author | wenzelm |
Sat, 08 Jul 2006 12:54:33 +0200 | |
changeset 20046 | 9c8909fc5865 |
parent 19705 | 08de66826677 |
child 20357 | 5fb92bd3aaea |
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 and Stefan Berghofer, TU Muenchen |
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|
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Gordon/HOL-style type definitions. |
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*) |
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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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type info = |
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{rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string, |
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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, |
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Abs_cases: thm, Rep_induct: thm, Abs_induct: thm}; |
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val get_info: theory -> string -> info option |
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val add_typedef: bool -> string option -> bstring * string list * mixfix -> |
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string -> (bstring * bstring) option -> tactic -> theory -> info * theory |
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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 -> info * theory |
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val typedef: (bool * string) * (bstring * string list * mixfix) * string |
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* (string * string) option -> theory -> Proof.state |
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val typedef_i: (bool * string) * (bstring * string list * mixfix) * term |
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* (string * string) option -> theory -> Proof.state |
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val setup: theory -> theory |
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end; |
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||
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structure TypedefPackage: TYPEDEF_PACKAGE = |
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struct |
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||
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||
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(** theory context references **) |
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||
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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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||
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||
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(** type declarations **) |
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||
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fun HOL_arity (raw_name, args, mx) thy = |
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thy |> AxClass.axiomatize_arity_i |
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(Sign.full_name thy (Syntax.type_name raw_name mx), |
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replicate (length args) HOLogic.typeS, HOLogic.typeS); |
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||
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fun add_typedecls decls thy = |
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thy |
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|> Theory.add_typedecls decls |
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|> can (Theory.assert_super HOL.thy) ? fold HOL_arity decls; |
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||
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||
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(** type definitions **) |
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||
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(* messages *) |
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||
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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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||
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||
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(* theory data *) |
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type info = |
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{rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string, |
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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, |
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Abs_cases: thm, Rep_induct: thm, Abs_induct: thm}; |
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structure TypedefData = TheoryDataFun |
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(struct |
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val name = "HOL/typedef"; |
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type T = info Symtab.table; |
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val empty = Symtab.empty; |
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val copy = I; |
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val extend = I; |
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fun merge _ tabs : T = Symtab.merge (K true) tabs; |
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fun print _ _ = (); |
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end); |
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val get_info = Symtab.lookup o TypedefData.get; |
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fun put_info name info = TypedefData.map (Symtab.update (name, info)); |
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||
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(* prepare_typedef *) |
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||
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fun read_term thy used s = |
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#1 (Thm.read_def_cterm (thy, K NONE, K NONE) used true (s, HOLogic.typeT)); |
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fun cert_term thy _ t = Thm.cterm_of thy t handle TERM (msg, _) => error msg; |
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fun err_in_typedef msg name = |
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cat_error msg ("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 full = Sign.full_name thy; |
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(*rhs*) |
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val full_name = full name; |
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val cset = prep_term thy vs raw_set; |
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val {T = setT, t = set, ...} = Thm.rep_cterm cset; |
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val rhs_tfrees = Term.add_tfrees set []; |
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val rhs_tfreesT = Term.add_tfreesT setT []; |
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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 thy 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 goal_pat = mk_nonempty (Var (the_default (name, 0) (Syntax.read_variable name), setT)); |
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|
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(*lhs*) |
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val defS = Sign.defaultS thy; |
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val lhs_tfrees = map (fn v => (v, the_default defS (AList.lookup (op =) rhs_tfrees v))) vs; |
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val args_setT = lhs_tfrees |
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|> filter (member (op =) rhs_tfrees andf (not o member (op =) rhs_tfreesT)) |
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|> map TFree; |
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||
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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) = the_default ("Rep_" ^ name, "Abs_" ^ name) opt_morphs; |
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val setT' = map Term.itselfT args_setT ---> setT; |
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val setC = Term.list_comb (Const (full_name, setT'), map Logic.mk_type args_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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val typedef_deps = Term.fold_aterms (fn Const c => insert (op =) c | _ => I) set' []; |
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fun add_def eq thy = |
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if def then |
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thy |
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|> PureThy.add_defs_i false [Thm.no_attributes eq] |
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|-> (fn [th] => pair (SOME th)) |
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else (NONE, thy); |
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fun typedef_result nonempty context = |
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Context.the_theory context |
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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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|> add_def (Logic.mk_defpair (setC, set)) |
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||>> PureThy.add_axioms_i [((typedef_name, typedef_prop), |
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[apsnd (fn cond_axm => nonempty RS cond_axm)])] |
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||> Theory.add_deps "" (dest_Const RepC) typedef_deps |
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||> Theory.add_deps "" (dest_Const AbsC) typedef_deps |
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|-> (fn (set_def, [type_definition]) => fn thy1 => |
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let |
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fun make th = Drule.standard (th OF [type_definition]); |
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val abs_inject = make Abs_inject; |
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val abs_inverse = make Abs_inverse; |
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val ([Rep, Rep_inverse, Abs_inverse, Rep_inject, Abs_inject, |
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Rep_cases, Abs_cases, Rep_induct, Abs_induct], thy2) = |
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thy1 |
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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", abs_inverse), []), |
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((Rep_name ^ "_inject", make Rep_inject), []), |
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((Abs_name ^ "_inject", abs_inject), []), |
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((Rep_name ^ "_cases", make Rep_cases), |
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[RuleCases.case_names [Rep_name], InductAttrib.cases_set full_name]), |
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((Abs_name ^ "_cases", make Abs_cases), |
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[RuleCases.case_names [Abs_name], InductAttrib.cases_type full_tname]), |
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((Rep_name ^ "_induct", make Rep_induct), |
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[RuleCases.case_names [Rep_name], InductAttrib.induct_set full_name]), |
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((Abs_name ^ "_induct", make Abs_induct), |
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[RuleCases.case_names [Abs_name], InductAttrib.induct_type full_tname])]) |
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||> Theory.parent_path; |
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val info = {rep_type = oldT, abs_type = newT, |
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Rep_name = full Rep_name, Abs_name = full Abs_name, |
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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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val thy3 = thy2 |> put_info full_tname info; |
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in (info, Context.Theory thy3) end); |
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|
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(* errors *) |
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||
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fun show_names pairs = commas_quote (map fst pairs); |
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||
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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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||
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val dup_lhs_tfrees = |
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(case duplicates (op =) lhs_tfrees of [] => [] |
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| dups => ["Duplicate type variables on lhs: " ^ show_names dups]); |
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||
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val extra_rhs_tfrees = |
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(case fold (remove (op =)) lhs_tfrees rhs_tfrees of [] => [] |
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| extras => ["Extra type variables on rhs: " ^ show_names extras]); |
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||
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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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||
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val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees; |
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val _ = if null errs then () else error (cat_lines errs); |
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225 |
|
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(*test theory errors now!*) |
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val test_thy = Theory.copy thy; |
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val _ = |
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Context.Theory test_thy |
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|> typedef_result (setmp quick_and_dirty true (SkipProof.make_thm test_thy) goal); |
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|
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in (cset, goal, goal_pat, typedef_result) end |
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handle ERROR msg => err_in_typedef msg name; |
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|
235 |
||
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(* add_typedef interfaces *) |
4866 | 237 |
|
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local |
239 |
||
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fun gen_typedef prep_term def opt_name typ set opt_morphs tac thy = |
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let |
17922 | 242 |
val name = the_default (#1 typ) opt_name; |
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val (cset, goal, _, typedef_result) = |
244 |
prepare_typedef prep_term def name typ set opt_morphs thy; |
|
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val _ = message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ..."); |
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val non_empty = Goal.prove_global thy [] [] goal (K tac) handle ERROR msg => |
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cat_error msg ("Failed to prove non-emptiness of " ^ quote (string_of_cterm cset)); |
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in |
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249 |
Context.Theory thy |
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250 |
|> typedef_result non_empty |
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||> Context.the_theory |
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252 |
end; |
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|
17339 | 254 |
in |
255 |
||
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val add_typedef = gen_typedef read_term; |
257 |
val add_typedef_i = gen_typedef cert_term; |
|
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|
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end; |
4866 | 260 |
|
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|
262 |
(* Isar typedef interface *) |
|
6383 | 263 |
|
17339 | 264 |
local |
265 |
||
266 |
fun gen_typedef prep_term ((def, name), typ, set, opt_morphs) thy = |
|
11822 | 267 |
let |
19705 | 268 |
val (_, goal, goal_pat, typedef_result) = |
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prepare_typedef prep_term def name typ set opt_morphs thy; |
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270 |
fun att (thy, th) = |
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let val ({type_definition, ...}, thy') = typedef_result th thy |
272 |
in (thy', type_definition) end; |
|
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in IsarThy.theorem_i PureThy.internalK ("", [att]) (goal, [goal_pat]) thy end; |
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|
275 |
in |
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6383 | 276 |
|
17339 | 277 |
val typedef = gen_typedef read_term; |
278 |
val typedef_i = gen_typedef cert_term; |
|
279 |
||
19705 | 280 |
end; |
15259 | 281 |
|
19459 | 282 |
val setup = TypedefData.init; |
15259 | 283 |
|
284 |
||
285 |
||
6383 | 286 |
(** outer syntax **) |
287 |
||
17057 | 288 |
local structure P = OuterParse and K = OuterKeyword in |
6383 | 289 |
|
6357 | 290 |
val typedeclP = |
12624 | 291 |
OuterSyntax.command "typedecl" "type declaration (HOL)" K.thy_decl |
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292 |
(P.type_args -- P.name -- P.opt_infix >> (fn ((vs, t), mx) => |
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Toplevel.theory (add_typedecls [(t, vs, mx)]))); |
294 |
||
6723 | 295 |
|
17339 | 296 |
val typedef_decl = |
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Scan.optional (P.$$$ "(" |-- |
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298 |
((P.$$$ "open" >> K false) -- Scan.option P.name || P.name >> (fn s => (true, SOME s))) |
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--| P.$$$ ")") (true, NONE) -- |
11744 | 300 |
(P.type_args -- P.name) -- P.opt_infix -- (P.$$$ "=" |-- P.term) -- |
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301 |
Scan.option (P.$$$ "morphisms" |-- P.!!! (P.name -- P.name)); |
6357 | 302 |
|
17339 | 303 |
fun mk_typedef ((((((def, opt_name), (vs, t)), mx), A), morphs)) = |
19473 | 304 |
typedef ((def, the_default (Syntax.type_name t mx) opt_name), (t, vs, mx), A, morphs); |
6357 | 305 |
|
306 |
val typedefP = |
|
6723 | 307 |
OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" K.thy_goal |
17339 | 308 |
(typedef_decl >> (Toplevel.print oo (Toplevel.theory_to_proof o mk_typedef))); |
6357 | 309 |
|
6723 | 310 |
|
11744 | 311 |
val _ = OuterSyntax.add_keywords ["morphisms"]; |
6357 | 312 |
val _ = OuterSyntax.add_parsers [typedeclP, typedefP]; |
313 |
||
4866 | 314 |
end; |
6383 | 315 |
|
316 |
end; |