diff -r 4b0563bc4b03 -r 7d8949da7d99 Quot/Nominal/Perm.thy --- a/Quot/Nominal/Perm.thy Wed Feb 24 17:32:43 2010 +0100 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,147 +0,0 @@ -theory Perm -imports "Nominal2_Atoms" -begin - -ML {* - open Datatype_Aux; (* typ_of_dtyp, DtRec, ... *) - fun permute ty = Const (@{const_name permute}, @{typ perm} --> ty --> ty); - val minus_perm = Const (@{const_name minus}, @{typ perm} --> @{typ perm}); -*} - -ML {* -fun prove_perm_empty lthy induct perm_def perm_frees = -let - val perm_types = map fastype_of perm_frees; - val perm_indnames = Datatype_Prop.make_tnames (map body_type perm_types); - val gl = - HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj - (map (fn ((perm, T), x) => HOLogic.mk_eq - (perm $ @{term "0 :: perm"} $ Free (x, T), - Free (x, T))) - (perm_frees ~~ - map body_type perm_types ~~ perm_indnames))); - fun tac _ = - EVERY [ - indtac induct perm_indnames 1, - ALLGOALS (asm_full_simp_tac (HOL_ss addsimps (@{thm permute_zero} :: perm_def))) - ]; -in - split_conj_thm (Goal.prove lthy perm_indnames [] gl tac) -end; -*} - -ML {* -fun prove_perm_append lthy induct perm_def perm_frees = -let - val add_perm = @{term "op + :: (perm \ perm \ perm)"} - val pi1 = Free ("pi1", @{typ perm}); - val pi2 = Free ("pi2", @{typ perm}); - val perm_types = map fastype_of perm_frees - val perm_indnames = Datatype_Prop.make_tnames (map body_type perm_types); - val gl = - (HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj - (map (fn ((perm, T), x) => - let - val lhs = perm $ (add_perm $ pi1 $ pi2) $ Free (x, T) - val rhs = perm $ pi1 $ (perm $ pi2 $ Free (x, T)) - in HOLogic.mk_eq (lhs, rhs) - end) - (perm_frees ~~ map body_type perm_types ~~ perm_indnames)))) - fun tac _ = - EVERY [ - indtac induct perm_indnames 1, - ALLGOALS (asm_full_simp_tac (HOL_ss addsimps (@{thm permute_plus} :: perm_def))) - ] -in - split_conj_thm (Goal.prove lthy ("pi1" :: "pi2" :: perm_indnames) [] gl tac) -end; -*} - -ML {* -(* TODO: full_name can be obtained from new_type_names with Datatype *) -fun define_raw_perms new_type_names full_tnames thy = -let - val {descr, induct, ...} = Datatype.the_info thy (hd full_tnames); - (* TODO: [] should be the sorts that we'll take from the specification *) - val sorts = []; - fun nth_dtyp i = typ_of_dtyp descr sorts (DtRec i); - val perm_names' = Datatype_Prop.indexify_names (map (fn (i, _) => - "permute_" ^ name_of_typ (nth_dtyp i)) descr); - val perm_types = map (fn (i, _) => - let val T = nth_dtyp i - in @{typ perm} --> T --> T end) descr; - val perm_names_types' = perm_names' ~~ perm_types; - val pi = Free ("pi", @{typ perm}); - fun perm_eq_constr i (cname, dts) = - let - val Ts = map (typ_of_dtyp descr sorts) dts; - val names = Name.variant_list ["pi"] (Datatype_Prop.make_tnames Ts); - val args = map Free (names ~~ Ts); - val c = Const (cname, Ts ---> (nth_dtyp i)); - fun perm_arg (dt, x) = - let val T = type_of x - in - if is_rec_type dt then - let val (Us, _) = strip_type T - in list_abs (map (pair "x") Us, - Free (nth perm_names_types' (body_index dt)) $ pi $ - list_comb (x, map (fn (i, U) => - (permute U) $ (minus_perm $ pi) $ Bound i) - ((length Us - 1 downto 0) ~~ Us))) - end - else (permute T) $ pi $ x - end; - in - (Attrib.empty_binding, HOLogic.mk_Trueprop (HOLogic.mk_eq - (Free (nth perm_names_types' i) $ - Free ("pi", @{typ perm}) $ list_comb (c, args), - list_comb (c, map perm_arg (dts ~~ args))))) - end; - fun perm_eq (i, (_, _, constrs)) = map (perm_eq_constr i) constrs; - val perm_eqs = maps perm_eq descr; - val lthy = - Theory_Target.instantiation (full_tnames, [], @{sort pt}) thy; - (* TODO: Use the version of prmrec that gives the names explicitely. *) - val ((_, perm_ldef), lthy') = - Primrec.add_primrec - (map (fn s => (Binding.name s, NONE, NoSyn)) perm_names') perm_eqs lthy; - val perm_frees = - (distinct (op =)) (map (fst o strip_comb o fst o HOLogic.dest_eq o HOLogic.dest_Trueprop o prop_of) perm_ldef); - val perm_empty_thms = List.take (prove_perm_empty lthy' induct perm_ldef perm_frees, length new_type_names); - val perm_append_thms = List.take (prove_perm_append lthy' induct perm_ldef perm_frees, length new_type_names) - val perms_name = space_implode "_" perm_names' - val perms_zero_bind = Binding.name (perms_name ^ "_zero") - val perms_append_bind = Binding.name (perms_name ^ "_append") - fun tac _ perm_thms = - (Class.intro_classes_tac []) THEN (ALLGOALS ( - simp_tac (HOL_ss addsimps perm_thms - ))); - fun morphism phi = map (Morphism.thm phi); - in - lthy' - |> snd o (Local_Theory.note ((perms_zero_bind, []), perm_empty_thms)) - |> snd o (Local_Theory.note ((perms_append_bind, []), perm_append_thms)) - |> Class_Target.prove_instantiation_exit_result morphism tac (perm_empty_thms @ perm_append_thms) - end - -*} - -(* Test -atom_decl name - -datatype rtrm1 = - rVr1 "name" -| rAp1 "rtrm1" "rtrm1 list" -| rLm1 "name" "rtrm1" -| rLt1 "bp" "rtrm1" "rtrm1" -and bp = - BUnit -| BVr "name" -| BPr "bp" "bp" - - -setup {* snd o define_raw_perms ["rtrm1", "bp"] ["Perm.rtrm1", "Perm.bp"] *} -print_theorems -*) - -end