--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/BNF/Tools/ctr_sugar.ML Tue Oct 01 14:05:25 2013 +0200
@@ -0,0 +1,956 @@
+(* 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 BNF_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 ctr 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) = map4 mk_goal ms ctrs 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;