(* Title: HOL/Tools/typedef_package.ML
ID: $Id$
Author: Markus Wenzel and Stefan Berghofer, TU Muenchen
Gordon/HOL-style type definitions: create a new syntactic type
represented by a non-empty subset.
*)
signature TYPEDEF_PACKAGE =
sig
val quiet_mode: bool ref
val add_typedecls: (bstring * string list * mixfix) list -> theory -> theory
type info =
{rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
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 get_info: theory -> string -> info option
val add_typedef: bool -> string option -> bstring * string list * mixfix ->
string -> (bstring * bstring) option -> tactic -> theory -> (string * info) * theory
val add_typedef_i: bool -> string option -> bstring * string list * mixfix ->
term -> (bstring * bstring) option -> tactic -> theory -> (string * info) * theory
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
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";
(** type declarations **)
fun HOL_arity (raw_name, args, mx) thy =
thy |> AxClass.axiomatize_arity_i
(Sign.full_name thy (Syntax.type_name raw_name mx),
replicate (length args) HOLogic.typeS, HOLogic.typeS);
fun add_typedecls decls thy =
thy
|> Theory.add_typedecls decls
|> can (Theory.assert_super HOL.thy) ? fold HOL_arity decls;
(** type definitions **)
(* messages *)
val quiet_mode = ref false;
fun message s = if ! quiet_mode then () else writeln s;
(* theory data *)
type info =
{rep_type: typ, abs_type: typ, Rep_name: string, Abs_name: string,
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 = TheoryDataFun
(struct
val name = "HOL/typedef";
type T = info Symtab.table;
val empty = Symtab.empty;
val copy = I;
val extend = I;
fun merge _ tabs : T = Symtab.merge (K true) tabs;
fun print _ _ = ();
end);
val get_info = Symtab.lookup o TypedefData.get;
fun put_info name info = TypedefData.map (Symtab.update (name, info));
(* prepare_typedef *)
fun err_in_typedef msg name =
cat_error msg ("The error(s) above occurred in typedef " ^ quote name);
fun declare_type_name a = Variable.declare_constraints (Logic.mk_type (TFree (a, dummyS)));
fun prepare_typedef prep_term def name (t, vs, mx) raw_set opt_morphs thy =
let
val _ = Theory.requires thy "Typedef" "typedefs";
val ctxt = ProofContext.init thy;
val full = Sign.full_name thy;
(*rhs*)
val full_name = full name;
val set = prep_term (ctxt |> fold declare_type_name vs) raw_set;
val setT = Term.fastype_of set;
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 (ProofContext.string_of_typ ctxt 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 (the_default (name, 0) (Syntax.read_variable name), 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
|> 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) = the_default ("Rep_" ^ name, "Abs_" ^ name) opt_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);
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'));
val typedef_deps = Term.fold_aterms (fn Const c => insert (op =) c | _ => I) set' [];
fun add_def eq thy =
if def then
thy
|> PureThy.add_defs_i false [Thm.no_attributes eq]
|-> (fn [th] => pair (SOME th))
else (NONE, thy);
fun typedef_result nonempty =
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)])
#> add_def (Logic.mk_defpair (setC, set))
##>> PureThy.add_axioms_i [((typedef_name, typedef_prop),
[apsnd (fn cond_axm => nonempty RS cond_axm)])]
##> Theory.add_deps "" (dest_Const RepC) typedef_deps
##> Theory.add_deps "" (dest_Const AbsC) typedef_deps
#-> (fn (set_def, [type_definition]) => fn thy1 =>
let
fun make th = Drule.standard (th OF [type_definition]);
val abs_inject = make Abs_inject;
val abs_inverse = make Abs_inverse;
val ([Rep, Rep_inverse, Abs_inverse, Rep_inject, Abs_inject,
Rep_cases, Abs_cases, Rep_induct, Abs_induct], thy2) =
thy1
|> Theory.add_path name
|> PureThy.add_thms
([((Rep_name, make Rep), []),
((Rep_name ^ "_inverse", make Rep_inverse), []),
((Abs_name ^ "_inverse", abs_inverse), []),
((Rep_name ^ "_inject", make Rep_inject), []),
((Abs_name ^ "_inject", abs_inject), []),
((Rep_name ^ "_cases", make Rep_cases),
[RuleCases.case_names [Rep_name], InductAttrib.cases_set full_name]),
((Abs_name ^ "_cases", make Abs_cases),
[RuleCases.case_names [Abs_name], InductAttrib.cases_type full_tname]),
((Rep_name ^ "_induct", make Rep_induct),
[RuleCases.case_names [Rep_name], InductAttrib.induct_set full_name]),
((Abs_name ^ "_induct", make Abs_induct),
[RuleCases.case_names [Abs_name], InductAttrib.induct_type full_tname])])
||> Theory.parent_path;
val info = {rep_type = oldT, abs_type = newT,
Rep_name = full Rep_name, Abs_name = full Abs_name,
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};
val thy3 = thy2 |> put_info full_tname info;
in ((full_tname, info), thy3) 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 (op =) 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
|> typedef_result (setmp quick_and_dirty true (SkipProof.make_thm test_thy) goal);
in (set, goal, goal_pat, typedef_result) end
handle ERROR msg => err_in_typedef msg name;
(* add_typedef interfaces *)
local
fun gen_typedef prep_term def opt_name typ set opt_morphs tac thy =
let
val string_of_term = ProofContext.string_of_term (ProofContext.init thy);
val name = the_default (#1 typ) opt_name;
val (set, goal, _, typedef_result) =
prepare_typedef prep_term def name typ set opt_morphs thy;
val _ = message ("Proving non-emptiness of set " ^ quote (string_of_term set) ^ " ...");
val non_empty = Goal.prove_global thy [] [] goal (K tac) handle ERROR msg =>
cat_error msg ("Failed to prove non-emptiness of " ^ quote (string_of_term set));
in typedef_result non_empty thy end;
in
val add_typedef = gen_typedef ProofContext.read_term;
val add_typedef_i = gen_typedef ProofContext.cert_term;
end;
(* Isar typedef interface *)
local
fun gen_typedef prep_term ((def, name), typ, set, opt_morphs) thy =
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;
in
val typedef = gen_typedef ProofContext.read_term;
val typedef_i = gen_typedef ProofContext.cert_term;
end;
val setup = TypedefData.init;
(** 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, the_default (Syntax.type_name t mx) opt_name), (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;