# HG changeset patch # User blanchet # Date 1514973989 -3600 # Node ID ac0b81ca3ed5955318ef55f80b673622e3297f69 # Parent cb96edae56efade8075acf62b5544cf302e09789 removed old 'add_datatype' ML functions diff -r cb96edae56ef -r ac0b81ca3ed5 src/HOL/Tools/Old_Datatype/old_datatype.ML --- a/src/HOL/Tools/Old_Datatype/old_datatype.ML Wed Jan 03 11:06:13 2018 +0100 +++ b/src/HOL/Tools/Old_Datatype/old_datatype.ML Wed Jan 03 11:06:29 2018 +0100 @@ -1,10 +1,7 @@ (* Title: HOL/Tools/Old_Datatype/old_datatype.ML Author: Stefan Berghofer, TU Muenchen -Datatype package: definitional introduction of datatypes -with proof of characteristic theorems: injectivity / distinctness -of constructors and induction. Main interface to datatypes -after full bootstrap of datatype package. +Pieces left from the old datatype package. *) signature OLD_DATATYPE = @@ -16,669 +13,16 @@ (binding * (string * string option) list * mixfix) * (binding * string list * mixfix) list val read_specs: spec_cmd list -> theory -> spec list * Proof.context val check_specs: spec list -> theory -> spec list * Proof.context - val add_datatype: config -> spec list -> theory -> string list * theory - val add_datatype_cmd: config -> spec_cmd list -> theory -> string list * theory end; structure Old_Datatype : OLD_DATATYPE = struct -(** auxiliary **) - val distinct_lemma = @{lemma "f x \ f y ==> x \ y" by iprover}; -val (_ $ (_ $ (_ $ (distinct_f $ _) $ _))) = hd (Thm.prems_of distinct_lemma); - -fun exh_thm_of (dt_info : Old_Datatype_Aux.info Symtab.table) tname = - #exhaust (the (Symtab.lookup dt_info tname)); - -val In0_inject = @{thm In0_inject}; -val In1_inject = @{thm In1_inject}; -val Scons_inject = @{thm Scons_inject}; -val Leaf_inject = @{thm Leaf_inject}; -val In0_eq = @{thm In0_eq}; -val In1_eq = @{thm In1_eq}; -val In0_not_In1 = @{thm In0_not_In1}; -val In1_not_In0 = @{thm In1_not_In0}; -val Lim_inject = @{thm Lim_inject}; -val Inl_inject = @{thm Inl_inject}; -val Inr_inject = @{thm Inr_inject}; -val Suml_inject = @{thm Suml_inject}; -val Sumr_inject = @{thm Sumr_inject}; - -val datatype_injI = - @{lemma "(\x. \y. f x = f y \ x = y) \ inj f" by (simp add: inj_on_def)}; - - -(** proof of characteristic theorems **) - -fun representation_proofs (config : Old_Datatype_Aux.config) - (dt_info : Old_Datatype_Aux.info Symtab.table) descr types_syntax constr_syntax case_names_induct - thy = - let - val descr' = flat descr; - val new_type_names = map (Binding.name_of o fst) types_syntax; - val big_name = space_implode "_" new_type_names; - val thy1 = Sign.add_path big_name thy; - val big_rec_name = "rep_set_" ^ big_name; - val rep_set_names' = - if length descr' = 1 then [big_rec_name] - else map (prefix (big_rec_name ^ "_") o string_of_int) (1 upto length descr'); - val rep_set_names = map (Sign.full_bname thy1) rep_set_names'; - - val tyvars = map (fn (_, (_, Ts, _)) => map Old_Datatype_Aux.dest_DtTFree Ts) (hd descr); - val leafTs' = Old_Datatype_Aux.get_nonrec_types descr'; - val branchTs = Old_Datatype_Aux.get_branching_types descr'; - val branchT = - if null branchTs then HOLogic.unitT - else Balanced_Tree.make (fn (T, U) => Type (@{type_name Sum_Type.sum}, [T, U])) branchTs; - val arities = remove (op =) 0 (Old_Datatype_Aux.get_arities descr'); - val unneeded_vars = - subtract (op =) (fold Term.add_tfreesT (leafTs' @ branchTs) []) (hd tyvars); - val leafTs = leafTs' @ map TFree unneeded_vars; - val recTs = Old_Datatype_Aux.get_rec_types descr'; - val (newTs, oldTs) = chop (length (hd descr)) recTs; - val sumT = - if null leafTs then HOLogic.unitT - else Balanced_Tree.make (fn (T, U) => Type (@{type_name Sum_Type.sum}, [T, U])) leafTs; - val Univ_elT = HOLogic.mk_setT (Type (@{type_name Old_Datatype.node}, [sumT, branchT])); - val UnivT = HOLogic.mk_setT Univ_elT; - val UnivT' = Univ_elT --> HOLogic.boolT; - val Collect = Const (@{const_name Collect}, UnivT' --> UnivT); - - val In0 = Const (@{const_name Old_Datatype.In0}, Univ_elT --> Univ_elT); - val In1 = Const (@{const_name Old_Datatype.In1}, Univ_elT --> Univ_elT); - val Leaf = Const (@{const_name Old_Datatype.Leaf}, sumT --> Univ_elT); - val Lim = Const (@{const_name Old_Datatype.Lim}, (branchT --> Univ_elT) --> Univ_elT); - - (* make injections needed for embedding types in leaves *) - - fun mk_inj T' x = - let - fun mk_inj' T n i = - if n = 1 then x - else - let - val n2 = n div 2; - val Type (_, [T1, T2]) = T; - in - if i <= n2 - then Const (@{const_name Inl}, T1 --> T) $ mk_inj' T1 n2 i - else Const (@{const_name Inr}, T2 --> T) $ mk_inj' T2 (n - n2) (i - n2) - end; - in mk_inj' sumT (length leafTs) (1 + find_index (fn T'' => T'' = T') leafTs) end; - - (* make injections for constructors *) - - fun mk_univ_inj ts = Balanced_Tree.access - {left = fn t => In0 $ t, - right = fn t => In1 $ t, - init = - if ts = [] then Const (@{const_name undefined}, Univ_elT) - else foldr1 (HOLogic.mk_binop @{const_name Old_Datatype.Scons}) ts}; - - (* function spaces *) - - fun mk_fun_inj T' x = - let - fun mk_inj T n i = - if n = 1 then x - else - let - val n2 = n div 2; - val Type (_, [T1, T2]) = T; - fun mkT U = (U --> Univ_elT) --> T --> Univ_elT; - in - if i <= n2 then Const (@{const_name Sum_Type.Suml}, mkT T1) $ mk_inj T1 n2 i - else Const (@{const_name Sum_Type.Sumr}, mkT T2) $ mk_inj T2 (n - n2) (i - n2) - end; - in mk_inj branchT (length branchTs) (1 + find_index (fn T'' => T'' = T') branchTs) end; - - fun mk_lim t Ts = fold_rev (fn T => fn t => Lim $ mk_fun_inj T (Abs ("x", T, t))) Ts t; - - (************** generate introduction rules for representing set **********) - - val _ = Old_Datatype_Aux.message config "Constructing representing sets ..."; - - (* make introduction rule for a single constructor *) - - fun make_intr s n (i, (_, cargs)) = - let - fun mk_prem dt (j, prems, ts) = - (case Old_Datatype_Aux.strip_dtyp dt of - (dts, Old_Datatype_Aux.DtRec k) => - let - val Ts = map (Old_Datatype_Aux.typ_of_dtyp descr') dts; - val free_t = - Old_Datatype_Aux.app_bnds (Old_Datatype_Aux.mk_Free "x" (Ts ---> Univ_elT) j) - (length Ts) - in - (j + 1, Logic.list_all (map (pair "x") Ts, - HOLogic.mk_Trueprop - (Free (nth rep_set_names' k, UnivT') $ free_t)) :: prems, - mk_lim free_t Ts :: ts) - end - | _ => - let val T = Old_Datatype_Aux.typ_of_dtyp descr' dt - in (j + 1, prems, (Leaf $ mk_inj T (Old_Datatype_Aux.mk_Free "x" T j)) :: ts) end); - - val (_, prems, ts) = fold_rev mk_prem cargs (1, [], []); - val concl = HOLogic.mk_Trueprop (Free (s, UnivT') $ mk_univ_inj ts n i); - in Logic.list_implies (prems, concl) end; - - val intr_ts = maps (fn ((_, (_, _, constrs)), rep_set_name) => - map (make_intr rep_set_name (length constrs)) - ((1 upto length constrs) ~~ constrs)) (descr' ~~ rep_set_names'); - - val ({raw_induct = rep_induct, intrs = rep_intrs, ...}, thy2) = - thy1 - |> Sign.concealed - |> Inductive.add_inductive_global - {quiet_mode = #quiet config, verbose = false, alt_name = Binding.name big_rec_name, - coind = false, no_elim = true, no_ind = false, skip_mono = true} - (map (fn s => ((Binding.name s, UnivT'), NoSyn)) rep_set_names') [] - (map (fn x => (Binding.empty_atts, x)) intr_ts) [] - ||> Sign.restore_naming thy1; - - (********************************* typedef ********************************) - - val (typedefs, thy3) = thy2 - |> Sign.parent_path - |> fold_map - (fn (((name, mx), tvs), c) => - Typedef.add_typedef_global {overloaded = false} (name, tvs, mx) - (Collect $ Const (c, UnivT')) NONE - (fn ctxt => - resolve_tac ctxt [exI] 1 THEN - resolve_tac ctxt [CollectI] 1 THEN - QUIET_BREADTH_FIRST (has_fewer_prems 1) - (resolve_tac ctxt rep_intrs 1))) - (types_syntax ~~ tyvars ~~ take (length newTs) rep_set_names) - ||> Sign.add_path big_name; - - (*********************** definition of constructors ***********************) - - val big_rep_name = big_name ^ "_Rep_"; - val rep_names' = map (fn i => big_rep_name ^ string_of_int i) (1 upto length (flat (tl descr))); - val all_rep_names = - map (#Rep_name o #1 o #2) typedefs @ - map (Sign.full_bname thy3) rep_names'; - - (* isomorphism declarations *) - - val iso_decls = map (fn (T, s) => (Binding.name s, T --> Univ_elT, NoSyn)) - (oldTs ~~ rep_names'); - - (* constructor definitions *) - - fun make_constr_def (typedef: Typedef.info) T n - ((cname, cargs), (cname', mx)) (thy, defs, eqns, i) = - let - fun constr_arg dt (j, l_args, r_args) = - let - val T = Old_Datatype_Aux.typ_of_dtyp descr' dt; - val free_t = Old_Datatype_Aux.mk_Free "x" T j; - in - (case (Old_Datatype_Aux.strip_dtyp dt, strip_type T) of - ((_, Old_Datatype_Aux.DtRec m), (Us, U)) => - (j + 1, free_t :: l_args, mk_lim - (Const (nth all_rep_names m, U --> Univ_elT) $ - Old_Datatype_Aux.app_bnds free_t (length Us)) Us :: r_args) - | _ => (j + 1, free_t :: l_args, (Leaf $ mk_inj T free_t) :: r_args)) - end; - - val (_, l_args, r_args) = fold_rev constr_arg cargs (1, [], []); - val constrT = map (Old_Datatype_Aux.typ_of_dtyp descr') cargs ---> T; - val ({Abs_name, Rep_name, ...}, _) = typedef; - val lhs = list_comb (Const (cname, constrT), l_args); - val rhs = mk_univ_inj r_args n i; - val def = Logic.mk_equals (lhs, Const (Abs_name, Univ_elT --> T) $ rhs); - val def_name = Thm.def_name (Long_Name.base_name cname); - val eqn = - HOLogic.mk_Trueprop (HOLogic.mk_eq (Const (Rep_name, T --> Univ_elT) $ lhs, rhs)); - val ([def_thm], thy') = - thy - |> Sign.add_consts [(cname', constrT, mx)] - |> (Global_Theory.add_defs false o map Thm.no_attributes) [(Binding.name def_name, def)]; - - in (thy', defs @ [def_thm], eqns @ [eqn], i + 1) end; - - (* constructor definitions for datatype *) - - fun dt_constr_defs (((((_, (_, _, constrs)), tname), typedef: Typedef.info), T), constr_syntax) - (thy, defs, eqns, rep_congs, dist_lemmas) = - let - val ctxt = Proof_Context.init_global thy; - val _ $ (_ $ (cong_f $ _) $ _) = Thm.concl_of arg_cong; - val rep_const = Thm.cterm_of ctxt (Const (#Rep_name (#1 typedef), T --> Univ_elT)); - val cong' = infer_instantiate ctxt [(#1 (dest_Var cong_f), rep_const)] arg_cong; - val dist = infer_instantiate ctxt [(#1 (dest_Var distinct_f), rep_const)] distinct_lemma; - val (thy', defs', eqns', _) = - fold (make_constr_def typedef T (length constrs)) - (constrs ~~ constr_syntax) (Sign.add_path tname thy, defs, [], 1); - in - (Sign.parent_path thy', defs', eqns @ [eqns'], - rep_congs @ [cong'], dist_lemmas @ [dist]) - end; - - val (thy4, constr_defs, constr_rep_eqns, rep_congs, dist_lemmas) = - fold dt_constr_defs - (hd descr ~~ new_type_names ~~ map #2 typedefs ~~ newTs ~~ constr_syntax) - (thy3 |> Sign.add_consts iso_decls |> Sign.parent_path, [], [], [], []); - - - (*********** isomorphisms for new types (introduced by typedef) ***********) - - val _ = Old_Datatype_Aux.message config "Proving isomorphism properties ..."; - - val collect_simp = rewrite_rule (Proof_Context.init_global thy4) [mk_meta_eq mem_Collect_eq]; - - val newT_iso_axms = typedefs |> map (fn (_, (_, {Abs_inverse, Rep_inverse, Rep, ...})) => - (collect_simp Abs_inverse, Rep_inverse, collect_simp Rep)); - - val newT_iso_inj_thms = typedefs |> map (fn (_, (_, {Abs_inject, Rep_inject, ...})) => - (collect_simp Abs_inject RS iffD1, Rep_inject RS iffD1)); - - (********* isomorphisms between existing types and "unfolded" types *******) - - (*---------------------------------------------------------------------*) - (* isomorphisms are defined using primrec-combinators: *) - (* generate appropriate functions for instantiating primrec-combinator *) - (* *) - (* e.g. Rep_dt_i = list_rec ... (%h t y. In1 (Scons (Leaf h) y)) *) - (* *) - (* also generate characteristic equations for isomorphisms *) - (* *) - (* e.g. Rep_dt_i (cons h t) = In1 (Scons (Rep_dt_j h) (Rep_dt_i t)) *) - (*---------------------------------------------------------------------*) - - fun make_iso_def k ks n (cname, cargs) (fs, eqns, i) = - let - val argTs = map (Old_Datatype_Aux.typ_of_dtyp descr') cargs; - val T = nth recTs k; - val rep_const = Const (nth all_rep_names k, T --> Univ_elT); - val constr = Const (cname, argTs ---> T); - - fun process_arg ks' dt (i2, i2', ts, Ts) = - let - val T' = Old_Datatype_Aux.typ_of_dtyp descr' dt; - val (Us, U) = strip_type T' - in - (case Old_Datatype_Aux.strip_dtyp dt of - (_, Old_Datatype_Aux.DtRec j) => - if member (op =) ks' j then - (i2 + 1, i2' + 1, ts @ [mk_lim (Old_Datatype_Aux.app_bnds - (Old_Datatype_Aux.mk_Free "y" (Us ---> Univ_elT) i2') (length Us)) Us], - Ts @ [Us ---> Univ_elT]) - else - (i2 + 1, i2', ts @ [mk_lim - (Const (nth all_rep_names j, U --> Univ_elT) $ - Old_Datatype_Aux.app_bnds - (Old_Datatype_Aux.mk_Free "x" T' i2) (length Us)) Us], Ts) - | _ => (i2 + 1, i2', ts @ [Leaf $ mk_inj T' (Old_Datatype_Aux.mk_Free "x" T' i2)], Ts)) - end; - - val (i2, i2', ts, Ts) = fold (process_arg ks) cargs (1, 1, [], []); - val xs = map (uncurry (Old_Datatype_Aux.mk_Free "x")) (argTs ~~ (1 upto (i2 - 1))); - val ys = map (uncurry (Old_Datatype_Aux.mk_Free "y")) (Ts ~~ (1 upto (i2' - 1))); - val f = fold_rev lambda (xs @ ys) (mk_univ_inj ts n i); - - val (_, _, ts', _) = fold (process_arg []) cargs (1, 1, [], []); - val eqn = HOLogic.mk_Trueprop (HOLogic.mk_eq - (rep_const $ list_comb (constr, xs), mk_univ_inj ts' n i)) - - in (fs @ [f], eqns @ [eqn], i + 1) end; - - (* define isomorphisms for all mutually recursive datatypes in list ds *) - - fun make_iso_defs ds (thy, char_thms) = - let - val ks = map fst ds; - val (_, (tname, _, _)) = hd ds; - val {rec_rewrites, rec_names, ...} = the (Symtab.lookup dt_info tname); - - fun process_dt (k, (_, _, constrs)) (fs, eqns, isos) = - let - val (fs', eqns', _) = fold (make_iso_def k ks (length constrs)) constrs (fs, eqns, 1); - val iso = (nth recTs k, nth all_rep_names k); - in (fs', eqns', isos @ [iso]) end; - - val (fs, eqns, isos) = fold process_dt ds ([], [], []); - val fTs = map fastype_of fs; - val defs = - map (fn (rec_name, (T, iso_name)) => - (Binding.name (Thm.def_name (Long_Name.base_name iso_name)), - Logic.mk_equals (Const (iso_name, T --> Univ_elT), - list_comb (Const (rec_name, fTs @ [T] ---> Univ_elT), fs)))) (rec_names ~~ isos); - val (def_thms, thy') = - (Global_Theory.add_defs false o map Thm.no_attributes) defs thy; - - (* prove characteristic equations *) - - val rewrites = def_thms @ map mk_meta_eq rec_rewrites; - val char_thms' = - map (fn eqn => Goal.prove_sorry_global thy' [] [] eqn - (fn {context = ctxt, ...} => - EVERY [rewrite_goals_tac ctxt rewrites, resolve_tac ctxt [refl] 1])) eqns; - - in (thy', char_thms' @ char_thms) end; - - val (thy5, iso_char_thms) = - fold_rev make_iso_defs (tl descr) (Sign.add_path big_name thy4, []); - - (* prove isomorphism properties *) - - fun mk_funs_inv thy thm = - let - val prop = Thm.prop_of thm; - val _ $ (_ $ ((S as Const (_, Type (_, [U, _]))) $ _ )) $ - (_ $ (_ $ (r $ (a $ _)) $ _)) = Type.legacy_freeze prop; - val used = Term.add_tfree_names a []; - - fun mk_thm i = - let - val Ts = map (TFree o rpair @{sort type}) (Name.variant_list used (replicate i "'t")); - val f = Free ("f", Ts ---> U); - in - Goal.prove_sorry_global thy [] [] - (Logic.mk_implies - (HOLogic.mk_Trueprop (HOLogic.list_all - (map (pair "x") Ts, S $ Old_Datatype_Aux.app_bnds f i)), - HOLogic.mk_Trueprop (HOLogic.mk_eq (fold_rev (Term.abs o pair "x") Ts - (r $ (a $ Old_Datatype_Aux.app_bnds f i)), f)))) - (fn {context = ctxt, ...} => - EVERY [REPEAT_DETERM_N i (resolve_tac ctxt @{thms ext} 1), - REPEAT (eresolve_tac ctxt [allE] 1), - resolve_tac ctxt [thm] 1, - assume_tac ctxt 1]) - end - in map (fn r => r RS subst) (thm :: map mk_thm arities) end; - - (* prove inj Rep_dt_i and Rep_dt_i x : rep_set_dt_i *) - - val fun_congs = - map (fn T => make_elim (Thm.instantiate' [SOME (Thm.global_ctyp_of thy5 T)] [] fun_cong)) branchTs; - - fun prove_iso_thms ds (inj_thms, elem_thms) = - let - val (_, (tname, _, _)) = hd ds; - val induct = #induct (the (Symtab.lookup dt_info tname)); - - fun mk_ind_concl (i, _) = - let - val T = nth recTs i; - val Rep_t = Const (nth all_rep_names i, T --> Univ_elT); - val rep_set_name = nth rep_set_names i; - val concl1 = - HOLogic.all_const T $ Abs ("y", T, HOLogic.imp $ - HOLogic.mk_eq (Rep_t $ Old_Datatype_Aux.mk_Free "x" T i, Rep_t $ Bound 0) $ - HOLogic.mk_eq (Old_Datatype_Aux.mk_Free "x" T i, Bound 0)); - val concl2 = Const (rep_set_name, UnivT') $ (Rep_t $ Old_Datatype_Aux.mk_Free "x" T i); - in (concl1, concl2) end; - - val (ind_concl1, ind_concl2) = split_list (map mk_ind_concl ds); - - val rewrites = map mk_meta_eq iso_char_thms; - val inj_thms' = map snd newT_iso_inj_thms @ map (fn r => r RS @{thm injD}) inj_thms; - - val inj_thm = - Goal.prove_sorry_global thy5 [] [] - (HOLogic.mk_Trueprop (Old_Datatype_Aux.mk_conj ind_concl1)) - (fn {context = ctxt, ...} => EVERY - [(Old_Datatype_Aux.ind_tac ctxt induct [] THEN_ALL_NEW - Object_Logic.atomize_prems_tac ctxt) 1, - REPEAT (EVERY - [resolve_tac ctxt [allI] 1, resolve_tac ctxt [impI] 1, - Old_Datatype_Aux.exh_tac ctxt (exh_thm_of dt_info) 1, - REPEAT (EVERY - [hyp_subst_tac ctxt 1, - rewrite_goals_tac ctxt rewrites, - REPEAT (dresolve_tac ctxt [In0_inject, In1_inject] 1), - (eresolve_tac ctxt [In0_not_In1 RS notE, In1_not_In0 RS notE] 1) - ORELSE (EVERY - [REPEAT (eresolve_tac ctxt (Scons_inject :: - map make_elim [Leaf_inject, Inl_inject, Inr_inject]) 1), - REPEAT (cong_tac ctxt 1), resolve_tac ctxt [refl] 1, - REPEAT (assume_tac ctxt 1 ORELSE (EVERY - [REPEAT (resolve_tac ctxt @{thms ext} 1), - REPEAT (eresolve_tac ctxt (mp :: allE :: - map make_elim (Suml_inject :: Sumr_inject :: - Lim_inject :: inj_thms') @ fun_congs) 1), - assume_tac ctxt 1]))])])])]); - - val inj_thms'' = map (fn r => r RS datatype_injI) (Old_Datatype_Aux.split_conj_thm inj_thm); - - val elem_thm = - Goal.prove_sorry_global thy5 [] [] - (HOLogic.mk_Trueprop (Old_Datatype_Aux.mk_conj ind_concl2)) - (fn {context = ctxt, ...} => - EVERY [ - (Old_Datatype_Aux.ind_tac ctxt induct [] THEN_ALL_NEW - Object_Logic.atomize_prems_tac ctxt) 1, - rewrite_goals_tac ctxt rewrites, - REPEAT ((resolve_tac ctxt rep_intrs THEN_ALL_NEW - ((REPEAT o eresolve_tac ctxt [allE]) THEN' ares_tac ctxt elem_thms)) 1)]); - - in (inj_thms'' @ inj_thms, elem_thms @ Old_Datatype_Aux.split_conj_thm elem_thm) end; - - val (iso_inj_thms_unfolded, iso_elem_thms) = - fold_rev prove_iso_thms (tl descr) ([], map #3 newT_iso_axms); - val iso_inj_thms = - map snd newT_iso_inj_thms @ map (fn r => r RS @{thm injD}) iso_inj_thms_unfolded; - - (* prove rep_set_dt_i x --> x : range Rep_dt_i *) - - fun mk_iso_t (((set_name, iso_name), i), T) = - let val isoT = T --> Univ_elT in - HOLogic.imp $ - (Const (set_name, UnivT') $ Old_Datatype_Aux.mk_Free "x" Univ_elT i) $ - (if i < length newTs then @{term True} - else HOLogic.mk_mem (Old_Datatype_Aux.mk_Free "x" Univ_elT i, - Const (@{const_name image}, isoT --> HOLogic.mk_setT T --> UnivT) $ - Const (iso_name, isoT) $ Const (@{const_abbrev UNIV}, HOLogic.mk_setT T))) - end; - - val iso_t = HOLogic.mk_Trueprop (Old_Datatype_Aux.mk_conj (map mk_iso_t - (rep_set_names ~~ all_rep_names ~~ (0 upto (length descr' - 1)) ~~ recTs))); - - (* all the theorems are proved by one single simultaneous induction *) - - val range_eqs = map (fn r => mk_meta_eq (r RS @{thm range_ex1_eq})) iso_inj_thms_unfolded; - - val iso_thms = - if length descr = 1 then [] - else - drop (length newTs) (Old_Datatype_Aux.split_conj_thm - (Goal.prove_sorry_global thy5 [] [] iso_t (fn {context = ctxt, ...} => EVERY - [(Old_Datatype_Aux.ind_tac ctxt rep_induct [] THEN_ALL_NEW - Object_Logic.atomize_prems_tac ctxt) 1, - REPEAT (resolve_tac ctxt [TrueI] 1), - rewrite_goals_tac ctxt (mk_meta_eq @{thm choice_eq} :: - Thm.symmetric (mk_meta_eq @{thm fun_eq_iff}) :: range_eqs), - rewrite_goals_tac ctxt (map Thm.symmetric range_eqs), - REPEAT (EVERY - [REPEAT (eresolve_tac ctxt ([rangeE, @{thm ex1_implies_ex} RS exE] @ - maps (mk_funs_inv thy5 o #1) newT_iso_axms) 1), - TRY (hyp_subst_tac ctxt 1), - resolve_tac ctxt [sym RS range_eqI] 1, - resolve_tac ctxt iso_char_thms 1])]))); - - val Abs_inverse_thms' = - map #1 newT_iso_axms @ - map2 (fn r_inj => fn r => @{thm f_the_inv_into_f} OF [r_inj, r RS mp]) - iso_inj_thms_unfolded iso_thms; - - val Abs_inverse_thms = maps (mk_funs_inv thy5) Abs_inverse_thms'; - - (******************* freeness theorems for constructors *******************) - - val _ = Old_Datatype_Aux.message config "Proving freeness of constructors ..."; - - (* prove theorem Rep_i (Constr_j ...) = Inj_j ... *) - - fun prove_constr_rep_thm eqn = - let - val inj_thms = map fst newT_iso_inj_thms; - val rewrites = @{thm o_def} :: constr_defs @ map (mk_meta_eq o #2) newT_iso_axms; - in - Goal.prove_sorry_global thy5 [] [] eqn - (fn {context = ctxt, ...} => EVERY - [resolve_tac ctxt inj_thms 1, - rewrite_goals_tac ctxt rewrites, - resolve_tac ctxt [refl] 3, - resolve_tac ctxt rep_intrs 2, - REPEAT (resolve_tac ctxt iso_elem_thms 1)]) - end; - - (*--------------------------------------------------------------*) - (* constr_rep_thms and rep_congs are used to prove distinctness *) - (* of constructors. *) - (*--------------------------------------------------------------*) - - val constr_rep_thms = map (map prove_constr_rep_thm) constr_rep_eqns; - - val dist_rewrites = - map (fn (rep_thms, dist_lemma) => - dist_lemma :: (rep_thms @ [In0_eq, In1_eq, In0_not_In1, In1_not_In0])) - (constr_rep_thms ~~ dist_lemmas); - - fun prove_distinct_thms dist_rewrites' = - let - fun prove [] = [] - | prove (t :: ts) = - let - val dist_thm = Goal.prove_sorry_global thy5 [] [] t (fn {context = ctxt, ...} => - EVERY [simp_tac (put_simpset HOL_ss ctxt addsimps dist_rewrites') 1]) - in dist_thm :: Drule.zero_var_indexes (dist_thm RS not_sym) :: prove ts end; - in prove end; - - val distinct_thms = - map2 (prove_distinct_thms) dist_rewrites (Old_Datatype_Prop.make_distincts descr); - - (* prove injectivity of constructors *) - - fun prove_constr_inj_thm rep_thms t = - let - val inj_thms = Scons_inject :: - map make_elim - (iso_inj_thms @ - [In0_inject, In1_inject, Leaf_inject, Inl_inject, Inr_inject, - Lim_inject, Suml_inject, Sumr_inject]) - in - Goal.prove_sorry_global thy5 [] [] t - (fn {context = ctxt, ...} => EVERY - [resolve_tac ctxt [iffI] 1, - REPEAT (eresolve_tac ctxt [conjE] 2), hyp_subst_tac ctxt 2, - resolve_tac ctxt [refl] 2, - dresolve_tac ctxt rep_congs 1, - dresolve_tac ctxt @{thms box_equals} 1, - REPEAT (resolve_tac ctxt rep_thms 1), - REPEAT (eresolve_tac ctxt inj_thms 1), - REPEAT (ares_tac ctxt [conjI] 1 ORELSE (EVERY [REPEAT (resolve_tac ctxt @{thms ext} 1), - REPEAT (eresolve_tac ctxt (make_elim fun_cong :: inj_thms) 1), - assume_tac ctxt 1]))]) - end; - - val constr_inject = - map (fn (ts, thms) => map (prove_constr_inj_thm thms) ts) - (Old_Datatype_Prop.make_injs descr ~~ constr_rep_thms); - - val ((constr_inject', distinct_thms'), thy6) = - thy5 - |> Sign.parent_path - |> Old_Datatype_Aux.store_thmss "inject" new_type_names constr_inject - ||>> Old_Datatype_Aux.store_thmss "distinct" new_type_names distinct_thms; - - (*************************** induction theorem ****************************) - - val _ = Old_Datatype_Aux.message config "Proving induction rule for datatypes ..."; - - val Rep_inverse_thms = - map (fn (_, iso, _) => iso RS subst) newT_iso_axms @ - map (fn r => r RS @{thm the_inv_f_f} RS subst) iso_inj_thms_unfolded; - val Rep_inverse_thms' = map (fn r => r RS @{thm the_inv_f_f}) iso_inj_thms_unfolded; - - fun mk_indrule_lemma (i, _) T = - let - val Rep_t = Const (nth all_rep_names i, T --> Univ_elT) $ Old_Datatype_Aux.mk_Free "x" T i; - val Abs_t = - if i < length newTs then - Const (#Abs_name (#1 (#2 (nth typedefs i))), Univ_elT --> T) - else - Const (@{const_name the_inv_into}, - [HOLogic.mk_setT T, T --> Univ_elT, Univ_elT] ---> T) $ - HOLogic.mk_UNIV T $ Const (nth all_rep_names i, T --> Univ_elT); - val prem = - HOLogic.imp $ - (Const (nth rep_set_names i, UnivT') $ Rep_t) $ - (Old_Datatype_Aux.mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ (Abs_t $ Rep_t)); - val concl = - Old_Datatype_Aux.mk_Free "P" (T --> HOLogic.boolT) (i + 1) $ - Old_Datatype_Aux.mk_Free "x" T i; - in (prem, concl) end; - - val (indrule_lemma_prems, indrule_lemma_concls) = - split_list (map2 mk_indrule_lemma descr' recTs); - - val indrule_lemma = - Goal.prove_sorry_global thy6 [] [] - (Logic.mk_implies - (HOLogic.mk_Trueprop (Old_Datatype_Aux.mk_conj indrule_lemma_prems), - HOLogic.mk_Trueprop (Old_Datatype_Aux.mk_conj indrule_lemma_concls))) - (fn {context = ctxt, ...} => - EVERY - [REPEAT (eresolve_tac ctxt [conjE] 1), - REPEAT (EVERY - [TRY (resolve_tac ctxt [conjI] 1), resolve_tac ctxt Rep_inverse_thms 1, - eresolve_tac ctxt [mp] 1, resolve_tac ctxt iso_elem_thms 1])]); - - val Ps = map head_of (HOLogic.dest_conj (HOLogic.dest_Trueprop (Thm.concl_of indrule_lemma))); - val frees = - if length Ps = 1 then [Free ("P", snd (dest_Var (hd Ps)))] - else map (Free o apfst fst o dest_Var) Ps; - - val dt_induct_prop = Old_Datatype_Prop.make_ind descr; - val dt_induct = - Goal.prove_sorry_global thy6 [] - (Logic.strip_imp_prems dt_induct_prop) - (Logic.strip_imp_concl dt_induct_prop) - (fn {context = ctxt, prems, ...} => - let - val indrule_lemma' = - infer_instantiate ctxt - (map (#1 o dest_Var) Ps ~~ map (Thm.cterm_of ctxt) frees) indrule_lemma; - in - EVERY - [resolve_tac ctxt [indrule_lemma'] 1, - (Old_Datatype_Aux.ind_tac ctxt rep_induct [] THEN_ALL_NEW - Object_Logic.atomize_prems_tac ctxt) 1, - EVERY (map (fn (prem, r) => (EVERY - [REPEAT (eresolve_tac ctxt Abs_inverse_thms 1), - simp_tac (put_simpset HOL_basic_ss ctxt - addsimps (Thm.symmetric r :: Rep_inverse_thms')) 1, - DEPTH_SOLVE_1 (ares_tac ctxt [prem] 1 ORELSE eresolve_tac ctxt [allE] 1)])) - (prems ~~ (constr_defs @ map mk_meta_eq iso_char_thms)))] - end); - - val ([(_, [dt_induct'])], thy7) = - thy6 - |> Global_Theory.note_thmss "" - [((Binding.qualify true big_name (Binding.name "induct"), [case_names_induct]), - [([dt_induct], [])])]; - in - ((constr_inject', distinct_thms', dt_induct'), thy7) - end; - - - -(** datatype definition **) - -(* specifications *) type spec_cmd = (binding * (string * string option) list * mixfix) * (binding * string list * mixfix) list; -local - fun parse_spec ctxt ((b, args, mx), constrs) = ((b, map (apsnd (Typedecl.read_constraint ctxt)) args, mx), constrs |> map (fn (c, Ts, mx') => (c, map (Syntax.parse_typ ctxt) Ts, mx'))); @@ -709,90 +53,9 @@ val specs = check_specs ctxt (map (parse ctxt) raw_specs); in (specs, ctxt) end; -in - val read_specs = prep_specs parse_spec; val check_specs = prep_specs (K I); -end; - - -(* main commands *) - -fun gen_add_datatype prep_specs config raw_specs thy = - let - val (dts, spec_ctxt) = prep_specs raw_specs thy; - val ((_, tyvars, _), _) :: _ = dts; - val string_of_tyvar = Syntax.string_of_typ spec_ctxt o TFree; - - val (new_dts, types_syntax) = dts |> map (fn ((tname, tvs, mx), _) => - let val full_tname = Sign.full_name thy tname in - (case duplicates (op =) tvs of - [] => - if eq_set (op =) (tyvars, tvs) then ((full_tname, tvs), (tname, mx)) - else error "Mutually recursive datatypes must have same type parameters" - | dups => - error ("Duplicate parameter(s) for datatype " ^ Binding.print tname ^ - " : " ^ commas (map string_of_tyvar dups))) - end) |> split_list; - val dt_names = map fst new_dts; - - val _ = - (case duplicates (op =) (map fst new_dts) of - [] => () - | dups => error ("Duplicate datatypes: " ^ commas_quote dups)); - - fun prep_dt_spec ((tname, tvs, _), constrs) (dts', constr_syntax, i) = - let - fun prep_constr (cname, cargs, mx) (constrs, constr_syntax') = - let - val _ = - (case subtract (op =) tvs (fold Term.add_tfreesT cargs []) of - [] => () - | vs => error ("Extra type variables on rhs: " ^ commas (map string_of_tyvar vs))); - val c = Sign.full_name_path thy (Binding.name_of tname) cname; - in - (constrs @ [(c, map (Old_Datatype_Aux.dtyp_of_typ new_dts) cargs)], - constr_syntax' @ [(cname, mx)]) - end handle ERROR msg => - cat_error msg ("The error above occurred in constructor " ^ Binding.print cname ^ - " of datatype " ^ Binding.print tname); - - val (constrs', constr_syntax') = fold prep_constr constrs ([], []); - in - (case duplicates (op =) (map fst constrs') of - [] => - (dts' @ [(i, (Sign.full_name thy tname, map Old_Datatype_Aux.DtTFree tvs, constrs'))], - constr_syntax @ [constr_syntax'], i + 1) - | dups => - error ("Duplicate constructors " ^ commas_quote dups ^ - " in datatype " ^ Binding.print tname)) - end; - - val (dts', constr_syntax, i) = fold prep_dt_spec dts ([], [], 0); - - val dt_info = Old_Datatype_Data.get_all thy; - val (descr, _) = Old_Datatype_Aux.unfold_datatypes spec_ctxt dts' dt_info dts' i; - val _ = - Old_Datatype_Aux.check_nonempty descr - handle (exn as Old_Datatype_Aux.Datatype_Empty s) => - if #strict config then error ("Nonemptiness check failed for datatype " ^ quote s) - else Exn.reraise exn; - - val _ = - Old_Datatype_Aux.message config - ("Constructing datatype(s) " ^ commas_quote (map (Binding.name_of o #1 o #1) dts)); - in - thy - |> representation_proofs config dt_info descr types_syntax constr_syntax - (Old_Datatype_Data.mk_case_names_induct (flat descr)) - |-> (fn (inject, distinct, induct) => - Old_Rep_Datatype.derive_datatype_props config dt_names descr induct inject distinct) - end; - -val add_datatype = gen_add_datatype check_specs; -val add_datatype_cmd = gen_add_datatype read_specs; - open Old_Datatype_Aux; end;