--- a/src/HOL/BNF/Tools/ctr_sugar.ML Thu Dec 05 17:52:12 2013 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,956 +0,0 @@
-(* Title: HOL/BNF/Tools/ctr_sugar.ML
- Author: Jasmin Blanchette, TU Muenchen
- Copyright 2012
-
-Wrapping existing freely generated type's constructors.
-*)
-
-signature CTR_SUGAR =
-sig
- type ctr_sugar =
- {ctrs: term list,
- casex: term,
- discs: term list,
- selss: term list list,
- exhaust: thm,
- nchotomy: thm,
- injects: thm list,
- distincts: thm list,
- case_thms: thm list,
- case_cong: thm,
- weak_case_cong: thm,
- split: thm,
- split_asm: thm,
- disc_thmss: thm list list,
- discIs: thm list,
- sel_thmss: thm list list,
- disc_exhausts: thm list,
- sel_exhausts: thm list,
- collapses: thm list,
- expands: thm list,
- sel_splits: thm list,
- sel_split_asms: thm list,
- case_conv_ifs: thm list};
-
- val morph_ctr_sugar: morphism -> ctr_sugar -> ctr_sugar
- val ctr_sugar_of: Proof.context -> string -> ctr_sugar option
- val ctr_sugars_of: Proof.context -> ctr_sugar list
-
- val rep_compat_prefix: string
-
- val mk_half_pairss: 'a list * 'a list -> ('a * 'a) list list
- val join_halves: int -> 'a list list -> 'a list list -> 'a list * 'a list list list
-
- val mk_ctr: typ list -> term -> term
- val mk_case: typ list -> typ -> term -> term
- val mk_disc_or_sel: typ list -> term -> term
- val name_of_ctr: term -> string
- val name_of_disc: term -> string
- val dest_ctr: Proof.context -> string -> term -> term * term list
- val dest_case: Proof.context -> string -> typ list -> term -> (term list * term list) option
-
- val wrap_free_constructors: ({prems: thm list, context: Proof.context} -> tactic) list list ->
- (((bool * bool) * term list) * binding) *
- (binding list * (binding list list * (binding * term) list list)) -> local_theory ->
- ctr_sugar * local_theory
- val parse_wrap_free_constructors_options: (bool * bool) parser
- val parse_bound_term: (binding * string) parser
-end;
-
-structure Ctr_Sugar : CTR_SUGAR =
-struct
-
-open Ctr_Sugar_Util
-open Ctr_Sugar_Tactics
-
-type ctr_sugar =
- {ctrs: term list,
- casex: term,
- discs: term list,
- selss: term list list,
- exhaust: thm,
- nchotomy: thm,
- injects: thm list,
- distincts: thm list,
- case_thms: thm list,
- case_cong: thm,
- weak_case_cong: thm,
- split: thm,
- split_asm: thm,
- disc_thmss: thm list list,
- discIs: thm list,
- sel_thmss: thm list list,
- disc_exhausts: thm list,
- sel_exhausts: thm list,
- collapses: thm list,
- expands: thm list,
- sel_splits: thm list,
- sel_split_asms: thm list,
- case_conv_ifs: thm list};
-
-fun eq_ctr_sugar ({ctrs = ctrs1, casex = case1, discs = discs1, selss = selss1, ...} : ctr_sugar,
- {ctrs = ctrs2, casex = case2, discs = discs2, selss = selss2, ...} : ctr_sugar) =
- ctrs1 = ctrs2 andalso case1 = case2 andalso discs1 = discs2 andalso selss1 = selss2;
-
-fun morph_ctr_sugar phi {ctrs, casex, discs, selss, exhaust, nchotomy, injects, distincts,
- case_thms, case_cong, weak_case_cong, split, split_asm, disc_thmss, discIs, sel_thmss,
- disc_exhausts, sel_exhausts, collapses, expands, sel_splits, sel_split_asms, case_conv_ifs} =
- {ctrs = map (Morphism.term phi) ctrs,
- casex = Morphism.term phi casex,
- discs = map (Morphism.term phi) discs,
- selss = map (map (Morphism.term phi)) selss,
- exhaust = Morphism.thm phi exhaust,
- nchotomy = Morphism.thm phi nchotomy,
- injects = map (Morphism.thm phi) injects,
- distincts = map (Morphism.thm phi) distincts,
- case_thms = map (Morphism.thm phi) case_thms,
- case_cong = Morphism.thm phi case_cong,
- weak_case_cong = Morphism.thm phi weak_case_cong,
- split = Morphism.thm phi split,
- split_asm = Morphism.thm phi split_asm,
- disc_thmss = map (map (Morphism.thm phi)) disc_thmss,
- discIs = map (Morphism.thm phi) discIs,
- sel_thmss = map (map (Morphism.thm phi)) sel_thmss,
- disc_exhausts = map (Morphism.thm phi) disc_exhausts,
- sel_exhausts = map (Morphism.thm phi) sel_exhausts,
- collapses = map (Morphism.thm phi) collapses,
- expands = map (Morphism.thm phi) expands,
- sel_splits = map (Morphism.thm phi) sel_splits,
- sel_split_asms = map (Morphism.thm phi) sel_split_asms,
- case_conv_ifs = map (Morphism.thm phi) case_conv_ifs};
-
-val transfer_ctr_sugar =
- morph_ctr_sugar o Morphism.thm_morphism o Thm.transfer o Proof_Context.theory_of;
-
-structure Data = Generic_Data
-(
- type T = ctr_sugar Symtab.table;
- val empty = Symtab.empty;
- val extend = I;
- val merge = Symtab.merge eq_ctr_sugar;
-);
-
-fun ctr_sugar_of ctxt =
- Symtab.lookup (Data.get (Context.Proof ctxt))
- #> Option.map (transfer_ctr_sugar ctxt);
-
-fun ctr_sugars_of ctxt =
- Symtab.fold (cons o transfer_ctr_sugar ctxt o snd) (Data.get (Context.Proof ctxt)) [];
-
-fun register_ctr_sugar key ctr_sugar =
- Local_Theory.declaration {syntax = false, pervasive = true}
- (fn phi => Data.map (Symtab.default (key, morph_ctr_sugar phi ctr_sugar)));
-
-val rep_compat_prefix = "new";
-
-val isN = "is_";
-val unN = "un_";
-fun mk_unN 1 1 suf = unN ^ suf
- | mk_unN _ l suf = unN ^ suf ^ string_of_int l;
-
-val caseN = "case";
-val case_congN = "case_cong";
-val case_conv_ifN = "case_conv_if";
-val collapseN = "collapse";
-val disc_excludeN = "disc_exclude";
-val disc_exhaustN = "disc_exhaust";
-val discN = "disc";
-val discIN = "discI";
-val distinctN = "distinct";
-val exhaustN = "exhaust";
-val expandN = "expand";
-val injectN = "inject";
-val nchotomyN = "nchotomy";
-val selN = "sel";
-val sel_exhaustN = "sel_exhaust";
-val sel_splitN = "sel_split";
-val sel_split_asmN = "sel_split_asm";
-val splitN = "split";
-val splitsN = "splits";
-val split_asmN = "split_asm";
-val weak_case_cong_thmsN = "weak_case_cong";
-
-val cong_attrs = @{attributes [cong]};
-val dest_attrs = @{attributes [dest]};
-val safe_elim_attrs = @{attributes [elim!]};
-val iff_attrs = @{attributes [iff]};
-val induct_simp_attrs = @{attributes [induct_simp]};
-val nitpick_attrs = @{attributes [nitpick_simp]};
-val simp_attrs = @{attributes [simp]};
-val code_nitpick_simp_simp_attrs = Code.add_default_eqn_attrib :: nitpick_attrs @ simp_attrs;
-
-fun unflat_lookup eq xs ys = map (fn xs' => permute_like eq xs xs' ys);
-
-fun mk_half_pairss' _ ([], []) = []
- | mk_half_pairss' indent (x :: xs, _ :: ys) =
- indent @ fold_rev (cons o single o pair x) ys (mk_half_pairss' ([] :: indent) (xs, ys));
-
-fun mk_half_pairss p = mk_half_pairss' [[]] p;
-
-fun join_halves n half_xss other_half_xss =
- let
- val xsss =
- map2 (map2 append) (Library.chop_groups n half_xss)
- (transpose (Library.chop_groups n other_half_xss))
- val xs = splice (flat half_xss) (flat other_half_xss);
- in (xs, xsss) end;
-
-fun mk_undefined T = Const (@{const_name undefined}, T);
-
-fun mk_ctr Ts t =
- let val Type (_, Ts0) = body_type (fastype_of t) in
- Term.subst_atomic_types (Ts0 ~~ Ts) t
- end;
-
-fun mk_case Ts T t =
- let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in
- Term.subst_atomic_types ((body, T) :: (Ts0 ~~ Ts)) t
- end;
-
-fun mk_disc_or_sel Ts t =
- Term.subst_atomic_types (snd (Term.dest_Type (domain_type (fastype_of t))) ~~ Ts) t;
-
-fun name_of_const what t =
- (case head_of t of
- Const (s, _) => s
- | Free (s, _) => s
- | _ => error ("Cannot extract name of " ^ what));
-
-val name_of_ctr = name_of_const "constructor";
-
-val notN = "not_";
-val eqN = "eq_";
-val neqN = "neq_";
-
-fun name_of_disc t =
- (case head_of t of
- Abs (_, _, @{const Not} $ (t' $ Bound 0)) =>
- Long_Name.map_base_name (prefix notN) (name_of_disc t')
- | Abs (_, _, Const (@{const_name HOL.eq}, _) $ Bound 0 $ t') =>
- Long_Name.map_base_name (prefix eqN) (name_of_disc t')
- | Abs (_, _, @{const Not} $ (Const (@{const_name HOL.eq}, _) $ Bound 0 $ t')) =>
- Long_Name.map_base_name (prefix neqN) (name_of_disc t')
- | t' => name_of_const "destructor" t');
-
-val base_name_of_ctr = Long_Name.base_name o name_of_ctr;
-
-fun dest_ctr ctxt s t =
- let
- val (f, args) = Term.strip_comb t;
- in
- (case ctr_sugar_of ctxt s of
- SOME {ctrs, ...} =>
- (case find_first (can (fo_match ctxt f)) ctrs of
- SOME f' => (f', args)
- | NONE => raise Fail "dest_ctr")
- | NONE => raise Fail "dest_ctr")
- end;
-
-fun dest_case ctxt s Ts t =
- (case Term.strip_comb t of
- (Const (c, _), args as _ :: _) =>
- (case ctr_sugar_of ctxt s of
- SOME {casex = Const (case_name, _), discs = discs0, selss = selss0, ...} =>
- if case_name = c then
- let val n = length discs0 in
- if n < length args then
- let
- val (branches, obj :: leftovers) = chop n args;
- val discs = map (mk_disc_or_sel Ts) discs0;
- val selss = map (map (mk_disc_or_sel Ts)) selss0;
- val conds = map (rapp obj) discs;
- val branch_argss = map (fn sels => map (rapp obj) sels @ leftovers) selss;
- val branches' = map2 (curry Term.betapplys) branches branch_argss;
- in
- SOME (conds, branches')
- end
- else
- NONE
- end
- else
- NONE
- | _ => NONE)
- | _ => NONE);
-
-fun eta_expand_arg xs f_xs = fold_rev Term.lambda xs f_xs;
-
-fun prepare_wrap_free_constructors prep_term ((((no_discs_sels, rep_compat), raw_ctrs),
- raw_case_binding), (raw_disc_bindings, (raw_sel_bindingss, raw_sel_defaultss))) no_defs_lthy =
- let
- (* TODO: sanity checks on arguments *)
-
- val n = length raw_ctrs;
- val ks = 1 upto n;
-
- val _ = if n > 0 then () else error "No constructors specified";
-
- val ctrs0 = map (prep_term no_defs_lthy) raw_ctrs;
- val sel_defaultss =
- pad_list [] n (map (map (apsnd (prep_term no_defs_lthy))) raw_sel_defaultss);
-
- val Type (fcT_name, As0) = body_type (fastype_of (hd ctrs0));
- val fc_b_name = Long_Name.base_name fcT_name;
- val fc_b = Binding.name fc_b_name;
-
- fun qualify mandatory =
- Binding.qualify mandatory fc_b_name o (rep_compat ? Binding.qualify false rep_compat_prefix);
-
- fun dest_TFree_or_TVar (TFree p) = p
- | dest_TFree_or_TVar (TVar ((s, _), S)) = (s, S)
- | dest_TFree_or_TVar _ = error "Invalid type argument";
-
- val (unsorted_As, B) =
- no_defs_lthy
- |> variant_tfrees (map (fst o dest_TFree_or_TVar) As0)
- ||> the_single o fst o mk_TFrees 1;
-
- val As = map2 (resort_tfree o snd o dest_TFree_or_TVar) As0 unsorted_As;
-
- val fcT = Type (fcT_name, As);
- val ctrs = map (mk_ctr As) ctrs0;
- val ctr_Tss = map (binder_types o fastype_of) ctrs;
-
- val ms = map length ctr_Tss;
-
- val raw_disc_bindings' = pad_list Binding.empty n raw_disc_bindings;
-
- fun can_definitely_rely_on_disc k = not (Binding.is_empty (nth raw_disc_bindings' (k - 1)));
- fun can_rely_on_disc k =
- can_definitely_rely_on_disc k orelse (k = 1 andalso not (can_definitely_rely_on_disc 2));
- fun should_omit_disc_binding k = n = 1 orelse (n = 2 andalso can_rely_on_disc (3 - k));
-
- fun is_disc_binding_valid b =
- not (Binding.is_empty b orelse Binding.eq_name (b, equal_binding));
-
- val standard_disc_binding = Binding.name o prefix isN o base_name_of_ctr;
-
- val disc_bindings =
- raw_disc_bindings'
- |> map4 (fn k => fn m => fn ctr => fn disc =>
- qualify false
- (if Binding.is_empty disc then
- if should_omit_disc_binding k then disc else standard_disc_binding ctr
- else if Binding.eq_name (disc, equal_binding) then
- if m = 0 then disc
- else error "Cannot use \"=\" syntax for discriminating nonnullary constructor"
- else if Binding.eq_name (disc, standard_binding) then
- standard_disc_binding ctr
- else
- disc)) ks ms ctrs0;
-
- fun standard_sel_binding m l = Binding.name o mk_unN m l o base_name_of_ctr;
-
- val sel_bindingss =
- pad_list [] n raw_sel_bindingss
- |> map3 (fn ctr => fn m => map2 (fn l => fn sel =>
- qualify false
- (if Binding.is_empty sel orelse Binding.eq_name (sel, standard_binding) then
- standard_sel_binding m l ctr
- else
- sel)) (1 upto m) o pad_list Binding.empty m) ctrs0 ms;
-
- val case_Ts = map (fn Ts => Ts ---> B) ctr_Tss;
-
- val ((((((((xss, xss'), yss), fs), gs), [u', v']), [w]), (p, p')), names_lthy) = no_defs_lthy |>
- mk_Freess' "x" ctr_Tss
- ||>> mk_Freess "y" ctr_Tss
- ||>> mk_Frees "f" case_Ts
- ||>> mk_Frees "g" case_Ts
- ||>> (apfst (map (rpair fcT)) oo Variable.variant_fixes) [fc_b_name, fc_b_name ^ "'"]
- ||>> mk_Frees "z" [B]
- ||>> yield_singleton (apfst (op ~~) oo mk_Frees' "P") HOLogic.boolT;
-
- val u = Free u';
- val v = Free v';
- val q = Free (fst p', mk_pred1T B);
-
- val xctrs = map2 (curry Term.list_comb) ctrs xss;
- val yctrs = map2 (curry Term.list_comb) ctrs yss;
-
- val xfs = map2 (curry Term.list_comb) fs xss;
- val xgs = map2 (curry Term.list_comb) gs xss;
-
- (* TODO: Eta-expension is for compatibility with the old datatype package (but it also provides
- nicer names). Consider removing. *)
- val eta_fs = map2 eta_expand_arg xss xfs;
- val eta_gs = map2 eta_expand_arg xss xgs;
-
- val case_binding =
- qualify false
- (if Binding.is_empty raw_case_binding orelse
- Binding.eq_name (raw_case_binding, standard_binding) then
- Binding.suffix_name ("_" ^ caseN) fc_b
- else
- raw_case_binding);
-
- fun mk_case_disj xctr xf xs =
- list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr), HOLogic.mk_eq (w, xf)));
-
- val case_rhs = fold_rev (fold_rev Term.lambda) [fs, [u]]
- (Const (@{const_name The}, (B --> HOLogic.boolT) --> B) $
- Term.lambda w (Library.foldr1 HOLogic.mk_disj (map3 mk_case_disj xctrs xfs xss)));
-
- val ((raw_case, (_, raw_case_def)), (lthy', lthy)) = no_defs_lthy
- |> Local_Theory.define ((case_binding, NoSyn), ((Thm.def_binding case_binding, []), case_rhs))
- ||> `Local_Theory.restore;
-
- val phi = Proof_Context.export_morphism lthy lthy';
-
- val case_def = Morphism.thm phi raw_case_def;
-
- val case0 = Morphism.term phi raw_case;
- val casex = mk_case As B case0;
-
- val fcase = Term.list_comb (casex, fs);
-
- val ufcase = fcase $ u;
- val vfcase = fcase $ v;
-
- val eta_fcase = Term.list_comb (casex, eta_fs);
- val eta_gcase = Term.list_comb (casex, eta_gs);
-
- val eta_ufcase = eta_fcase $ u;
- val eta_vgcase = eta_gcase $ v;
-
- fun mk_uu_eq () = HOLogic.mk_eq (u, u);
-
- val uv_eq = mk_Trueprop_eq (u, v);
-
- val exist_xs_u_eq_ctrs =
- map2 (fn xctr => fn xs => list_exists_free xs (HOLogic.mk_eq (u, xctr))) xctrs xss;
-
- val unique_disc_no_def = TrueI; (*arbitrary marker*)
- val alternate_disc_no_def = FalseE; (*arbitrary marker*)
-
- fun alternate_disc_lhs get_udisc k =
- HOLogic.mk_not
- (let val b = nth disc_bindings (k - 1) in
- if is_disc_binding_valid b then get_udisc b (k - 1) else nth exist_xs_u_eq_ctrs (k - 1)
- end);
-
- val (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy') =
- if no_discs_sels then
- (true, [], [], [], [], [], lthy)
- else
- let
- fun disc_free b = Free (Binding.name_of b, mk_pred1T fcT);
-
- fun disc_spec b exist_xs_u_eq_ctr = mk_Trueprop_eq (disc_free b $ u, exist_xs_u_eq_ctr);
-
- fun alternate_disc k =
- Term.lambda u (alternate_disc_lhs (K o rapp u o disc_free) (3 - k));
-
- fun mk_sel_case_args b proto_sels T =
- map2 (fn Ts => fn k =>
- (case AList.lookup (op =) proto_sels k of
- NONE =>
- (case AList.lookup Binding.eq_name (rev (nth sel_defaultss (k - 1))) b of
- NONE => fold_rev (Term.lambda o curry Free Name.uu) Ts (mk_undefined T)
- | SOME t => t |> Type.constraint (Ts ---> T) |> Syntax.check_term lthy)
- | SOME (xs, x) => fold_rev Term.lambda xs x)) ctr_Tss ks;
-
- fun sel_spec b proto_sels =
- let
- val _ =
- (case duplicates (op =) (map fst proto_sels) of
- k :: _ => error ("Duplicate selector name " ^ quote (Binding.name_of b) ^
- " for constructor " ^
- quote (Syntax.string_of_term lthy (nth ctrs (k - 1))))
- | [] => ())
- val T =
- (case distinct (op =) (map (fastype_of o snd o snd) proto_sels) of
- [T] => T
- | T :: T' :: _ => error ("Inconsistent range type for selector " ^
- quote (Binding.name_of b) ^ ": " ^ quote (Syntax.string_of_typ lthy T) ^ " vs. "
- ^ quote (Syntax.string_of_typ lthy T')));
- in
- mk_Trueprop_eq (Free (Binding.name_of b, fcT --> T) $ u,
- Term.list_comb (mk_case As T case0, mk_sel_case_args b proto_sels T) $ u)
- end;
-
- val sel_bindings = flat sel_bindingss;
- val uniq_sel_bindings = distinct Binding.eq_name sel_bindings;
- val all_sels_distinct = (length uniq_sel_bindings = length sel_bindings);
-
- val sel_binding_index =
- if all_sels_distinct then 1 upto length sel_bindings
- else map (fn b => find_index (curry Binding.eq_name b) uniq_sel_bindings) sel_bindings;
-
- val proto_sels = flat (map3 (fn k => fn xs => map (fn x => (k, (xs, x)))) ks xss xss);
- val sel_infos =
- AList.group (op =) (sel_binding_index ~~ proto_sels)
- |> sort (int_ord o pairself fst)
- |> map snd |> curry (op ~~) uniq_sel_bindings;
- val sel_bindings = map fst sel_infos;
-
- fun unflat_selss xs = unflat_lookup Binding.eq_name sel_bindings xs sel_bindingss;
-
- val (((raw_discs, raw_disc_defs), (raw_sels, raw_sel_defs)), (lthy', lthy)) =
- lthy
- |> apfst split_list o fold_map3 (fn k => fn exist_xs_u_eq_ctr => fn b =>
- if Binding.is_empty b then
- if n = 1 then pair (Term.lambda u (mk_uu_eq ()), unique_disc_no_def)
- else pair (alternate_disc k, alternate_disc_no_def)
- else if Binding.eq_name (b, equal_binding) then
- pair (Term.lambda u exist_xs_u_eq_ctr, refl)
- else
- Specification.definition (SOME (b, NONE, NoSyn),
- ((Thm.def_binding b, []), disc_spec b exist_xs_u_eq_ctr)) #>> apsnd snd)
- ks exist_xs_u_eq_ctrs disc_bindings
- ||>> apfst split_list o fold_map (fn (b, proto_sels) =>
- Specification.definition (SOME (b, NONE, NoSyn),
- ((Thm.def_binding b, []), sel_spec b proto_sels)) #>> apsnd snd) sel_infos
- ||> `Local_Theory.restore;
-
- val phi = Proof_Context.export_morphism lthy lthy';
-
- val disc_defs = map (Morphism.thm phi) raw_disc_defs;
- val sel_defs = map (Morphism.thm phi) raw_sel_defs;
- val sel_defss = unflat_selss sel_defs;
-
- val discs0 = map (Morphism.term phi) raw_discs;
- val selss0 = unflat_selss (map (Morphism.term phi) raw_sels);
-
- val discs = map (mk_disc_or_sel As) discs0;
- val selss = map (map (mk_disc_or_sel As)) selss0;
- in
- (all_sels_distinct, discs, selss, disc_defs, sel_defs, sel_defss, lthy')
- end;
-
- fun mk_imp_p Qs = Logic.list_implies (Qs, HOLogic.mk_Trueprop p);
-
- val exhaust_goal =
- let fun mk_prem xctr xs = fold_rev Logic.all xs (mk_imp_p [mk_Trueprop_eq (u, xctr)]) in
- fold_rev Logic.all [p, u] (mk_imp_p (map2 mk_prem xctrs xss))
- end;
-
- val inject_goalss =
- let
- fun mk_goal _ _ [] [] = []
- | mk_goal xctr yctr xs ys =
- [fold_rev Logic.all (xs @ ys) (mk_Trueprop_eq (HOLogic.mk_eq (xctr, yctr),
- Library.foldr1 HOLogic.mk_conj (map2 (curry HOLogic.mk_eq) xs ys)))];
- in
- map4 mk_goal xctrs yctrs xss yss
- end;
-
- val half_distinct_goalss =
- let
- fun mk_goal ((xs, xc), (xs', xc')) =
- fold_rev Logic.all (xs @ xs')
- (HOLogic.mk_Trueprop (HOLogic.mk_not (HOLogic.mk_eq (xc, xc'))));
- in
- map (map mk_goal) (mk_half_pairss (`I (xss ~~ xctrs)))
- end;
-
- val goalss = [exhaust_goal] :: inject_goalss @ half_distinct_goalss;
-
- fun after_qed thmss lthy =
- let
- val ([exhaust_thm], (inject_thmss, half_distinct_thmss)) = (hd thmss, chop n (tl thmss));
-
- val inject_thms = flat inject_thmss;
-
- val rho_As = map (pairself (certifyT lthy)) (map Logic.varifyT_global As ~~ As);
-
- fun inst_thm t thm =
- Drule.instantiate' [] [SOME (certify lthy t)]
- (Thm.instantiate (rho_As, []) (Drule.zero_var_indexes thm));
-
- val uexhaust_thm = inst_thm u exhaust_thm;
-
- val exhaust_cases = map base_name_of_ctr ctrs;
-
- val other_half_distinct_thmss = map (map (fn thm => thm RS not_sym)) half_distinct_thmss;
-
- val (distinct_thms, (distinct_thmsss', distinct_thmsss)) =
- join_halves n half_distinct_thmss other_half_distinct_thmss ||> `transpose;
-
- val nchotomy_thm =
- let
- val goal =
- HOLogic.mk_Trueprop (HOLogic.mk_all (fst u', snd u',
- Library.foldr1 HOLogic.mk_disj exist_xs_u_eq_ctrs));
- in
- Goal.prove_sorry lthy [] [] goal (fn _ => mk_nchotomy_tac n exhaust_thm)
- |> Thm.close_derivation
- end;
-
- val case_thms =
- let
- val goals =
- map3 (fn xctr => fn xf => fn xs =>
- fold_rev Logic.all (fs @ xs) (mk_Trueprop_eq (fcase $ xctr, xf))) xctrs xfs xss;
- in
- map4 (fn k => fn goal => fn injects => fn distinctss =>
- Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
- mk_case_tac ctxt n k case_def injects distinctss)
- |> Thm.close_derivation)
- ks goals inject_thmss distinct_thmsss
- end;
-
- val (case_cong_thm, weak_case_cong_thm) =
- let
- fun mk_prem xctr xs xf xg =
- fold_rev Logic.all xs (Logic.mk_implies (mk_Trueprop_eq (v, xctr),
- mk_Trueprop_eq (xf, xg)));
-
- val goal =
- Logic.list_implies (uv_eq :: map4 mk_prem xctrs xss xfs xgs,
- mk_Trueprop_eq (eta_ufcase, eta_vgcase));
- val weak_goal = Logic.mk_implies (uv_eq, mk_Trueprop_eq (ufcase, vfcase));
- in
- (Goal.prove_sorry lthy [] [] goal (fn _ => mk_case_cong_tac lthy uexhaust_thm case_thms),
- Goal.prove_sorry lthy [] [] weak_goal (K (etac arg_cong 1)))
- |> pairself (Thm.close_derivation #> singleton (Proof_Context.export names_lthy lthy))
- end;
-
- val split_lhs = q $ ufcase;
-
- fun mk_split_conjunct xctr xs f_xs =
- list_all_free xs (HOLogic.mk_imp (HOLogic.mk_eq (u, xctr), q $ f_xs));
- fun mk_split_disjunct xctr xs f_xs =
- list_exists_free xs (HOLogic.mk_conj (HOLogic.mk_eq (u, xctr),
- HOLogic.mk_not (q $ f_xs)));
-
- fun mk_split_goal xctrs xss xfs =
- mk_Trueprop_eq (split_lhs, Library.foldr1 HOLogic.mk_conj
- (map3 mk_split_conjunct xctrs xss xfs));
- fun mk_split_asm_goal xctrs xss xfs =
- mk_Trueprop_eq (split_lhs, HOLogic.mk_not (Library.foldr1 HOLogic.mk_disj
- (map3 mk_split_disjunct xctrs xss xfs)));
-
- fun prove_split selss goal =
- Goal.prove_sorry lthy [] [] goal (fn _ =>
- mk_split_tac lthy uexhaust_thm case_thms selss inject_thmss distinct_thmsss)
- |> Thm.close_derivation
- |> singleton (Proof_Context.export names_lthy lthy);
-
- fun prove_split_asm asm_goal split_thm =
- Goal.prove_sorry lthy [] [] asm_goal (fn {context = ctxt, ...} =>
- mk_split_asm_tac ctxt split_thm)
- |> Thm.close_derivation
- |> singleton (Proof_Context.export names_lthy lthy);
-
- val (split_thm, split_asm_thm) =
- let
- val goal = mk_split_goal xctrs xss xfs;
- val asm_goal = mk_split_asm_goal xctrs xss xfs;
-
- val thm = prove_split (replicate n []) goal;
- val asm_thm = prove_split_asm asm_goal thm;
- in
- (thm, asm_thm)
- end;
-
- val (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms, nontriv_discI_thms,
- disc_exclude_thms, disc_exhaust_thms, sel_exhaust_thms, all_collapse_thms,
- safe_collapse_thms, expand_thms, sel_split_thms, sel_split_asm_thms,
- case_conv_if_thms) =
- if no_discs_sels then
- ([], [], [], [], [], [], [], [], [], [], [], [], [], [], [])
- else
- let
- val udiscs = map (rapp u) discs;
- val uselss = map (map (rapp u)) selss;
- val usel_ctrs = map2 (curry Term.list_comb) ctrs uselss;
- val usel_fs = map2 (curry Term.list_comb) fs uselss;
-
- val vdiscs = map (rapp v) discs;
- val vselss = map (map (rapp v)) selss;
-
- fun make_sel_thm xs' case_thm sel_def =
- zero_var_indexes (Drule.gen_all (Drule.rename_bvars' (map (SOME o fst) xs')
- (Drule.forall_intr_vars (case_thm RS (sel_def RS trans)))));
-
- val sel_thmss = map3 (map oo make_sel_thm) xss' case_thms sel_defss;
-
- fun has_undefined_rhs thm =
- (case snd (HOLogic.dest_eq (HOLogic.dest_Trueprop (prop_of thm))) of
- Const (@{const_name undefined}, _) => true
- | _ => false);
-
- val all_sel_thms =
- (if all_sels_distinct andalso forall null sel_defaultss then
- flat sel_thmss
- else
- map_product (fn s => fn (xs', c) => make_sel_thm xs' c s) sel_defs
- (xss' ~~ case_thms))
- |> filter_out has_undefined_rhs;
-
- fun mk_unique_disc_def () =
- let
- val m = the_single ms;
- val goal = mk_Trueprop_eq (mk_uu_eq (), the_single exist_xs_u_eq_ctrs);
- in
- Goal.prove_sorry lthy [] [] goal (fn _ => mk_unique_disc_def_tac m uexhaust_thm)
- |> Thm.close_derivation
- |> singleton (Proof_Context.export names_lthy lthy)
- end;
-
- fun mk_alternate_disc_def k =
- let
- val goal =
- mk_Trueprop_eq (alternate_disc_lhs (K (nth udiscs)) (3 - k),
- nth exist_xs_u_eq_ctrs (k - 1));
- in
- Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
- mk_alternate_disc_def_tac ctxt k (nth disc_defs (2 - k))
- (nth distinct_thms (2 - k)) uexhaust_thm)
- |> Thm.close_derivation
- |> singleton (Proof_Context.export names_lthy lthy)
- end;
-
- val has_alternate_disc_def =
- exists (fn def => Thm.eq_thm_prop (def, alternate_disc_no_def)) disc_defs;
-
- val disc_defs' =
- map2 (fn k => fn def =>
- if Thm.eq_thm_prop (def, unique_disc_no_def) then mk_unique_disc_def ()
- else if Thm.eq_thm_prop (def, alternate_disc_no_def) then mk_alternate_disc_def k
- else def) ks disc_defs;
-
- val discD_thms = map (fn def => def RS iffD1) disc_defs';
- val discI_thms =
- map2 (fn m => fn def => funpow m (fn thm => exI RS thm) (def RS iffD2)) ms
- disc_defs';
- val not_discI_thms =
- map2 (fn m => fn def => funpow m (fn thm => allI RS thm)
- (unfold_thms lthy @{thms not_ex} (def RS @{thm ssubst[of _ _ Not]})))
- ms disc_defs';
-
- val (disc_thmss', disc_thmss) =
- let
- fun mk_thm discI _ [] = refl RS discI
- | mk_thm _ not_discI [distinct] = distinct RS not_discI;
- fun mk_thms discI not_discI distinctss = map (mk_thm discI not_discI) distinctss;
- in
- map3 mk_thms discI_thms not_discI_thms distinct_thmsss' |> `transpose
- end;
-
- val nontriv_disc_thms =
- flat (map2 (fn b => if is_disc_binding_valid b then I else K [])
- disc_bindings disc_thmss);
-
- fun is_discI_boring b =
- (n = 1 andalso Binding.is_empty b) orelse Binding.eq_name (b, equal_binding);
-
- val nontriv_discI_thms =
- flat (map2 (fn b => if is_discI_boring b then K [] else single) disc_bindings
- discI_thms);
-
- val (disc_exclude_thms, (disc_exclude_thmsss', disc_exclude_thmsss)) =
- let
- fun mk_goal [] = []
- | mk_goal [((_, udisc), (_, udisc'))] =
- [Logic.all u (Logic.mk_implies (HOLogic.mk_Trueprop udisc,
- HOLogic.mk_Trueprop (HOLogic.mk_not udisc')))];
-
- fun prove tac goal =
- Goal.prove_sorry lthy [] [] goal (K tac)
- |> Thm.close_derivation;
-
- val half_pairss = mk_half_pairss (`I (ms ~~ discD_thms ~~ udiscs));
-
- val half_goalss = map mk_goal half_pairss;
- val half_thmss =
- map3 (fn [] => K (K []) | [goal] => fn [(((m, discD), _), _)] =>
- fn disc_thm => [prove (mk_half_disc_exclude_tac lthy m discD disc_thm) goal])
- half_goalss half_pairss (flat disc_thmss');
-
- val other_half_goalss = map (mk_goal o map swap) half_pairss;
- val other_half_thmss =
- map2 (map2 (prove o mk_other_half_disc_exclude_tac)) half_thmss
- other_half_goalss;
- in
- join_halves n half_thmss other_half_thmss ||> `transpose
- |>> has_alternate_disc_def ? K []
- end;
-
- val disc_exhaust_thm =
- let
- fun mk_prem udisc = mk_imp_p [HOLogic.mk_Trueprop udisc];
- val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem udiscs));
- in
- Goal.prove_sorry lthy [] [] goal (fn _ =>
- mk_disc_exhaust_tac n exhaust_thm discI_thms)
- |> Thm.close_derivation
- end;
-
- val (safe_collapse_thms, all_collapse_thms) =
- let
- fun mk_goal m udisc usel_ctr =
- let
- val prem = HOLogic.mk_Trueprop udisc;
- val concl = mk_Trueprop_eq ((usel_ctr, u) |> m = 0 ? swap);
- in
- (prem aconv concl, Logic.all u (Logic.mk_implies (prem, concl)))
- end;
- val (trivs, goals) = map3 mk_goal ms udiscs usel_ctrs |> split_list;
- val thms =
- map5 (fn m => fn discD => fn sel_thms => fn triv => fn goal =>
- Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
- mk_collapse_tac ctxt m discD sel_thms ORELSE HEADGOAL atac)
- |> Thm.close_derivation
- |> not triv ? perhaps (try (fn thm => refl RS thm)))
- ms discD_thms sel_thmss trivs goals;
- in
- (map_filter (fn (true, _) => NONE | (false, thm) => SOME thm) (trivs ~~ thms),
- thms)
- end;
-
- val swapped_all_collapse_thms =
- map2 (fn m => fn thm => if m = 0 then thm else thm RS sym) ms all_collapse_thms;
-
- val sel_exhaust_thm =
- let
- fun mk_prem usel_ctr = mk_imp_p [mk_Trueprop_eq (u, usel_ctr)];
- val goal = fold_rev Logic.all [p, u] (mk_imp_p (map mk_prem usel_ctrs));
- in
- Goal.prove_sorry lthy [] [] goal (fn _ =>
- mk_sel_exhaust_tac n disc_exhaust_thm swapped_all_collapse_thms)
- |> Thm.close_derivation
- end;
-
- val expand_thm =
- let
- fun mk_prems k udisc usels vdisc vsels =
- (if k = n then [] else [mk_Trueprop_eq (udisc, vdisc)]) @
- (if null usels then
- []
- else
- [Logic.list_implies
- (if n = 1 then [] else map HOLogic.mk_Trueprop [udisc, vdisc],
- HOLogic.mk_Trueprop (Library.foldr1 HOLogic.mk_conj
- (map2 (curry HOLogic.mk_eq) usels vsels)))]);
-
- val goal =
- Library.foldr Logic.list_implies
- (map5 mk_prems ks udiscs uselss vdiscs vselss, uv_eq);
- val uncollapse_thms =
- map2 (fn thm => fn [] => thm | _ => thm RS sym) all_collapse_thms uselss;
- in
- Goal.prove_sorry lthy [] [] goal (fn _ =>
- mk_expand_tac lthy n ms (inst_thm u disc_exhaust_thm)
- (inst_thm v disc_exhaust_thm) uncollapse_thms disc_exclude_thmsss
- disc_exclude_thmsss')
- |> Thm.close_derivation
- |> singleton (Proof_Context.export names_lthy lthy)
- end;
-
- val (sel_split_thm, sel_split_asm_thm) =
- let
- val zss = map (K []) xss;
- val goal = mk_split_goal usel_ctrs zss usel_fs;
- val asm_goal = mk_split_asm_goal usel_ctrs zss usel_fs;
-
- val thm = prove_split sel_thmss goal;
- val asm_thm = prove_split_asm asm_goal thm;
- in
- (thm, asm_thm)
- end;
-
- val case_conv_if_thm =
- let
- val goal = mk_Trueprop_eq (ufcase, mk_IfN B udiscs usel_fs);
- in
- Goal.prove_sorry lthy [] [] goal (fn {context = ctxt, ...} =>
- mk_case_conv_if_tac ctxt n uexhaust_thm case_thms disc_thmss' sel_thmss)
- |> Thm.close_derivation
- |> singleton (Proof_Context.export names_lthy lthy)
- end;
- in
- (all_sel_thms, sel_thmss, disc_thmss, nontriv_disc_thms, discI_thms,
- nontriv_discI_thms, disc_exclude_thms, [disc_exhaust_thm], [sel_exhaust_thm],
- all_collapse_thms, safe_collapse_thms, [expand_thm], [sel_split_thm],
- [sel_split_asm_thm], [case_conv_if_thm])
- end;
-
- val exhaust_case_names_attr = Attrib.internal (K (Rule_Cases.case_names exhaust_cases));
- val cases_type_attr = Attrib.internal (K (Induct.cases_type fcT_name));
-
- val notes =
- [(caseN, case_thms, code_nitpick_simp_simp_attrs),
- (case_congN, [case_cong_thm], []),
- (case_conv_ifN, case_conv_if_thms, []),
- (collapseN, safe_collapse_thms, simp_attrs),
- (discN, nontriv_disc_thms, simp_attrs),
- (discIN, nontriv_discI_thms, []),
- (disc_excludeN, disc_exclude_thms, dest_attrs),
- (disc_exhaustN, disc_exhaust_thms, [exhaust_case_names_attr]),
- (distinctN, distinct_thms, simp_attrs @ induct_simp_attrs),
- (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]),
- (expandN, expand_thms, []),
- (injectN, inject_thms, iff_attrs @ induct_simp_attrs),
- (nchotomyN, [nchotomy_thm], []),
- (selN, all_sel_thms, code_nitpick_simp_simp_attrs),
- (sel_exhaustN, sel_exhaust_thms, [exhaust_case_names_attr]),
- (sel_splitN, sel_split_thms, []),
- (sel_split_asmN, sel_split_asm_thms, []),
- (splitN, [split_thm], []),
- (split_asmN, [split_asm_thm], []),
- (splitsN, [split_thm, split_asm_thm], []),
- (weak_case_cong_thmsN, [weak_case_cong_thm], cong_attrs)]
- |> filter_out (null o #2)
- |> map (fn (thmN, thms, attrs) =>
- ((qualify true (Binding.name thmN), attrs), [(thms, [])]));
-
- val notes' =
- [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs)]
- |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])]));
-
- val ctr_sugar =
- {ctrs = ctrs, casex = casex, discs = discs, selss = selss, exhaust = exhaust_thm,
- nchotomy = nchotomy_thm, injects = inject_thms, distincts = distinct_thms,
- case_thms = case_thms, case_cong = case_cong_thm, weak_case_cong = weak_case_cong_thm,
- split = split_thm, split_asm = split_asm_thm, disc_thmss = disc_thmss,
- discIs = discI_thms, sel_thmss = sel_thmss, disc_exhausts = disc_exhaust_thms,
- sel_exhausts = sel_exhaust_thms, collapses = all_collapse_thms, expands = expand_thms,
- sel_splits = sel_split_thms, sel_split_asms = sel_split_asm_thms,
- case_conv_ifs = case_conv_if_thms};
- in
- (ctr_sugar,
- lthy
- |> not rep_compat ?
- (Local_Theory.declaration {syntax = false, pervasive = true}
- (fn phi => Case_Translation.register
- (Morphism.term phi casex) (map (Morphism.term phi) ctrs)))
- |> Local_Theory.notes (notes' @ notes) |> snd
- |> register_ctr_sugar fcT_name ctr_sugar)
- end;
- in
- (goalss, after_qed, lthy')
- end;
-
-fun wrap_free_constructors tacss = (fn (goalss, after_qed, lthy) =>
- map2 (map2 (Thm.close_derivation oo Goal.prove_sorry lthy [] [])) goalss tacss
- |> (fn thms => after_qed thms lthy)) oo prepare_wrap_free_constructors (K I);
-
-val wrap_free_constructors_cmd = (fn (goalss, after_qed, lthy) =>
- Proof.theorem NONE (snd oo after_qed) (map (map (rpair [])) goalss) lthy) oo
- prepare_wrap_free_constructors Syntax.read_term;
-
-fun parse_bracket_list parser = @{keyword "["} |-- Parse.list parser --| @{keyword "]"};
-
-val parse_bindings = parse_bracket_list parse_binding;
-val parse_bindingss = parse_bracket_list parse_bindings;
-
-val parse_bound_term = (parse_binding --| @{keyword ":"}) -- Parse.term;
-val parse_bound_terms = parse_bracket_list parse_bound_term;
-val parse_bound_termss = parse_bracket_list parse_bound_terms;
-
-val parse_wrap_free_constructors_options =
- Scan.optional (@{keyword "("} |-- Parse.list1 ((@{keyword "no_discs_sels"} >> K (true, false)) ||
- (@{keyword "rep_compat"} >> K (false, true))) --| @{keyword ")"}
- >> (pairself (exists I) o split_list)) (false, false);
-
-val _ =
- Outer_Syntax.local_theory_to_proof @{command_spec "wrap_free_constructors"}
- "wrap an existing freely generated type's constructors"
- ((parse_wrap_free_constructors_options -- (@{keyword "["} |-- Parse.list Parse.term --|
- @{keyword "]"}) --
- parse_binding -- Scan.optional (parse_bindings -- Scan.optional (parse_bindingss --
- Scan.optional parse_bound_termss []) ([], [])) ([], ([], [])))
- >> wrap_free_constructors_cmd);
-
-end;