(* Title: HOL/Tools/recdef_package.ML
Author: Markus Wenzel, TU Muenchen
Wrapper module for Konrad Slind's TFL package.
*)
signature RECDEF_PACKAGE =
sig
val get_recdef: theory -> string
-> {simps: thm list, rules: thm list list, induct: thm, tcs: term list} option
val get_hints: Proof.context -> {simps: thm list, congs: (string * thm) list, wfs: thm list}
val simp_add: attribute
val simp_del: attribute
val cong_add: attribute
val cong_del: attribute
val wf_add: attribute
val wf_del: attribute
val add_recdef: bool -> xstring -> string -> ((binding * string) * Attrib.src list) list ->
Attrib.src option -> theory -> theory
* {simps: thm list, rules: thm list list, induct: thm, tcs: term list}
val add_recdef_i: bool -> xstring -> term -> ((binding * term) * attribute list) list ->
theory -> theory * {simps: thm list, rules: thm list list, induct: thm, tcs: term list}
val defer_recdef: xstring -> string list -> (Facts.ref * Attrib.src list) list
-> theory -> theory * {induct_rules: thm}
val defer_recdef_i: xstring -> term list -> thm list -> theory -> theory * {induct_rules: thm}
val recdef_tc: bstring * Attrib.src list -> xstring -> int option -> bool ->
local_theory -> Proof.state
val recdef_tc_i: bstring * Attrib.src list -> string -> int option -> bool ->
local_theory -> Proof.state
val setup: theory -> theory
end;
structure RecdefPackage: RECDEF_PACKAGE =
struct
(** recdef hints **)
(* type hints *)
type hints = {simps: thm list, congs: (string * thm) list, wfs: thm list};
fun mk_hints (simps, congs, wfs) = {simps = simps, congs = congs, wfs = wfs}: hints;
fun map_hints f ({simps, congs, wfs}: hints) = mk_hints (f (simps, congs, wfs));
fun map_simps f = map_hints (fn (simps, congs, wfs) => (f simps, congs, wfs));
fun map_congs f = map_hints (fn (simps, congs, wfs) => (simps, f congs, wfs));
fun map_wfs f = map_hints (fn (simps, congs, wfs) => (simps, congs, f wfs));
fun pretty_hints ({simps, congs, wfs}: hints) =
[Pretty.big_list "recdef simp hints:" (map Display.pretty_thm simps),
Pretty.big_list "recdef cong hints:" (map Display.pretty_thm (map snd congs)),
Pretty.big_list "recdef wf hints:" (map Display.pretty_thm wfs)];
(* congruence rules *)
local
val cong_head =
fst o Term.dest_Const o Term.head_of o fst o Logic.dest_equals o Thm.concl_of;
fun prep_cong raw_thm =
let val thm = safe_mk_meta_eq raw_thm in (cong_head thm, thm) end;
in
fun add_cong raw_thm congs =
let
val (c, thm) = prep_cong raw_thm;
val _ = if AList.defined (op =) congs c
then warning ("Overwriting recdef congruence rule for " ^ quote c)
else ();
in AList.update (op =) (c, thm) congs end;
fun del_cong raw_thm congs =
let
val (c, thm) = prep_cong raw_thm;
val _ = if AList.defined (op =) congs c
then ()
else warning ("No recdef congruence rule for " ^ quote c);
in AList.delete (op =) c congs end;
end;
(** global and local recdef data **)
(* theory data *)
type recdef_info = {simps: thm list, rules: thm list list, induct: thm, tcs: term list};
structure GlobalRecdefData = TheoryDataFun
(
type T = recdef_info Symtab.table * hints;
val empty = (Symtab.empty, mk_hints ([], [], [])): T;
val copy = I;
val extend = I;
fun merge _
((tab1, {simps = simps1, congs = congs1, wfs = wfs1}),
(tab2, {simps = simps2, congs = congs2, wfs = wfs2})) : T =
(Symtab.merge (K true) (tab1, tab2),
mk_hints (Thm.merge_thms (simps1, simps2),
AList.merge (op =) Thm.eq_thm (congs1, congs2),
Thm.merge_thms (wfs1, wfs2)));
);
val get_recdef = Symtab.lookup o #1 o GlobalRecdefData.get;
fun put_recdef name info thy =
let
val (tab, hints) = GlobalRecdefData.get thy;
val tab' = Symtab.update_new (name, info) tab
handle Symtab.DUP _ => error ("Duplicate recursive function definition " ^ quote name);
in GlobalRecdefData.put (tab', hints) thy end;
val get_global_hints = #2 o GlobalRecdefData.get;
(* proof data *)
structure LocalRecdefData = ProofDataFun
(
type T = hints;
val init = get_global_hints;
);
val get_hints = LocalRecdefData.get;
fun map_hints f = Context.mapping (GlobalRecdefData.map (apsnd f)) (LocalRecdefData.map f);
(* attributes *)
fun attrib f = Thm.declaration_attribute (map_hints o f);
val simp_add = attrib (map_simps o Thm.add_thm);
val simp_del = attrib (map_simps o Thm.del_thm);
val cong_add = attrib (map_congs o add_cong);
val cong_del = attrib (map_congs o del_cong);
val wf_add = attrib (map_wfs o Thm.add_thm);
val wf_del = attrib (map_wfs o Thm.del_thm);
(* modifiers *)
val recdef_simpN = "recdef_simp";
val recdef_congN = "recdef_cong";
val recdef_wfN = "recdef_wf";
val recdef_modifiers =
[Args.$$$ recdef_simpN -- Args.colon >> K ((I, simp_add): Method.modifier),
Args.$$$ recdef_simpN -- Args.add -- Args.colon >> K (I, simp_add),
Args.$$$ recdef_simpN -- Args.del -- Args.colon >> K (I, simp_del),
Args.$$$ recdef_congN -- Args.colon >> K (I, cong_add),
Args.$$$ recdef_congN -- Args.add -- Args.colon >> K (I, cong_add),
Args.$$$ recdef_congN -- Args.del -- Args.colon >> K (I, cong_del),
Args.$$$ recdef_wfN -- Args.colon >> K (I, wf_add),
Args.$$$ recdef_wfN -- Args.add -- Args.colon >> K (I, wf_add),
Args.$$$ recdef_wfN -- Args.del -- Args.colon >> K (I, wf_del)] @
Clasimp.clasimp_modifiers;
(** prepare_hints(_i) **)
fun prepare_hints thy opt_src =
let
val ctxt0 = ProofContext.init thy;
val ctxt =
(case opt_src of
NONE => ctxt0
| SOME src => Method.only_sectioned_args recdef_modifiers I src ctxt0);
val {simps, congs, wfs} = get_hints ctxt;
val cs = local_claset_of ctxt;
val ss = local_simpset_of ctxt addsimps simps;
in (cs, ss, rev (map snd congs), wfs) end;
fun prepare_hints_i thy () =
let
val ctxt0 = ProofContext.init thy;
val {simps, congs, wfs} = get_global_hints thy;
in (local_claset_of ctxt0, local_simpset_of ctxt0 addsimps simps, rev (map snd congs), wfs) end;
(** add_recdef(_i) **)
fun requires_recdef thy = Theory.requires thy "Recdef" "recursive functions";
fun gen_add_recdef tfl_fn prep_att prep_hints not_permissive raw_name R eq_srcs hints thy =
let
val _ = requires_recdef thy;
val name = Sign.intern_const thy raw_name;
val bname = Long_Name.base_name name;
val _ = writeln ("Defining recursive function " ^ quote name ^ " ...");
val ((eq_names, eqs), raw_eq_atts) = apfst split_list (split_list eq_srcs);
val eq_atts = map (map (prep_att thy)) raw_eq_atts;
val (cs, ss, congs, wfs) = prep_hints thy hints;
(*We must remove imp_cong to prevent looping when the induction rule
is simplified. Many induction rules have nested implications that would
give rise to looping conditional rewriting.*)
val (thy, {rules = rules_idx, induct, tcs}) =
tfl_fn not_permissive thy cs (ss delcongs [imp_cong])
congs wfs name R eqs;
val rules = (map o map) fst (partition_eq (eq_snd (op = : int * int -> bool)) rules_idx);
val simp_att = if null tcs then [Simplifier.simp_add, Nitpick_Const_Simp_Thms.add,
Code.add_default_eqn_attribute] else [];
val ((simps' :: rules', [induct']), thy) =
thy
|> Sign.add_path bname
|> PureThy.add_thmss
(((Binding.name "simps", List.concat rules), simp_att) :: ((eq_names ~~ rules) ~~ eq_atts))
||>> PureThy.add_thms [((Binding.name "induct", induct), [])];
val result = {simps = simps', rules = rules', induct = induct', tcs = tcs};
val thy =
thy
|> put_recdef name result
|> Sign.parent_path;
in (thy, result) end;
val add_recdef = gen_add_recdef Tfl.define Attrib.attribute prepare_hints;
fun add_recdef_i x y z w = gen_add_recdef Tfl.define_i (K I) prepare_hints_i x y z w ();
(** defer_recdef(_i) **)
fun gen_defer_recdef tfl_fn eval_thms raw_name eqs raw_congs thy =
let
val name = Sign.intern_const thy raw_name;
val bname = Long_Name.base_name name;
val _ = requires_recdef thy;
val _ = writeln ("Deferred recursive function " ^ quote name ^ " ...");
val congs = eval_thms (ProofContext.init thy) raw_congs;
val (thy2, induct_rules) = tfl_fn thy congs name eqs;
val ([induct_rules'], thy3) =
thy2
|> Sign.add_path bname
|> PureThy.add_thms [((Binding.name "induct_rules", induct_rules), [])]
||> Sign.parent_path;
in (thy3, {induct_rules = induct_rules'}) end;
val defer_recdef = gen_defer_recdef Tfl.defer Attrib.eval_thms;
val defer_recdef_i = gen_defer_recdef Tfl.defer_i (K I);
(** recdef_tc(_i) **)
fun gen_recdef_tc prep_att prep_name (bname, raw_atts) raw_name opt_i int lthy =
let
val thy = ProofContext.theory_of lthy;
val name = prep_name thy raw_name;
val atts = map (prep_att thy) raw_atts;
val tcs =
(case get_recdef thy name of
NONE => error ("No recdef definition of constant: " ^ quote name)
| SOME {tcs, ...} => tcs);
val i = the_default 1 opt_i;
val tc = nth tcs (i - 1) handle Subscript =>
error ("No termination condition #" ^ string_of_int i ^
" in recdef definition of " ^ quote name);
in
Specification.theorem Thm.internalK NONE (K I) (Binding.name bname, atts)
[] (Element.Shows [(Attrib.empty_binding, [(HOLogic.mk_Trueprop tc, [])])]) int lthy
end;
val recdef_tc = gen_recdef_tc Attrib.intern_src Sign.intern_const;
val recdef_tc_i = gen_recdef_tc (K I) (K I);
(** package setup **)
(* setup theory *)
val setup =
Attrib.setup @{binding recdef_simp} (Attrib.add_del simp_add simp_del)
"declaration of recdef simp rule" #>
Attrib.setup @{binding recdef_cong} (Attrib.add_del cong_add cong_del)
"declaration of recdef cong rule" #>
Attrib.setup @{binding recdef_wf} (Attrib.add_del wf_add wf_del)
"declaration of recdef wf rule";
(* outer syntax *)
local structure P = OuterParse and K = OuterKeyword in
val _ = List.app OuterKeyword.keyword ["permissive", "congs", "hints"];
val hints =
P.$$$ "(" |-- P.!!! (P.position (P.$$$ "hints" -- Args.parse) --| P.$$$ ")") >> Args.src;
val recdef_decl =
Scan.optional (P.$$$ "(" -- P.!!! (P.$$$ "permissive" -- P.$$$ ")") >> K false) true --
P.name -- P.term -- Scan.repeat1 (SpecParse.opt_thm_name ":" -- P.prop)
-- Scan.option hints
>> (fn ((((p, f), R), eqs), src) => #1 o add_recdef p f R (map P.triple_swap eqs) src);
val _ =
OuterSyntax.command "recdef" "define general recursive functions (TFL)" K.thy_decl
(recdef_decl >> Toplevel.theory);
val defer_recdef_decl =
P.name -- Scan.repeat1 P.prop --
Scan.optional (P.$$$ "(" |-- P.$$$ "congs" |-- P.!!! (SpecParse.xthms1 --| P.$$$ ")")) []
>> (fn ((f, eqs), congs) => #1 o defer_recdef f eqs congs);
val _ =
OuterSyntax.command "defer_recdef" "defer general recursive functions (TFL)" K.thy_decl
(defer_recdef_decl >> Toplevel.theory);
val _ =
OuterSyntax.local_theory_to_proof' "recdef_tc" "recommence proof of termination condition (TFL)"
K.thy_goal
((SpecParse.opt_thm_name ":" >> apfst Binding.name_of) -- P.xname --
Scan.option (P.$$$ "(" |-- P.nat --| P.$$$ ")")
>> (fn ((thm_name, name), i) => recdef_tc thm_name name i));
end;
end;