccfc7c193d2b
modify nominal packages to better respect set/pred distinction
huffman
parents:
44241
diff
changeset
|
1180 |
Term.range_type T --> |
26806 | 1181 |
HOLogic.boolT) $ (f $ Free ("x", fsT'))))) fresh_fs @ |
32952 | 1182 |
maps (fn (((i, (_, _, constrs)), (_, idxss)), T) => |
18658 | 1183 |
map (make_ind_prem fsT' (fn T => fn t => fn u => HOLogic.Not $ |
1184 |
HOLogic.mk_mem (t, the (AList.lookup op = fresh_fs T) $ u)) i T) |
|
32952 | 1185 |
(constrs ~~ idxss)) (descr'' ~~ ndescr ~~ recTs); |
38795
848be46708dc
formerly unnamed infix conjunction and disjunction now named HOL.conj and HOL.disj
haftmann
parents:
38715
diff
changeset
|
1186 |
val ind_concl' = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop @{const_name HOL.conj}) |
18658 | 1187 |
(map (fn ((((i, _), T), tname), z) => |
1188 |
make_pred fsT' i T $ Free (z, fsT') $ Free (tname, T)) |
|
1189 |
(descr'' ~~ recTs ~~ tnames ~~ zs))); |
|
1190 |
val induct' = Logic.list_implies (ind_prems', ind_concl'); |
|
1191 |
||
1192 |
val aux_ind_vars = |
|
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
1193 |
(Datatype_Prop.indexify_names (replicate (length dt_atomTs) "pi") ~~ |
18658 | 1194 |
map mk_permT dt_atomTs) @ [("z", fsT')]; |
1195 |
val aux_ind_Ts = rev (map snd aux_ind_vars); |
|
38795
848be46708dc
formerly unnamed infix conjunction and disjunction now named HOL.conj and HOL.disj
haftmann
parents:
38715
diff
changeset
|
1196 |
val aux_ind_concl = HOLogic.mk_Trueprop (foldr1 (HOLogic.mk_binop @{const_name HOL.conj}) |
18658 | 1197 |
(map (fn (((i, _), T), tname) => |
1198 |
HOLogic.list_all (aux_ind_vars, make_pred fsT' i T $ Bound 0 $ |
|
22311 | 1199 |
fold_rev (mk_perm aux_ind_Ts) (map Bound (length dt_atomTs downto 1)) |
1200 |
(Free (tname, T)))) |
|
18658 | 1201 |
(descr'' ~~ recTs ~~ tnames))); |
1202 |
||
28731 | 1203 |
val fin_set_supp = map (fn s => |
1204 |
at_inst_of thy9 s RS at_fin_set_supp) dt_atoms; |
|
1205 |
val fin_set_fresh = map (fn s => |
|
1206 |
at_inst_of thy9 s RS at_fin_set_fresh) dt_atoms; |
|
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1207 |
val pt1_atoms = map (fn Type (s, _) => |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1208 |
Global_Theory.get_thm thy9 ("pt_" ^ Long_Name.base_name s ^ "1")) dt_atomTs; |
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1209 |
val pt2_atoms = map (fn Type (s, _) => |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1210 |
Global_Theory.get_thm thy9 ("pt_" ^ Long_Name.base_name s ^ "2") RS sym) dt_atomTs; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1211 |
val exists_fresh' = Global_Theory.get_thms thy9 "exists_fresh'"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1212 |
val fs_atoms = Global_Theory.get_thms thy9 "fin_supp"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1213 |
val abs_supp = Global_Theory.get_thms thy9 "abs_supp"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1214 |
val perm_fresh_fresh = Global_Theory.get_thms thy9 "perm_fresh_fresh"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1215 |
val calc_atm = Global_Theory.get_thms thy9 "calc_atm"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1216 |
val fresh_atm = Global_Theory.get_thms thy9 "fresh_atm"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1217 |
val fresh_left = Global_Theory.get_thms thy9 "fresh_left"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1218 |
val perm_swap = Global_Theory.get_thms thy9 "perm_swap"; |
18658 | 1219 |
|
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1220 |
fun obtain_fresh_name' ths ts T (freshs1, freshs2, ctxt) = |
18658 | 1221 |
let |
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1222 |
val p = foldr1 HOLogic.mk_prod (ts @ freshs1); |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1223 |
val ex = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1224 |
(HOLogic.exists_const T $ Abs ("x", T, |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1225 |
fresh_const T (fastype_of p) $ |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1226 |
Bound 0 $ p))) |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1227 |
(fn _ => EVERY |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1228 |
[resolve_tac exists_fresh' 1, |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1229 |
simp_tac (HOL_ss addsimps (supp_prod :: finite_Un :: fs_atoms @ |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1230 |
fin_set_supp @ ths)) 1]); |
32202 | 1231 |
val (([(_, cx)], ths), ctxt') = Obtain.result |
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1232 |
(fn _ => EVERY |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1233 |
[etac exE 1, |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1234 |
full_simp_tac (HOL_ss addsimps (fresh_prod :: fresh_atm)) 1, |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1235 |
REPEAT (etac conjE 1)]) |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1236 |
[ex] ctxt |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1237 |
in (freshs1 @ [term_of cx], freshs2 @ ths, ctxt') end; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1238 |
|
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1239 |
fun fresh_fresh_inst thy a b = |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1240 |
let |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1241 |
val T = fastype_of a; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1242 |
val SOME th = find_first (fn th => case prop_of th of |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1243 |
_ $ (_ $ (Const (_, Type (_, [U, _])) $ _ $ _)) $ _ => U = T |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1244 |
| _ => false) perm_fresh_fresh |
18658 | 1245 |
in |
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1246 |
Drule.instantiate' [] |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1247 |
[SOME (cterm_of thy a), NONE, SOME (cterm_of thy b)] th |
18658 | 1248 |
end; |
18104
dbe58b104cb9
added thms perm, distinct and fresh to the simplifier.
urbanc
parents:
18068
diff
changeset
|
1249 |
|
28731 | 1250 |
val fs_cp_sort = |
1251 |
map (fs_class_of thy9) dt_atoms @ |
|
33040 | 1252 |
maps (fn s => map (cp_class_of thy9 s) (remove (op =) s dt_atoms)) dt_atoms; |
28731 | 1253 |
|
19710 | 1254 |
(********************************************************************** |
1255 |
The subgoals occurring in the proof of induct_aux have the |
|
1256 |
following parameters: |
|
1257 |
||
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1258 |
x_1 ... x_k p_1 ... p_m z |
19710 | 1259 |
|
1260 |
where |
|
1261 |
||
1262 |
x_i : constructor arguments (introduced by weak induction rule) |
|
1263 |
p_i : permutations (one for each atom type in the data type) |
|
1264 |
z : freshness context |
|
1265 |
***********************************************************************) |
|
1266 |
||
1267 |
val _ = warning "proving strong induction theorem ..."; |
|
1268 |
||
28731 | 1269 |
val induct_aux = Goal.prove_global thy9 [] |
1270 |
(map (augment_sort thy9 fs_cp_sort) ind_prems') |
|
1271 |
(augment_sort thy9 fs_cp_sort ind_concl') (fn {prems, context} => |
|
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1272 |
let |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1273 |
val (prems1, prems2) = chop (length dt_atomTs) prems; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1274 |
val ind_ss2 = HOL_ss addsimps |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1275 |
finite_Diff :: abs_fresh @ abs_supp @ fs_atoms; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1276 |
val ind_ss1 = ind_ss2 addsimps fresh_left @ calc_atm @ |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1277 |
fresh_atm @ rev_simps @ app_simps; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1278 |
val ind_ss3 = HOL_ss addsimps abs_fun_eq1 :: |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1279 |
abs_perm @ calc_atm @ perm_swap; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1280 |
val ind_ss4 = HOL_basic_ss addsimps fresh_left @ prems1 @ |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1281 |
fin_set_fresh @ calc_atm; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1282 |
val ind_ss5 = HOL_basic_ss addsimps pt1_atoms; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1283 |
val ind_ss6 = HOL_basic_ss addsimps flat perm_simps'; |
28731 | 1284 |
val th = Goal.prove context [] [] |
1285 |
(augment_sort thy9 fs_cp_sort aux_ind_concl) |
|
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1286 |
(fn {context = context1, ...} => |
45735 | 1287 |
EVERY (Datatype_Aux.ind_tac dt_induct tnames 1 :: |
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1288 |
maps (fn ((_, (_, _, constrs)), (_, constrs')) => |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1289 |
map (fn ((cname, cargs), is) => |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1290 |
REPEAT (rtac allI 1) THEN |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1291 |
SUBPROOF (fn {prems = iprems, params, concl, |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1292 |
context = context2, ...} => |
18658 | 1293 |
let |
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1294 |
val concl' = term_of concl; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1295 |
val _ $ (_ $ _ $ u) = concl'; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1296 |
val U = fastype_of u; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1297 |
val (xs, params') = |
32202 | 1298 |
chop (length cargs) (map (term_of o #2) params); |
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1299 |
val Ts = map fastype_of xs; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1300 |
val cnstr = Const (cname, Ts ---> U); |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1301 |
val (pis, z) = split_last params'; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1302 |
val mk_pi = fold_rev (mk_perm []) pis; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1303 |
val xs' = partition_cargs is xs; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1304 |
val xs'' = map (fn (ts, u) => (map mk_pi ts, mk_pi u)) xs'; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1305 |
val ts = maps (fn (ts, u) => ts @ [u]) xs''; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1306 |
val (freshs1, freshs2, context3) = fold (fn t => |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1307 |
let val T = fastype_of t |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1308 |
in obtain_fresh_name' prems1 |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1309 |
(the (AList.lookup op = fresh_fs T) $ z :: ts) T |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1310 |
end) (maps fst xs') ([], [], context2); |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1311 |
val freshs1' = unflat (map fst xs') freshs1; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1312 |
val freshs2' = map (Simplifier.simplify ind_ss4) |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1313 |
(mk_not_sym freshs2); |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1314 |
val ind_ss1' = ind_ss1 addsimps freshs2'; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1315 |
val ind_ss3' = ind_ss3 addsimps freshs2'; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1316 |
val rename_eq = |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1317 |
if forall (null o fst) xs' then [] |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1318 |
else [Goal.prove context3 [] [] |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1319 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1320 |
(list_comb (cnstr, ts), |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1321 |
list_comb (cnstr, maps (fn ((bs, t), cs) => |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1322 |
cs @ [fold_rev (mk_perm []) (map perm_of_pair |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1323 |
(bs ~~ cs)) t]) (xs'' ~~ freshs1'))))) |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1324 |
(fn _ => EVERY |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1325 |
(simp_tac (HOL_ss addsimps flat inject_thms) 1 :: |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1326 |
REPEAT (FIRSTGOAL (rtac conjI)) :: |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1327 |
maps (fn ((bs, t), cs) => |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1328 |
if null bs then [] |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1329 |
else rtac sym 1 :: maps (fn (b, c) => |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1330 |
[rtac trans 1, rtac sym 1, |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1331 |
rtac (fresh_fresh_inst thy9 b c) 1, |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1332 |
simp_tac ind_ss1' 1, |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1333 |
simp_tac ind_ss2 1, |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1334 |
simp_tac ind_ss3' 1]) (bs ~~ cs)) |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1335 |
(xs'' ~~ freshs1')))]; |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1336 |
val th = Goal.prove context3 [] [] concl' (fn _ => EVERY |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1337 |
[simp_tac (ind_ss6 addsimps rename_eq) 1, |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1338 |
cut_facts_tac iprems 1, |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1339 |
(resolve_tac prems THEN_ALL_NEW |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1340 |
SUBGOAL (fn (t, i) => case Logic.strip_assums_concl t of |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1341 |
_ $ (Const ("Nominal.fresh", _) $ _ $ _) => |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1342 |
simp_tac ind_ss1' i |
38558 | 1343 |
| _ $ (Const (@{const_name Not}, _) $ _) => |
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1344 |
resolve_tac freshs2' i |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1345 |
| _ => asm_simp_tac (HOL_basic_ss addsimps |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1346 |
pt2_atoms addsimprocs [perm_simproc]) i)) 1]) |
42361 | 1347 |
val final = Proof_Context.export context3 context2 [th] |
18658 | 1348 |
in |
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1349 |
resolve_tac final 1 |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1350 |
end) context1 1) (constrs ~~ constrs')) (descr'' ~~ ndescr))) |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1351 |
in |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1352 |
EVERY |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1353 |
[cut_facts_tac [th] 1, |
27228
4f7976a6ffc3
allE_Nil: only one copy, proven in regular theory source;
wenzelm
parents:
27153
diff
changeset
|
1354 |
REPEAT (eresolve_tac [conjE, @{thm allE_Nil}] 1), |
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1355 |
REPEAT (etac allE 1), |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1356 |
REPEAT (TRY (rtac conjI 1) THEN asm_full_simp_tac ind_ss5 1)] |
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1357 |
end); |
18658 | 1358 |
|
1359 |
val induct_aux' = Thm.instantiate ([], |
|
28731 | 1360 |
map (fn (s, v as Var (_, T)) => |
1361 |
(cterm_of thy9 v, cterm_of thy9 (Free (s, T)))) |
|
1362 |
(pnames ~~ map head_of (HOLogic.dest_conj |
|
1363 |
(HOLogic.dest_Trueprop (concl_of induct_aux)))) @ |
|
18658 | 1364 |
map (fn (_, f) => |
35845
e5980f0ad025
renamed varify/unvarify operations to varify_global/unvarify_global to emphasize that these only work in a global situation;
wenzelm
parents:
35842
diff
changeset
|
1365 |
let val f' = Logic.varify_global f |
18658 | 1366 |
in (cterm_of thy9 f', |
19494 | 1367 |
cterm_of thy9 (Const ("Nominal.supp", fastype_of f'))) |
18658 | 1368 |
end) fresh_fs) induct_aux; |
1369 |
||
28731 | 1370 |
val induct = Goal.prove_global thy9 [] |
1371 |
(map (augment_sort thy9 fs_cp_sort) ind_prems) |
|
1372 |
(augment_sort thy9 fs_cp_sort ind_concl) |
|
26711 | 1373 |
(fn {prems, ...} => EVERY |
18658 | 1374 |
[rtac induct_aux' 1, |
25951
6ebe26bfed18
Reimplemented proof of strong induction theorem.
berghofe
parents:
25823
diff
changeset
|
1375 |
REPEAT (resolve_tac fs_atoms 1), |
18658 | 1376 |
REPEAT ((resolve_tac prems THEN_ALL_NEW |
39159 | 1377 |
(etac @{thm meta_spec} ORELSE' full_simp_tac (HOL_basic_ss addsimps [fresh_def]))) 1)]) |
18658 | 1378 |
|
1379 |
val (_, thy10) = thy9 |> |
|
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24459
diff
changeset
|
1380 |
Sign.add_path big_name |> |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1381 |
Global_Theory.add_thms [((Binding.name "strong_induct'", induct_aux), [])] ||>> |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1382 |
Global_Theory.add_thms [((Binding.name "strong_induct", induct), [case_names_induct])] ||>> |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1383 |
Global_Theory.add_thmss [((Binding.name "strong_inducts", projections induct), [case_names_induct])]; |
18658 | 1384 |
|
19322
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1385 |
(**** recursion combinator ****) |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1386 |
|
19322
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1387 |
val _ = warning "defining recursion combinator ..."; |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1388 |
|
45741 | 1389 |
val used = fold Term.add_tfree_namesT recTs []; |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1390 |
|
45822 | 1391 |
val (rec_result_Ts', rec_fn_Ts') = Datatype_Prop.make_primrec_Ts descr' used; |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1392 |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
1393 |
val rec_sort = if null dt_atomTs then HOLogic.typeS else |
36428
874843c1e96e
really minimize sorts after certification -- looks like this is intended here;
wenzelm
parents:
35994
diff
changeset
|
1394 |
Sign.minimize_sort thy10 (Sign.certify_sort thy10 pt_cp_sort); |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1395 |
|
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1396 |
val rec_result_Ts = map (fn TFree (s, _) => TFree (s, rec_sort)) rec_result_Ts'; |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1397 |
val rec_fn_Ts = map (typ_subst_atomic (rec_result_Ts' ~~ rec_result_Ts)) rec_fn_Ts'; |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1398 |
|
21021 | 1399 |
val rec_set_Ts = map (fn (T1, T2) => |
1400 |
rec_fn_Ts @ [T1, T2] ---> HOLogic.boolT) (recTs ~~ rec_result_Ts); |
|
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1401 |
|
19322
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1402 |
val big_rec_name = big_name ^ "_rec_set"; |
21021 | 1403 |
val rec_set_names' = |
1404 |
if length descr'' = 1 then [big_rec_name] else |
|
1405 |
map ((curry (op ^) (big_rec_name ^ "_")) o string_of_int) |
|
1406 |
(1 upto (length descr'')); |
|
28965 | 1407 |
val rec_set_names = map (Sign.full_bname thy10) rec_set_names'; |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1408 |
|
45838 | 1409 |
val rec_fns = map (uncurry (Datatype_Aux.mk_Free "f")) |
19322
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1410 |
(rec_fn_Ts ~~ (1 upto (length rec_fn_Ts))); |
21021 | 1411 |
val rec_sets' = map (fn c => list_comb (Free c, rec_fns)) |
1412 |
(rec_set_names' ~~ rec_set_Ts); |
|
19322
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1413 |
val rec_sets = map (fn c => list_comb (Const c, rec_fns)) |
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1414 |
(rec_set_names ~~ rec_set_Ts); |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1415 |
|
19322
bf84bdf05f14
Replaced iteration combinator by recursion combinator.
berghofe
parents:
19275
diff
changeset
|
1416 |
(* introduction rules for graph of recursion function *) |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1417 |
|
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1418 |
val rec_preds = map (fn (a, T) => |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1419 |
Free (a, T --> HOLogic.boolT)) (pnames ~~ rec_result_Ts); |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1420 |
|
20267 | 1421 |
fun mk_fresh3 rs [] = [] |
32952 | 1422 |
| mk_fresh3 rs ((p as (ys, z)) :: yss) = maps (fn y as (_, T) => |
1423 |
map_filter (fn ((_, (_, x)), r as (_, U)) => if z = x then NONE |
|
20267 | 1424 |
else SOME (HOLogic.mk_Trueprop |
32952 | 1425 |
(fresh_const T U $ Free y $ Free r))) rs) ys @ |
20267 | 1426 |
mk_fresh3 rs yss; |
1427 |
||
21088 | 1428 |
(* FIXME: avoid collisions with other variable names? *) |
1429 |
val rec_ctxt = Free ("z", fsT'); |
|
1430 |
||
33244 | 1431 |
fun make_rec_intr T p rec_set ((cname, cargs), idxs) |
1432 |
(rec_intr_ts, rec_prems, rec_prems', rec_eq_prems, l) = |
|
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1433 |
let |
45838 | 1434 |
val Ts = map (Datatype_Aux.typ_of_dtyp descr'') cargs; |
19851
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1435 |
val frees = map (fn i => "x" ^ string_of_int i) (1 upto length Ts) ~~ Ts; |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1436 |
val frees' = partition_cargs idxs frees; |
32952 | 1437 |
val binders = maps fst frees'; |
20411
dd8a1cda2eaf
Added premises concerning finite support of recursion results to FCBs.
berghofe
parents:
20397
diff
changeset
|
1438 |
val atomTs = distinct op = (maps (map snd o fst) frees'); |
32952 | 1439 |
val recs = map_filter |
45896 | 1440 |
(fn ((_, Datatype.DtRec i), p) => SOME (i, p) | _ => NONE) |
19851
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1441 |
(partition_cargs idxs cargs ~~ frees'); |
10162c01bd78
Completely rewrote code for defining graph of recursion combinator.
berghofe
parents:
19833
diff
changeset
|
1442 |
val frees'' = map (fn i => "y" ^ string_of_int i) (1 upto length recs) ~~ |
42364 | 1443 |
map (fn (i, _) => nth rec_result_Ts i) recs; |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1444 |
val prems1 = map (fn ((i, (_, x)), y) => HOLogic.mk_Trueprop |
42364 | 1445 |
(nth rec_sets' i $ Free x $ Free y)) (recs ~~ frees''); |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1446 |
val prems2 = |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1447 |
map (fn f => map (fn p as (_, T) => HOLogic.mk_Trueprop |
25823 | 1448 |
(fresh_const T (fastype_of f) $ Free p $ f)) binders) rec_fns; |
21088 | 1449 |
val prems3 = mk_fresh1 [] binders @ mk_fresh2 [] frees'; |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1450 |
val prems4 = map (fn ((i, _), y) => |
42364 | 1451 |
HOLogic.mk_Trueprop (nth rec_preds i $ Free y)) (recs ~~ frees''); |
20267 | 1452 |
val prems5 = mk_fresh3 (recs ~~ frees'') frees'; |
20411
dd8a1cda2eaf
Added premises concerning finite support of recursion results to FCBs.
berghofe
parents:
20397
diff
changeset
|
1453 |
val prems6 = maps (fn aT => map (fn y as (_, T) => HOLogic.mk_Trueprop |
22274 | 1454 |
(Const ("Finite_Set.finite", HOLogic.mk_setT aT --> HOLogic.boolT) $ |
1455 |
(Const ("Nominal.supp", T --> HOLogic.mk_setT aT) $ Free y))) |
|
20411
dd8a1cda2eaf
Added premises concerning finite support of recursion results to FCBs.
berghofe
parents:
20397
diff
changeset
|
1456 |
frees'') atomTs; |
21088 | 1457 |
val prems7 = map (fn x as (_, T) => HOLogic.mk_Trueprop |
25823 | 1458 |
(fresh_const T fsT' $ Free x $ rec_ctxt)) binders; |
42364 | 1459 |
val result = list_comb (nth rec_fns l, map Free (frees @ frees'')); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1460 |
val result_freshs = map (fn p as (_, T) => |
25823 | 1461 |
fresh_const T (fastype_of result) $ Free p $ result) binders; |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1462 |
val P = HOLogic.mk_Trueprop (p $ result) |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1463 |
in |
32952 | 1464 |
(rec_intr_ts @ [Logic.list_implies (flat prems2 @ prems3 @ prems1, |
21021 | 1465 |
HOLogic.mk_Trueprop (rec_set $ |
1466 |
list_comb (Const (cname, Ts ---> T), map Free frees) $ result))], |
|
46215
0da9433f959e
discontinued old-style Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset
|
1467 |
rec_prems @ [fold_rev (Logic.all o Free) (frees @ frees'') (Logic.list_implies (prems4, P))], |
0da9433f959e
discontinued old-style Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset
|
1468 |
rec_prems' @ map (fn fr => fold_rev (Logic.all o Free) (frees @ frees'') |
0da9433f959e
discontinued old-style Term.list_all_free in favour of plain Logic.all;
wenzelm
parents:
46161
diff
changeset
|
1469 |
(Logic.list_implies (nth prems2 l @ prems3 @ prems5 @ prems7 @ prems6 @ [P], |
21054
6048c085c3ae
Split up FCBs into separate formulae for each binder.
berghofe
parents:
21021
diff
changeset
|
1470 |
HOLogic.mk_Trueprop fr))) result_freshs, |
32952 | 1471 |
rec_eq_prems @ [flat prems2 @ prems3], |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1472 |
l + 1) |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1473 |
end; |
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1474 |
|
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1475 |
val (rec_intr_ts, rec_prems, rec_prems', rec_eq_prems, _) = |
33244 | 1476 |
fold (fn ((((d, d'), T), p), rec_set) => |
1477 |
fold (make_rec_intr T p rec_set) (#3 (snd d) ~~ snd d')) |
|
1478 |
(descr'' ~~ ndescr ~~ recTs ~~ rec_preds ~~ rec_sets') |
|
1479 |
([], [], [], [], 0); |
|
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1480 |
|
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
1481 |
val ({intrs = rec_intrs, elims = rec_elims, raw_induct = rec_induct, ...}, thy11) = |
33278 | 1482 |
thy10 |
1483 |
|> Sign.map_naming Name_Space.conceal |
|
33726
0878aecbf119
eliminated slightly odd name space grouping -- now managed by Isar toplevel;
wenzelm
parents:
33669
diff
changeset
|
1484 |
|> Inductive.add_inductive_global |
33669 | 1485 |
{quiet_mode = #quiet config, verbose = false, alt_name = Binding.name big_rec_name, |
1486 |
coind = false, no_elim = false, no_ind = false, skip_mono = true, fork_mono = false} |
|
28965 | 1487 |
(map (fn (s, T) => ((Binding.name s, T), NoSyn)) (rec_set_names' ~~ rec_set_Ts)) |
26128 | 1488 |
(map dest_Free rec_fns) |
33278 | 1489 |
(map (fn x => (Attrib.empty_binding, x)) rec_intr_ts) [] |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1490 |
||> Global_Theory.hide_fact true (Long_Name.append (Sign.full_bname thy10 big_rec_name) "induct") |
33278 | 1491 |
||> Sign.restore_naming thy10; |
19251
6bc0dda66f32
First version of function for defining graph of iteration combinator.
berghofe
parents:
19134
diff
changeset
|
1492 |
|
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1493 |
(** equivariance **) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1494 |
|
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1495 |
val fresh_bij = Global_Theory.get_thms thy11 "fresh_bij"; |
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1496 |
val perm_bij = Global_Theory.get_thms thy11 "perm_bij"; |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1497 |
|
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1498 |
val (rec_equiv_thms, rec_equiv_thms') = ListPair.unzip (map (fn aT => |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1499 |
let |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1500 |
val permT = mk_permT aT; |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1501 |
val pi = Free ("pi", permT); |
45838 | 1502 |
val rec_fns_pi = map (mk_perm [] pi o uncurry (Datatype_Aux.mk_Free "f")) |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1503 |
(rec_fn_Ts ~~ (1 upto (length rec_fn_Ts))); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1504 |
val rec_sets_pi = map (fn c => list_comb (Const c, rec_fns_pi)) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1505 |
(rec_set_names ~~ rec_set_Ts); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1506 |
val ps = map (fn ((((T, U), R), R'), i) => |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1507 |
let |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1508 |
val x = Free ("x" ^ string_of_int i, T); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1509 |
val y = Free ("y" ^ string_of_int i, U) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1510 |
in |
22311 | 1511 |
(R $ x $ y, R' $ mk_perm [] pi x $ mk_perm [] pi y) |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1512 |
end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ rec_sets_pi ~~ (1 upto length recTs)); |
45838 | 1513 |
val ths = map (fn th => Drule.export_without_context (th RS mp)) (Datatype_Aux.split_conj_thm |
20046 | 1514 |
(Goal.prove_global thy11 [] [] |
28731 | 1515 |
(augment_sort thy1 pt_cp_sort |
1516 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj (map HOLogic.mk_imp ps)))) |
|
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1517 |
(fn _ => rtac rec_induct 1 THEN REPEAT |
35232
f588e1169c8b
renamed Simplifier.theory_context to Simplifier.global_context to emphasize that this is not the real thing;
wenzelm
parents:
35021
diff
changeset
|
1518 |
(simp_tac (Simplifier.global_context thy11 HOL_basic_ss |
27450
d45d2850aaed
Replaced all but one occurrence of perm_simp_tac by perm_simproc_app,
berghofe
parents:
27300
diff
changeset
|
1519 |
addsimps flat perm_simps' |
d45d2850aaed
Replaced all but one occurrence of perm_simp_tac by perm_simproc_app,
berghofe
parents:
27300
diff
changeset
|
1520 |
addsimprocs [NominalPermeq.perm_simproc_app]) 1 THEN |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1521 |
(resolve_tac rec_intrs THEN_ALL_NEW |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1522 |
asm_simp_tac (HOL_ss addsimps (fresh_bij @ perm_bij))) 1)))) |
20046 | 1523 |
val ths' = map (fn ((P, Q), th) => |
1524 |
Goal.prove_global thy11 [] [] |
|
28731 | 1525 |
(augment_sort thy1 pt_cp_sort |
1526 |
(Logic.mk_implies (HOLogic.mk_Trueprop Q, HOLogic.mk_Trueprop P))) |
|
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1527 |
(fn _ => dtac (Thm.instantiate ([], |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1528 |
[(cterm_of thy11 (Var (("pi", 0), permT)), |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1529 |
cterm_of thy11 (Const ("List.rev", permT --> permT) $ pi))]) th) 1 THEN |
20046 | 1530 |
NominalPermeq.perm_simp_tac HOL_ss 1)) (ps ~~ ths) |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1531 |
in (ths, ths') end) dt_atomTs); |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1532 |
|
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1533 |
(** finite support **) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1534 |
|
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1535 |
val rec_fin_supp_thms = map (fn aT => |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1536 |
let |
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset
|
1537 |
val name = Long_Name.base_name (fst (dest_Type aT)); |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1538 |
val fs_name = Global_Theory.get_thm thy11 ("fs_" ^ name ^ "1"); |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1539 |
val aset = HOLogic.mk_setT aT; |
22274 | 1540 |
val finite = Const ("Finite_Set.finite", aset --> HOLogic.boolT); |
1541 |
val fins = map (fn (f, T) => HOLogic.mk_Trueprop |
|
1542 |
(finite $ (Const ("Nominal.supp", T --> aset) $ f))) |
|
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1543 |
(rec_fns ~~ rec_fn_Ts) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1544 |
in |
45838 | 1545 |
map (fn th => Drule.export_without_context (th RS mp)) (Datatype_Aux.split_conj_thm |
28731 | 1546 |
(Goal.prove_global thy11 [] |
1547 |
(map (augment_sort thy11 fs_cp_sort) fins) |
|
1548 |
(augment_sort thy11 fs_cp_sort |
|
1549 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
|
1550 |
(map (fn (((T, U), R), i) => |
|
1551 |
let |
|
1552 |
val x = Free ("x" ^ string_of_int i, T); |
|
1553 |
val y = Free ("y" ^ string_of_int i, U) |
|
1554 |
in |
|
1555 |
HOLogic.mk_imp (R $ x $ y, |
|
1556 |
finite $ (Const ("Nominal.supp", U --> aset) $ y)) |
|
1557 |
end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ |
|
1558 |
(1 upto length recTs)))))) |
|
26711 | 1559 |
(fn {prems = fins, ...} => |
1560 |
(rtac rec_induct THEN_ALL_NEW cut_facts_tac fins) 1 THEN REPEAT |
|
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1561 |
(NominalPermeq.finite_guess_tac (HOL_ss addsimps [fs_name]) 1)))) |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1562 |
end) dt_atomTs; |
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
1563 |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1564 |
(** freshness **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1565 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1566 |
val finite_premss = map (fn aT => |
22274 | 1567 |
map (fn (f, T) => HOLogic.mk_Trueprop |
1568 |
(Const ("Finite_Set.finite", HOLogic.mk_setT aT --> HOLogic.boolT) $ |
|
1569 |
(Const ("Nominal.supp", T --> HOLogic.mk_setT aT) $ f))) |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1570 |
(rec_fns ~~ rec_fn_Ts)) dt_atomTs; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1571 |
|
28731 | 1572 |
val rec_fns' = map (augment_sort thy11 fs_cp_sort) rec_fns; |
1573 |
||
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1574 |
val rec_fresh_thms = map (fn ((aT, eqvt_ths), finite_prems) => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1575 |
let |
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset
|
1576 |
val name = Long_Name.base_name (fst (dest_Type aT)); |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1577 |
val fs_name = Global_Theory.get_thm thy11 ("fs_" ^ name ^ "1"); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1578 |
val a = Free ("a", aT); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1579 |
val freshs = map (fn (f, fT) => HOLogic.mk_Trueprop |
25823 | 1580 |
(fresh_const aT fT $ a $ f)) (rec_fns ~~ rec_fn_Ts) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1581 |
in |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1582 |
map (fn (((T, U), R), eqvt_th) => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1583 |
let |
28731 | 1584 |
val x = Free ("x", augment_sort_typ thy11 fs_cp_sort T); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1585 |
val y = Free ("y", U); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1586 |
val y' = Free ("y'", U) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1587 |
in |
42361 | 1588 |
Drule.export_without_context (Goal.prove (Proof_Context.init_global thy11) [] |
28731 | 1589 |
(map (augment_sort thy11 fs_cp_sort) |
1590 |
(finite_prems @ |
|
1591 |
[HOLogic.mk_Trueprop (R $ x $ y), |
|
1592 |
HOLogic.mk_Trueprop (HOLogic.mk_all ("y'", U, |
|
1593 |
HOLogic.mk_imp (R $ x $ y', HOLogic.mk_eq (y', y)))), |
|
1594 |
HOLogic.mk_Trueprop (fresh_const aT T $ a $ x)] @ |
|
1595 |
freshs)) |
|
25823 | 1596 |
(HOLogic.mk_Trueprop (fresh_const aT U $ a $ y)) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1597 |
(fn {prems, context} => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1598 |
let |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1599 |
val (finite_prems, rec_prem :: unique_prem :: |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1600 |
fresh_prems) = chop (length finite_prems) prems; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1601 |
val unique_prem' = unique_prem RS spec RS mp; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1602 |
val unique = [unique_prem', unique_prem' RS sym] MRS trans; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1603 |
val _ $ (_ $ (_ $ S $ _)) $ _ = prop_of supports_fresh; |
28731 | 1604 |
val tuple = foldr1 HOLogic.mk_prod (x :: rec_fns') |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1605 |
in EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1606 |
[rtac (Drule.cterm_instantiate |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1607 |
[(cterm_of thy11 S, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1608 |
cterm_of thy11 (Const ("Nominal.supp", |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1609 |
fastype_of tuple --> HOLogic.mk_setT aT) $ tuple))] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1610 |
supports_fresh) 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1611 |
simp_tac (HOL_basic_ss addsimps |
36945 | 1612 |
[supports_def, Thm.symmetric fresh_def, fresh_prod]) 1, |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1613 |
REPEAT_DETERM (resolve_tac [allI, impI] 1), |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1614 |
REPEAT_DETERM (etac conjE 1), |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1615 |
rtac unique 1, |
32202 | 1616 |
SUBPROOF (fn {prems = prems', params = [(_, a), (_, b)], ...} => EVERY |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1617 |
[cut_facts_tac [rec_prem] 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1618 |
rtac (Thm.instantiate ([], |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1619 |
[(cterm_of thy11 (Var (("pi", 0), mk_permT aT)), |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1620 |
cterm_of thy11 (perm_of_pair (term_of a, term_of b)))]) eqvt_th) 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1621 |
asm_simp_tac (HOL_ss addsimps |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1622 |
(prems' @ perm_swap @ perm_fresh_fresh)) 1]) context 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1623 |
rtac rec_prem 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1624 |
simp_tac (HOL_ss addsimps (fs_name :: |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1625 |
supp_prod :: finite_Un :: finite_prems)) 1, |
36945 | 1626 |
simp_tac (HOL_ss addsimps (Thm.symmetric fresh_def :: |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1627 |
fresh_prod :: fresh_prems)) 1] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1628 |
end)) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1629 |
end) (recTs ~~ rec_result_Ts ~~ rec_sets ~~ eqvt_ths) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1630 |
end) (dt_atomTs ~~ rec_equiv_thms' ~~ finite_premss); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1631 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1632 |
(** uniqueness **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1633 |
|
21088 | 1634 |
val fun_tuple = foldr1 HOLogic.mk_prod (rec_ctxt :: rec_fns); |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1635 |
val fun_tupleT = fastype_of fun_tuple; |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1636 |
val rec_unique_frees = |
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
1637 |
Datatype_Prop.indexify_names (replicate (length recTs) "x") ~~ recTs; |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1638 |
val rec_unique_frees'' = map (fn (s, T) => (s ^ "'", T)) rec_unique_frees; |
20267 | 1639 |
val rec_unique_frees' = |
33968
f94fb13ecbb3
modernized structures and tuned headers of datatype package modules; joined former datatype.ML and datatype_rep_proofs.ML
haftmann
parents:
33957
diff
changeset
|
1640 |
Datatype_Prop.indexify_names (replicate (length recTs) "y") ~~ rec_result_Ts; |
21021 | 1641 |
val rec_unique_concls = map (fn ((x, U), R) => |
38558 | 1642 |
Const (@{const_name Ex1}, (U --> HOLogic.boolT) --> HOLogic.boolT) $ |
21021 | 1643 |
Abs ("y", U, R $ Free x $ Bound 0)) |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1644 |
(rec_unique_frees ~~ rec_result_Ts ~~ rec_sets); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1645 |
|
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1646 |
val induct_aux_rec = Drule.cterm_instantiate |
28731 | 1647 |
(map (pairself (cterm_of thy11) o apsnd (augment_sort thy11 fs_cp_sort)) |
35845
e5980f0ad025
renamed varify/unvarify operations to varify_global/unvarify_global to emphasize that these only work in a global situation;
wenzelm
parents:
35842
diff
changeset
|
1648 |
(map (fn (aT, f) => (Logic.varify_global f, Abs ("z", HOLogic.unitT, |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1649 |
Const ("Nominal.supp", fun_tupleT --> HOLogic.mk_setT aT) $ fun_tuple))) |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1650 |
fresh_fs @ |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1651 |
map (fn (((P, T), (x, U)), Q) => |
35845
e5980f0ad025
renamed varify/unvarify operations to varify_global/unvarify_global to emphasize that these only work in a global situation;
wenzelm
parents:
35842
diff
changeset
|
1652 |
(Var ((P, 0), Logic.varifyT_global (fsT' --> T --> HOLogic.boolT)), |
44241 | 1653 |
Abs ("z", HOLogic.unitT, absfree (x, U) Q))) |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1654 |
(pnames ~~ recTs ~~ rec_unique_frees ~~ rec_unique_concls) @ |
35845
e5980f0ad025
renamed varify/unvarify operations to varify_global/unvarify_global to emphasize that these only work in a global situation;
wenzelm
parents:
35842
diff
changeset
|
1655 |
map (fn (s, T) => (Var ((s, 0), Logic.varifyT_global T), Free (s, T))) |
20145
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1656 |
rec_unique_frees)) induct_aux; |
922b4e7b8efd
Started implementing uniqueness proof for recursion
berghofe
parents:
20071
diff
changeset
|
1657 |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1658 |
fun obtain_fresh_name vs ths rec_fin_supp T (freshs1, freshs2, ctxt) = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1659 |
let |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1660 |
val p = foldr1 HOLogic.mk_prod (vs @ freshs1); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1661 |
val ex = Goal.prove ctxt [] [] (HOLogic.mk_Trueprop |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1662 |
(HOLogic.exists_const T $ Abs ("x", T, |
25823 | 1663 |
fresh_const T (fastype_of p) $ Bound 0 $ p))) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1664 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1665 |
[cut_facts_tac ths 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1666 |
REPEAT_DETERM (dresolve_tac (the (AList.lookup op = rec_fin_supp T)) 1), |
21377
c29146dc14f1
replaced exists_fresh lemma with a version formulated with obtains;
urbanc
parents:
21365
diff
changeset
|
1667 |
resolve_tac exists_fresh' 1, |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1668 |
asm_simp_tac (HOL_ss addsimps (supp_prod :: finite_Un :: fs_atoms)) 1]); |
32202 | 1669 |
val (([(_, cx)], ths), ctxt') = Obtain.result |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1670 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1671 |
[etac exE 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1672 |
full_simp_tac (HOL_ss addsimps (fresh_prod :: fresh_atm)) 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1673 |
REPEAT (etac conjE 1)]) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1674 |
[ex] ctxt |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1675 |
in (freshs1 @ [term_of cx], freshs2 @ ths, ctxt') end; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1676 |
|
21088 | 1677 |
val finite_ctxt_prems = map (fn aT => |
22274 | 1678 |
HOLogic.mk_Trueprop |
1679 |
(Const ("Finite_Set.finite", HOLogic.mk_setT aT --> HOLogic.boolT) $ |
|
1680 |
(Const ("Nominal.supp", fsT' --> HOLogic.mk_setT aT) $ rec_ctxt))) dt_atomTs; |
|
21088 | 1681 |
|
45838 | 1682 |
val rec_unique_thms = Datatype_Aux.split_conj_thm (Goal.prove |
42361 | 1683 |
(Proof_Context.init_global thy11) (map fst rec_unique_frees) |
28731 | 1684 |
(map (augment_sort thy11 fs_cp_sort) |
32952 | 1685 |
(flat finite_premss @ finite_ctxt_prems @ rec_prems @ rec_prems')) |
28731 | 1686 |
(augment_sort thy11 fs_cp_sort |
1687 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj rec_unique_concls))) |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1688 |
(fn {prems, context} => |
20267 | 1689 |
let |
1690 |
val k = length rec_fns; |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1691 |
val (finite_thss, ths1) = fold_map (fn T => fn xs => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1692 |
apfst (pair T) (chop k xs)) dt_atomTs prems; |
21088 | 1693 |
val (finite_ctxt_ths, ths2) = chop (length dt_atomTs) ths1; |
1694 |
val (P_ind_ths, fcbs) = chop k ths2; |
|
45838 | 1695 |
val P_ths = map (fn th => th RS mp) (Datatype_Aux.split_conj_thm |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1696 |
(Goal.prove context |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1697 |
(map fst (rec_unique_frees'' @ rec_unique_frees')) [] |
28731 | 1698 |
(augment_sort thy11 fs_cp_sort |
1699 |
(HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj |
|
1700 |
(map (fn (((x, y), S), P) => HOLogic.mk_imp |
|
1701 |
(S $ Free x $ Free y, P $ (Free y))) |
|
1702 |
(rec_unique_frees'' ~~ rec_unique_frees' ~~ |
|
1703 |
rec_sets ~~ rec_preds))))) |
|
20267 | 1704 |
(fn _ => |
1705 |
rtac rec_induct 1 THEN |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1706 |
REPEAT ((resolve_tac P_ind_ths THEN_ALL_NEW assume_tac) 1)))); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1707 |
val rec_fin_supp_thms' = map |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1708 |
(fn (ths, (T, fin_ths)) => (T, map (curry op MRS fin_ths) ths)) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1709 |
(rec_fin_supp_thms ~~ finite_thss); |
20267 | 1710 |
in EVERY |
1711 |
([rtac induct_aux_rec 1] @ |
|
21088 | 1712 |
maps (fn ((_, finite_ths), finite_th) => |
1713 |
[cut_facts_tac (finite_th :: finite_ths) 1, |
|
1714 |
asm_simp_tac (HOL_ss addsimps [supp_prod, finite_Un]) 1]) |
|
1715 |
(finite_thss ~~ finite_ctxt_ths) @ |
|
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1716 |
maps (fn ((_, idxss), elim) => maps (fn idxs => |
36945 | 1717 |
[full_simp_tac (HOL_ss addsimps [Thm.symmetric fresh_def, supp_prod, Un_iff]) 1, |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1718 |
REPEAT_DETERM (eresolve_tac [conjE, ex1E] 1), |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1719 |
rtac ex1I 1, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1720 |
(resolve_tac rec_intrs THEN_ALL_NEW atac) 1, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1721 |
rotate_tac ~1 1, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1722 |
((DETERM o etac elim) THEN_ALL_NEW full_simp_tac |
32952 | 1723 |
(HOL_ss addsimps flat distinct_thms)) 1] @ |
21021 | 1724 |
(if null idxs then [] else [hyp_subst_tac 1, |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1725 |
SUBPROOF (fn {asms, concl, prems = prems', params, context = context', ...} => |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1726 |
let |
21021 | 1727 |
val SOME prem = find_first (can (HOLogic.dest_eq o |
1728 |
HOLogic.dest_Trueprop o prop_of)) prems'; |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1729 |
val _ $ (_ $ lhs $ rhs) = prop_of prem; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1730 |
val _ $ (_ $ lhs' $ rhs') = term_of concl; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1731 |
val rT = fastype_of lhs'; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1732 |
val (c, cargsl) = strip_comb lhs; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1733 |
val cargsl' = partition_cargs idxs cargsl; |
32952 | 1734 |
val boundsl = maps fst cargsl'; |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1735 |
val (_, cargsr) = strip_comb rhs; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1736 |
val cargsr' = partition_cargs idxs cargsr; |
32952 | 1737 |
val boundsr = maps fst cargsr'; |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1738 |
val (params1, _ :: params2) = |
32202 | 1739 |
chop (length params div 2) (map (term_of o #2) params); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1740 |
val params' = params1 @ params2; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1741 |
val rec_prems = filter (fn th => case prop_of th of |
28731 | 1742 |
_ $ p => (case head_of p of |
36692
54b64d4ad524
farewell to old-style mem infixes -- type inference in situations with mem_int and mem_string should provide enough information to resolve the type of (op =)
haftmann
parents:
36610
diff
changeset
|
1743 |
Const (s, _) => member (op =) rec_set_names s |
28731 | 1744 |
| _ => false) |
1745 |
| _ => false) prems'; |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1746 |
val fresh_prems = filter (fn th => case prop_of th of |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1747 |
_ $ (Const ("Nominal.fresh", _) $ _ $ _) => true |
38558 | 1748 |
| _ $ (Const (@{const_name Not}, _) $ _) => true |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1749 |
| _ => false) prems'; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1750 |
val Ts = map fastype_of boundsl; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1751 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1752 |
val _ = warning "step 1: obtaining fresh names"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1753 |
val (freshs1, freshs2, context'') = fold |
28731 | 1754 |
(obtain_fresh_name (rec_ctxt :: rec_fns' @ params') |
32952 | 1755 |
(maps snd finite_thss @ finite_ctxt_ths @ rec_prems) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1756 |
rec_fin_supp_thms') |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1757 |
Ts ([], [], context'); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1758 |
val pi1 = map perm_of_pair (boundsl ~~ freshs1); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1759 |
val rpi1 = rev pi1; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1760 |
val pi2 = map perm_of_pair (boundsr ~~ freshs1); |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1761 |
val rpi2 = rev pi2; |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1762 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1763 |
val fresh_prems' = mk_not_sym fresh_prems; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1764 |
val freshs2' = mk_not_sym freshs2; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1765 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1766 |
(** as, bs, cs # K as ts, K bs us **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1767 |
val _ = warning "step 2: as, bs, cs # K as ts, K bs us"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1768 |
val prove_fresh_ss = HOL_ss addsimps |
32952 | 1769 |
(finite_Diff :: flat fresh_thms @ |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1770 |
fs_atoms @ abs_fresh @ abs_supp @ fresh_atm); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1771 |
(* FIXME: avoid asm_full_simp_tac ? *) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1772 |
fun prove_fresh ths y x = Goal.prove context'' [] [] |
25823 | 1773 |
(HOLogic.mk_Trueprop (fresh_const |
1774 |
(fastype_of x) (fastype_of y) $ x $ y)) |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1775 |
(fn _ => cut_facts_tac ths 1 THEN asm_full_simp_tac prove_fresh_ss 1); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1776 |
val constr_fresh_thms = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1777 |
map (prove_fresh fresh_prems lhs) boundsl @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1778 |
map (prove_fresh fresh_prems rhs) boundsr @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1779 |
map (prove_fresh freshs2 lhs) freshs1 @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1780 |
map (prove_fresh freshs2 rhs) freshs1; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1781 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1782 |
(** pi1 o (K as ts) = pi2 o (K bs us) **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1783 |
val _ = warning "step 3: pi1 o (K as ts) = pi2 o (K bs us)"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1784 |
val pi1_pi2_eq = Goal.prove context'' [] [] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1785 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
22311 | 1786 |
(fold_rev (mk_perm []) pi1 lhs, fold_rev (mk_perm []) pi2 rhs))) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1787 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1788 |
[cut_facts_tac constr_fresh_thms 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1789 |
asm_simp_tac (HOL_basic_ss addsimps perm_fresh_fresh) 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1790 |
rtac prem 1]); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1791 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1792 |
(** pi1 o ts = pi2 o us **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1793 |
val _ = warning "step 4: pi1 o ts = pi2 o us"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1794 |
val pi1_pi2_eqs = map (fn (t, u) => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1795 |
Goal.prove context'' [] [] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1796 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
22311 | 1797 |
(fold_rev (mk_perm []) pi1 t, fold_rev (mk_perm []) pi2 u))) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1798 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1799 |
[cut_facts_tac [pi1_pi2_eq] 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1800 |
asm_full_simp_tac (HOL_ss addsimps |
32952 | 1801 |
(calc_atm @ flat perm_simps' @ |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1802 |
fresh_prems' @ freshs2' @ abs_perm @ |
32952 | 1803 |
alpha @ flat inject_thms)) 1])) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1804 |
(map snd cargsl' ~~ map snd cargsr'); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1805 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1806 |
(** pi1^-1 o pi2 o us = ts **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1807 |
val _ = warning "step 5: pi1^-1 o pi2 o us = ts"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1808 |
val rpi1_pi2_eqs = map (fn ((t, u), eq) => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1809 |
Goal.prove context'' [] [] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1810 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
22311 | 1811 |
(fold_rev (mk_perm []) (rpi1 @ pi2) u, t))) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1812 |
(fn _ => simp_tac (HOL_ss addsimps |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1813 |
((eq RS sym) :: perm_swap)) 1)) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1814 |
(map snd cargsl' ~~ map snd cargsr' ~~ pi1_pi2_eqs); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1815 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1816 |
val (rec_prems1, rec_prems2) = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1817 |
chop (length rec_prems div 2) rec_prems; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1818 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1819 |
(** (ts, pi1^-1 o pi2 o vs) in rec_set **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1820 |
val _ = warning "step 6: (ts, pi1^-1 o pi2 o vs) in rec_set"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1821 |
val rec_prems' = map (fn th => |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1822 |
let |
21021 | 1823 |
val _ $ (S $ x $ y) = prop_of th; |
28731 | 1824 |
val Const (s, _) = head_of S; |
1825 |
val k = find_index (equal s) rec_set_names; |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1826 |
val pi = rpi1 @ pi2; |
22311 | 1827 |
fun mk_pi z = fold_rev (mk_perm []) pi z; |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1828 |
fun eqvt_tac p = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1829 |
let |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1830 |
val U as Type (_, [Type (_, [T, _])]) = fastype_of p; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1831 |
val l = find_index (equal T) dt_atomTs; |
42364 | 1832 |
val th = nth (nth rec_equiv_thms' l) k; |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1833 |
val th' = Thm.instantiate ([], |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1834 |
[(cterm_of thy11 (Var (("pi", 0), U)), |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1835 |
cterm_of thy11 p)]) th; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1836 |
in rtac th' 1 end; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1837 |
val th' = Goal.prove context'' [] [] |
21021 | 1838 |
(HOLogic.mk_Trueprop (S $ mk_pi x $ mk_pi y)) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1839 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1840 |
(map eqvt_tac pi @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1841 |
[simp_tac (HOL_ss addsimps (fresh_prems' @ freshs2' @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1842 |
perm_swap @ perm_fresh_fresh)) 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1843 |
rtac th 1])) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1844 |
in |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1845 |
Simplifier.simplify |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1846 |
(HOL_basic_ss addsimps rpi1_pi2_eqs) th' |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1847 |
end) rec_prems2; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1848 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1849 |
val ihs = filter (fn th => case prop_of th of |
38558 | 1850 |
_ $ (Const (@{const_name All}, _) $ _) => true | _ => false) prems'; |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1851 |
|
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1852 |
(** pi1 o rs = pi2 o vs , rs = pi1^-1 o pi2 o vs **) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1853 |
val _ = warning "step 7: pi1 o rs = pi2 o vs , rs = pi1^-1 o pi2 o vs"; |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1854 |
val rec_eqns = map (fn (th, ih) => |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1855 |
let |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1856 |
val th' = th RS (ih RS spec RS mp) RS sym; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1857 |
val _ $ (_ $ lhs $ rhs) = prop_of th'; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1858 |
fun strip_perm (_ $ _ $ t) = strip_perm t |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1859 |
| strip_perm t = t; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1860 |
in |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1861 |
Goal.prove context'' [] [] |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1862 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
22311 | 1863 |
(fold_rev (mk_perm []) pi1 lhs, |
1864 |
fold_rev (mk_perm []) pi2 (strip_perm rhs)))) |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1865 |
(fn _ => simp_tac (HOL_basic_ss addsimps |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1866 |
(th' :: perm_swap)) 1) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1867 |
end) (rec_prems' ~~ ihs); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1868 |
|
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1869 |
(** as # rs **) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1870 |
val _ = warning "step 8: as # rs"; |
32952 | 1871 |
val rec_freshs = |
1872 |
maps (fn (rec_prem, ih) => |
|
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1873 |
let |
21021 | 1874 |
val _ $ (S $ x $ (y as Free (_, T))) = |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1875 |
prop_of rec_prem; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1876 |
val k = find_index (equal S) rec_sets; |
32952 | 1877 |
val atoms = flat (map_filter (fn (bs, z) => |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1878 |
if z = x then NONE else SOME bs) cargsl') |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1879 |
in |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1880 |
map (fn a as Free (_, aT) => |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1881 |
let val l = find_index (equal aT) dt_atomTs; |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1882 |
in |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1883 |
Goal.prove context'' [] [] |
25823 | 1884 |
(HOLogic.mk_Trueprop (fresh_const aT T $ a $ y)) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1885 |
(fn _ => EVERY |
42364 | 1886 |
(rtac (nth (nth rec_fresh_thms l) k) 1 :: |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1887 |
map (fn th => rtac th 1) |
42364 | 1888 |
(snd (nth finite_thss l)) @ |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1889 |
[rtac rec_prem 1, rtac ih 1, |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1890 |
REPEAT_DETERM (resolve_tac fresh_prems 1)])) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1891 |
end) atoms |
32952 | 1892 |
end) (rec_prems1 ~~ ihs); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1893 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1894 |
(** as # fK as ts rs , bs # fK bs us vs **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1895 |
val _ = warning "step 9: as # fK as ts rs , bs # fK bs us vs"; |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1896 |
fun prove_fresh_result (a as Free (_, aT)) = |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1897 |
Goal.prove context'' [] [] |
25823 | 1898 |
(HOLogic.mk_Trueprop (fresh_const aT rT $ a $ rhs')) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1899 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1900 |
[resolve_tac fcbs 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1901 |
REPEAT_DETERM (resolve_tac |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1902 |
(fresh_prems @ rec_freshs) 1), |
20411
dd8a1cda2eaf
Added premises concerning finite support of recursion results to FCBs.
berghofe
parents:
20397
diff
changeset
|
1903 |
REPEAT_DETERM (resolve_tac (maps snd rec_fin_supp_thms') 1 |
dd8a1cda2eaf
Added premises concerning finite support of recursion results to FCBs.
berghofe
parents:
20397
diff
changeset
|
1904 |
THEN resolve_tac rec_prems 1), |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1905 |
resolve_tac P_ind_ths 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1906 |
REPEAT_DETERM (resolve_tac (P_ths @ rec_prems) 1)]); |
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
1907 |
|
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1908 |
val fresh_results'' = map prove_fresh_result boundsl; |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1909 |
|
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1910 |
fun prove_fresh_result'' ((a as Free (_, aT), b), th) = |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1911 |
let val th' = Goal.prove context'' [] [] |
25823 | 1912 |
(HOLogic.mk_Trueprop (fresh_const aT rT $ |
22311 | 1913 |
fold_rev (mk_perm []) (rpi2 @ pi1) a $ |
1914 |
fold_rev (mk_perm []) (rpi2 @ pi1) rhs')) |
|
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1915 |
(fn _ => simp_tac (HOL_ss addsimps fresh_bij) 1 THEN |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1916 |
rtac th 1) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1917 |
in |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1918 |
Goal.prove context'' [] [] |
25823 | 1919 |
(HOLogic.mk_Trueprop (fresh_const aT rT $ b $ lhs')) |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1920 |
(fn _ => EVERY |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1921 |
[cut_facts_tac [th'] 1, |
35232
f588e1169c8b
renamed Simplifier.theory_context to Simplifier.global_context to emphasize that this is not the real thing;
wenzelm
parents:
35021
diff
changeset
|
1922 |
full_simp_tac (Simplifier.global_context thy11 HOL_ss |
25998
f38dc602a926
Tuned uniqueness proof for recursion combinator.
berghofe
parents:
25985
diff
changeset
|
1923 |
addsimps rec_eqns @ pi1_pi2_eqs @ perm_swap |
f38dc602a926
Tuned uniqueness proof for recursion combinator.
berghofe
parents:
25985
diff
changeset
|
1924 |
addsimprocs [NominalPermeq.perm_simproc_app]) 1, |
21073
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1925 |
full_simp_tac (HOL_ss addsimps (calc_atm @ |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1926 |
fresh_prems' @ freshs2' @ perm_fresh_fresh)) 1]) |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1927 |
end; |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1928 |
|
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1929 |
val fresh_results = fresh_results'' @ map prove_fresh_result'' |
be0a17371ba6
Proof of "bs # fK bs us vs" no longer depends on FCBs.
berghofe
parents:
21055
diff
changeset
|
1930 |
(boundsl ~~ boundsr ~~ fresh_results''); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1931 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1932 |
(** cs # fK as ts rs , cs # fK bs us vs **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1933 |
val _ = warning "step 10: cs # fK as ts rs , cs # fK bs us vs"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1934 |
fun prove_fresh_result' recs t (a as Free (_, aT)) = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1935 |
Goal.prove context'' [] [] |
25823 | 1936 |
(HOLogic.mk_Trueprop (fresh_const aT rT $ a $ t)) |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1937 |
(fn _ => EVERY |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1938 |
[cut_facts_tac recs 1, |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1939 |
REPEAT_DETERM (dresolve_tac |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1940 |
(the (AList.lookup op = rec_fin_supp_thms' aT)) 1), |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1941 |
NominalPermeq.fresh_guess_tac |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1942 |
(HOL_ss addsimps (freshs2 @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1943 |
fs_atoms @ fresh_atm @ |
32952 | 1944 |
maps snd finite_thss)) 1]); |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1945 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1946 |
val fresh_results' = |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1947 |
map (prove_fresh_result' rec_prems1 rhs') freshs1 @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1948 |
map (prove_fresh_result' rec_prems2 lhs') freshs1; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1949 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1950 |
(** pi1 o (fK as ts rs) = pi2 o (fK bs us vs) **) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1951 |
val _ = warning "step 11: pi1 o (fK as ts rs) = pi2 o (fK bs us vs)"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1952 |
val pi1_pi2_result = Goal.prove context'' [] [] |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1953 |
(HOLogic.mk_Trueprop (HOLogic.mk_eq |
22311 | 1954 |
(fold_rev (mk_perm []) pi1 rhs', fold_rev (mk_perm []) pi2 lhs'))) |
27450
d45d2850aaed
Replaced all but one occurrence of perm_simp_tac by perm_simproc_app,
berghofe
parents:
27300
diff
changeset
|
1955 |
(fn _ => simp_tac (Simplifier.context context'' HOL_ss |
d45d2850aaed
Replaced all but one occurrence of perm_simp_tac by perm_simproc_app,
berghofe
parents:
27300
diff
changeset
|
1956 |
addsimps pi1_pi2_eqs @ rec_eqns |
d45d2850aaed
Replaced all but one occurrence of perm_simp_tac by perm_simproc_app,
berghofe
parents:
27300
diff
changeset
|
1957 |
addsimprocs [NominalPermeq.perm_simproc_app]) 1 THEN |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1958 |
TRY (simp_tac (HOL_ss addsimps |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1959 |
(fresh_prems' @ freshs2' @ calc_atm @ perm_fresh_fresh)) 1)); |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1960 |
|
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1961 |
val _ = warning "final result"; |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1962 |
val final = Goal.prove context'' [] [] (term_of concl) |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1963 |
(fn _ => cut_facts_tac [pi1_pi2_result RS sym] 1 THEN |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1964 |
full_simp_tac (HOL_basic_ss addsimps perm_fresh_fresh @ |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1965 |
fresh_results @ fresh_results') 1); |
42361 | 1966 |
val final' = Proof_Context.export context'' context' [final]; |
20376
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1967 |
val _ = warning "finished!" |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1968 |
in |
53b31f7c1d87
Finished implementation of uniqueness proof for recursion combinator.
berghofe
parents:
20267
diff
changeset
|
1969 |
resolve_tac final' 1 |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1970 |
end) context 1])) idxss) (ndescr ~~ rec_elims)) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1971 |
end)); |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1972 |
|
46161 | 1973 |
val rec_total_thms = map (fn r => r RS @{thm theI'}) rec_unique_thms; |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1974 |
|
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1975 |
(* define primrec combinators *) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1976 |
|
45701 | 1977 |
val big_reccomb_name = space_implode "_" new_type_names ^ "_rec"; |
28965 | 1978 |
val reccomb_names = map (Sign.full_bname thy11) |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1979 |
(if length descr'' = 1 then [big_reccomb_name] else |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1980 |
(map ((curry (op ^) (big_reccomb_name ^ "_")) o string_of_int) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1981 |
(1 upto (length descr'')))); |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1982 |
val reccombs = map (fn ((name, T), T') => list_comb |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1983 |
(Const (name, rec_fn_Ts @ [T] ---> T'), rec_fns)) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1984 |
(reccomb_names ~~ recTs ~~ rec_result_Ts); |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1985 |
|
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1986 |
val (reccomb_defs, thy12) = |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1987 |
thy11 |
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24459
diff
changeset
|
1988 |
|> Sign.add_consts_i (map (fn ((name, T), T') => |
30364
577edc39b501
moved basic algebra of long names from structure NameSpace to Long_Name;
wenzelm
parents:
30345
diff
changeset
|
1989 |
(Binding.name (Long_Name.base_name name), rec_fn_Ts @ [T] ---> T', NoSyn)) |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1990 |
(reccomb_names ~~ recTs ~~ rec_result_Ts)) |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
1991 |
|> (Global_Theory.add_defs false o map Thm.no_attributes) (map (fn ((((name, comb), set), T), T') => |
44241 | 1992 |
(Binding.name (Long_Name.base_name name ^ "_def"), Logic.mk_equals (comb, absfree ("x", T) |
1993 |
(Const (@{const_name The}, (T' --> HOLogic.boolT) --> T') $ absfree ("y", T') |
|
1994 |
(set $ Free ("x", T) $ Free ("y", T')))))) |
|
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1995 |
(reccomb_names ~~ reccombs ~~ rec_sets ~~ recTs ~~ rec_result_Ts)); |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1996 |
|
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1997 |
(* prove characteristic equations for primrec combinators *) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1998 |
|
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
1999 |
val rec_thms = map (fn (prems, concl) => |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2000 |
let |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2001 |
val _ $ (_ $ (_ $ x) $ _) = concl; |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2002 |
val (_, cargs) = strip_comb x; |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2003 |
val ps = map (fn (x as Free (_, T), i) => |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2004 |
(Free ("x" ^ string_of_int i, T), x)) (cargs ~~ (1 upto length cargs)); |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2005 |
val concl' = subst_atomic_types (rec_result_Ts' ~~ rec_result_Ts) concl; |
32952 | 2006 |
val prems' = flat finite_premss @ finite_ctxt_prems @ |
21088 | 2007 |
rec_prems @ rec_prems' @ map (subst_atomic ps) prems; |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2008 |
fun solve rules prems = resolve_tac rules THEN_ALL_NEW |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2009 |
(resolve_tac prems THEN_ALL_NEW atac) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2010 |
in |
28731 | 2011 |
Goal.prove_global thy12 [] |
2012 |
(map (augment_sort thy12 fs_cp_sort) prems') |
|
2013 |
(augment_sort thy12 fs_cp_sort concl') |
|
26711 | 2014 |
(fn {prems, ...} => EVERY |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2015 |
[rewrite_goals_tac reccomb_defs, |
46161 | 2016 |
rtac @{thm the1_equality} 1, |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2017 |
solve rec_unique_thms prems 1, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2018 |
resolve_tac rec_intrs 1, |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2019 |
REPEAT (solve (prems @ rec_total_thms) prems 1)]) |
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2020 |
end) (rec_eq_prems ~~ |
45879
71b8d0d170b1
avoid fragile Sign.intern_const -- pass internal names directly;
wenzelm
parents:
45863
diff
changeset
|
2021 |
Datatype_Prop.make_primrecs reccomb_names descr' thy12); |
21365
4ee8e2702241
InductivePackage.add_inductive_i: canonical argument order;
wenzelm
parents:
21291
diff
changeset
|
2022 |
|
45822 | 2023 |
val dt_infos = map_index (make_dt_info pdescr induct reccomb_names rec_thms) |
33063 | 2024 |
(descr1 ~~ distinct_thms ~~ inject_thms); |
21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset
|
2025 |
|
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
2026 |
(* FIXME: theorems are stored in database for testing only *) |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2027 |
val (_, thy13) = thy12 |> |
39557
fe5722fce758
renamed structure PureThy to Pure_Thy and moved most content to Global_Theory, to emphasize that this is global-only;
wenzelm
parents:
39159
diff
changeset
|
2028 |
Global_Theory.add_thmss |
32952 | 2029 |
[((Binding.name "rec_equiv", flat rec_equiv_thms), []), |
2030 |
((Binding.name "rec_equiv'", flat rec_equiv_thms'), []), |
|
2031 |
((Binding.name "rec_fin_supp", flat rec_fin_supp_thms), []), |
|
2032 |
((Binding.name "rec_fresh", flat rec_fresh_thms), []), |
|
35021
c839a4c670c6
renamed old-style Drule.standard to Drule.export_without_context, to emphasize that this is in no way a standard operation;
wenzelm
parents:
33968
diff
changeset
|
2033 |
((Binding.name "rec_unique", map Drule.export_without_context rec_unique_thms), []), |
29585 | 2034 |
((Binding.name "recs", rec_thms), [])] ||> |
24712
64ed05609568
proper Sign operations instead of Theory aliases;
wenzelm
parents:
24459
diff
changeset
|
2035 |
Sign.parent_path ||> |
21540
f3faed8276e6
Additional information about nominal datatypes (descriptor,
berghofe
parents:
21516
diff
changeset
|
2036 |
map_nominal_datatypes (fold Symtab.update dt_infos); |
19985
d39c554cf750
Implemented proofs of equivariance and finite support
berghofe
parents:
19874
diff
changeset
|
2037 |
|
17870 | 2038 |
in |
20397
243293620225
- Fixed bug that caused uniqueness proof for recursion
berghofe
parents:
20376
diff
changeset
|
2039 |
thy13 |
17870 | 2040 |
end; |
2041 |
||
45863 | 2042 |
val nominal_datatype = gen_nominal_datatype Datatype.check_specs; |
2043 |
val nominal_datatype_cmd = gen_nominal_datatype Datatype.read_specs; |
|
17870 | 2044 |
|
24867 | 2045 |
val _ = |
45863 | 2046 |
Outer_Syntax.command "nominal_datatype" "define nominal datatypes" Keyword.thy_decl |
2047 |
(Parse.and_list1 Datatype.spec_cmd >> |
|
2048 |
(Toplevel.theory o nominal_datatype_cmd Datatype.default_config)); |
|
17870 | 2049 |
|
18261
1318955d57ac
Corrected treatment of non-recursive abstraction types.
berghofe
parents:
18246
diff
changeset
|
2050 |
end |