(* Title: HOL/Tools/typedef_package.ML
ID: $Id$
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: 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";
(** 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
thy
|> Theory.add_typedecls decls
|> can (Theory.assert_super HOL.thy) ? Theory.add_arities_i (map arity_of decls)
end;
(** type definitions **)
(* messages *)
val quiet_mode = ref false;
fun message s = if ! quiet_mode then () else writeln s;
(* 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)));
(* 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 opt_name typ set opt_morphs tac thy =
let
val name = the_default (#1 typ) opt_name;
val (cset, goal, _, typedef_result) =
prepare_typedef prep_term def name typ set opt_morphs thy;
val _ = message ("Proving non-emptiness of set " ^ quote (string_of_cterm cset) ^ " ...");
val non_empty = Goal.prove thy [] [] goal (K tac) handle ERROR_MESSAGE msg =>
error (msg ^ "\nFailed to prove non-emptiness of " ^ quote (string_of_cterm cset));
val ((thy', _), result) = (thy, non_empty) |> typedef_result;
in (thy', result) end;
in
val add_typedef = gen_typedef read_term;
val add_typedef_i = gen_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;