--- a/src/HOL/Tools/inductive_set_package.ML Thu Jun 18 18:31:14 2009 -0700
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,566 +0,0 @@
-(* Title: HOL/Tools/inductive_set_package.ML
- Author: Stefan Berghofer, TU Muenchen
-
-Wrapper for defining inductive sets using package for inductive predicates,
-including infrastructure for converting between predicates and sets.
-*)
-
-signature INDUCTIVE_SET_PACKAGE =
-sig
- val to_set_att: thm list -> attribute
- val to_pred_att: thm list -> attribute
- val pred_set_conv_att: attribute
- val add_inductive_i:
- InductivePackage.inductive_flags ->
- ((binding * typ) * mixfix) list ->
- (string * typ) list ->
- (Attrib.binding * term) list -> thm list ->
- local_theory -> InductivePackage.inductive_result * local_theory
- val add_inductive: bool -> bool ->
- (binding * string option * mixfix) list ->
- (binding * string option * mixfix) list ->
- (Attrib.binding * string) list -> (Facts.ref * Attrib.src list) list ->
- bool -> local_theory -> InductivePackage.inductive_result * local_theory
- val codegen_preproc: theory -> thm list -> thm list
- val setup: theory -> theory
-end;
-
-structure InductiveSetPackage: INDUCTIVE_SET_PACKAGE =
-struct
-
-(**** simplify {(x1, ..., xn). (x1, ..., xn) : S} to S ****)
-
-val collect_mem_simproc =
- Simplifier.simproc (theory "Set") "Collect_mem" ["Collect t"] (fn thy => fn ss =>
- fn S as Const ("Collect", Type ("fun", [_, T])) $ t =>
- let val (u, Ts, ps) = HOLogic.strip_split t
- in case u of
- (c as Const ("op :", _)) $ q $ S' =>
- (case try (HOLogic.dest_tuple' ps) q of
- NONE => NONE
- | SOME ts =>
- if not (loose_bvar (S', 0)) andalso
- ts = map Bound (length ps downto 0)
- then
- let val simp = full_simp_tac (Simplifier.inherit_context ss
- (HOL_basic_ss addsimps [split_paired_all, split_conv])) 1
- in
- SOME (Goal.prove (Simplifier.the_context ss) [] []
- (Const ("==", T --> T --> propT) $ S $ S')
- (K (EVERY
- [rtac eq_reflection 1, rtac @{thm subset_antisym} 1,
- rtac subsetI 1, dtac CollectD 1, simp,
- rtac subsetI 1, rtac CollectI 1, simp])))
- end
- else NONE)
- | _ => NONE
- end
- | _ => NONE);
-
-(***********************************************************************************)
-(* simplifies (%x y. (x, y) : S & P x y) to (%x y. (x, y) : S Int {(x, y). P x y}) *)
-(* and (%x y. (x, y) : S | P x y) to (%x y. (x, y) : S Un {(x, y). P x y}) *)
-(* used for converting "strong" (co)induction rules *)
-(***********************************************************************************)
-
-val anyt = Free ("t", TFree ("'t", []));
-
-fun strong_ind_simproc tab =
- Simplifier.simproc_i @{theory HOL} "strong_ind" [anyt] (fn thy => fn ss => fn t =>
- let
- fun close p t f =
- let val vs = Term.add_vars t []
- in Drule.instantiate' [] (rev (map (SOME o cterm_of thy o Var) vs))
- (p (fold (Logic.all o Var) vs t) f)
- end;
- fun mkop "op &" T x = SOME (Const (@{const_name "Int"}, T --> T --> T), x)
- | mkop "op |" T x = SOME (Const (@{const_name "Un"}, T --> T --> T), x)
- | mkop _ _ _ = NONE;
- fun mk_collect p T t =
- let val U = HOLogic.dest_setT T
- in HOLogic.Collect_const U $
- HOLogic.ap_split' (HOLogic.prod_factors p) U HOLogic.boolT t
- end;
- fun decomp (Const (s, _) $ ((m as Const ("op :",
- Type (_, [_, Type (_, [T, _])]))) $ p $ S) $ u) =
- mkop s T (m, p, S, mk_collect p T (head_of u))
- | decomp (Const (s, _) $ u $ ((m as Const ("op :",
- Type (_, [_, Type (_, [T, _])]))) $ p $ S)) =
- mkop s T (m, p, mk_collect p T (head_of u), S)
- | decomp _ = NONE;
- val simp = full_simp_tac (Simplifier.inherit_context ss
- (HOL_basic_ss addsimps [mem_Collect_eq, split_conv])) 1;
- fun mk_rew t = (case strip_abs_vars t of
- [] => NONE
- | xs => (case decomp (strip_abs_body t) of
- NONE => NONE
- | SOME (bop, (m, p, S, S')) =>
- SOME (close (Goal.prove (Simplifier.the_context ss) [] [])
- (Logic.mk_equals (t, list_abs (xs, m $ p $ (bop $ S $ S'))))
- (K (EVERY
- [rtac eq_reflection 1, REPEAT (rtac ext 1), rtac iffI 1,
- EVERY [etac conjE 1, rtac IntI 1, simp, simp,
- etac IntE 1, rtac conjI 1, simp, simp] ORELSE
- EVERY [etac disjE 1, rtac UnI1 1, simp, rtac UnI2 1, simp,
- etac UnE 1, rtac disjI1 1, simp, rtac disjI2 1, simp]])))
- handle ERROR _ => NONE))
- in
- case strip_comb t of
- (h as Const (name, _), ts) => (case Symtab.lookup tab name of
- SOME _ =>
- let val rews = map mk_rew ts
- in
- if forall is_none rews then NONE
- else SOME (fold (fn th1 => fn th2 => combination th2 th1)
- (map2 (fn SOME r => K r | NONE => reflexive o cterm_of thy)
- rews ts) (reflexive (cterm_of thy h)))
- end
- | NONE => NONE)
- | _ => NONE
- end);
-
-(* only eta contract terms occurring as arguments of functions satisfying p *)
-fun eta_contract p =
- let
- fun eta b (Abs (a, T, body)) =
- (case eta b body of
- body' as (f $ Bound 0) =>
- if loose_bvar1 (f, 0) orelse not b then Abs (a, T, body')
- else incr_boundvars ~1 f
- | body' => Abs (a, T, body'))
- | eta b (t $ u) = eta b t $ eta (p (head_of t)) u
- | eta b t = t
- in eta false end;
-
-fun eta_contract_thm p =
- Conv.fconv_rule (Conv.then_conv (Thm.beta_conversion true, fn ct =>
- Thm.transitive (Thm.eta_conversion ct)
- (Thm.symmetric (Thm.eta_conversion
- (cterm_of (theory_of_cterm ct) (eta_contract p (term_of ct)))))));
-
-
-(***********************************************************)
-(* rules for converting between predicate and set notation *)
-(* *)
-(* rules for converting predicates to sets have the form *)
-(* P (%x y. (x, y) : s) = (%x y. (x, y) : S s) *)
-(* *)
-(* rules for converting sets to predicates have the form *)
-(* S {(x, y). p x y} = {(x, y). P p x y} *)
-(* *)
-(* where s and p are parameters *)
-(***********************************************************)
-
-structure PredSetConvData = GenericDataFun
-(
- type T =
- {(* rules for converting predicates to sets *)
- to_set_simps: thm list,
- (* rules for converting sets to predicates *)
- to_pred_simps: thm list,
- (* arities of functions of type t set => ... => u set *)
- set_arities: (typ * (int list list option list * int list list option)) list Symtab.table,
- (* arities of functions of type (t => ... => bool) => u => ... => bool *)
- pred_arities: (typ * (int list list option list * int list list option)) list Symtab.table};
- val empty = {to_set_simps = [], to_pred_simps = [],
- set_arities = Symtab.empty, pred_arities = Symtab.empty};
- val extend = I;
- fun merge _
- ({to_set_simps = to_set_simps1, to_pred_simps = to_pred_simps1,
- set_arities = set_arities1, pred_arities = pred_arities1},
- {to_set_simps = to_set_simps2, to_pred_simps = to_pred_simps2,
- set_arities = set_arities2, pred_arities = pred_arities2}) : T =
- {to_set_simps = Thm.merge_thms (to_set_simps1, to_set_simps2),
- to_pred_simps = Thm.merge_thms (to_pred_simps1, to_pred_simps2),
- set_arities = Symtab.merge_list op = (set_arities1, set_arities2),
- pred_arities = Symtab.merge_list op = (pred_arities1, pred_arities2)};
-);
-
-fun name_type_of (Free p) = SOME p
- | name_type_of (Const p) = SOME p
- | name_type_of _ = NONE;
-
-fun map_type f (Free (s, T)) = Free (s, f T)
- | map_type f (Var (ixn, T)) = Var (ixn, f T)
- | map_type f _ = error "map_type";
-
-fun find_most_specific is_inst f eq xs T =
- find_first (fn U => is_inst (T, f U)
- andalso forall (fn U' => eq (f U, f U') orelse not
- (is_inst (T, f U') andalso is_inst (f U', f U)))
- xs) xs;
-
-fun lookup_arity thy arities (s, T) = case Symtab.lookup arities s of
- NONE => NONE
- | SOME xs => find_most_specific (Sign.typ_instance thy) fst (op =) xs T;
-
-fun lookup_rule thy f rules = find_most_specific
- (swap #> Pattern.matches thy) (f #> fst) (op aconv) rules;
-
-fun infer_arities thy arities (optf, t) fs = case strip_comb t of
- (Abs (s, T, u), []) => infer_arities thy arities (NONE, u) fs
- | (Abs _, _) => infer_arities thy arities (NONE, Envir.beta_norm t) fs
- | (u, ts) => (case Option.map (lookup_arity thy arities) (name_type_of u) of
- SOME (SOME (_, (arity, _))) =>
- (fold (infer_arities thy arities) (arity ~~ List.take (ts, length arity)) fs
- handle Subscript => error "infer_arities: bad term")
- | _ => fold (infer_arities thy arities) (map (pair NONE) ts)
- (case optf of
- NONE => fs
- | SOME f => AList.update op = (u, the_default f
- (Option.map (curry op inter f) (AList.lookup op = fs u))) fs));
-
-
-(**************************************************************)
-(* derive the to_pred equation from the to_set equation *)
-(* *)
-(* 1. instantiate each set parameter with {(x, y). p x y} *)
-(* 2. apply %P. {(x, y). P x y} to both sides of the equation *)
-(* 3. simplify *)
-(**************************************************************)
-
-fun mk_to_pred_inst thy fs =
- map (fn (x, ps) =>
- let
- val U = HOLogic.dest_setT (fastype_of x);
- val x' = map_type (K (HOLogic.prodT_factors' ps U ---> HOLogic.boolT)) x
- in
- (cterm_of thy x,
- cterm_of thy (HOLogic.Collect_const U $
- HOLogic.ap_split' ps U HOLogic.boolT x'))
- end) fs;
-
-fun mk_to_pred_eq p fs optfs' T thm =
- let
- val thy = theory_of_thm thm;
- val insts = mk_to_pred_inst thy fs;
- val thm' = Thm.instantiate ([], insts) thm;
- val thm'' = (case optfs' of
- NONE => thm' RS sym
- | SOME fs' =>
- let
- val (_, U) = split_last (binder_types T);
- val Ts = HOLogic.prodT_factors' fs' U;
- (* FIXME: should cterm_instantiate increment indexes? *)
- val arg_cong' = Thm.incr_indexes (Thm.maxidx_of thm + 1) arg_cong;
- val (arg_cong_f, _) = arg_cong' |> cprop_of |> Drule.strip_imp_concl |>
- Thm.dest_comb |> snd |> Drule.strip_comb |> snd |> hd |> Thm.dest_comb
- in
- thm' RS (Drule.cterm_instantiate [(arg_cong_f,
- cterm_of thy (Abs ("P", Ts ---> HOLogic.boolT,
- HOLogic.Collect_const U $ HOLogic.ap_split' fs' U
- HOLogic.boolT (Bound 0))))] arg_cong' RS sym)
- end)
- in
- Simplifier.simplify (HOL_basic_ss addsimps [mem_Collect_eq, split_conv]
- addsimprocs [collect_mem_simproc]) thm'' |>
- zero_var_indexes |> eta_contract_thm (equal p)
- end;
-
-
-(**** declare rules for converting predicates to sets ****)
-
-fun add ctxt thm (tab as {to_set_simps, to_pred_simps, set_arities, pred_arities}) =
- case prop_of thm of
- Const ("Trueprop", _) $ (Const ("op =", Type (_, [T, _])) $ lhs $ rhs) =>
- (case body_type T of
- Type ("bool", []) =>
- let
- val thy = Context.theory_of ctxt;
- fun factors_of t fs = case strip_abs_body t of
- Const ("op :", _) $ u $ S =>
- if is_Free S orelse is_Var S then
- let val ps = HOLogic.prod_factors u
- in (SOME ps, (S, ps) :: fs) end
- else (NONE, fs)
- | _ => (NONE, fs);
- val (h, ts) = strip_comb lhs
- val (pfs, fs) = fold_map factors_of ts [];
- val ((h', ts'), fs') = (case rhs of
- Abs _ => (case strip_abs_body rhs of
- Const ("op :", _) $ u $ S =>
- (strip_comb S, SOME (HOLogic.prod_factors u))
- | _ => error "member symbol on right-hand side expected")
- | _ => (strip_comb rhs, NONE))
- in
- case (name_type_of h, name_type_of h') of
- (SOME (s, T), SOME (s', T')) =>
- if exists (fn (U, _) =>
- Sign.typ_instance thy (T', U) andalso
- Sign.typ_instance thy (U, T'))
- (Symtab.lookup_list set_arities s')
- then
- (warning ("Ignoring conversion rule for operator " ^ s'); tab)
- else
- {to_set_simps = thm :: to_set_simps,
- to_pred_simps =
- mk_to_pred_eq h fs fs' T' thm :: to_pred_simps,
- set_arities = Symtab.insert_list op = (s',
- (T', (map (AList.lookup op = fs) ts', fs'))) set_arities,
- pred_arities = Symtab.insert_list op = (s,
- (T, (pfs, fs'))) pred_arities}
- | _ => error "set / predicate constant expected"
- end
- | _ => error "equation between predicates expected")
- | _ => error "equation expected";
-
-val pred_set_conv_att = Thm.declaration_attribute
- (fn thm => fn ctxt => PredSetConvData.map (add ctxt thm) ctxt);
-
-
-(**** convert theorem in set notation to predicate notation ****)
-
-fun is_pred tab t =
- case Option.map (Symtab.lookup tab o fst) (name_type_of t) of
- SOME (SOME _) => true | _ => false;
-
-fun to_pred_simproc rules =
- let val rules' = map mk_meta_eq rules
- in
- Simplifier.simproc_i @{theory HOL} "to_pred" [anyt]
- (fn thy => K (lookup_rule thy (prop_of #> Logic.dest_equals) rules'))
- end;
-
-fun to_pred_proc thy rules t = case lookup_rule thy I rules t of
- NONE => NONE
- | SOME (lhs, rhs) =>
- SOME (Envir.subst_vars
- (Pattern.match thy (lhs, t) (Vartab.empty, Vartab.empty)) rhs);
-
-fun to_pred thms ctxt thm =
- let
- val thy = Context.theory_of ctxt;
- val {to_pred_simps, set_arities, pred_arities, ...} =
- fold (add ctxt) thms (PredSetConvData.get ctxt);
- val fs = filter (is_Var o fst)
- (infer_arities thy set_arities (NONE, prop_of thm) []);
- (* instantiate each set parameter with {(x, y). p x y} *)
- val insts = mk_to_pred_inst thy fs
- in
- thm |>
- Thm.instantiate ([], insts) |>
- Simplifier.full_simplify (HOL_basic_ss addsimprocs
- [to_pred_simproc (mem_Collect_eq :: split_conv :: to_pred_simps)]) |>
- eta_contract_thm (is_pred pred_arities) |>
- RuleCases.save thm
- end;
-
-val to_pred_att = Thm.rule_attribute o to_pred;
-
-
-(**** convert theorem in predicate notation to set notation ****)
-
-fun to_set thms ctxt thm =
- let
- val thy = Context.theory_of ctxt;
- val {to_set_simps, pred_arities, ...} =
- fold (add ctxt) thms (PredSetConvData.get ctxt);
- val fs = filter (is_Var o fst)
- (infer_arities thy pred_arities (NONE, prop_of thm) []);
- (* instantiate each predicate parameter with %x y. (x, y) : s *)
- val insts = map (fn (x, ps) =>
- let
- val Ts = binder_types (fastype_of x);
- val T = HOLogic.mk_tupleT ps Ts;
- val x' = map_type (K (HOLogic.mk_setT T)) x
- in
- (cterm_of thy x,
- cterm_of thy (list_abs (map (pair "x") Ts, HOLogic.mk_mem
- (HOLogic.mk_tuple' ps T (map Bound (length ps downto 0)), x'))))
- end) fs
- in
- thm |>
- Thm.instantiate ([], insts) |>
- Simplifier.full_simplify (HOL_basic_ss addsimps to_set_simps
- addsimprocs [strong_ind_simproc pred_arities, collect_mem_simproc]) |>
- RuleCases.save thm
- end;
-
-val to_set_att = Thm.rule_attribute o to_set;
-
-
-(**** preprocessor for code generator ****)
-
-fun codegen_preproc thy =
- let
- val {to_pred_simps, set_arities, pred_arities, ...} =
- PredSetConvData.get (Context.Theory thy);
- fun preproc thm =
- if exists_Const (fn (s, _) => case Symtab.lookup set_arities s of
- NONE => false
- | SOME arities => exists (fn (_, (xs, _)) =>
- forall is_none xs) arities) (prop_of thm)
- then
- thm |>
- Simplifier.full_simplify (HOL_basic_ss addsimprocs
- [to_pred_simproc (mem_Collect_eq :: split_conv :: to_pred_simps)]) |>
- eta_contract_thm (is_pred pred_arities)
- else thm
- in map preproc end;
-
-fun code_ind_att optmod = to_pred_att [] #> InductiveCodegen.add optmod NONE;
-
-
-(**** definition of inductive sets ****)
-
-fun add_ind_set_def
- {quiet_mode, verbose, kind, alt_name, coind, no_elim, no_ind, skip_mono, fork_mono}
- cs intros monos params cnames_syn ctxt =
- let
- val thy = ProofContext.theory_of ctxt;
- val {set_arities, pred_arities, to_pred_simps, ...} =
- PredSetConvData.get (Context.Proof ctxt);
- fun infer (Abs (_, _, t)) = infer t
- | infer (Const ("op :", _) $ t $ u) =
- infer_arities thy set_arities (SOME (HOLogic.prod_factors t), u)
- | infer (t $ u) = infer t #> infer u
- | infer _ = I;
- val new_arities = filter_out
- (fn (x as Free (_, T), _) => x mem params andalso length (binder_types T) > 1
- | _ => false) (fold (snd #> infer) intros []);
- val params' = map (fn x => (case AList.lookup op = new_arities x of
- SOME fs =>
- let
- val T = HOLogic.dest_setT (fastype_of x);
- val Ts = HOLogic.prodT_factors' fs T;
- val x' = map_type (K (Ts ---> HOLogic.boolT)) x
- in
- (x, (x',
- (HOLogic.Collect_const T $
- HOLogic.ap_split' fs T HOLogic.boolT x',
- list_abs (map (pair "x") Ts, HOLogic.mk_mem
- (HOLogic.mk_tuple' fs T (map Bound (length fs downto 0)),
- x)))))
- end
- | NONE => (x, (x, (x, x))))) params;
- val (params1, (params2, params3)) =
- params' |> map snd |> split_list ||> split_list;
- val paramTs = map fastype_of params;
-
- (* equations for converting sets to predicates *)
- val ((cs', cs_info), eqns) = cs |> map (fn c as Free (s, T) =>
- let
- val fs = the_default [] (AList.lookup op = new_arities c);
- val (Us, U) = split_last (binder_types T);
- val _ = Us = paramTs orelse error (Pretty.string_of (Pretty.chunks
- [Pretty.str "Argument types",
- Pretty.block (Pretty.commas (map (Syntax.pretty_typ ctxt) Us)),
- Pretty.str ("of " ^ s ^ " do not agree with types"),
- Pretty.block (Pretty.commas (map (Syntax.pretty_typ ctxt) paramTs)),
- Pretty.str "of declared parameters"]));
- val Ts = HOLogic.prodT_factors' fs U;
- val c' = Free (s ^ "p",
- map fastype_of params1 @ Ts ---> HOLogic.boolT)
- in
- ((c', (fs, U, Ts)),
- (list_comb (c, params2),
- HOLogic.Collect_const U $ HOLogic.ap_split' fs U HOLogic.boolT
- (list_comb (c', params1))))
- end) |> split_list |>> split_list;
- val eqns' = eqns @
- map (prop_of #> HOLogic.dest_Trueprop #> HOLogic.dest_eq)
- (mem_Collect_eq :: split_conv :: to_pred_simps);
-
- (* predicate version of the introduction rules *)
- val intros' =
- map (fn (name_atts, t) => (name_atts,
- t |>
- map_aterms (fn u =>
- (case AList.lookup op = params' u of
- SOME (_, (u', _)) => u'
- | NONE => u)) |>
- Pattern.rewrite_term thy [] [to_pred_proc thy eqns'] |>
- eta_contract (member op = cs' orf is_pred pred_arities))) intros;
- val cnames_syn' = map (fn (b, _) => (Binding.suffix_name "p" b, NoSyn)) cnames_syn;
- val monos' = map (to_pred [] (Context.Proof ctxt)) monos;
- val ({preds, intrs, elims, raw_induct, ...}, ctxt1) =
- InductivePackage.add_ind_def
- {quiet_mode = quiet_mode, verbose = verbose, kind = kind, alt_name = Binding.empty,
- coind = coind, no_elim = no_elim, no_ind = no_ind,
- skip_mono = skip_mono, fork_mono = fork_mono}
- cs' intros' monos' params1 cnames_syn' ctxt;
-
- (* define inductive sets using previously defined predicates *)
- val (defs, ctxt2) = fold_map (LocalTheory.define Thm.internalK)
- (map (fn ((c_syn, (fs, U, _)), p) => (c_syn, (Attrib.empty_binding,
- fold_rev lambda params (HOLogic.Collect_const U $
- HOLogic.ap_split' fs U HOLogic.boolT (list_comb (p, params3))))))
- (cnames_syn ~~ cs_info ~~ preds)) ctxt1;
-
- (* prove theorems for converting predicate to set notation *)
- val ctxt3 = fold
- (fn (((p, c as Free (s, _)), (fs, U, Ts)), (_, (_, def))) => fn ctxt =>
- let val conv_thm =
- Goal.prove ctxt (map (fst o dest_Free) params) []
- (HOLogic.mk_Trueprop (HOLogic.mk_eq
- (list_comb (p, params3),
- list_abs (map (pair "x") Ts, HOLogic.mk_mem
- (HOLogic.mk_tuple' fs U (map Bound (length fs downto 0)),
- list_comb (c, params))))))
- (K (REPEAT (rtac ext 1) THEN simp_tac (HOL_basic_ss addsimps
- [def, mem_Collect_eq, split_conv]) 1))
- in
- ctxt |> LocalTheory.note kind ((Binding.name (s ^ "p_" ^ s ^ "_eq"),
- [Attrib.internal (K pred_set_conv_att)]),
- [conv_thm]) |> snd
- end) (preds ~~ cs ~~ cs_info ~~ defs) ctxt2;
-
- (* convert theorems to set notation *)
- val rec_name =
- if Binding.is_empty alt_name then
- Binding.name (space_implode "_" (map (Binding.name_of o fst) cnames_syn))
- else alt_name;
- val cnames = map (LocalTheory.full_name ctxt3 o #1) cnames_syn; (* FIXME *)
- val (intr_names, intr_atts) = split_list (map fst intros);
- val raw_induct' = to_set [] (Context.Proof ctxt3) raw_induct;
- val (intrs', elims', induct, ctxt4) =
- InductivePackage.declare_rules kind rec_name coind no_ind cnames
- (map (to_set [] (Context.Proof ctxt3)) intrs) intr_names intr_atts
- (map (fn th => (to_set [] (Context.Proof ctxt3) th,
- map fst (fst (RuleCases.get th)))) elims)
- raw_induct' ctxt3
- in
- ({intrs = intrs', elims = elims', induct = induct,
- raw_induct = raw_induct', preds = map fst defs},
- ctxt4)
- end;
-
-val add_inductive_i = InductivePackage.gen_add_inductive_i add_ind_set_def;
-val add_inductive = InductivePackage.gen_add_inductive add_ind_set_def;
-
-val mono_add_att = to_pred_att [] #> InductivePackage.mono_add;
-val mono_del_att = to_pred_att [] #> InductivePackage.mono_del;
-
-
-(** package setup **)
-
-(* setup theory *)
-
-val setup =
- Attrib.setup @{binding pred_set_conv} (Scan.succeed pred_set_conv_att)
- "declare rules for converting between predicate and set notation" #>
- Attrib.setup @{binding to_set} (Attrib.thms >> to_set_att) "convert rule to set notation" #>
- Attrib.setup @{binding to_pred} (Attrib.thms >> to_pred_att) "convert rule to predicate notation" #>
- Code.add_attribute ("ind_set",
- Scan.option (Args.$$$ "target" |-- Args.colon |-- Args.name) >> code_ind_att) #>
- Codegen.add_preprocessor codegen_preproc #>
- Attrib.setup @{binding mono_set} (Attrib.add_del mono_add_att mono_del_att)
- "declaration of monotonicity rule for set operators" #>
- Context.theory_map (Simplifier.map_ss (fn ss => ss addsimprocs [collect_mem_simproc]));
-
-
-(* outer syntax *)
-
-local structure P = OuterParse and K = OuterKeyword in
-
-val ind_set_decl = InductivePackage.gen_ind_decl add_ind_set_def;
-
-val _ =
- OuterSyntax.local_theory' "inductive_set" "define inductive sets" K.thy_decl (ind_set_decl false);
-
-val _ =
- OuterSyntax.local_theory' "coinductive_set" "define coinductive sets" K.thy_decl (ind_set_decl true);
-
-end;
-
-end;