--- 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 \<noteq> f y ==> x \<noteq> 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 "(\<And>x. \<forall>y. f x = f y \<longrightarrow> x = y) \<Longrightarrow> 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;