# HG changeset patch # User wenzelm # Date 1268487736 -3600 # Node ID 4f3660a3e5afcb37b68726a32331a368557bb480 # Parent d3726291f252d7612e62189ea9375238f8662849 localized typedef; Typedef.get_info can yield multiple typedef interpretations, even in a global context; misc tuning and modernization; diff -r d3726291f252 -r 4f3660a3e5af src/HOL/Tools/typedef.ML --- a/src/HOL/Tools/typedef.ML Sat Mar 13 14:41:37 2010 +0100 +++ b/src/HOL/Tools/typedef.ML Sat Mar 13 14:42:16 2010 +0100 @@ -2,7 +2,7 @@ Author: Markus Wenzel and Stefan Berghofer, TU Muenchen Gordon/HOL-style type definitions: create a new syntactic type -represented by a non-empty subset. +represented by a non-empty set. *) signature TYPEDEF = @@ -12,16 +12,19 @@ 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 transform_info: morphism -> info -> info + val get_info: Proof.context -> string -> info list + val get_info_global: theory -> string -> info list + val interpretation: (string -> theory -> theory) -> theory -> theory + val setup: theory -> theory val add_typedef: bool -> binding option -> binding * string list * mixfix -> + term -> (binding * binding) option -> tactic -> local_theory -> (string * info) * local_theory + val add_typedef_global: bool -> binding option -> binding * string list * mixfix -> term -> (binding * binding) option -> tactic -> theory -> (string * info) * theory val typedef: (bool * binding) * (binding * string list * mixfix) * term * - (binding * binding) option -> theory -> Proof.state + (binding * binding) option -> local_theory -> Proof.state val typedef_cmd: (bool * binding) * (binding * string list * mixfix) * string * - (binding * binding) option -> theory -> Proof.state - val get_info: theory -> string -> info option - val the_info: theory -> string -> info - val interpretation: (string -> theory -> theory) -> theory -> theory - val setup: theory -> theory + (binding * binding) option -> local_theory -> Proof.state end; structure Typedef: TYPEDEF = @@ -32,207 +35,261 @@ (* theory data *) type info = - {rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string, inhabited: thm, - type_definition: thm, set_def: thm option, Rep: thm, Rep_inverse: thm, + {(*global part*) + rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string, + (*local part*) + inhabited: thm, 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}; -structure TypedefData = Theory_Data +fun transform_info phi (info: info) = + let + val thm = Morphism.thm phi; + val {rep_type, abs_type, Rep_name, Abs_name, inhabited, type_definition, + set_def, Rep, Rep_inverse, Abs_inverse, Rep_inject, Abs_inject, + Rep_cases, Abs_cases, Rep_induct, Abs_induct} = info; + in + {rep_type = rep_type, abs_type = abs_type, Rep_name = Rep_name, Abs_name = Abs_name, + inhabited = thm inhabited, type_definition = thm type_definition, + set_def = Option.map thm set_def, Rep = thm Rep, Rep_inverse = thm Rep_inverse, + Abs_inverse = thm Abs_inverse, Rep_inject = thm Rep_inject, Abs_inject = thm Abs_inject, + Rep_cases = thm Rep_cases, Abs_cases = thm Abs_cases, Rep_induct = thm Rep_induct, + Abs_induct = thm Abs_induct} + end; + +structure Data = Generic_Data ( - type T = info Symtab.table; + type T = info list Symtab.table; val empty = Symtab.empty; val extend = I; - fun merge data = Symtab.merge (K true) data; + fun merge data = Symtab.merge_list (K true) data; ); -val get_info = Symtab.lookup o TypedefData.get; +val get_info = Symtab.lookup_list o Data.get o Context.Proof; +val get_info_global = Symtab.lookup_list o Data.get o Context.Theory; + +fun put_info name info = Data.map (Symtab.cons_list (name, info)); + + +(* global interpretation *) + +structure Typedef_Interpretation = Interpretation(type T = string val eq = op =); +val interpretation = Typedef_Interpretation.interpretation; + +val setup = Typedef_Interpretation.init; + + +(* primitive typedef axiomatization -- for fresh typedecl *) + +fun mk_inhabited A = + let val T = HOLogic.dest_setT (Term.fastype_of A) + in HOLogic.mk_Trueprop (HOLogic.exists_const T $ Abs ("x", T, HOLogic.mk_mem (Bound 0, A))) end; + +fun mk_typedef newT oldT RepC AbsC A = + let + val typedefC = + Const (@{const_name type_definition}, + (newT --> oldT) --> (oldT --> newT) --> HOLogic.mk_setT oldT --> HOLogic.boolT); + in Logic.mk_implies (mk_inhabited A, HOLogic.mk_Trueprop (typedefC $ RepC $ AbsC $ A)) end; -fun the_info thy name = - (case get_info thy name of - SOME info => info - | NONE => error ("Unknown typedef " ^ quote name)); +fun primitive_typedef typedef_name newT oldT Rep_name Abs_name A thy = + let + (* errors *) + + fun show_names pairs = commas_quote (map fst pairs); + + val lhs_tfrees = Term.add_tfreesT newT []; + val rhs_tfrees = Term.add_tfreesT oldT []; + val _ = + (case fold (remove (op =)) lhs_tfrees rhs_tfrees of [] => () + | extras => error ("Extra type variables in representing set: " ^ show_names extras)); + + val _ = + (case Term.add_frees A [] of [] => [] + | xs => error ("Illegal variables in representing set: " ^ show_names xs)); -fun put_info name info = TypedefData.map (Symtab.update (name, info)); + + (* axiomatization *) + + val ((RepC, AbsC), consts_thy) = thy + |> Sign.declare_const ((Rep_name, newT --> oldT), NoSyn) + ||>> Sign.declare_const ((Abs_name, oldT --> newT), NoSyn); + + val typedef_deps = Term.add_consts A []; + + val (axiom, axiom_thy) = consts_thy + |> Thm.add_axiom (typedef_name, mk_typedef newT oldT RepC AbsC A) + ||> Theory.add_deps "" (dest_Const RepC) typedef_deps + ||> Theory.add_deps "" (dest_Const AbsC) typedef_deps; + + in ((RepC, AbsC, axiom), axiom_thy) end; (* prepare_typedef *) fun declare_type_name a = Variable.declare_constraints (Logic.mk_type (TFree (a, dummyS))); -structure Typedef_Interpretation = Interpretation(type T = string val eq = op =); -val interpretation = Typedef_Interpretation.interpretation; - -fun prepare_typedef prep_term def name (tname, vs, mx) raw_set opt_morphs thy = +fun prepare_typedef prep_term def_set name (tname, vs, mx) raw_set opt_morphs lthy = let - val _ = Theory.requires thy "Typedef" "typedefs"; - val ctxt = ProofContext.init thy; - - val full = Sign.full_name thy; - val full_name = full name; + val full_name = Local_Theory.full_name lthy name; val bname = Binding.name_of name; - (*rhs*) - val set = prep_term (ctxt |> fold declare_type_name vs) raw_set; + + (* rhs *) + + val set = prep_term (lthy |> fold declare_type_name vs) raw_set; val setT = Term.fastype_of set; + val oldT = HOLogic.dest_setT setT handle TYPE _ => + error ("Not a set type: " ^ quote (Syntax.string_of_typ lthy setT)); + + val goal = mk_inhabited set; + val goal_pat = mk_inhabited (Var (the_default (bname, 0) (Syntax.read_variable bname), setT)); + + + (* lhs *) + + val (newT, typedecl_lthy) = lthy + |> Typedecl.typedecl_wrt [set] (tname, vs, mx) + ||> Variable.declare_term set; + + val Type (full_tname, type_args) = newT; + val lhs_tfrees = map Term.dest_TFree type_args; + + + (* set definition *) + + (* FIXME let Local_Theory.define handle hidden polymorphism (!??!) *) + 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 (Syntax.string_of_typ ctxt setT)); - (*lhs*) - val defS = Sign.defaultS thy; - val lhs_tfrees = map (fn v => (v, the_default defS (AList.lookup (op =) rhs_tfrees v))) vs; - val args_setT = lhs_tfrees + val set_argsT = lhs_tfrees |> filter (member (op =) rhs_tfrees andf (not o member (op =) rhs_tfreesT)) |> map TFree; + val set_args = map Logic.mk_type set_argsT; - val full_tname = full tname; - val newT = Type (full_tname, map TFree lhs_tfrees); + val ((set', set_def), set_lthy) = + if def_set then + typedecl_lthy + |> Local_Theory.define + ((name, NoSyn), ((Thm.def_binding name, []), fold_rev lambda set_args set)) + |>> (fn (s, (_, set_def)) => (Term.list_comb (s, set_args), SOME set_def)) + else ((set, NONE), typedecl_lthy); + + + (* axiomatization *) val (Rep_name, Abs_name) = (case opt_morphs of NONE => (Binding.prefix_name "Rep_" name, Binding.prefix_name "Abs_" name) | SOME morphs => morphs); - val setT' = map Term.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); - (*inhabitance*) - fun mk_inhabited A = - HOLogic.mk_Trueprop (HOLogic.mk_exists ("x", oldT, HOLogic.mk_mem (Free ("x", oldT), A))); - val set' = if def then setC else set; - val goal' = mk_inhabited set'; - val goal = mk_inhabited set; - val goal_pat = mk_inhabited (Var (the_default (bname, 0) (Syntax.read_variable bname), setT)); - - (*axiomatization*) val typedef_name = Binding.prefix_name "type_definition_" name; - val typedefC = - Const (@{const_name type_definition}, - (newT --> oldT) --> (oldT --> newT) --> setT --> HOLogic.boolT); - val typedef_prop = Logic.mk_implies (goal', HOLogic.mk_Trueprop (typedefC $ RepC $ AbsC $ set')); - val typedef_deps = Term.add_consts set' []; - (*set definition*) - fun add_def theory = - if def then - theory - |> Sign.add_consts_i [(name, setT', NoSyn)] - |> PureThy.add_defs false [((Thm.def_binding name, Logic.mk_equals (setC, set)), [])] - |-> (fn [th] => pair (SOME th)) - else (NONE, theory); - fun contract_def NONE th = th - | contract_def (SOME def_eq) th = - let - val cert = Thm.cterm_of (Thm.theory_of_thm def_eq); - val goal_eq = MetaSimplifier.rewrite true [def_eq] (cert goal'); - in Drule.export_without_context (Drule.equal_elim_rule2 OF [goal_eq, th]) end; + val ((RepC, AbsC, typedef), typedef_lthy) = + let + val thy = ProofContext.theory_of set_lthy; + val cert = Thm.cterm_of thy; + val (defs, A) = + Local_Defs.export_cterm set_lthy (ProofContext.init thy) (cert set') ||> Thm.term_of; - fun typedef_result inhabited = - Typedecl.typedecl_global (tname, vs, mx) - #> snd - #> Sign.add_consts_i - [(Rep_name, newT --> oldT, NoSyn), - (Abs_name, oldT --> newT, NoSyn)] - #> add_def - #-> (fn set_def => - PureThy.add_axioms [((typedef_name, typedef_prop), - [Thm.rule_attribute (K (fn cond_axm => contract_def set_def inhabited RS cond_axm))])] - ##>> pair set_def) - ##> Theory.add_deps "" (dest_Const RepC) typedef_deps - ##> Theory.add_deps "" (dest_Const AbsC) typedef_deps - #-> (fn ([type_definition], set_def) => fn thy1 => - let - fun make th = Drule.export_without_context (th OF [type_definition]); - val ([Rep, Rep_inverse, Abs_inverse, Rep_inject, Abs_inject, - Rep_cases, Abs_cases, Rep_induct, Abs_induct], thy2) = - thy1 - |> Sign.add_path (Binding.name_of name) - |> PureThy.add_thms - [((Rep_name, make @{thm type_definition.Rep}), []), - ((Binding.suffix_name "_inverse" Rep_name, make @{thm type_definition.Rep_inverse}), []), - ((Binding.suffix_name "_inverse" Abs_name, make @{thm type_definition.Abs_inverse}), []), - ((Binding.suffix_name "_inject" Rep_name, make @{thm type_definition.Rep_inject}), []), - ((Binding.suffix_name "_inject" Abs_name, make @{thm type_definition.Abs_inject}), []), - ((Binding.suffix_name "_cases" Rep_name, make @{thm type_definition.Rep_cases}), - [Rule_Cases.case_names [Binding.name_of Rep_name], Induct.cases_pred full_name]), - ((Binding.suffix_name "_cases" Abs_name, make @{thm type_definition.Abs_cases}), - [Rule_Cases.case_names [Binding.name_of Abs_name], Induct.cases_type full_tname]), - ((Binding.suffix_name "_induct" Rep_name, make @{thm type_definition.Rep_induct}), - [Rule_Cases.case_names [Binding.name_of Rep_name], Induct.induct_pred full_name]), - ((Binding.suffix_name "_induct" Abs_name, make @{thm type_definition.Abs_induct}), - [Rule_Cases.case_names [Binding.name_of Abs_name], Induct.induct_type full_tname])] - ||> Sign.restore_naming thy1; - val info = {rep_type = oldT, abs_type = newT, - Rep_name = full Rep_name, Abs_name = full Abs_name, - inhabited = inhabited, 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 - thy2 - |> put_info full_tname info - |> Typedef_Interpretation.data full_tname - |> pair (full_tname, info) - end); + val ((RepC, AbsC, axiom), axiom_lthy) = set_lthy |> + Local_Theory.theory_result (primitive_typedef typedef_name newT oldT Rep_name Abs_name A); + + val cert = Thm.cterm_of (ProofContext.theory_of axiom_lthy); + val typedef = + Local_Defs.contract axiom_lthy defs (cert (mk_typedef newT oldT RepC AbsC set')) axiom; + in ((RepC, AbsC, typedef), axiom_lthy) end; + + val alias_lthy = typedef_lthy + |> Local_Theory.const_alias Rep_name (#1 (Term.dest_Const RepC)) + |> Local_Theory.const_alias Abs_name (#1 (Term.dest_Const AbsC)); - (* errors *) - - fun show_names pairs = commas_quote (map fst pairs); + (* result *) - val illegal_vars = - if null (Term.add_vars set []) andalso null (Term.add_tvars set []) then [] - else ["Illegal schematic variable(s) on rhs"]; - - val dup_lhs_tfrees = - (case duplicates (op =) lhs_tfrees of [] => [] - | dups => ["Duplicate type variables on lhs: " ^ show_names dups]); + fun note_qualify ((b, atts), th) = + Local_Theory.note ((Binding.qualify false bname b, map (Attrib.internal o K) atts), [th]) + #>> (fn (_, [th']) => th'); - 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.add_frees set [] of [] => [] - | xs => ["Illegal variables on rhs: " ^ show_names xs]); + fun typedef_result inhabited lthy1 = + let + val cert = Thm.cterm_of (ProofContext.theory_of lthy1); + val inhabited' = + Local_Defs.contract lthy1 (the_list set_def) (cert (mk_inhabited set')) inhabited; + val typedef' = inhabited' RS typedef; + fun make th = Goal.norm_result (typedef' RS th); + val (((((((((((_, [type_definition]), Rep), Rep_inverse), Abs_inverse), Rep_inject), + Abs_inject), Rep_cases), Abs_cases), Rep_induct), Abs_induct), lthy2) = lthy1 + |> Local_Theory.note ((typedef_name, []), [typedef']) + ||>> note_qualify ((Rep_name, []), make @{thm type_definition.Rep}) + ||>> note_qualify ((Binding.suffix_name "_inverse" Rep_name, []), + make @{thm type_definition.Rep_inverse}) + ||>> note_qualify ((Binding.suffix_name "_inverse" Abs_name, []), + make @{thm type_definition.Abs_inverse}) + ||>> note_qualify ((Binding.suffix_name "_inject" Rep_name, []), + make @{thm type_definition.Rep_inject}) + ||>> note_qualify ((Binding.suffix_name "_inject" Abs_name, []), + make @{thm type_definition.Abs_inject}) + ||>> note_qualify ((Binding.suffix_name "_cases" Rep_name, + [Rule_Cases.case_names [Binding.name_of Rep_name], Induct.cases_pred full_name]), + make @{thm type_definition.Rep_cases}) + ||>> note_qualify ((Binding.suffix_name "_cases" Abs_name, + [Rule_Cases.case_names [Binding.name_of Abs_name], Induct.cases_type full_tname]), + make @{thm type_definition.Abs_cases}) + ||>> note_qualify ((Binding.suffix_name "_induct" Rep_name, + [Rule_Cases.case_names [Binding.name_of Rep_name], Induct.induct_pred full_name]), + make @{thm type_definition.Rep_induct}) + ||>> note_qualify ((Binding.suffix_name "_induct" Abs_name, + [Rule_Cases.case_names [Binding.name_of Abs_name], Induct.induct_type full_tname]), + make @{thm type_definition.Abs_induct}); - val errs = illegal_vars @ dup_lhs_tfrees @ extra_rhs_tfrees @ illegal_frees; - val _ = if null errs then () else error (cat_lines errs); + val info = {rep_type = oldT, abs_type = newT, + Rep_name = #1 (Term.dest_Const RepC), Abs_name = #1 (Term.dest_Const AbsC), + inhabited = inhabited, 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 + lthy2 + |> Local_Theory.declaration true (fn phi => put_info full_tname (transform_info phi info)) + |> Local_Theory.theory (Typedef_Interpretation.data full_tname) + |> pair (full_tname, info) + end; - (*test theory errors now!*) - val test_thy = Theory.copy thy; - val _ = typedef_result (Skip_Proof.make_thm test_thy goal) test_thy; - - in (set, goal, goal_pat, typedef_result) end + in ((goal, goal_pat, typedef_result), alias_lthy) end handle ERROR msg => cat_error msg ("The error(s) above occurred in typedef " ^ quote (Binding.str_of name)); (* add_typedef: tactic interface *) -fun add_typedef def opt_name typ set opt_morphs tac thy = +fun add_typedef def opt_name typ set opt_morphs tac lthy = let val name = the_default (#1 typ) opt_name; - val (set, goal, _, typedef_result) = - prepare_typedef Syntax.check_term def name typ set opt_morphs thy; - val inhabited = Goal.prove_global thy [] [] goal (K tac) - handle ERROR msg => cat_error msg - ("Failed to prove non-emptiness of " ^ quote (Syntax.string_of_term_global thy set)); - in typedef_result inhabited thy end; + val ((goal, _, typedef_result), lthy') = + prepare_typedef Syntax.check_term def name typ set opt_morphs lthy; + val inhabited = + Goal.prove lthy' [] [] goal (K tac) + |> Goal.norm_result |> Thm.close_derivation; + in typedef_result inhabited lthy' end; + +fun add_typedef_global def opt_name typ set opt_morphs tac = + Theory_Target.init NONE + #> add_typedef def opt_name typ set opt_morphs tac + #> Local_Theory.exit_result_global (apsnd o transform_info); (* typedef: proof interface *) local -fun gen_typedef prep_term ((def, name), typ, set, opt_morphs) thy = +fun gen_typedef prep_term ((def, name), typ, set, opt_morphs) lthy = let - val (_, goal, goal_pat, typedef_result) = - prepare_typedef prep_term def name typ set opt_morphs thy; - fun after_qed [[th]] = ProofContext.theory (snd o typedef_result th); - in Proof.theorem_i NONE after_qed [[(goal, [goal_pat])]] (ProofContext.init thy) end; + val ((goal, goal_pat, typedef_result), lthy') = + prepare_typedef prep_term def name typ set opt_morphs lthy; + fun after_qed [[th]] = snd o typedef_result th; + in Proof.theorem_i NONE after_qed [[(goal, [goal_pat])]] lthy' end; in @@ -250,7 +307,7 @@ val _ = OuterKeyword.keyword "morphisms"; val _ = - OuterSyntax.command "typedef" "HOL type definition (requires non-emptiness proof)" + OuterSyntax.local_theory_to_proof "typedef" "HOL type definition (requires non-emptiness proof)" OuterKeyword.thy_goal (Scan.optional (P.$$$ "(" |-- ((P.$$$ "open" >> K false) -- Scan.option P.binding || @@ -258,11 +315,9 @@ (P.type_args -- P.binding) -- P.opt_mixfix -- (P.$$$ "=" |-- P.term) -- Scan.option (P.$$$ "morphisms" |-- P.!!! (P.binding -- P.binding)) >> (fn ((((((def, opt_name), (vs, t)), mx), A), morphs)) => - Toplevel.print o Toplevel.theory_to_proof - (typedef_cmd ((def, the_default t opt_name), (t, vs, mx), A, morphs)))); + typedef_cmd ((def, the_default t opt_name), (t, vs, mx), A, morphs))); end; -val setup = Typedef_Interpretation.init; +end; -end;