diff --git a/src/HOL/Library/Saturated.thy b/src/HOL/Library/Saturated.thy --- a/src/HOL/Library/Saturated.thy +++ b/src/HOL/Library/Saturated.thy @@ -1,269 +1,254 @@ (* Title: HOL/Library/Saturated.thy Author: Brian Huffman Author: Peter Gammie Author: Florian Haftmann *) section \Saturated arithmetic\ theory Saturated imports Numeral_Type Type_Length begin subsection \The type of saturated naturals\ typedef (overloaded) ('a::len) sat = "{.. LENGTH('a)}" morphisms nat_of Abs_sat by auto lemma sat_eqI: "nat_of m = nat_of n \ m = n" by (simp add: nat_of_inject) lemma sat_eq_iff: "m = n \ nat_of m = nat_of n" by (simp add: nat_of_inject) lemma Abs_sat_nat_of [code abstype]: "Abs_sat (nat_of n) = n" by (fact nat_of_inverse) definition Abs_sat' :: "nat \ 'a::len sat" where "Abs_sat' n = Abs_sat (min (LENGTH('a)) n)" lemma nat_of_Abs_sat' [simp]: "nat_of (Abs_sat' n :: ('a::len) sat) = min (LENGTH('a)) n" unfolding Abs_sat'_def by (rule Abs_sat_inverse) simp lemma nat_of_le_len_of [simp]: "nat_of (n :: ('a::len) sat) \ LENGTH('a)" using nat_of [where x = n] by simp lemma min_len_of_nat_of [simp]: "min (LENGTH('a)) (nat_of (n::('a::len) sat)) = nat_of n" by (rule min.absorb2 [OF nat_of_le_len_of]) lemma min_nat_of_len_of [simp]: "min (nat_of (n::('a::len) sat)) (LENGTH('a)) = nat_of n" by (subst min.commute) simp lemma Abs_sat'_nat_of [simp]: "Abs_sat' (nat_of n) = n" by (simp add: Abs_sat'_def nat_of_inverse) instantiation sat :: (len) linorder begin definition less_eq_sat_def: "x \ y \ nat_of x \ nat_of y" definition less_sat_def: "x < y \ nat_of x < nat_of y" instance by standard (auto simp add: less_eq_sat_def less_sat_def not_le sat_eq_iff min.coboundedI1 mult.commute) end instantiation sat :: (len) "{minus, comm_semiring_1}" begin definition "0 = Abs_sat' 0" definition "1 = Abs_sat' 1" lemma nat_of_zero_sat [simp, code abstract]: "nat_of 0 = 0" by (simp add: zero_sat_def) lemma nat_of_one_sat [simp, code abstract]: "nat_of 1 = min 1 (LENGTH('a))" by (simp add: one_sat_def) definition "x + y = Abs_sat' (nat_of x + nat_of y)" lemma nat_of_plus_sat [simp, code abstract]: "nat_of (x + y) = min (nat_of x + nat_of y) (LENGTH('a))" by (simp add: plus_sat_def) definition "x - y = Abs_sat' (nat_of x - nat_of y)" lemma nat_of_minus_sat [simp, code abstract]: "nat_of (x - y) = nat_of x - nat_of y" proof - from nat_of_le_len_of [of x] have "nat_of x - nat_of y \ LENGTH('a)" by arith then show ?thesis by (simp add: minus_sat_def) qed definition "x * y = Abs_sat' (nat_of x * nat_of y)" lemma nat_of_times_sat [simp, code abstract]: "nat_of (x * y) = min (nat_of x * nat_of y) (LENGTH('a))" by (simp add: times_sat_def) instance proof fix a b c :: "'a::len sat" show "a * b * c = a * (b * c)" proof(cases "a = 0") case True thus ?thesis by (simp add: sat_eq_iff) next case False show ?thesis proof(cases "c = 0") case True thus ?thesis by (simp add: sat_eq_iff) next case False with \a \ 0\ show ?thesis by (simp add: sat_eq_iff nat_mult_min_left nat_mult_min_right mult.assoc min.assoc min.absorb2) qed qed show "1 * a = a" - apply (simp add: sat_eq_iff) - apply (metis One_nat_def len_gt_0 less_Suc0 less_zeroE linorder_not_less min.absorb_iff1 min_nat_of_len_of nat_mult_1_right mult.commute) - done + by (simp add: sat_eq_iff min_def not_le not_less) show "(a + b) * c = a * c + b * c" proof(cases "c = 0") case True thus ?thesis by (simp add: sat_eq_iff) next case False thus ?thesis by (simp add: sat_eq_iff nat_mult_min_left add_mult_distrib min_add_distrib_left min_add_distrib_right min.assoc min.absorb2) qed qed (simp_all add: sat_eq_iff mult.commute) end instantiation sat :: (len) ordered_comm_semiring begin instance by standard (auto simp add: less_eq_sat_def less_sat_def not_le sat_eq_iff min.coboundedI1 mult.commute) end lemma Abs_sat'_eq_of_nat: "Abs_sat' n = of_nat n" by (rule sat_eqI, induct n, simp_all) abbreviation Sat :: "nat \ 'a::len sat" where "Sat \ of_nat" lemma nat_of_Sat [simp]: "nat_of (Sat n :: ('a::len) sat) = min (LENGTH('a)) n" by (rule nat_of_Abs_sat' [unfolded Abs_sat'_eq_of_nat]) lemma [code_abbrev]: "of_nat (numeral k) = (numeral k :: 'a::len sat)" by simp context begin qualified definition sat_of_nat :: "nat \ ('a::len) sat" where [code_abbrev]: "sat_of_nat = of_nat" lemma [code abstract]: "nat_of (sat_of_nat n :: ('a::len) sat) = min (LENGTH('a)) n" by (simp add: sat_of_nat_def) end instance sat :: (len) finite proof show "finite (UNIV::'a sat set)" unfolding type_definition.univ [OF type_definition_sat] using finite by simp qed instantiation sat :: (len) equal begin definition "HOL.equal A B \ nat_of A = nat_of B" instance by standard (simp add: equal_sat_def nat_of_inject) end instantiation sat :: (len) "{bounded_lattice, distrib_lattice}" begin definition "(inf :: 'a sat \ 'a sat \ 'a sat) = min" definition "(sup :: 'a sat \ 'a sat \ 'a sat) = max" definition "bot = (0 :: 'a sat)" definition "top = Sat (LENGTH('a))" instance by standard (simp_all add: inf_sat_def sup_sat_def bot_sat_def top_sat_def max_min_distrib2, simp_all add: less_eq_sat_def) end instantiation sat :: (len) "{Inf, Sup}" begin -definition "Inf = (semilattice_neutr_set.F min top :: 'a sat set \ 'a sat)" -definition "Sup = (semilattice_neutr_set.F max bot :: 'a sat set \ 'a sat)" +global_interpretation Inf_sat: semilattice_neutr_set min \top :: 'a sat\ + defines Inf_sat = Inf_sat.F + by standard (simp add: min_def) + +global_interpretation Sup_sat: semilattice_neutr_set max \bot :: 'a sat\ + defines Sup_sat = Sup_sat.F + by standard (simp add: max_def bot.extremum_unique) instance .. end -interpretation Inf_sat: semilattice_neutr_set min "top :: 'a::len sat" - rewrites "semilattice_neutr_set.F min (top :: 'a sat) = Inf" -proof - - show "semilattice_neutr_set min (top :: 'a sat)" - by standard (simp add: min_def) - show "semilattice_neutr_set.F min (top :: 'a sat) = Inf" - by (simp add: Inf_sat_def) -qed - -interpretation Sup_sat: semilattice_neutr_set max "bot :: 'a::len sat" - rewrites "semilattice_neutr_set.F max (bot :: 'a sat) = Sup" -proof - - show "semilattice_neutr_set max (bot :: 'a sat)" - by standard (simp add: max_def bot.extremum_unique) - show "semilattice_neutr_set.F max (bot :: 'a sat) = Sup" - by (simp add: Sup_sat_def) -qed - instance sat :: (len) complete_lattice proof fix x :: "'a sat" fix A :: "'a sat set" note finite moreover assume "x \ A" ultimately show "Inf A \ x" by (induct A) (auto intro: min.coboundedI2) next fix z :: "'a sat" fix A :: "'a sat set" note finite moreover assume z: "\x. x \ A \ z \ x" ultimately show "z \ Inf A" by (induct A) simp_all next fix x :: "'a sat" fix A :: "'a sat set" note finite moreover assume "x \ A" ultimately show "x \ Sup A" by (induct A) (auto intro: max.coboundedI2) next fix z :: "'a sat" fix A :: "'a sat set" note finite moreover assume z: "\x. x \ A \ x \ z" ultimately show "Sup A \ z" by (induct A) auto next show "Inf {} = (top::'a sat)" by (auto simp: top_sat_def) show "Sup {} = (bot::'a sat)" by (auto simp: bot_sat_def) qed end diff --git a/src/Pure/Isar/class.ML b/src/Pure/Isar/class.ML --- a/src/Pure/Isar/class.ML +++ b/src/Pure/Isar/class.ML @@ -1,836 +1,844 @@ (* Title: Pure/Isar/class.ML Author: Florian Haftmann, TU Muenchen Type classes derived from primitive axclasses and locales. *) signature CLASS = sig (*classes*) val is_class: theory -> class -> bool val these_params: theory -> sort -> (string * (class * (string * typ))) list val base_sort: theory -> class -> sort val rules: theory -> class -> thm option * thm val these_defs: theory -> sort -> thm list val these_operations: theory -> sort -> (string * (class * ((typ * term) * bool))) list val print_classes: Proof.context -> unit val init: class -> theory -> Proof.context val begin: class list -> sort -> Proof.context -> Proof.context val const: class -> (binding * mixfix) * term -> term list * term list -> local_theory -> local_theory val abbrev: class -> Syntax.mode -> (binding * mixfix) * term -> local_theory -> (term * term) * local_theory val redeclare_operations: theory -> sort -> Proof.context -> Proof.context val class_prefix: string -> string val register: class -> class list -> ((string * typ) * (string * typ)) list -> sort -> morphism -> morphism -> thm option -> thm option -> thm -> theory -> theory (*instances*) val instantiation: string list * (string * sort) list * sort -> theory -> local_theory val instantiation_instance: (local_theory -> local_theory) -> local_theory -> Proof.state val prove_instantiation_instance: (Proof.context -> tactic) -> local_theory -> local_theory val prove_instantiation_exit: (Proof.context -> tactic) -> local_theory -> theory val prove_instantiation_exit_result: (morphism -> 'a -> 'b) -> (Proof.context -> 'b -> tactic) -> 'a -> local_theory -> 'b * theory val read_multi_arity: theory -> xstring list * xstring list * xstring -> string list * (string * sort) list * sort val instantiation_cmd: xstring list * xstring list * xstring -> theory -> local_theory val instance_arity_cmd: xstring list * xstring list * xstring -> theory -> Proof.state val theory_map_result: string list * (string * sort) list * sort -> (morphism -> 'a -> 'b) -> (local_theory -> 'a * local_theory) -> (Proof.context -> 'b -> tactic) -> theory -> 'b * theory (*subclasses*) val classrel: class * class -> theory -> Proof.state val classrel_cmd: xstring * xstring -> theory -> Proof.state val register_subclass: class * class -> morphism option -> Element.witness option -> morphism -> local_theory -> local_theory (*tactics*) val intro_classes_tac: Proof.context -> thm list -> tactic val standard_intro_classes_tac: Proof.context -> thm list -> tactic (*diagnostics*) val pretty_specification: theory -> class -> Pretty.T list end; structure Class: CLASS = struct (** class data **) datatype class_data = Class_Data of { (* static part *) consts: (string * string) list (*locale parameter ~> constant name*), base_sort: sort, base_morph: morphism (*static part of canonical morphism*), export_morph: morphism, assm_intro: thm option, of_class: thm, axiom: thm option, (* dynamic part *) defs: thm list, operations: (string * (class * ((typ * term) * bool))) list (* n.b. params = logical parameters of class operations = operations participating in user-space type system *) }; fun make_class_data ((consts, base_sort, base_morph, export_morph, assm_intro, of_class, axiom), (defs, operations)) = Class_Data {consts = consts, base_sort = base_sort, base_morph = base_morph, export_morph = export_morph, assm_intro = assm_intro, of_class = of_class, axiom = axiom, defs = defs, operations = operations}; fun map_class_data f (Class_Data {consts, base_sort, base_morph, export_morph, assm_intro, of_class, axiom, defs, operations}) = make_class_data (f ((consts, base_sort, base_morph, export_morph, assm_intro, of_class, axiom), (defs, operations))); fun merge_class_data _ (Class_Data {consts = consts, base_sort = base_sort, base_morph = base_morph, export_morph = export_morph, assm_intro = assm_intro, of_class = of_class, axiom = axiom, defs = defs1, operations = operations1}, Class_Data {consts = _, base_sort = _, base_morph = _, export_morph = _, assm_intro = _, of_class = _, axiom = _, defs = defs2, operations = operations2}) = make_class_data ((consts, base_sort, base_morph, export_morph, assm_intro, of_class, axiom), (Thm.merge_thms (defs1, defs2), AList.merge (op =) (K true) (operations1, operations2))); structure Class_Data = Theory_Data ( type T = class_data Graph.T val empty = Graph.empty; val extend = I; val merge = Graph.join merge_class_data; ); (* queries *) fun lookup_class_data thy class = (case try (Graph.get_node (Class_Data.get thy)) class of SOME (Class_Data data) => SOME data | NONE => NONE); fun the_class_data thy class = (case lookup_class_data thy class of NONE => error ("Undeclared class " ^ quote class) | SOME data => data); val is_class = is_some oo lookup_class_data; val ancestry = Graph.all_succs o Class_Data.get; val heritage = Graph.all_preds o Class_Data.get; fun these_params thy = let fun params class = let val const_typs = (#params o Axclass.get_info thy) class; val const_names = (#consts o the_class_data thy) class; in (map o apsnd) (fn c => (class, (c, (the o AList.lookup (op =) const_typs) c))) const_names end; in maps params o ancestry thy end; val base_sort = #base_sort oo the_class_data; fun rules thy class = let val {axiom, of_class, ...} = the_class_data thy class in (axiom, of_class) end; fun all_assm_intros thy = Graph.fold (fn (_, (Class_Data {assm_intro, ...}, _)) => fold (insert Thm.eq_thm) (the_list assm_intro)) (Class_Data.get thy) []; fun these_defs thy = maps (#defs o the_class_data thy) o ancestry thy; fun these_operations thy = maps (#operations o the_class_data thy) o ancestry thy; val base_morphism = #base_morph oo the_class_data; fun morphism thy class = (case Element.eq_morphism thy (these_defs thy [class]) of SOME eq_morph => base_morphism thy class $> eq_morph | NONE => base_morphism thy class); val export_morphism = #export_morph oo the_class_data; fun pretty_param ctxt (c, ty) = Pretty.block [Name_Space.pretty ctxt (Proof_Context.const_space ctxt) c, Pretty.str " ::", Pretty.brk 1, Syntax.pretty_typ ctxt ty]; fun print_classes ctxt = let val thy = Proof_Context.theory_of ctxt; val algebra = Sign.classes_of thy; val class_space = Proof_Context.class_space ctxt; val type_space = Proof_Context.type_space ctxt; val arities = Symtab.empty |> Symtab.fold (fn (tyco, arities) => fold (fn (class, _) => Symtab.map_default (class, []) (insert (op =) tyco)) arities) (Sorts.arities_of algebra); fun prt_supersort class = Syntax.pretty_sort ctxt (Sign.minimize_sort thy (Sign.super_classes thy class)); fun prt_arity class tyco = let val Ss = Sorts.mg_domain algebra tyco [class]; in Syntax.pretty_arity ctxt (tyco, Ss, [class]) end; fun prt_param (c, ty) = pretty_param ctxt (c, Type.strip_sorts_dummy ty); fun prt_entry class = Pretty.block ([Pretty.keyword1 "class", Pretty.brk 1, Name_Space.pretty ctxt class_space class, Pretty.str ":", Pretty.fbrk, Pretty.block [Pretty.str "supersort: ", prt_supersort class]] @ (case (these o Option.map #params o try (Axclass.get_info thy)) class of [] => [] | params => [Pretty.fbrk, Pretty.big_list "parameters:" (map prt_param params)]) @ (case (these o Symtab.lookup arities) class of [] => [] | ars => [Pretty.fbrk, Pretty.big_list "instances:" (map (prt_arity class) (sort (Name_Space.extern_ord ctxt type_space) ars))])); in Sorts.all_classes algebra |> sort (Name_Space.extern_ord ctxt class_space) |> map prt_entry |> Pretty.writeln_chunks2 end; (* updaters *) fun register class sups params base_sort base_morph export_morph some_axiom some_assm_intro of_class thy = let val operations = map (fn (v_ty as (_, ty), (c, _)) => (c, (class, ((ty, Free v_ty), false)))) params; val add_class = Graph.new_node (class, make_class_data (((map o apply2) fst params, base_sort, base_morph, export_morph, Option.map Thm.trim_context some_assm_intro, Thm.trim_context of_class, Option.map Thm.trim_context some_axiom), ([], operations))) #> fold (curry Graph.add_edge class) sups; in Class_Data.map add_class thy end; fun activate_defs class thms thy = (case Element.eq_morphism thy thms of SOME eq_morph => fold (fn cls => fn thy => Context.theory_map (Locale.amend_registration {inst = (cls, base_morphism thy cls), mixin = SOME (eq_morph, true), export = export_morphism thy cls}) thy) (heritage thy [class]) thy | NONE => thy); fun register_operation class (c, t) input_only thy = let val base_sort = base_sort thy class; val prep_typ = map_type_tfree (fn (v, sort) => if Name.aT = v then TFree (v, base_sort) else TVar ((v, 0), sort)); val t' = map_types prep_typ t; val ty' = Term.fastype_of t'; in thy |> (Class_Data.map o Graph.map_node class o map_class_data o apsnd o apsnd) (cons (c, (class, ((ty', t'), input_only)))) end; fun register_def class def_thm thy = let val sym_thm = Thm.trim_context (Thm.symmetric def_thm) in thy |> (Class_Data.map o Graph.map_node class o map_class_data o apsnd o apfst) (cons sym_thm) |> activate_defs class [sym_thm] end; (** classes and class target **) (* class context syntax *) fun make_rewrite t c_ty = let - val (vs, t') = strip_abs t; + val vs = strip_abs_vars t; val vts = map snd vs |> Name.invent_names Name.context Name.uu |> map (fn (v, T) => Var ((v, 0), T)); in (betapplys (t, vts), betapplys (Const c_ty, vts)) end; fun these_unchecks thy = these_operations thy #> map_filter (fn (c, (_, ((ty, t), input_only))) => if input_only then NONE else SOME (make_rewrite t (c, ty))); fun these_unchecks_reversed thy = these_operations thy #> map (fn (c, (_, ((ty, t), _))) => (Const (c, ty), t)); fun redeclare_const thy c = let val b = Long_Name.base_name c in Sign.intern_const thy b = c ? Variable.declare_const (b, c) end; fun synchronize_class_syntax sort base_sort ctxt = let val thy = Proof_Context.theory_of ctxt; val algebra = Sign.classes_of thy; val operations = these_operations thy sort; fun subst_class_typ sort = map_type_tfree (K (TVar ((Name.aT, 0), sort))); val primary_constraints = (map o apsnd) (subst_class_typ base_sort o fst o fst o snd) operations; val secondary_constraints = (map o apsnd) (fn (class, ((ty, _), _)) => subst_class_typ [class] ty) operations; fun improve (c, ty) = (case AList.lookup (op =) primary_constraints c of SOME ty' => (case try (Type.raw_match (ty', ty)) Vartab.empty of SOME tyenv => (case Vartab.lookup tyenv (Name.aT, 0) of SOME (_, ty' as TVar (vi, sort)) => if Type_Infer.is_param vi andalso Sorts.sort_le algebra (base_sort, sort) then SOME (ty', Term.aT base_sort) else NONE | _ => NONE) | NONE => NONE) | NONE => NONE); fun subst (c, _) = Option.map (fst o snd) (AList.lookup (op =) operations c); val unchecks = these_unchecks thy sort; in ctxt |> fold (redeclare_const thy o fst) primary_constraints |> Overloading.map_improvable_syntax (K {primary_constraints = primary_constraints, secondary_constraints = secondary_constraints, improve = improve, subst = subst, no_subst_in_abbrev_mode = true, unchecks = unchecks}) |> Overloading.set_primary_constraints end; fun synchronize_class_syntax_target class lthy = lthy |> Local_Theory.map_contexts (K (synchronize_class_syntax [class] (base_sort (Proof_Context.theory_of lthy) class))); fun redeclare_operations thy sort = fold (redeclare_const thy o fst) (these_operations thy sort); fun begin sort base_sort ctxt = ctxt |> Variable.declare_term (Logic.mk_type (Term.aT base_sort)) |> synchronize_class_syntax sort base_sort |> Overloading.activate_improvable_syntax; fun init class thy = thy |> Locale.init class |> begin [class] (base_sort thy class); (* class target *) val class_prefix = Logic.const_of_class o Long_Name.base_name; fun guess_morphism_identity (b, rhs) phi1 phi2 = let (*FIXME proper concept to identify morphism instead of educated guess*) val name_of_binding = Name_Space.full_name Name_Space.global_naming; val n1 = (name_of_binding o Morphism.binding phi1) b; val n2 = (name_of_binding o Morphism.binding phi2) b; val rhs1 = Morphism.term phi1 rhs; val rhs2 = Morphism.term phi2 rhs; in n1 = n2 andalso Term.aconv_untyped (rhs1, rhs2) end; fun target_const class phi0 prmode (b, rhs) lthy = let val export = Variable.export_morphism lthy (Local_Theory.target_of lthy); val guess_identity = guess_morphism_identity (b, rhs) export; val guess_canonical = guess_morphism_identity (b, rhs) (export $> phi0); in lthy |> Generic_Target.locale_target_const class (not o (guess_identity orf guess_canonical)) prmode ((b, NoSyn), rhs) end; local fun dangling_params_for lthy class (type_params, term_params) = let val class_param_names = map fst (these_params (Proof_Context.theory_of lthy) [class]); val dangling_term_params = subtract (fn (v, Free (w, _)) => v = w | _ => false) class_param_names term_params; in (type_params, dangling_term_params) end; fun global_def (b, eq) thy = let val ((_, def_thm), thy') = thy |> Thm.add_def_global false false (b, eq); val def_thm' = def_thm |> Thm.forall_intr_frees |> Thm.forall_elim_vars 0 |> Thm.varifyT_global; val (_, thy'') = thy' |> Global_Theory.store_thm (b, def_thm'); in (def_thm', thy'') end; fun canonical_const class phi dangling_params ((b, mx), rhs) thy = let val b_def = Binding.suffix_name "_dict" b; val c = Sign.full_name thy b; val ty = map Term.fastype_of dangling_params ---> Term.fastype_of rhs; val def_eq = Logic.mk_equals (list_comb (Const (c, ty), dangling_params), rhs) |> map_types Type.strip_sorts; in thy |> Sign.declare_const_global ((b, Type.strip_sorts ty), mx) |> snd |> global_def (b_def, def_eq) |-> (fn def_thm => register_def class def_thm) |> null dangling_params ? register_operation class (c, rhs) false |> Sign.add_const_constraint (c, SOME ty) end; in fun const class ((b, mx), lhs) params lthy = let val phi = morphism (Proof_Context.theory_of lthy) class; val dangling_params = map (Morphism.term phi) (uncurry append (dangling_params_for lthy class params)); in lthy |> target_const class phi Syntax.mode_default (b, lhs) |> Local_Theory.raw_theory (canonical_const class phi dangling_params ((Morphism.binding phi b, if null dangling_params then mx else NoSyn), Morphism.term phi lhs)) |> Generic_Target.standard_const (fn (this, other) => other <> 0 andalso this <> other) Syntax.mode_default ((b, if null dangling_params then NoSyn else mx), lhs) |> synchronize_class_syntax_target class end; end; local fun canonical_abbrev class phi prmode with_syntax ((b, mx), rhs) thy = let val c = Sign.full_name thy b; val constrain = map_atyps (fn T as TFree (v, _) => if v = Name.aT then TFree (v, [class]) else T | T => T); val rhs' = map_types constrain rhs; in thy |> Sign.add_abbrev (#1 prmode) (b, Logic.varify_types_global rhs') |> snd |> with_syntax ? Sign.notation true prmode [(Const (c, fastype_of rhs), mx)] |> with_syntax ? register_operation class (c, rhs) (#1 prmode = Print_Mode.input) |> Sign.add_const_constraint (c, SOME (fastype_of rhs')) end; fun canonical_abbrev_target class phi prmode ((b, mx), rhs) lthy = let val thy = Proof_Context.theory_of lthy; val preprocess = perhaps (try (Pattern.rewrite_term_top thy (these_unchecks thy [class]) [])); - val (global_rhs, (extra_tfrees, (type_params, term_params))) = + val (global_rhs, (_, (_, term_params))) = Generic_Target.export_abbrev lthy preprocess rhs; val mx' = Generic_Target.check_mixfix_global (b, null term_params) mx; in lthy |> Local_Theory.raw_theory (canonical_abbrev class phi prmode (null term_params) ((Morphism.binding phi b, mx'), Logic.unvarify_types_global global_rhs)) end; fun further_abbrev_target class phi prmode (b, mx) rhs params = Generic_Target.background_abbrev (b, rhs) (snd params) #-> (fn (lhs, _) => target_const class phi prmode (b, lhs) #> Generic_Target.standard_const (fn (this, other) => other <> 0 andalso this <> other) prmode ((b, mx), lhs)) in fun abbrev class prmode ((b, mx), rhs) lthy = let val thy = Proof_Context.theory_of lthy; val phi = morphism thy class; val rhs_generic = perhaps (try (Pattern.rewrite_term_top thy (these_unchecks_reversed thy [class]) [])) rhs; in lthy |> canonical_abbrev_target class phi prmode ((b, mx), rhs) |> Generic_Target.abbrev (further_abbrev_target class phi) prmode ((b, mx), rhs_generic) ||> synchronize_class_syntax_target class end; end; (* subclasses *) fun register_subclass (sub, sup) some_dep_morph some_witn export lthy = let val thy = Proof_Context.theory_of lthy; val intros = (snd o rules thy) sup :: map_filter I [Option.map (Drule.export_without_context_open o Element.conclude_witness lthy) some_witn, (fst o rules thy) sub]; val classrel = Goal.prove_sorry_global thy [] [] (Logic.mk_classrel (sub, sup)) (fn {context = ctxt, ...} => EVERY (map (TRYALL o resolve_tac ctxt o single) intros)); val diff_sort = Sign.complete_sort thy [sup] |> subtract (op =) (Sign.complete_sort thy [sub]) |> filter (is_class thy); val add_dependency = (case some_dep_morph of SOME dep_morph => Locale.add_dependency sub {inst = (sup, dep_morph $> Element.satisfy_morphism (the_list some_witn)), mixin = NONE, export = export} | NONE => I); in lthy |> Local_Theory.raw_theory (Axclass.add_classrel classrel #> Class_Data.map (Graph.add_edge (sub, sup)) #> activate_defs sub (these_defs thy diff_sort)) |> add_dependency |> synchronize_class_syntax_target sub end; local fun gen_classrel mk_prop classrel thy = let fun after_qed results = Proof_Context.background_theory ((fold o fold) Axclass.add_classrel results); in thy |> Proof_Context.init_global |> Proof.theorem NONE after_qed [[(mk_prop thy classrel, [])]] end; in val classrel = gen_classrel (Logic.mk_classrel oo Axclass.cert_classrel); val classrel_cmd = gen_classrel (Logic.mk_classrel oo Axclass.read_classrel); end; (*local*) (** instantiation target **) (* bookkeeping *) datatype instantiation = Instantiation of { arities: string list * (string * sort) list * sort, params: ((string * string) * (string * typ)) list (*(instantiation parameter, type constructor), (local instantiation parameter, typ)*) } fun make_instantiation (arities, params) = Instantiation {arities = arities, params = params}; val empty_instantiation = make_instantiation (([], [], []), []); structure Instantiation = Proof_Data ( type T = instantiation; fun init _ = empty_instantiation; ); val get_instantiation = (fn Instantiation data => data) o Instantiation.get o Local_Theory.target_of; fun map_instantiation f = (Local_Theory.target o Instantiation.map) (fn Instantiation {arities, params} => make_instantiation (f (arities, params))); fun the_instantiation lthy = (case get_instantiation lthy of {arities = ([], [], []), ...} => error "No instantiation target" | data => data); val instantiation_params = #params o get_instantiation; fun instantiation_param lthy b = instantiation_params lthy |> find_first (fn (_, (v, _)) => Binding.name_of b = v) |> Option.map (fst o fst); fun read_multi_arity thy (raw_tycos, raw_sorts, raw_sort) = let val ctxt = Proof_Context.init_global thy; val all_arities = map (fn raw_tyco => Proof_Context.read_arity ctxt (raw_tyco, raw_sorts, raw_sort)) raw_tycos; val tycos = map #1 all_arities; val (_, sorts, sort) = hd all_arities; val vs = Name.invent_names Name.context Name.aT sorts; in (tycos, vs, sort) end; (* syntax *) fun synchronize_inst_syntax ctxt = let val Instantiation {params, ...} = Instantiation.get ctxt; val lookup_inst_param = Axclass.lookup_inst_param (Sign.consts_of (Proof_Context.theory_of ctxt)) params; fun subst (c, ty) = (case lookup_inst_param (c, ty) of SOME (v_ty as (_, ty)) => SOME (ty, Free v_ty) | NONE => NONE); val unchecks = map (fn ((c, _), v_ty as (_, ty)) => (Free v_ty, Const (c, ty))) params; in ctxt |> Overloading.map_improvable_syntax (fn {primary_constraints, improve, ...} => {primary_constraints = primary_constraints, secondary_constraints = [], improve = improve, subst = subst, no_subst_in_abbrev_mode = false, unchecks = unchecks}) end; fun resort_terms ctxt algebra consts constraints ts = let fun matchings (Const (c_ty as (c, _))) = (case constraints c of NONE => I | SOME sorts => fold2 (curry (Sorts.meet_sort algebra)) (Consts.typargs consts c_ty) sorts) | matchings _ = I; val tvartab = (fold o fold_aterms) matchings ts Vartab.empty handle Sorts.CLASS_ERROR e => error (Sorts.class_error (Context.Proof ctxt) e); val inst = map_type_tvar (fn (vi, sort) => TVar (vi, the_default sort (Vartab.lookup tvartab vi))); in if Vartab.is_empty tvartab then ts else (map o map_types) inst ts end; (* target *) fun define_overloaded (c, U) b (b_def, rhs) lthy = let val name = Binding.name_of b; val pos = Binding.pos_of b; val _ = if Context_Position.is_reported lthy pos then Position.report_text pos Markup.class_parameter (Pretty.string_of (Pretty.block [Pretty.keyword1 "class", Pretty.brk 1, Pretty.str "parameter", Pretty.brk 1, pretty_param lthy (c, U)])) else (); in lthy |> Local_Theory.background_theory_result (Axclass.declare_overloaded (c, U) ##>> Axclass.define_overloaded b_def (c, rhs)) ||> (map_instantiation o apsnd) (filter_out (fn (_, (v', _)) => v' = name)) ||> Local_Theory.map_contexts (K synchronize_inst_syntax) end; fun foundation (((b, U), mx), (b_def, rhs)) params lthy = (case instantiation_param lthy b of SOME c => if Mixfix.is_empty mx then lthy |> define_overloaded (c, U) b (b_def, rhs) else error ("Illegal mixfix syntax for overloaded constant " ^ quote c) | NONE => lthy |> Generic_Target.theory_target_foundation (((b, U), mx), (b_def, rhs)) params); fun pretty lthy = let val {arities = (tycos, vs, sort), params} = the_instantiation lthy; fun pr_arity tyco = Syntax.pretty_arity lthy (tyco, map snd vs, sort); fun pr_param ((c, _), (v, ty)) = Pretty.block (Pretty.breaks [Pretty.str v, Pretty.str "==", Proof_Context.pretty_const lthy c, Pretty.str "::", Syntax.pretty_typ lthy ty]); in [Pretty.block (Pretty.fbreaks (Pretty.keyword1 "instantiation" :: map pr_arity tycos @ map pr_param params))] end; fun conclude lthy = let val (tycos, vs, sort) = #arities (the_instantiation lthy); val thy = Proof_Context.theory_of lthy; val _ = tycos |> List.app (fn tyco => if Sign.of_sort thy (Type (tyco, map TFree vs), sort) then () else error ("Missing instance proof for type " ^ quote (Proof_Context.markup_type lthy tyco))); in lthy end; +fun registration thy_ctxt {inst, mixin, export} lthy = + lthy + |> Locale.add_registration_theory + {inst = inst, + mixin = mixin, + export = export $> Proof_Context.export_morphism lthy thy_ctxt} + (*handle fixed types variables on target context properly*); + fun instantiation (tycos, vs, sort) thy = let val _ = if null tycos then error "At least one arity must be given" else (); val class_params = these_params thy (filter (can (Axclass.get_info thy)) sort); fun get_param tyco (param, (_, (c, ty))) = if can (Axclass.param_of_inst thy) (c, tyco) then NONE else SOME ((c, tyco), (param ^ "_" ^ Long_Name.base_name tyco, map_atyps (K (Type (tyco, map TFree vs))) ty)); val params = map_product get_param tycos class_params |> map_filter I; val _ = if null params andalso forall (fn tyco => can (Sign.arity_sorts thy tyco) sort) tycos then error "No parameters and no pending instance proof obligations in instantiation." else (); val primary_constraints = map (apsnd (map_atyps (K (TVar ((Name.aT, 0), [])))) o snd o snd) class_params; val algebra = Sign.classes_of thy |> fold (fn tyco => Sorts.add_arities (Context.Theory thy) (tyco, map (fn class => (class, map snd vs)) sort)) tycos; val consts = Sign.consts_of thy; val improve_constraints = AList.lookup (op =) (map (fn (_, (class, (c, _))) => (c, [[class]])) class_params); fun resort_check ctxt ts = resort_terms ctxt algebra consts improve_constraints ts; val lookup_inst_param = Axclass.lookup_inst_param consts params; fun improve (c, ty) = (case lookup_inst_param (c, ty) of SOME (_, ty') => if Sign.typ_instance thy (ty', ty) then SOME (ty, ty') else NONE | NONE => NONE); in thy |> Local_Theory.init {background_naming = Sign.naming_of thy, setup = Proof_Context.init_global #> Instantiation.put (make_instantiation ((tycos, vs, sort), params)) #> fold (Variable.declare_typ o TFree) vs #> fold (Variable.declare_names o Free o snd) params #> (Overloading.map_improvable_syntax) (K {primary_constraints = primary_constraints, secondary_constraints = [], improve = improve, subst = K NONE, no_subst_in_abbrev_mode = false, unchecks = []}) #> Overloading.activate_improvable_syntax #> Context.proof_map (Syntax_Phases.term_check 0 "resorting" resort_check) #> synchronize_inst_syntax, conclude = conclude} {define = Generic_Target.define foundation, notes = Generic_Target.notes Generic_Target.theory_target_notes, abbrev = Generic_Target.abbrev Generic_Target.theory_target_abbrev, declaration = K Generic_Target.theory_declaration, - theory_registration = Locale.add_registration_theory, + theory_registration = registration (Proof_Context.init_global thy), locale_dependency = fn _ => error "Not possible in instantiation target", pretty = pretty} end; fun instantiation_cmd arities thy = instantiation (read_multi_arity thy arities) thy; fun gen_instantiation_instance do_proof after_qed lthy = let val (tycos, vs, sort) = (#arities o the_instantiation) lthy; val arities_proof = maps (fn tyco => Logic.mk_arities (tyco, map snd vs, sort)) tycos; fun after_qed' results = Local_Theory.background_theory (fold (Axclass.add_arity o Thm.varifyT_global) results) #> after_qed; in lthy |> do_proof after_qed' arities_proof end; val instantiation_instance = gen_instantiation_instance (fn after_qed => fn ts => Proof.theorem NONE (after_qed o map the_single) (map (fn t => [(t, [])]) ts)); fun prove_instantiation_instance tac = gen_instantiation_instance (fn after_qed => fn ts => fn lthy => after_qed (map (fn t => Goal.prove lthy [] [] t (fn {context, ...} => tac context)) ts) lthy) I; fun prove_instantiation_exit tac = prove_instantiation_instance tac #> Local_Theory.exit_global; fun prove_instantiation_exit_result f tac x lthy = let val morph = Proof_Context.export_morphism lthy (Proof_Context.init_global (Proof_Context.theory_of lthy)); val y = f morph x; in lthy |> prove_instantiation_exit (fn ctxt => tac ctxt y) |> pair y end; fun theory_map_result arities f g tac = instantiation arities #> g #-> prove_instantiation_exit_result f tac; (* simplified instantiation interface with no class parameter *) fun instance_arity_cmd raw_arities thy = let val (tycos, vs, sort) = read_multi_arity thy raw_arities; val sorts = map snd vs; val arities = maps (fn tyco => Logic.mk_arities (tyco, sorts, sort)) tycos; fun after_qed results = Proof_Context.background_theory ((fold o fold) Axclass.add_arity results); in thy |> Proof_Context.init_global |> Proof.theorem NONE after_qed (map (fn t => [(t, [])]) arities) end; (** tactics and methods **) fun intro_classes_tac ctxt facts st = let val thy = Proof_Context.theory_of ctxt; val classes = Sign.all_classes thy; val class_trivs = map (Thm.class_triv thy) classes; val class_intros = map_filter (try (#intro o Axclass.get_info thy)) classes; val assm_intros = all_assm_intros thy; in Method.intros_tac ctxt (class_trivs @ class_intros @ assm_intros) facts st end; fun standard_intro_classes_tac ctxt facts st = if null facts andalso not (Thm.no_prems st) then (intro_classes_tac ctxt [] ORELSE Locale.intro_locales_tac {strict = true, eager = true} ctxt []) st else no_tac st; fun standard_tac ctxt facts = HEADGOAL (Method.some_rule_tac ctxt [] facts) ORELSE standard_intro_classes_tac ctxt facts; val _ = Theory.setup (Method.setup \<^binding>\intro_classes\ (Scan.succeed (METHOD o intro_classes_tac)) "back-chain introduction rules of classes" #> Method.setup \<^binding>\standard\ (Scan.succeed (METHOD o standard_tac)) "standard proof step: Pure intro/elim rule or class introduction"); (** diagnostics **) fun pretty_specification thy class = if is_class thy class then let val class_ctxt = init class thy; val prt_class = Name_Space.pretty class_ctxt (Proof_Context.class_space class_ctxt); val super_classes = Sign.minimize_sort thy (Sign.super_classes thy class); val fix_args = #params (Axclass.get_info thy class) |> map (fn (c, T) => (Binding.name (Long_Name.base_name c), SOME T, NoSyn)); val fixes = if null fix_args then [] else [Element.Fixes fix_args]; val assumes = Locale.hyp_spec_of thy class; val header = [Pretty.keyword1 "class", Pretty.brk 1, prt_class class, Pretty.str " =", Pretty.brk 1] @ Pretty.separate " +" (map prt_class super_classes) @ (if null super_classes then [] else [Pretty.str " +"]); val body = if null fixes andalso null assumes then [] else maps (Element.pretty_ctxt_no_attribs class_ctxt) (fixes @ assumes) |> maps (fn prt => [Pretty.fbrk, prt]); in if null body then [] else [Pretty.block (header @ body)] end else []; end;