author | blanchet |
Thu, 05 Dec 2013 14:11:45 +0100 | |
changeset 54634 | 366297517091 |
parent 54626 | 8a5e82425e55 |
child 54635 | 30666a281ae3 |
permissions | -rw-r--r-- |
(* Title: HOL/Tools/ctr_sugar.ML Author: Jasmin Blanchette, TU Muenchen Copyright 2012, 2013 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_eq_ifs: thm list}; val morph_ctr_sugar: morphism -> ctr_sugar -> ctr_sugar val transfer_ctr_sugar: Proof.context -> ctr_sugar -> ctr_sugar val ctr_sugar_of: Proof.context -> string -> ctr_sugar option val ctr_sugars_of: Proof.context -> ctr_sugar list val ctr_sugar_of_case: Proof.context -> string -> ctr_sugar option val register_ctr_sugar: string -> ctr_sugar -> local_theory -> local_theory val register_ctr_sugar_global: string -> ctr_sugar -> theory -> theory 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 * 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 * bool)) parser val parse_bound_term: (binding * string) parser end; structure Ctr_Sugar : CTR_SUGAR = struct open Ctr_Sugar_Util open Ctr_Sugar_Tactics open Ctr_Sugar_Code 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_eq_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_eq_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_eq_ifs = map (Morphism.thm phi) case_eq_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 ctr_sugar_of_case ctxt s = find_first (fn {casex = Const (s', _), ...} => s' = s | _ => false) (ctr_sugars_of 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))); fun register_ctr_sugar_global key ctr_sugar = Context.theory_map (Data.map (Symtab.default (key, 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_eq_ifN = "case_eq_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 inductsimp_attrs = @{attributes [induct_simp]}; val nitpicksimp_attrs = @{attributes [nitpick_simp]}; val simp_attrs = @{attributes [simp]}; val code_nitpicksimp_attrs = Code.add_default_eqn_attrib :: nitpicksimp_attrs; val code_nitpicksimp_simp_attrs = code_nitpicksimp_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 subst_nonatomic_types (Ts0 ~~ Ts) t end; fun mk_case Ts T t = let val (Type (_, Ts0), body) = strip_type (fastype_of t) |>> List.last in subst_nonatomic_types ((body, T) :: (Ts0 ~~ Ts)) t end; fun mk_disc_or_sel Ts t = subst_nonatomic_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, (no_code, 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 sS) = sS | 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.prefix_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), ((Binding.conceal (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_eq_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_eq_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_eq_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_eq_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 anonymous_notes = [(map (fn th => th RS notE) distinct_thms, safe_elim_attrs), (map (fn th => th RS @{thm eq_False[THEN iffD2]} handle THM _ => th RS @{thm eq_True[THEN iffD2]}) nontriv_disc_thms, code_nitpicksimp_attrs)] |> map (fn (thms, attrs) => ((Binding.empty, attrs), [(thms, [])])); val notes = [(caseN, case_thms, code_nitpicksimp_simp_attrs), (case_congN, [case_cong_thm], []), (case_eq_ifN, case_eq_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 @ inductsimp_attrs), (exhaustN, [exhaust_thm], [exhaust_case_names_attr, cases_type_attr]), (expandN, expand_thms, []), (injectN, inject_thms, iff_attrs @ inductsimp_attrs), (nchotomyN, [nchotomy_thm], []), (selN, all_sel_thms, code_nitpicksimp_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 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_eq_ifs = case_eq_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 (anonymous_notes @ notes) |> snd |> register_ctr_sugar fcT_name ctr_sugar |> (not no_code andalso null (Thm.hyps_of (hd case_thms))) ? Local_Theory.background_theory (add_ctr_code fcT_name As (map dest_Const ctrs) inject_thms distinct_thms case_thms)) 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 (Parse.reserved "no_discs_sels" >> K 0 || Parse.reserved "no_code" >> K 1 || Parse.reserved "rep_compat" >> K 2) --| @{keyword ")"} >> (fn js => (member (op =) js 0, (member (op =) js 1, member (op =) js 2)))) (false, (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;