(* Title: HOL/Tools/typedef_package.ML ID: $Id: typedef_package.ML,v 1.61 2005/09/15 15:16:58 wenzelm Exp $ Author: Markus Wenzel and Stefan Berghofer, TU Muenchen Gordon/HOL-style type definitions. *) signature TYPEDEF_PACKAGE = sig val quiet_mode: bool ref val add_typedecls: (bstring * string list * mixfix) list -> theory -> theory val add_typedef_x: string -> bstring * string list * mixfix -> string -> string list -> thm list -> tactic option -> theory -> theory val add_typedef: bool -> string option -> bstring * string list * mixfix -> string -> (bstring * bstring) option -> tactic -> theory -> theory * {type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm, Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm, Rep_induct: thm, Abs_induct: thm} val add_typedef_i: bool -> string option -> bstring * string list * mixfix -> term -> (bstring * bstring) option -> tactic -> theory -> theory * {type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm, Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm, Rep_induct: thm, Abs_induct: thm} val typedef: (bool * string) * (bstring * string list * mixfix) * string * (string * string) option -> theory -> Proof.state val typedef_i: (bool * string) * (bstring * string list * mixfix) * term * (string * string) option -> theory -> Proof.state val setup: (theory -> theory) list end; structure TypedefPackage: TYPEDEF_PACKAGE = struct (** theory context references **) val type_definitionN = "Typedef.type_definition"; val Rep = thm "type_definition.Rep"; val Rep_inverse = thm "type_definition.Rep_inverse"; val Abs_inverse = thm "type_definition.Abs_inverse"; val Rep_inject = thm "type_definition.Rep_inject"; val Abs_inject = thm "type_definition.Abs_inject"; val Rep_cases = thm "type_definition.Rep_cases"; val Abs_cases = thm "type_definition.Abs_cases"; val Rep_induct = thm "type_definition.Rep_induct"; val Abs_induct = thm "type_definition.Abs_induct"; (** theory data **) structure TypedefData = TheoryDataFun (struct val name = "HOL/typedef"; type T = (typ * typ * string * string) Symtab.table; val empty = Symtab.empty; val copy = I; val extend = I; fun merge _ (tabs: T * T) = Symtab.merge (op =) tabs; fun print _ _ = (); end); fun put_typedef newT oldT Abs_name Rep_name = TypedefData.map (Symtab.update_new (fst (dest_Type newT), (newT, oldT, Abs_name, Rep_name))); (** type declarations **) fun add_typedecls decls thy = let fun arity_of (raw_name, args, mx) = (Sign.full_name thy (Syntax.type_name raw_name mx), replicate (length args) HOLogic.typeS, HOLogic.typeS); in if can (Theory.assert_super HOL.thy) thy then thy |> Theory.add_typedecls decls |> Theory.add_arities_i (map arity_of decls) else thy |> Theory.add_typedecls decls end; (** type definitions **) (* messages *) val quiet_mode = ref false; fun message s = if ! quiet_mode then () else writeln s; (* prove_nonempty -- tactical version *) (*exception ERROR*) fun prove_nonempty thy cset goal (witn1_tac, witn_names, witn_thms, witn2_tac) = let val is_def = Logic.is_equals o #prop o Thm.rep_thm; val thms = PureThy.get_thmss thy (map Name witn_names) @ witn_thms; val tac = witn1_tac THEN TRY (rewrite_goals_tac (List.filter is_def thms)) THEN TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN if_none witn2_tac (TRY (ALLGOALS (CLASET' blast_tac))); in message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ..."); Tactic.prove thy [] [] goal (K tac) end handle ERROR => error ("Failed to prove non-emptiness of " ^ quote (string_of_cterm cset)); (* prepare_typedef *) fun read_term thy used s = #1 (Thm.read_def_cterm (thy, K NONE, K NONE) used true (s, HOLogic.typeT)); fun cert_term thy _ t = Thm.cterm_of thy t handle TERM (msg, _) => error msg; fun err_in_typedef name = error ("The error(s) above occurred in typedef " ^ quote name); fun prepare_typedef prep_term def name (t, vs, mx) raw_set opt_morphs thy = let val _ = Theory.requires thy "Typedef" "typedefs"; val full = Sign.full_name thy; (*rhs*) val full_name = full name; val cset = prep_term thy vs raw_set; val {T = setT, t = set, ...} = Thm.rep_cterm cset; val rhs_tfrees = Term.add_tfrees set []; val rhs_tfreesT = Term.add_tfreesT setT []; val oldT = HOLogic.dest_setT setT handle TYPE _ => error ("Not a set type: " ^ quote (Sign.string_of_typ thy setT)); fun mk_nonempty A = HOLogic.mk_Trueprop (HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), A))); val goal = mk_nonempty set; val goal_pat = mk_nonempty (Var (if_none (Syntax.read_variable name) (name, 0), setT)); (*lhs*) val defS = Sign.defaultS thy; val lhs_tfrees = map (fn v => (v, if_none (AList.lookup (op =) rhs_tfrees v) defS)) vs; val args_setT = lhs_tfrees |> filter (member (op =) rhs_tfrees andf (not o member (op =) rhs_tfreesT)) |> map TFree; val tname = Syntax.type_name t mx; val full_tname = full tname; val newT = Type (full_tname, map TFree lhs_tfrees); val (Rep_name, Abs_name) = if_none opt_morphs ("Rep_" ^ name, "Abs_" ^ name); val setT' = map itselfT args_setT ---> setT; val setC = Term.list_comb (Const (full_name, setT'), map Logic.mk_type args_setT); val RepC = Const (full Rep_name, newT --> oldT); val AbsC = Const (full Abs_name, oldT --> newT); val x_new = Free ("x", newT); val y_old = Free ("y", oldT); val set' = if def then setC else set; val typedef_name = "type_definition_" ^ name; val typedefC = Const (type_definitionN, (newT --> oldT) --> (oldT --> newT) --> setT --> HOLogic.boolT); val typedef_prop = Logic.mk_implies (goal, HOLogic.mk_Trueprop (typedefC $ RepC $ AbsC $ set')); fun typedef_result (theory, nonempty) = theory |> put_typedef newT oldT (full Abs_name) (full Rep_name) |> add_typedecls [(t, vs, mx)] |> Theory.add_consts_i ((if def then [(name, setT', NoSyn)] else []) @ [(Rep_name, newT --> oldT, NoSyn), (Abs_name, oldT --> newT, NoSyn)]) |> (if def then (apsnd (SOME o hd) oo (PureThy.add_defs_i false o map Thm.no_attributes)) [Logic.mk_defpair (setC, set)] else rpair NONE) |>>> PureThy.add_axioms_i [((typedef_name, typedef_prop), [apsnd (fn cond_axm => Drule.standard (nonempty RS cond_axm))])] |>> Theory.add_finals_i false [RepC, AbsC] |> (fn (theory', (set_def, [type_definition])) => let fun make th = Drule.standard (th OF [type_definition]); val (theory'', [Rep, Rep_inverse, Abs_inverse, Rep_inject, Abs_inject, Rep_cases, Abs_cases, Rep_induct, Abs_induct]) = theory' |> Theory.add_path name |> PureThy.add_thms ([((Rep_name, make Rep), []), ((Rep_name ^ "_inverse", make Rep_inverse), []), ((Abs_name ^ "_inverse", make Abs_inverse), []), ((Rep_name ^ "_inject", make Rep_inject), []), ((Abs_name ^ "_inject", make Abs_inject), []), ((Rep_name ^ "_cases", make Rep_cases), [RuleCases.case_names [Rep_name], InductAttrib.cases_set_global full_name]), ((Abs_name ^ "_cases", make Abs_cases), [RuleCases.case_names [Abs_name], InductAttrib.cases_type_global full_tname]), ((Rep_name ^ "_induct", make Rep_induct), [RuleCases.case_names [Rep_name], InductAttrib.induct_set_global full_name]), ((Abs_name ^ "_induct", make Abs_induct), [RuleCases.case_names [Abs_name], InductAttrib.induct_type_global full_tname])]) |>> Theory.parent_path; val result = {type_definition = type_definition, set_def = set_def, Rep = Rep, Rep_inverse = Rep_inverse, Abs_inverse = Abs_inverse, Rep_inject = Rep_inject, Abs_inject = Abs_inject, Rep_cases = Rep_cases, Abs_cases = Abs_cases, Rep_induct = Rep_induct, Abs_induct = Abs_induct}; in ((theory'', type_definition), result) end); (* errors *) fun show_names pairs = commas_quote (map fst pairs); val illegal_vars = if null (term_vars set) andalso null (term_tvars set) then [] else ["Illegal schematic variable(s) on rhs"]; val dup_lhs_tfrees = (case duplicates lhs_tfrees of [] => [] | dups => ["Duplicate type variables on lhs: " ^ show_names dups]); val extra_rhs_tfrees = (case fold (remove (op =)) lhs_tfrees rhs_tfrees of [] => [] | extras => ["Extra type variables on rhs: " ^ show_names extras]); val illegal_frees = (case term_frees set of [] => [] | xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]); val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees; val _ = if null errs then () else error (cat_lines errs); (*test theory errors now!*) val test_thy = Theory.copy thy; val _ = (test_thy, setmp quick_and_dirty true (SkipProof.make_thm test_thy) goal) |> typedef_result; in (cset, goal, goal_pat, typedef_result) end handle ERROR => err_in_typedef name; (* add_typedef interfaces *) local fun gen_typedef prep_term def name typ set opt_morphs tac1 names thms tac2 thy = let val (cset, goal, _, typedef_result) = prepare_typedef prep_term def name typ set opt_morphs thy; val non_empty = prove_nonempty thy cset goal (tac1, names, thms, tac2); val ((thy', _), result) = (thy, non_empty) |> typedef_result; in (thy', result) end; fun sane_typedef prep_term def opt_name typ set opt_morphs tac = gen_typedef prep_term def (if_none opt_name (#1 typ)) typ set opt_morphs all_tac [] [] (SOME tac); in fun add_typedef_x name typ set names thms tac = #1 o gen_typedef read_term true name typ set NONE (Tactic.rtac exI 1) names thms tac; val add_typedef = sane_typedef read_term; val add_typedef_i = sane_typedef cert_term; end; (* Isar typedef interface *) local fun gen_typedef prep_term ((def, name), typ, set, opt_morphs) thy = let val (_, goal, goal_pat, att_result) = prepare_typedef prep_term def name typ set opt_morphs thy; val att = #1 o att_result; in IsarThy.theorem_i Drule.internalK ("", [att]) (goal, ([goal_pat], [])) thy end; in val typedef = gen_typedef read_term; val typedef_i = gen_typedef cert_term; end; (** trivial code generator **) fun typedef_codegen thy defs gr dep module brack t = let fun get_name (Type (tname, _)) = tname | get_name _ = ""; fun mk_fun s T ts = let val (gr', _) = Codegen.invoke_tycodegen thy defs dep module false (gr, T); val (gr'', ps) = foldl_map (Codegen.invoke_codegen thy defs dep module true) (gr', ts); val id = Codegen.mk_qual_id module (Codegen.get_const_id s gr'') in SOME (gr'', Codegen.mk_app brack (Pretty.str id) ps) end; fun lookup f T = (case Symtab.lookup (TypedefData.get thy) (get_name T) of NONE => "" | SOME s => f s); in (case strip_comb t of (Const (s, Type ("fun", [T, U])), ts) => if lookup #4 T = s andalso is_none (Codegen.get_assoc_type thy (get_name T)) then mk_fun s T ts else if lookup #3 U = s andalso is_none (Codegen.get_assoc_type thy (get_name U)) then mk_fun s U ts else NONE | _ => NONE) end; fun mk_tyexpr [] s = Pretty.str s | mk_tyexpr [p] s = Pretty.block [p, Pretty.str (" " ^ s)] | mk_tyexpr ps s = Pretty.list "(" (") " ^ s) ps; fun typedef_tycodegen thy defs gr dep module brack (Type (s, Ts)) = (case Symtab.lookup (TypedefData.get thy) s of NONE => NONE | SOME (newT as Type (tname, Us), oldT, Abs_name, Rep_name) => if is_some (Codegen.get_assoc_type thy tname) then NONE else let val module' = Codegen.if_library (Codegen.thyname_of_type tname thy) module; val node_id = tname ^ " (type)"; val (gr', (((qs, (_, Abs_id)), (_, Rep_id)), ty_id)) = foldl_map (Codegen.invoke_tycodegen thy defs dep module (length Ts = 1)) (gr, Ts) |>>> Codegen.mk_const_id module' Abs_name |>>> Codegen.mk_const_id module' Rep_name |>>> Codegen.mk_type_id module' s; val tyexpr = mk_tyexpr qs (Codegen.mk_qual_id module ty_id) in SOME (case try (Codegen.get_node gr') node_id of NONE => let val (gr'', p :: ps) = foldl_map (Codegen.invoke_tycodegen thy defs node_id module' false) (Codegen.add_edge (node_id, dep) (Codegen.new_node (node_id, (NONE, "", "")) gr'), oldT :: Us); val s = Pretty.string_of (Pretty.block [Pretty.str "datatype ", mk_tyexpr ps (snd ty_id), Pretty.str " =", Pretty.brk 1, Pretty.str (Abs_id ^ " of"), Pretty.brk 1, p, Pretty.str ";"]) ^ "\n\n" ^ Pretty.string_of (Pretty.block [Pretty.str ("fun " ^ Rep_id), Pretty.brk 1, Pretty.str ("(" ^ Abs_id), Pretty.brk 1, Pretty.str "x) = x;"]) ^ "\n\n" ^ (if "term_of" mem !Codegen.mode then Pretty.string_of (Pretty.block [Pretty.str "fun ", Codegen.mk_term_of gr'' module' false newT, Pretty.brk 1, Pretty.str ("(" ^ Abs_id), Pretty.brk 1, Pretty.str "x) =", Pretty.brk 1, Pretty.block [Pretty.str ("Const (\"" ^ Abs_name ^ "\","), Pretty.brk 1, Codegen.mk_type false (oldT --> newT), Pretty.str ")"], Pretty.str " $", Pretty.brk 1, Codegen.mk_term_of gr'' module' false oldT, Pretty.brk 1, Pretty.str "x;"]) ^ "\n\n" else "") ^ (if "test" mem !Codegen.mode then Pretty.string_of (Pretty.block [Pretty.str "fun ", Codegen.mk_gen gr'' module' false [] "" newT, Pretty.brk 1, Pretty.str "i =", Pretty.brk 1, Pretty.block [Pretty.str (Abs_id ^ " ("), Codegen.mk_gen gr'' module' false [] "" oldT, Pretty.brk 1, Pretty.str "i);"]]) ^ "\n\n" else "") in Codegen.map_node node_id (K (NONE, module', s)) gr'' end | SOME _ => Codegen.add_edge (node_id, dep) gr', tyexpr) end) | typedef_tycodegen thy defs gr dep module brack _ = NONE; val setup = [TypedefData.init, Codegen.add_codegen "typedef" typedef_codegen, Codegen.add_tycodegen "typedef" typedef_tycodegen]; (** outer syntax **) local structure P = OuterParse and K = OuterKeyword in val typedeclP = OuterSyntax.command "typedecl" "type declaration (HOL)" K.thy_decl (P.type_args -- P.name -- P.opt_infix >> (fn ((vs, t), mx) => Toplevel.theory (add_typedecls [(t, vs, mx)]))); val typedef_decl = Scan.optional (P.$$$ "(" |-- ((P.$$$ "open" >> K false) -- Scan.option P.name || P.name >> (fn s => (true, SOME s))) --| P.$$$ ")") (true, NONE) -- (P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) -- Scan.option (P.$$$ "morphisms" |-- P.!!! (P.name -- P.name)); fun mk_typedef ((((((def, opt_name), (vs, t)), mx), A), morphs)) = typedef ((def, if_none opt_name (Syntax.type_name t mx)), (t, vs, mx), A, morphs); val typedefP = OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal (typedef_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef))); val _ = OuterSyntax.add_keywords ["morphisms"]; val _ = OuterSyntax.add_parsers [typedeclP, typedefP]; end; end;