author | nipkow |
Mon, 16 Aug 2004 14:22:27 +0200 | |
changeset 15131 | c69542757a4d |
parent 14981 | e73f8140af78 |
child 15259 | 6aa593317905 |
permissions | -rw-r--r-- |
4866 | 1 |
(* Title: HOL/Tools/typedef_package.ML |
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ID: $Id$ |
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Author: Markus Wenzel, TU Muenchen |
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Gordon/HOL-style type definitions. |
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*) |
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signature TYPEDEF_PACKAGE = |
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sig |
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val quiet_mode: bool ref |
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val add_typedecls: (bstring * string list * mixfix) list -> theory -> theory |
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val add_typedef_x: string -> bstring * string list * mixfix -> |
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string -> string list -> thm list -> tactic option -> theory -> theory |
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val add_typedef: bool -> string option -> bstring * string list * mixfix -> |
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string -> (bstring * bstring) option -> tactic -> theory -> theory * |
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{type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm, |
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Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm, |
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Rep_induct: thm, Abs_induct: thm} |
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val add_typedef_i: bool -> string option -> bstring * string list * mixfix -> |
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term -> (bstring * bstring) option -> tactic -> theory -> theory * |
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{type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm, |
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Abs_inverse: thm, Rep_inject: thm, Abs_inject: thm, Rep_cases: thm, Abs_cases: thm, |
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Rep_induct: thm, Abs_induct: thm} |
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val typedef_proof: (bool * string) * (bstring * string list * mixfix) * string |
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* (string * string) option -> bool -> theory -> ProofHistory.T |
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val typedef_proof_i: (bool * string) * (bstring * string list * mixfix) * term |
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* (string * string) option -> bool -> theory -> ProofHistory.T |
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end; |
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structure TypedefPackage: TYPEDEF_PACKAGE = |
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struct |
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(** theory context references **) |
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val type_definitionN = "Typedef.type_definition"; |
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val Rep = thm "type_definition.Rep"; |
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val Rep_inverse = thm "type_definition.Rep_inverse"; |
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val Abs_inverse = thm "type_definition.Abs_inverse"; |
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val Rep_inject = thm "type_definition.Rep_inject"; |
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val Abs_inject = thm "type_definition.Abs_inject"; |
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val Rep_cases = thm "type_definition.Rep_cases"; |
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val Abs_cases = thm "type_definition.Abs_cases"; |
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val Rep_induct = thm "type_definition.Rep_induct"; |
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val Abs_induct = thm "type_definition.Abs_induct"; |
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(** type declarations **) |
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fun add_typedecls decls thy = |
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let |
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val full = Sign.full_name (Theory.sign_of thy); |
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fun arity_of (raw_name, args, mx) = |
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(full (Syntax.type_name raw_name mx), replicate (length args) HOLogic.typeS, HOLogic.typeS); |
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in |
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if can (Theory.assert_super HOL.thy) thy then |
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thy |
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|> PureThy.add_typedecls decls |
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|> Theory.add_arities_i (map arity_of decls) |
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else thy |> PureThy.add_typedecls decls |
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end; |
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(** type definitions **) |
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(* messages *) |
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val quiet_mode = ref false; |
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fun message s = if ! quiet_mode then () else writeln s; |
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(* prove_nonempty -- tactical version *) (*exception ERROR*) |
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fun prove_nonempty thy cset goal (witn1_tac, witn_names, witn_thms, witn2_tac) = |
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let |
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val is_def = Logic.is_equals o #prop o Thm.rep_thm; |
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val thms = PureThy.get_thmss thy witn_names @ witn_thms; |
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val tac = |
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witn1_tac THEN |
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TRY (rewrite_goals_tac (filter is_def thms)) THEN |
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TRY (REPEAT_FIRST (resolve_tac (filter_out is_def thms))) THEN |
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if_none witn2_tac (TRY (ALLGOALS (CLASET' blast_tac))); |
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in |
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message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ..."); |
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Tactic.prove (Theory.sign_of thy) [] [] goal (K tac) |
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end handle ERROR => error ("Failed to prove non-emptiness of " ^ quote (string_of_cterm cset)); |
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(* prepare_typedef *) |
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fun read_term sg used s = |
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#1 (Thm.read_def_cterm (sg, K None, K None) used true (s, HOLogic.typeT)); |
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fun cert_term sg _ t = Thm.cterm_of sg t handle TERM (msg, _) => error msg; |
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fun err_in_typedef name = |
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error ("The error(s) above occurred in typedef " ^ quote name); |
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fun prepare_typedef prep_term def name (t, vs, mx) raw_set opt_morphs thy = |
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let |
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val _ = Theory.requires thy "Typedef" "typedefs"; |
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val sign = Theory.sign_of thy; |
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val full = Sign.full_name sign; |
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(*rhs*) |
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val full_name = full name; |
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val cset = prep_term sign vs raw_set; |
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val {T = setT, t = set, ...} = Thm.rep_cterm cset; |
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val rhs_tfrees = term_tfrees set; |
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val oldT = HOLogic.dest_setT setT handle TYPE _ => |
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error ("Not a set type: " ^ quote (Sign.string_of_typ sign setT)); |
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fun mk_nonempty A = |
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HOLogic.mk_Trueprop (HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), A))); |
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val goal = mk_nonempty set; |
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val vname = take_suffix Symbol.is_digit (Symbol.explode name) |
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|> apfst implode |> apsnd (#1 o Library.read_int); |
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val goal_pat = mk_nonempty (Var (vname, setT)); |
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(*lhs*) |
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val lhs_tfrees = map (fn v => (v, if_none (assoc (rhs_tfrees, v)) HOLogic.typeS)) vs; |
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val tname = Syntax.type_name t mx; |
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val full_tname = full tname; |
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val newT = Type (full_tname, map TFree lhs_tfrees); |
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val (Rep_name, Abs_name) = if_none opt_morphs ("Rep_" ^ name, "Abs_" ^ name); |
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val setC = Const (full_name, setT); |
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val RepC = Const (full Rep_name, newT --> oldT); |
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val AbsC = Const (full Abs_name, oldT --> newT); |
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val x_new = Free ("x", newT); |
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val y_old = Free ("y", oldT); |
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val set' = if def then setC else set; |
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val typedef_name = "type_definition_" ^ name; |
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val typedefC = |
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Const (type_definitionN, (newT --> oldT) --> (oldT --> newT) --> setT --> HOLogic.boolT); |
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val typedef_prop = |
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Logic.mk_implies (goal, HOLogic.mk_Trueprop (typedefC $ RepC $ AbsC $ set')); |
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fun typedef_result (theory, nonempty) = |
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theory |
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|> add_typedecls [(t, vs, mx)] |
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|> Theory.add_consts_i |
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((if def then [(name, setT, NoSyn)] else []) @ |
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[(Rep_name, newT --> oldT, NoSyn), |
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(Abs_name, oldT --> newT, NoSyn)]) |
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|> (if def then (apsnd (Some o hd) oo (PureThy.add_defs_i false o map Thm.no_attributes)) |
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[Logic.mk_defpair (setC, set)] |
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else rpair None) |
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|>>> PureThy.add_axioms_i [((typedef_name, typedef_prop), |
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[apsnd (fn cond_axm => Drule.standard (nonempty RS cond_axm))])] |
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|>> Theory.add_finals_i false [RepC, AbsC] |
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|> (fn (theory', (set_def, [type_definition])) => |
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let |
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fun make th = Drule.standard (th OF [type_definition]); |
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val (theory'', [Rep, Rep_inverse, Abs_inverse, Rep_inject, Abs_inject, |
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Rep_cases, Abs_cases, Rep_induct, Abs_induct]) = |
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theory' |
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|> Theory.add_path name |
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|> PureThy.add_thms |
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([((Rep_name, make Rep), []), |
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((Rep_name ^ "_inverse", make Rep_inverse), []), |
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((Abs_name ^ "_inverse", make Abs_inverse), []), |
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((Rep_name ^ "_inject", make Rep_inject), []), |
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((Abs_name ^ "_inject", make Abs_inject), []), |
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((Rep_name ^ "_cases", make Rep_cases), |
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[RuleCases.case_names [Rep_name], InductAttrib.cases_set_global full_name]), |
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((Abs_name ^ "_cases", make Abs_cases), |
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[RuleCases.case_names [Abs_name], InductAttrib.cases_type_global full_tname]), |
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((Rep_name ^ "_induct", make Rep_induct), |
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[RuleCases.case_names [Rep_name], InductAttrib.induct_set_global full_name]), |
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((Abs_name ^ "_induct", make Abs_induct), |
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parents:
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diff
changeset
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[RuleCases.case_names [Abs_name], InductAttrib.induct_type_global full_tname])]) |
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|>> Theory.parent_path; |
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val result = {type_definition = type_definition, set_def = set_def, |
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Rep = Rep, Rep_inverse = Rep_inverse, Abs_inverse = Abs_inverse, |
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Rep_inject = Rep_inject, Abs_inject = Abs_inject, Rep_cases = Rep_cases, |
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Abs_cases = Abs_cases, Rep_induct = Rep_induct, Abs_induct = Abs_induct}; |
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in ((theory'', type_definition), result) end); |
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(* errors *) |
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fun show_names pairs = commas_quote (map fst pairs); |
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val illegal_vars = |
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if null (term_vars set) andalso null (term_tvars set) then [] |
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else ["Illegal schematic variable(s) on rhs"]; |
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val dup_lhs_tfrees = |
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(case duplicates lhs_tfrees of [] => [] |
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| dups => ["Duplicate type variables on lhs: " ^ show_names dups]); |
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val extra_rhs_tfrees = |
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(case gen_rems (op =) (rhs_tfrees, lhs_tfrees) of [] => [] |
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| extras => ["Extra type variables on rhs: " ^ show_names extras]); |
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val illegal_frees = |
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(case term_frees set of [] => [] |
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| xs => ["Illegal variables on rhs: " ^ show_names (map dest_Free xs)]); |
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val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees; |
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parents:
10697
diff
changeset
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val _ = if null errs then () else error (cat_lines errs); |
f280d4b29a2c
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parents:
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(*test theory errors now!*) |
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val test_thy = Theory.copy thy; |
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val _ = (test_thy, |
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setmp quick_and_dirty true (SkipProof.make_thm test_thy) goal) |> typedef_result; |
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parents:
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changeset
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in (cset, goal, goal_pat, typedef_result) end |
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wenzelm
parents:
10697
diff
changeset
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handle ERROR => err_in_typedef name; |
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(* add_typedef interfaces *) |
4866 | 219 |
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fun gen_typedef prep_term def name typ set opt_morphs tac1 names thms tac2 thy = |
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let |
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val (cset, goal, _, typedef_result) = |
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prepare_typedef prep_term def name typ set opt_morphs thy; |
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val non_empty = prove_nonempty thy cset goal (tac1, names, thms, tac2); |
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val ((thy', _), result) = (thy, non_empty) |> typedef_result; |
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in (thy', result) end; |
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fun sane_typedef prep_term def opt_name typ set opt_morphs tac = |
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gen_typedef prep_term def |
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(if_none opt_name (#1 typ)) typ set opt_morphs all_tac [] [] (Some tac); |
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fun add_typedef_x name typ set names thms tac = |
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#1 o gen_typedef read_term true name typ set None (Tactic.rtac exI 1) names thms tac; |
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val add_typedef = sane_typedef read_term; |
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val add_typedef_i = sane_typedef cert_term; |
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(* typedef_proof interface *) |
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fun gen_typedef_proof prep_term ((def, name), typ, set, opt_morphs) int thy = |
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let |
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val (_, goal, goal_pat, att_result) = |
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13443 | 244 |
prepare_typedef prep_term def name typ set opt_morphs thy; |
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val att = #1 o att_result; |
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in thy |> IsarThy.theorem_i Drule.internalK (("", [att]), (goal, ([goal_pat], []))) int end; |
6383 | 247 |
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val typedef_proof = gen_typedef_proof read_term; |
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val typedef_proof_i = gen_typedef_proof cert_term; |
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(** outer syntax **) |
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6723 | 255 |
local structure P = OuterParse and K = OuterSyntax.Keyword in |
6383 | 256 |
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val typedeclP = |
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OuterSyntax.command "typedecl" "type declaration (HOL)" K.thy_decl |
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259 |
(P.type_args -- P.name -- P.opt_infix >> (fn ((vs, t), mx) => |
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Toplevel.theory (add_typedecls [(t, vs, mx)]))); |
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6723 | 262 |
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6383 | 263 |
val typedef_proof_decl = |
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Scan.optional (P.$$$ "(" |-- P.!!! |
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(((P.$$$ "open" >> K false) -- Scan.option P.name || P.name >> (fn s => (true, Some s))) |
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--| P.$$$ ")")) (true, None) -- |
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(P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) -- |
12876
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wenzelm
parents:
12694
diff
changeset
|
268 |
Scan.option (P.$$$ "morphisms" |-- P.!!! (P.name -- P.name)); |
6357 | 269 |
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13443 | 270 |
fun mk_typedef_proof ((((((def, opt_name), (vs, t)), mx), A), morphs)) = |
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typedef_proof ((def, if_none opt_name (Syntax.type_name t mx)), (t, vs, mx), A, morphs); |
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6357 | 272 |
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273 |
val typedefP = |
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6723 | 274 |
OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal |
6383 | 275 |
(typedef_proof_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef_proof))); |
6357 | 276 |
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6723 | 277 |
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11744 | 278 |
val _ = OuterSyntax.add_keywords ["morphisms"]; |
6357 | 279 |
val _ = OuterSyntax.add_parsers [typedeclP, typedefP]; |
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4866 | 281 |
end; |
6383 | 282 |
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283 |
end; |