--- a/src/HOL/Tools/inductive_package.ML Fri Oct 13 18:24:02 2006 +0200
+++ b/src/HOL/Tools/inductive_package.ML Fri Oct 13 18:27:27 2006 +0200
@@ -8,53 +8,42 @@
Features:
* least or greatest fixedpoints
- * user-specified product and sum constructions
* mutually recursive definitions
* definitions involving arbitrary monotone operators
* automatically proves introduction and elimination rules
-The recursive sets must *already* be declared as constants in the
-current theory!
-
Introduction rules have the form
- [| ti:M(Sj), ..., P(x), ... |] ==> t: Sk
+ [| M Pj ti, ..., Q x, ... |] ==> Pk t
where M is some monotone operator (usually the identity)
- P(x) is any side condition on the free variables
+ Q x is any side condition on the free variables
ti, t are any terms
- Sj, Sk are two of the sets being defined in mutual recursion
-
-Sums are used only for mutual recursion. Products are used only to
-derive "streamlined" induction rules for relations.
+ Pj, Pk are two of the predicates being defined in mutual recursion
*)
signature INDUCTIVE_PACKAGE =
sig
val quiet_mode: bool ref
val trace: bool ref
- val unify_consts: theory -> term list -> term list -> term list * term list
- val split_rule_vars: term list -> thm -> thm
- val get_inductive: theory -> string -> ({names: string list, coind: bool} *
- {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
- intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}) option
- val the_mk_cases: theory -> string -> string -> thm
- val print_inductives: theory -> unit
+ type inductive_result
+ type inductive_info
+ val get_inductive: Context.generic -> string -> inductive_info option
+ val the_mk_cases: Context.generic -> string -> string -> thm
+ val print_inductives: Context.generic -> unit
val mono_add: attribute
val mono_del: attribute
- val get_monos: theory -> thm list
+ val get_monos: Context.generic -> thm list
val inductive_forall_name: string
val inductive_forall_def: thm
val rulify: thm -> thm
val inductive_cases: ((bstring * Attrib.src list) * string list) list -> theory -> theory
val inductive_cases_i: ((bstring * attribute list) * term list) list -> theory -> theory
- val add_inductive_i: bool -> bool -> bstring -> bool -> bool -> bool -> term list ->
- ((bstring * term) * attribute list) list -> thm list -> theory -> theory *
- {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
- intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
- val add_inductive: bool -> bool -> string list ->
- ((bstring * string) * Attrib.src list) list -> (thmref * Attrib.src list) list ->
- theory -> theory *
- {defs: thm list, elims: thm list, raw_induct: thm, induct: thm,
- intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm}
+ val add_inductive_i: bool -> bstring -> bool -> bool -> bool -> (string * typ option * mixfix) list ->
+ (string * typ option) list -> ((bstring * Attrib.src list) * term) list -> thm list ->
+ local_theory -> local_theory * inductive_result
+ val add_inductive: bool -> bool -> (string * string option * mixfix) list ->
+ (string * string option * mixfix) list ->
+ ((bstring * Attrib.src list) * string) list -> (thmref * Attrib.src list) list ->
+ local_theory -> local_theory * inductive_result
val setup: theory -> theory
end;
@@ -67,8 +56,6 @@
val mono_name = "Orderings.mono";
val gfp_name = "FixedPoint.gfp";
val lfp_name = "FixedPoint.lfp";
-val vimage_name = "Set.vimage";
-val Const _ $ (vimage_f $ _) $ _ = HOLogic.dest_Trueprop (Thm.concl_of vimageD);
val inductive_forall_name = "HOL.induct_forall";
val inductive_forall_def = thm "induct_forall_def";
@@ -79,29 +66,41 @@
val inductive_rulify = thms "induct_rulify";
val inductive_rulify_fallback = thms "induct_rulify_fallback";
+val notTrueE = TrueI RSN (2, notE);
+val notFalseI = Seq.hd (atac 1 notI);
+val simp_thms' = map (fn s => mk_meta_eq (the (find_first
+ (equal (term_of (read_cterm HOL.thy (s, propT))) o prop_of) simp_thms)))
+ ["(~True) = False", "(~False) = True",
+ "(True --> ?P) = ?P", "(False --> ?P) = True",
+ "(?P & True) = ?P", "(True & ?P) = ?P"];
+
(** theory data **)
-type inductive_info =
- {names: string list, coind: bool} * {defs: thm list, elims: thm list, raw_induct: thm,
- induct: thm, intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm};
+type inductive_result =
+ {preds: term list, defs: thm list, elims: thm list, raw_induct: thm,
+ induct: thm, intrs: thm list, mk_cases: string -> thm, mono: thm, unfold: thm};
-structure InductiveData = TheoryDataFun
+type inductive_info =
+ {names: string list, coind: bool} * inductive_result;
+
+structure InductiveData = GenericDataFun
(struct
- val name = "HOL/inductive";
+ val name = "HOL/inductive2";
type T = inductive_info Symtab.table * thm list;
val empty = (Symtab.empty, []);
- val copy = I;
val extend = I;
fun merge _ ((tab1, monos1), (tab2, monos2)) =
(Symtab.merge (K true) (tab1, tab2), Drule.merge_rules (monos1, monos2));
- fun print thy (tab, monos) =
+ fun print generic (tab, monos) =
[Pretty.strs ("(co)inductives:" ::
- map #1 (NameSpace.extern_table (Sign.const_space thy, tab))),
- Pretty.big_list "monotonicity rules:" (map (Display.pretty_thm_sg thy) monos)]
+ map #1 (NameSpace.extern_table
+ (Sign.const_space (Context.theory_of generic), tab))), (* FIXME? *)
+ Pretty.big_list "monotonicity rules:"
+ (map (ProofContext.pretty_thm (Context.proof_of generic)) monos)]
|> Pretty.chunks |> Pretty.writeln;
end);
@@ -114,14 +113,14 @@
fun the_inductive thy name =
(case get_inductive thy name of
- NONE => error ("Unknown (co)inductive set " ^ quote name)
+ NONE => error ("Unknown (co)inductive predicate " ^ quote name)
| SOME info => info);
val the_mk_cases = (#mk_cases o #2) oo the_inductive;
fun put_inductives names info = InductiveData.map (apfst (fn tab =>
fold (fn name => Symtab.update_new (name, info)) names tab
- handle Symtab.DUP dup => error ("Duplicate definition of (co)inductive set " ^ quote dup)));
+ handle Symtab.DUP dup => error ("Duplicate definition of (co)inductive predicate " ^ quote dup)));
@@ -132,10 +131,10 @@
fun mk_mono thm =
let
- fun eq2mono thm' = [standard (thm' RS (thm' RS eq_to_mono))] @
+ fun eq2mono thm' = [(*standard*) (thm' RS (thm' RS eq_to_mono))] @
(case concl_of thm of
(_ $ (_ $ (Const ("Not", _) $ _) $ _)) => []
- | _ => [standard (thm' RS (thm' RS eq_to_mono2))]);
+ | _ => [(*standard*) (thm' RS (thm' RS eq_to_mono2))]);
val concl = concl_of thm
in
if can Logic.dest_equals concl then
@@ -149,10 +148,10 @@
(* attributes *)
val mono_add = Thm.declaration_attribute (fn th =>
- Context.mapping (map_monos (fold Drule.add_rule (mk_mono th))) I);
+ map_monos (fold Drule.add_rule (mk_mono th)));
val mono_del = Thm.declaration_attribute (fn th =>
- Context.mapping (map_monos (fold Drule.del_rule (mk_mono th))) I);
+ map_monos (fold Drule.del_rule (mk_mono th)));
@@ -166,104 +165,46 @@
fun coind_prefix true = "co"
| coind_prefix false = "";
+fun log b m n = if m >= n then 0 else 1 + log b (b * m) n;
-(*the following code ensures that each recursive set always has the
- same type in all introduction rules*)
-fun unify_consts thy cs intr_ts =
- (let
- val add_term_consts_2 = fold_aterms (fn Const c => insert (op =) c | _ => I);
- fun varify (t, (i, ts)) =
- let val t' = map_types (Logic.incr_tvar (i + 1)) (#1 (Type.varify (t, [])))
- in (maxidx_of_term t', t'::ts) end;
- val (i, cs') = foldr varify (~1, []) cs;
- val (i', intr_ts') = foldr varify (i, []) intr_ts;
- val rec_consts = fold add_term_consts_2 cs' [];
- val intr_consts = fold add_term_consts_2 intr_ts' [];
- fun unify (cname, cT) =
- let val consts = map snd (List.filter (fn c => fst c = cname) intr_consts)
- in fold (Sign.typ_unify thy) ((replicate (length consts) cT) ~~ consts) end;
- val (env, _) = fold unify rec_consts (Vartab.empty, i');
- val subst = Type.freeze o map_types (Envir.norm_type env)
+fun make_bool_args f g [] i = []
+ | make_bool_args f g (x :: xs) i =
+ (if i mod 2 = 0 then f x else g x) :: make_bool_args f g xs (i div 2);
+
+fun make_bool_args' xs =
+ make_bool_args (K HOLogic.false_const) (K HOLogic.true_const) xs;
+
+fun find_arg T x [] = sys_error "find_arg"
+ | find_arg T x ((p as (_, (SOME _, _))) :: ps) =
+ apsnd (cons p) (find_arg T x ps)
+ | find_arg T x ((p as (U, (NONE, y))) :: ps) =
+ if T = U then (y, (U, (SOME x, y)) :: ps)
+ else apsnd (cons p) (find_arg T x ps);
- in (map subst cs', map subst intr_ts')
- end) handle Type.TUNIFY =>
- (warning "Occurrences of recursive constant have non-unifiable types"; (cs, intr_ts));
+fun make_args Ts xs =
+ map (fn (T, (NONE, ())) => Const ("arbitrary", T) | (_, (SOME t, ())) => t)
+ (fold (fn (t, T) => snd o find_arg T t) xs (map (rpair (NONE, ())) Ts));
+fun make_args' Ts xs Us =
+ fst (fold_map (fn T => find_arg T ()) Us (Ts ~~ map (pair NONE) xs));
-(*make injections used in mutually recursive definitions*)
-fun mk_inj cs sumT c x =
+fun dest_predicate cs params t =
let
- fun mk_inj' T n i =
- if n = 1 then x else
- let val n2 = n div 2;
- val Type (_, [T1, T2]) = T
- in
- if i <= n2 then
- Const ("Sum_Type.Inl", T1 --> T) $ (mk_inj' T1 n2 i)
- else
- Const ("Sum_Type.Inr", T2 --> T) $ (mk_inj' T2 (n - n2) (i - n2))
- end
- in mk_inj' sumT (length cs) (1 + find_index_eq c cs)
+ val k = length params;
+ val (c, ts) = strip_comb t;
+ val (xs, ys) = chop k ts;
+ val i = find_index_eq c cs;
+ in
+ if xs = params andalso i >= 0 then
+ SOME (c, i, ys, chop (length ys)
+ (List.drop (binder_types (fastype_of c), k)))
+ else NONE
end;
-(*make "vimage" terms for selecting out components of mutually rec.def*)
-fun mk_vimage cs sumT t c = if length cs < 2 then t else
- let
- val cT = HOLogic.dest_setT (fastype_of c);
- val vimageT = [cT --> sumT, HOLogic.mk_setT sumT] ---> HOLogic.mk_setT cT
- in
- Const (vimage_name, vimageT) $
- Abs ("y", cT, mk_inj cs sumT c (Bound 0)) $ t
- end;
-
-(** proper splitting **)
-
-fun prod_factors p (Const ("Pair", _) $ t $ u) =
- p :: prod_factors (1::p) t @ prod_factors (2::p) u
- | prod_factors p _ = [];
-
-fun mg_prod_factors ts (t $ u) fs = if t mem ts then
- let val f = prod_factors [] u
- in AList.update (op =) (t, f inter (AList.lookup (op =) fs t) |> the_default f) fs end
- else mg_prod_factors ts u (mg_prod_factors ts t fs)
- | mg_prod_factors ts (Abs (_, _, t)) fs = mg_prod_factors ts t fs
- | mg_prod_factors ts _ fs = fs;
-
-fun prodT_factors p ps (T as Type ("*", [T1, T2])) =
- if p mem ps then prodT_factors (1::p) ps T1 @ prodT_factors (2::p) ps T2
- else [T]
- | prodT_factors _ _ T = [T];
+fun mk_names a 0 = []
+ | mk_names a 1 = [a]
+ | mk_names a n = map (fn i => a ^ string_of_int i) (1 upto n);
-fun ap_split p ps (Type ("*", [T1, T2])) T3 u =
- if p mem ps then HOLogic.split_const (T1, T2, T3) $
- Abs ("v", T1, ap_split (2::p) ps T2 T3 (ap_split (1::p) ps T1
- (prodT_factors (2::p) ps T2 ---> T3) (incr_boundvars 1 u) $ Bound 0))
- else u
- | ap_split _ _ _ _ u = u;
-
-fun mk_tuple p ps (Type ("*", [T1, T2])) (tms as t::_) =
- if p mem ps then HOLogic.mk_prod (mk_tuple (1::p) ps T1 tms,
- mk_tuple (2::p) ps T2 (Library.drop (length (prodT_factors (1::p) ps T1), tms)))
- else t
- | mk_tuple _ _ _ (t::_) = t;
-
-fun split_rule_var' ((t as Var (v, Type ("fun", [T1, T2])), ps), rl) =
- let val T' = prodT_factors [] ps T1 ---> T2
- val newt = ap_split [] ps T1 T2 (Var (v, T'))
- val cterm = Thm.cterm_of (Thm.theory_of_thm rl)
- in
- instantiate ([], [(cterm t, cterm newt)]) rl
- end
- | split_rule_var' (_, rl) = rl;
-
-val remove_split = rewrite_rule [split_conv RS eq_reflection];
-
-fun split_rule_vars vs rl = standard (remove_split (foldr split_rule_var'
- rl (mg_prod_factors vs (Thm.prop_of rl) [])));
-
-fun split_rule vs rl = standard (remove_split (foldr split_rule_var'
- rl (List.mapPartial (fn (t as Var ((a, _), _)) =>
- Option.map (pair t) (AList.lookup (op =) vs a)) (term_vars (Thm.prop_of rl)))));
(** process rules **)
@@ -278,261 +219,200 @@
error (cat_lines ["Ill-formed premise", Sign.string_of_term thy p,
"in introduction rule " ^ quote name, Sign.string_of_term thy t, msg]);
-val bad_concl = "Conclusion of introduction rule must have form \"t : S_i\"";
+val bad_concl = "Conclusion of introduction rule must be an inductive predicate";
-val all_not_allowed =
- "Introduction rule must not have a leading \"!!\" quantifier";
+val bad_ind_occ = "Inductive predicate occurs in argument of inductive predicate";
+
+val bad_app = "Inductive predicate must be applied to parameter(s) ";
fun atomize_term thy = MetaSimplifier.rewrite_term thy inductive_atomize [];
in
-fun check_rule thy cs ((name, rule), att) =
+fun check_rule thy cs params ((name, att), rule) =
let
- val concl = Logic.strip_imp_concl rule;
- val prems = Logic.strip_imp_prems rule;
+ val params' = Term.variant_frees rule (Logic.strip_params rule);
+ val frees = rev (map Free params');
+ val concl = subst_bounds (frees, Logic.strip_assums_concl rule);
+ val prems = map (curry subst_bounds frees) (Logic.strip_assums_hyp rule);
val aprems = map (atomize_term thy) prems;
- val arule = Logic.list_implies (aprems, concl);
+ val arule = list_all_free (params', Logic.list_implies (aprems, concl));
+
+ fun check_ind err t = case dest_predicate cs params t of
+ NONE => err (bad_app ^
+ commas (map (Sign.string_of_term thy) params))
+ | SOME (_, _, ys, _) =>
+ if exists (fn c => exists (fn t => Logic.occs (c, t)) ys) cs
+ then err bad_ind_occ else ();
+
+ fun check_prem' prem t =
+ if head_of t mem cs then
+ check_ind (err_in_prem thy name rule prem) t
+ else (case t of
+ Abs (_, _, t) => check_prem' prem t
+ | t $ u => (check_prem' prem t; check_prem' prem u)
+ | _ => ());
fun check_prem (prem, aprem) =
- if can HOLogic.dest_Trueprop aprem then ()
+ if can HOLogic.dest_Trueprop aprem then check_prem' prem prem
else err_in_prem thy name rule prem "Non-atomic premise";
in
(case concl of
- Const ("Trueprop", _) $ (Const ("op :", _) $ t $ u) =>
- if u mem cs then
- if exists (Logic.occs o rpair t) cs then
- err_in_rule thy name rule "Recursion term on left of member symbol"
- else List.app check_prem (prems ~~ aprems)
- else err_in_rule thy name rule bad_concl
- | Const ("all", _) $ _ => err_in_rule thy name rule all_not_allowed
- | _ => err_in_rule thy name rule bad_concl);
- ((name, arule), att)
+ Const ("Trueprop", _) $ t =>
+ if head_of t mem cs then
+ (check_ind (err_in_rule thy name rule) t;
+ List.app check_prem (prems ~~ aprems))
+ else err_in_rule thy name rule bad_concl
+ | _ => err_in_rule thy name rule bad_concl);
+ ((name, att), arule)
end;
val rulify = (* FIXME norm_hhf *)
hol_simplify inductive_conj
#> hol_simplify inductive_rulify
#> hol_simplify inductive_rulify_fallback
- #> standard;
+ (*#> standard*);
end;
-(** properties of (co)inductive sets **)
-
-(* elimination rules *)
-
-fun mk_elims cs cTs params intr_ts intr_names =
- let
- val used = foldr add_term_names [] intr_ts;
- val [aname, pname] = Name.variant_list used ["a", "P"];
- val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
-
- fun dest_intr r =
- let val Const ("op :", _) $ t $ u =
- HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
- in (u, t, Logic.strip_imp_prems r) end;
-
- val intrs = map dest_intr intr_ts ~~ intr_names;
-
- fun mk_elim (c, T) =
- let
- val a = Free (aname, T);
-
- fun mk_elim_prem (_, t, ts) =
- list_all_free (map dest_Free ((foldr add_term_frees [] (t::ts)) \\ params),
- Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_eq (a, t)) :: ts, P));
- val c_intrs = (List.filter (equal c o #1 o #1) intrs);
- in
- (Logic.list_implies (HOLogic.mk_Trueprop (HOLogic.mk_mem (a, c)) ::
- map mk_elim_prem (map #1 c_intrs), P), map #2 c_intrs)
- end
- in
- map mk_elim (cs ~~ cTs)
- end;
-
-
-(* premises and conclusions of induction rules *)
-
-fun mk_indrule cs cTs params intr_ts =
- let
- val used = foldr add_term_names [] intr_ts;
-
- (* predicates for induction rule *)
-
- val preds = map Free (Name.variant_list used (if length cs < 2 then ["P"] else
- map (fn i => "P" ^ string_of_int i) (1 upto length cs)) ~~
- map (fn T => T --> HOLogic.boolT) cTs);
-
- (* transform an introduction rule into a premise for induction rule *)
-
- fun mk_ind_prem r =
- let
- val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
-
- val pred_of = AList.lookup (op aconv) (cs ~~ preds);
-
- fun subst (s as ((m as Const ("op :", T)) $ t $ u)) =
- (case pred_of u of
- NONE => (m $ fst (subst t) $ fst (subst u), NONE)
- | SOME P => (HOLogic.mk_binop inductive_conj_name (s, P $ t), SOME (s, P $ t)))
- | subst s =
- (case pred_of s of
- SOME P => (HOLogic.mk_binop "op Int"
- (s, HOLogic.Collect_const (HOLogic.dest_setT
- (fastype_of s)) $ P), NONE)
- | NONE => (case s of
- (t $ u) => (fst (subst t) $ fst (subst u), NONE)
- | (Abs (a, T, t)) => (Abs (a, T, fst (subst t)), NONE)
- | _ => (s, NONE)));
-
- fun mk_prem (s, prems) = (case subst s of
- (_, SOME (t, u)) => t :: u :: prems
- | (t, _) => t :: prems);
-
- val Const ("op :", _) $ t $ u =
- HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
-
- in list_all_free (frees,
- Logic.list_implies (map HOLogic.mk_Trueprop (foldr mk_prem
- [] (map HOLogic.dest_Trueprop (Logic.strip_imp_prems r))),
- HOLogic.mk_Trueprop (valOf (pred_of u) $ t)))
- end;
-
- val ind_prems = map mk_ind_prem intr_ts;
-
- val factors = Library.fold (mg_prod_factors preds) ind_prems [];
-
- (* make conclusions for induction rules *)
-
- fun mk_ind_concl ((c, P), (ts, x)) =
- let val T = HOLogic.dest_setT (fastype_of c);
- val ps = AList.lookup (op =) factors P |> the_default [];
- val Ts = prodT_factors [] ps T;
- val (frees, x') = foldr (fn (T', (fs, s)) =>
- ((Free (s, T'))::fs, Symbol.bump_string s)) ([], x) Ts;
- val tuple = mk_tuple [] ps T frees;
- in ((HOLogic.mk_binop "op -->"
- (HOLogic.mk_mem (tuple, c), P $ tuple))::ts, x')
- end;
-
- val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
- (fst (foldr mk_ind_concl ([], "xa") (cs ~~ preds))))
-
- in (preds, ind_prems, mutual_ind_concl,
- map (apfst (fst o dest_Free)) factors)
- end;
-
+(** properties of (co)inductive predicates **)
(* prepare cases and induct rules *)
-fun add_cases_induct no_elim no_induct coind names elims induct =
+fun add_cases_induct no_elim no_induct coind rec_name names elims induct =
let
- fun cases_spec name elim thy =
- thy
- |> Theory.parent_path
- |> Theory.add_path (Sign.base_name name)
- |> PureThy.add_thms [(("cases", elim), [InductAttrib.cases_set name])] |> snd
- |> Theory.restore_naming thy;
+ fun cases_spec name elim =
+ LocalTheory.note ((NameSpace.append (Sign.base_name name) "cases",
+ [Attrib.internal (InductAttrib.cases_set name)]), [elim]) #> snd;
val cases_specs = if no_elim then [] else map2 cases_spec names elims;
val induct_att = if coind then InductAttrib.coinduct_set else InductAttrib.induct_set;
- fun induct_specs thy =
- if no_induct then thy
+ fun induct_specs ctxt =
+ if no_induct then ctxt
else
let
- val ctxt = ProofContext.init thy;
val rules = names ~~ ProjectRule.projects ctxt (1 upto length names) induct;
val inducts = map (RuleCases.save induct o standard o #2) rules;
in
- thy
- |> PureThy.add_thms (rules |> map (fn (name, th) =>
- (("", th), [RuleCases.consumes 1, induct_att name]))) |> snd
- |> PureThy.add_thmss
- [((coind_prefix coind ^ "inducts", inducts), [RuleCases.consumes 1])] |> snd
+ ctxt |>
+ LocalTheory.notes (rules |> map (fn (name, th) =>
+ (("", [Attrib.internal (RuleCases.consumes 1),
+ Attrib.internal (induct_att name)]), [([th], [])]))) |> snd |>
+ LocalTheory.note ((NameSpace.append rec_name
+ (coind_prefix coind ^ "inducts"),
+ [Attrib.internal (RuleCases.consumes 1)]), inducts) |> snd
end;
in Library.apply cases_specs #> induct_specs end;
-(** proofs for (co)inductive sets **)
+(** proofs for (co)inductive predicates **)
(* prove monotonicity -- NOT subject to quick_and_dirty! *)
-fun prove_mono setT fp_fun monos thy =
+fun prove_mono predT fp_fun monos ctxt =
(message " Proving monotonicity ...";
- Goal.prove_global thy [] [] (*NO quick_and_dirty here!*)
+ Goal.prove ctxt [] [] (*NO quick_and_dirty here!*)
(HOLogic.mk_Trueprop
- (Const (mono_name, (setT --> setT) --> HOLogic.boolT) $ fp_fun))
+ (Const (mono_name, (predT --> predT) --> HOLogic.boolT) $ fp_fun))
(fn _ => EVERY [rtac monoI 1,
- REPEAT (ares_tac (List.concat (map mk_mono monos) @ get_monos thy) 1)]));
+ REPEAT (resolve_tac [le_funI, le_boolI'] 1),
+ REPEAT (FIRST
+ [atac 1,
+ resolve_tac (List.concat (map mk_mono monos) @
+ get_monos (Context.Proof ctxt)) 1,
+ etac le_funE 1, dtac le_boolD 1])]));
(* prove introduction rules *)
-fun prove_intrs coind mono fp_def intr_ts rec_sets_defs ctxt =
+fun prove_intrs coind mono fp_def k intr_ts rec_preds_defs ctxt =
let
val _ = clean_message " Proving the introduction rules ...";
- val unfold = standard' (mono RS (fp_def RS
- (if coind then def_gfp_unfold else def_lfp_unfold)));
+ val unfold = funpow k (fn th => th RS fun_cong)
+ (mono RS (fp_def RS
+ (if coind then def_gfp_unfold else def_lfp_unfold)));
fun select_disj 1 1 = []
| select_disj _ 1 = [rtac disjI1]
| select_disj n i = (rtac disjI2)::(select_disj (n - 1) (i - 1));
- val intrs = (1 upto (length intr_ts) ~~ intr_ts) |> map (fn (i, intr) =>
+ val rules = [refl, TrueI, notFalseI, exI, conjI];
+
+ val intrs = map_index (fn (i, intr) =>
rulify (SkipProof.prove ctxt [] [] intr (fn _ => EVERY
- [rewrite_goals_tac rec_sets_defs,
- stac unfold 1,
- REPEAT (resolve_tac [vimageI2, CollectI] 1),
- (*Now 1-2 subgoals: the disjunction, perhaps equality.*)
- EVERY1 (select_disj (length intr_ts) i),
+ [rewrite_goals_tac rec_preds_defs,
+ rtac (unfold RS iffD2) 1,
+ EVERY1 (select_disj (length intr_ts) (i + 1)),
(*Not ares_tac, since refl must be tried before any equality assumptions;
backtracking may occur if the premises have extra variables!*)
- DEPTH_SOLVE_1 (resolve_tac [refl, exI, conjI] 1 APPEND assume_tac 1),
- (*Now solve the equations like Inl 0 = Inl ?b2*)
- REPEAT (rtac refl 1)])))
+ DEPTH_SOLVE_1 (resolve_tac rules 1 APPEND assume_tac 1)]))) intr_ts
in (intrs, unfold) end;
(* prove elimination rules *)
-fun prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs ctxt =
+fun prove_elims cs params intr_ts intr_names unfold rec_preds_defs ctxt =
let
val _ = clean_message " Proving the elimination rules ...";
- val rules1 = [CollectE, disjE, make_elim vimageD, exE, FalseE];
- val rules2 = [conjE, Inl_neq_Inr, Inr_neq_Inl] @ map make_elim [Inl_inject, Inr_inject];
- in
- mk_elims cs cTs params intr_ts intr_names |> map (fn (t, cases) =>
- SkipProof.prove ctxt [] (Logic.strip_imp_prems t) (Logic.strip_imp_concl t)
- (fn {prems, ...} => EVERY
- [cut_facts_tac [hd prems] 1,
- rewrite_goals_tac rec_sets_defs,
- dtac (unfold RS subst) 1,
- REPEAT (FIRSTGOAL (eresolve_tac rules1)),
- REPEAT (FIRSTGOAL (eresolve_tac rules2)),
- EVERY (map (fn prem =>
- DEPTH_SOLVE_1 (ares_tac [rewrite_rule rec_sets_defs prem, conjI] 1)) (tl prems))])
- |> rulify
- |> RuleCases.name cases)
- end;
+ val ([pname], ctxt') = Variable.variant_fixes ["P"] ctxt;
+ val P = HOLogic.mk_Trueprop (Free (pname, HOLogic.boolT));
+
+ fun dest_intr r =
+ (the (dest_predicate cs params (HOLogic.dest_Trueprop (Logic.strip_assums_concl r))),
+ Logic.strip_assums_hyp r, Logic.strip_params r);
+
+ val intrs = map dest_intr intr_ts ~~ intr_names;
+
+ val rules1 = [disjE, exE, FalseE];
+ val rules2 = [conjE, FalseE, notTrueE];
+
+ fun prove_elim c =
+ let
+ val Ts = List.drop (binder_types (fastype_of c), length params);
+ val (anames, ctxt'') = Variable.variant_fixes (mk_names "a" (length Ts)) ctxt';
+ val frees = map Free (anames ~~ Ts);
+
+ fun mk_elim_prem ((_, _, us, _), ts, params') =
+ list_all (params',
+ Logic.list_implies (map (HOLogic.mk_Trueprop o HOLogic.mk_eq)
+ (frees ~~ us) @ ts, P));
+ val c_intrs = (List.filter (equal c o #1 o #1 o #1) intrs);
+ val prems = HOLogic.mk_Trueprop (list_comb (c, params @ frees)) ::
+ map mk_elim_prem (map #1 c_intrs)
+ in
+ SkipProof.prove ctxt'' [] prems P
+ (fn {prems, ...} => EVERY
+ [cut_facts_tac [hd prems] 1,
+ rewrite_goals_tac rec_preds_defs,
+ dtac (unfold RS iffD1) 1,
+ REPEAT (FIRSTGOAL (eresolve_tac rules1)),
+ REPEAT (FIRSTGOAL (eresolve_tac rules2)),
+ EVERY (map (fn prem =>
+ DEPTH_SOLVE_1 (ares_tac [rewrite_rule rec_preds_defs prem, conjI] 1)) (tl prems))])
+ |> rulify
+ |> singleton (ProofContext.export ctxt'' ctxt)
+ |> RuleCases.name (map #2 c_intrs)
+ end
+
+ in map prove_elim cs end;
(* derivation of simplified elimination rules *)
local
-(*cprop should have the form t:Si where Si is an inductive set*)
-val mk_cases_err = "mk_cases: proposition not of form \"t : S_i\"";
+(*cprop should have the form "Si t" where Si is an inductive predicate*)
+val mk_cases_err = "mk_cases: proposition not an inductive predicate";
(*delete needless equality assumptions*)
val refl_thin = prove_goal HOL.thy "!!P. a = a ==> P ==> P" (fn _ => [assume_tac 1]);
-val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE, Pair_inject];
+val elim_rls = [asm_rl, FalseE, refl_thin, conjE, exE];
val elim_tac = REPEAT o Tactic.eresolve_tac elim_rls;
fun simp_case_tac solved ss i =
@@ -556,11 +436,11 @@
fun mk_cases elims s =
mk_cases_i elims (simpset()) (Thm.read_cterm (Thm.theory_of_thm (hd elims)) (s, propT));
-fun smart_mk_cases thy ss cprop =
+fun smart_mk_cases ctxt ss cprop =
let
- val c = #1 (Term.dest_Const (Term.head_of (#2 (HOLogic.dest_mem (HOLogic.dest_Trueprop
- (Logic.strip_imp_concl (Thm.term_of cprop))))))) handle TERM _ => error mk_cases_err;
- val (_, {elims, ...}) = the_inductive thy c;
+ val c = #1 (Term.dest_Const (Term.head_of (HOLogic.dest_Trueprop
+ (Logic.strip_imp_concl (Thm.term_of cprop))))) handle TERM _ => error mk_cases_err;
+ val (_, {elims, ...}) = the_inductive ctxt c;
in mk_cases_i elims ss cprop end;
end;
@@ -571,7 +451,7 @@
fun gen_inductive_cases prep_att prep_prop args thy =
let
val cert_prop = Thm.cterm_of thy o prep_prop (ProofContext.init thy);
- val mk_cases = smart_mk_cases thy (Simplifier.simpset_of thy) o cert_prop;
+ val mk_cases = smart_mk_cases (Context.Theory thy) (Simplifier.simpset_of thy) o cert_prop;
val facts = args |> map (fn ((a, atts), props) =>
((a, map (prep_att thy) atts), map (Thm.no_attributes o single o mk_cases) props));
@@ -588,33 +468,70 @@
val thy = ProofContext.theory_of ctxt;
val ss = local_simpset_of ctxt;
val cprops = map (Thm.cterm_of thy o ProofContext.read_prop ctxt) raw_props;
- in Method.erule 0 (map (smart_mk_cases thy ss) cprops) end;
+ in Method.erule 0 (map (smart_mk_cases (Context.Theory thy) ss) cprops) end;
val mk_cases_args = Method.syntax (Scan.lift (Scan.repeat1 Args.name));
(* prove induction rule *)
-fun prove_indrule cs cTs sumT rec_const params intr_ts mono
- fp_def rec_sets_defs ctxt =
+fun prove_indrule cs argTs bs xs rec_const params intr_ts mono
+ fp_def rec_preds_defs ctxt =
let
val _ = clean_message " Proving the induction rule ...";
val thy = ProofContext.theory_of ctxt;
- val sum_case_rewrites =
- (if Context.theory_name thy = "Datatype" then
- PureThy.get_thms thy (Name "sum.cases")
- else
- (case ThyInfo.lookup_theory "Datatype" of
- NONE => []
- | SOME thy' =>
- if Theory.subthy (thy', thy) then
- PureThy.get_thms thy' (Name "sum.cases")
- else []))
- |> map mk_meta_eq;
+ (* predicates for induction rule *)
+
+ val (pnames, ctxt') = Variable.variant_fixes (mk_names "P" (length cs)) ctxt;
+ val preds = map Free (pnames ~~
+ map (fn c => List.drop (binder_types (fastype_of c), length params) --->
+ HOLogic.boolT) cs);
+
+ (* transform an introduction rule into a premise for induction rule *)
+
+ fun mk_ind_prem r =
+ let
+ fun subst s = (case dest_predicate cs params s of
+ SOME (_, i, ys, (_, Ts)) =>
+ let
+ val k = length Ts;
+ val bs = map Bound (k - 1 downto 0);
+ val P = list_comb (List.nth (preds, i), ys @ bs);
+ val Q = list_abs (mk_names "x" k ~~ Ts,
+ HOLogic.mk_binop inductive_conj_name (list_comb (s, bs), P))
+ in (Q, case Ts of [] => SOME (s, P) | _ => NONE) end
+ | NONE => (case s of
+ (t $ u) => (fst (subst t) $ fst (subst u), NONE)
+ | (Abs (a, T, t)) => (Abs (a, T, fst (subst t)), NONE)
+ | _ => (s, NONE)));
- val (preds, ind_prems, mutual_ind_concl, factors) =
- mk_indrule cs cTs params intr_ts;
+ fun mk_prem (s, prems) = (case subst s of
+ (_, SOME (t, u)) => t :: u :: prems
+ | (t, _) => t :: prems);
+
+ val SOME (_, i, ys, _) = dest_predicate cs params
+ (HOLogic.dest_Trueprop (Logic.strip_assums_concl r))
+
+ in list_all_free (Logic.strip_params r,
+ Logic.list_implies (map HOLogic.mk_Trueprop (foldr mk_prem
+ [] (map HOLogic.dest_Trueprop (Logic.strip_assums_hyp r))),
+ HOLogic.mk_Trueprop (list_comb (List.nth (preds, i), ys))))
+ end;
+
+ val ind_prems = map mk_ind_prem intr_ts;
+
+ (* make conclusions for induction rules *)
+
+ val Tss = map (binder_types o fastype_of) preds;
+ val (xnames, ctxt'') =
+ Variable.variant_fixes (mk_names "x" (length (flat Tss))) ctxt';
+ val mutual_ind_concl = HOLogic.mk_Trueprop (foldr1 HOLogic.mk_conj
+ (map (fn (((xnames, Ts), c), P) =>
+ let val frees = map Free (xnames ~~ Ts)
+ in HOLogic.mk_imp
+ (list_comb (c, params @ frees), list_comb (P, frees))
+ end) (unflat Tss xnames ~~ Tss ~~ cs ~~ preds)));
val dummy = if !trace then
(writeln "ind_prems = ";
@@ -623,31 +540,13 @@
(* make predicate for instantiation of abstract induction rule *)
- fun mk_ind_pred _ [P] = P
- | mk_ind_pred T Ps =
- let val n = (length Ps) div 2;
- val Type (_, [T1, T2]) = T
- in Const ("Datatype.sum.sum_case",
- [T1 --> HOLogic.boolT, T2 --> HOLogic.boolT, T] ---> HOLogic.boolT) $
- mk_ind_pred T1 (Library.take (n, Ps)) $ mk_ind_pred T2 (Library.drop (n, Ps))
- end;
-
- val ind_pred = mk_ind_pred sumT preds;
+ val ind_pred = fold_rev lambda (bs @ xs) (foldr1 HOLogic.mk_conj
+ (map_index (fn (i, P) => foldr HOLogic.mk_imp
+ (list_comb (P, make_args' argTs xs (binder_types (fastype_of P))))
+ (make_bool_args HOLogic.mk_not I bs i)) preds));
val ind_concl = HOLogic.mk_Trueprop
- (HOLogic.all_const sumT $ Abs ("x", sumT, HOLogic.mk_binop "op -->"
- (HOLogic.mk_mem (Bound 0, rec_const), ind_pred $ Bound 0)));
-
- (* simplification rules for vimage and Collect *)
-
- val vimage_simps = if length cs < 2 then [] else
- map (fn c => standard (SkipProof.prove ctxt [] []
- (HOLogic.mk_Trueprop (HOLogic.mk_eq
- (mk_vimage cs sumT (HOLogic.Collect_const sumT $ ind_pred) c,
- HOLogic.Collect_const (HOLogic.dest_setT (fastype_of c)) $
- List.nth (preds, find_index_eq c cs))))
- (fn _ => EVERY
- [rtac vimage_Collect 1, rewrite_goals_tac sum_case_rewrites, rtac refl 1]))) cs;
+ (HOLogic.mk_binrel "Orderings.less_eq" (rec_const, ind_pred));
val raw_fp_induct = (mono RS (fp_def RS def_lfp_induct));
@@ -655,131 +554,147 @@
(writeln "raw_fp_induct = "; print_thm raw_fp_induct)
else ();
- val induct = standard (SkipProof.prove ctxt [] ind_prems ind_concl
+ val induct = SkipProof.prove ctxt'' [] ind_prems ind_concl
(fn {prems, ...} => EVERY
[rewrite_goals_tac [inductive_conj_def],
- rtac (impI RS allI) 1,
- DETERM (etac raw_fp_induct 1),
- rewrite_goals_tac (map mk_meta_eq (vimage_Int::Int_Collect::vimage_simps)),
- fold_goals_tac rec_sets_defs,
- (*This CollectE and disjE separates out the introduction rules*)
- REPEAT (FIRSTGOAL (eresolve_tac [CollectE, disjE, exE, FalseE])),
+ DETERM (rtac raw_fp_induct 1),
+ REPEAT (resolve_tac [le_funI, le_boolI] 1),
+ rewrite_goals_tac (map mk_meta_eq [meet_fun_eq, meet_bool_eq] @ simp_thms'),
+ (*This disjE separates out the introduction rules*)
+ REPEAT (FIRSTGOAL (eresolve_tac [disjE, exE, FalseE])),
(*Now break down the individual cases. No disjE here in case
some premise involves disjunction.*)
REPEAT (FIRSTGOAL (etac conjE ORELSE' bound_hyp_subst_tac)),
- rewrite_goals_tac sum_case_rewrites,
- EVERY (map (fn prem =>
- DEPTH_SOLVE_1 (ares_tac [rewrite_rule [inductive_conj_def] prem, conjI, refl] 1)) prems)]));
+ REPEAT (FIRSTGOAL
+ (resolve_tac [conjI, impI] ORELSE' (etac notE THEN' atac))),
+ EVERY (map (fn prem => DEPTH_SOLVE_1 (ares_tac [rewrite_rule
+ (inductive_conj_def :: rec_preds_defs) prem, conjI, refl] 1)) prems)]);
- val lemma = standard (SkipProof.prove ctxt [] []
+ val lemma = SkipProof.prove ctxt'' [] []
(Logic.mk_implies (ind_concl, mutual_ind_concl)) (fn _ => EVERY
- [rewrite_goals_tac rec_sets_defs,
+ [rewrite_goals_tac rec_preds_defs,
REPEAT (EVERY
[REPEAT (resolve_tac [conjI, impI] 1),
- TRY (dtac vimageD 1), etac allE 1, dtac mp 1, atac 1,
- rewrite_goals_tac sum_case_rewrites,
- atac 1])]))
+ REPEAT (eresolve_tac [le_funE, le_boolE] 1),
+ atac 1,
+ rewrite_goals_tac simp_thms',
+ atac 1])])
- in standard (split_rule factors (induct RS lemma)) end;
+ in singleton (ProofContext.export ctxt'' ctxt) (induct RS lemma) end;
-(** specification of (co)inductive sets **)
-
-fun cond_declare_consts declare_consts cs paramTs cnames =
- if declare_consts then
- Theory.add_consts_i (map (fn (c, n) => (Sign.base_name n, paramTs ---> fastype_of c, NoSyn)) (cs ~~ cnames))
- else I;
+(** specification of (co)inductive predicates **)
-fun mk_ind_def declare_consts alt_name coind cs intr_ts monos thy
- params paramTs cTs cnames =
+fun mk_ind_def alt_name coind cs intr_ts monos
+ params cnames_syn ctxt =
let
- val sumT = fold_bal (fn (T, U) => Type ("+", [T, U])) cTs;
- val setT = HOLogic.mk_setT sumT;
-
val fp_name = if coind then gfp_name else lfp_name;
- val used = foldr add_term_names [] intr_ts;
- val [sname, xname] = Name.variant_list used ["S", "x"];
+ val argTs = fold (fn c => fn Ts => Ts @
+ (List.drop (binder_types (fastype_of c), length params) \\ Ts)) cs [];
+ val k = log 2 1 (length cs);
+ val predT = replicate k HOLogic.boolT ---> argTs ---> HOLogic.boolT;
+ val p :: xs = map Free (Variable.variant_frees ctxt intr_ts
+ (("p", predT) :: (mk_names "x" (length argTs) ~~ argTs)));
+ val bs = map Free (Variable.variant_frees ctxt (p :: xs @ intr_ts)
+ (map (rpair HOLogic.boolT) (mk_names "b" k)));
+
+ fun subst t = (case dest_predicate cs params t of
+ SOME (_, i, ts, (Ts, Us)) =>
+ let val zs = map Bound (length Us - 1 downto 0)
+ in
+ list_abs (map (pair "z") Us, list_comb (p,
+ make_bool_args' bs i @ make_args argTs ((ts ~~ Ts) @ (zs ~~ Us))))
+ end
+ | NONE => (case t of
+ t1 $ t2 => subst t1 $ subst t2
+ | Abs (x, T, u) => Abs (x, T, subst u)
+ | _ => t));
(* transform an introduction rule into a conjunction *)
- (* [| t : ... S_i ... ; ... |] ==> u : S_j *)
+ (* [| p_i t; ... |] ==> p_j u *)
(* is transformed into *)
- (* x = Inj_j u & t : ... Inj_i -`` S ... & ... *)
+ (* b_j & x_j = u & p b_j t & ... *)
fun transform_rule r =
let
- val frees = map dest_Free ((add_term_frees (r, [])) \\ params);
- val subst = subst_free
- (cs ~~ (map (mk_vimage cs sumT (Free (sname, setT))) cs));
- val Const ("op :", _) $ t $ u =
- HOLogic.dest_Trueprop (Logic.strip_imp_concl r)
+ val SOME (_, i, ts, (Ts, _)) = dest_predicate cs params
+ (HOLogic.dest_Trueprop (Logic.strip_assums_concl r))
- in foldr (fn ((x, T), P) => HOLogic.mk_exists (x, T, P))
+ in foldr (fn ((x, T), P) => HOLogic.exists_const T $ (Abs (x, T, P)))
(foldr1 HOLogic.mk_conj
- (((HOLogic.eq_const sumT) $ Free (xname, sumT) $ (mk_inj cs sumT u t))::
- (map (subst o HOLogic.dest_Trueprop)
- (Logic.strip_imp_prems r)))) frees
+ (make_bool_args HOLogic.mk_not I bs i @
+ map HOLogic.mk_eq (make_args' argTs xs Ts ~~ ts) @
+ map (subst o HOLogic.dest_Trueprop)
+ (Logic.strip_assums_hyp r))) (Logic.strip_params r)
end
(* make a disjunction of all introduction rules *)
- val fp_fun = absfree (sname, setT, (HOLogic.Collect_const sumT) $
- absfree (xname, sumT, if null intr_ts then HOLogic.false_const
- else foldr1 HOLogic.mk_disj (map transform_rule intr_ts)));
+ val fp_fun = fold_rev lambda (p :: bs @ xs)
+ (if null intr_ts then HOLogic.false_const
+ else foldr1 HOLogic.mk_disj (map transform_rule intr_ts));
- (* add definiton of recursive sets to theory *)
+ (* add definiton of recursive predicates to theory *)
val rec_name = if alt_name = "" then
- space_implode "_" (map Sign.base_name cnames) else alt_name;
- val full_rec_name = if length cs < 2 then hd cnames
- else Sign.full_name thy rec_name;
-
- val rec_const = list_comb
- (Const (full_rec_name, paramTs ---> setT), params);
-
- val fp_def_term = Logic.mk_equals (rec_const,
- Const (fp_name, (setT --> setT) --> setT) $ fp_fun);
-
- val def_terms = fp_def_term :: (if length cs < 2 then [] else
- map (fn c => Logic.mk_equals (c, mk_vimage cs sumT rec_const c)) cs);
+ space_implode "_" (map fst cnames_syn) else alt_name;
- val ([fp_def :: rec_sets_defs], thy') =
- thy
- |> cond_declare_consts declare_consts cs paramTs cnames
- |> (if length cs < 2 then I
- else Theory.add_consts_i [(rec_name, paramTs ---> setT, NoSyn)])
- |> Theory.add_path rec_name
- |> PureThy.add_defss_i false [(("defs", def_terms), [])];
+ val ((rec_const, (_, fp_def)), ctxt') = ctxt |>
+ Variable.add_fixes (map (fst o dest_Free) params) |> snd |>
+ fold Variable.declare_term intr_ts |>
+ LocalTheory.def
+ ((rec_name, case cnames_syn of [(_, syn)] => syn | _ => NoSyn),
+ (("", []), fold_rev lambda params
+ (Const (fp_name, (predT --> predT) --> predT) $ fp_fun)));
+ val fp_def' = Simplifier.rewrite (HOL_basic_ss addsimps [fp_def])
+ (cterm_of (ProofContext.theory_of ctxt') (list_comb (rec_const, params)));
+ val specs = if length cs < 2 then [] else
+ map_index (fn (i, (name_mx, c)) =>
+ let
+ val Ts = List.drop (binder_types (fastype_of c), length params);
+ val xs = map Free (Variable.variant_frees ctxt intr_ts
+ (mk_names "x" (length Ts) ~~ Ts))
+ in
+ (name_mx, (("", []), fold_rev lambda (params @ xs)
+ (list_comb (rec_const, params @ make_bool_args' bs i @
+ make_args argTs (xs ~~ Ts)))))
+ end) (cnames_syn ~~ cs);
+ val (consts_defs, ctxt'') = fold_map LocalTheory.def specs ctxt';
+ val preds = (case cs of [_] => [rec_const] | _ => map #1 consts_defs);
- val mono = prove_mono setT fp_fun monos thy'
+ val mono = prove_mono predT fp_fun monos ctxt''
- in (thy', rec_name, mono, fp_def, rec_sets_defs, rec_const, sumT) end;
+ in (ctxt'', rec_name, mono, fp_def', map (#2 o #2) consts_defs,
+ list_comb (rec_const, params), preds, argTs, bs, xs)
+ end;
-fun add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs
- intros monos thy params paramTs cTs cnames induct_cases =
+fun add_ind_def verbose alt_name coind no_elim no_ind cs
+ intros monos params cnames_syn induct_cases ctxt =
let
val _ =
- if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive set(s) " ^
- commas_quote (map Sign.base_name cnames)) else ();
-
- val ((intr_names, intr_ts), intr_atts) = apfst split_list (split_list intros);
+ if verbose then message ("Proofs for " ^ coind_prefix coind ^ "inductive predicate(s) " ^
+ commas_quote (map fst cnames_syn)) else ();
- val (thy1, rec_name, mono, fp_def, rec_sets_defs, rec_const, sumT) =
- mk_ind_def declare_consts alt_name coind cs intr_ts monos thy
- params paramTs cTs cnames;
- val ctxt1 = ProofContext.init thy1;
+ val ((intr_names, intr_atts), intr_ts) = apfst split_list (split_list intros);
+
+ val (ctxt1, rec_name, mono, fp_def, rec_preds_defs, rec_const, preds,
+ argTs, bs, xs) = mk_ind_def alt_name coind cs intr_ts
+ monos params cnames_syn ctxt;
- val (intrs, unfold) = prove_intrs coind mono fp_def intr_ts rec_sets_defs ctxt1;
- val elims = if no_elim then [] else
- prove_elims cs cTs params intr_ts intr_names unfold rec_sets_defs ctxt1;
- val raw_induct = if no_ind then Drule.asm_rl else
- if coind then standard (rule_by_tactic
- (rewrite_tac [mk_meta_eq vimage_Un] THEN
- fold_tac rec_sets_defs) (mono RS (fp_def RS def_Collect_coinduct)))
- else
- prove_indrule cs cTs sumT rec_const params intr_ts mono fp_def
- rec_sets_defs ctxt1;
+ val (intrs, unfold) = prove_intrs coind mono fp_def (length bs + length xs)
+ intr_ts rec_preds_defs ctxt1;
+ val elims = ProofContext.export ctxt1 ctxt (if no_elim then [] else
+ prove_elims cs params intr_ts intr_names unfold rec_preds_defs ctxt1);
+ val raw_induct = singleton (ProofContext.export ctxt1 ctxt)
+ (if no_ind then Drule.asm_rl else
+ if coind then ObjectLogic.rulify (rule_by_tactic
+ (rewrite_tac [le_fun_def, le_bool_def] THEN
+ fold_tac rec_preds_defs) (mono RS (fp_def RS def_coinduct)))
+ else
+ prove_indrule cs argTs bs xs rec_const params intr_ts mono fp_def
+ rec_preds_defs ctxt1);
val induct =
if coind then
(raw_induct, [RuleCases.case_names [rec_name],
@@ -789,20 +704,23 @@
(raw_induct, [RuleCases.case_names induct_cases, RuleCases.consumes 0])
else (raw_induct RSN (2, rev_mp), [RuleCases.case_names induct_cases, RuleCases.consumes 1]);
- val (intrs', thy2) =
- thy1
- |> PureThy.add_thms ((intr_names ~~ intrs) ~~ intr_atts);
- val (([_, elims'], [induct']), thy3) =
- thy2
- |> PureThy.add_thmss
- [(("intros", intrs'), []),
- (("elims", elims), [RuleCases.consumes 1])]
- ||>> PureThy.add_thms
- [((coind_prefix coind ^ "induct", rulify (#1 induct)), #2 induct)];
- in (thy3,
- {defs = fp_def :: rec_sets_defs,
- mono = mono,
- unfold = unfold,
+ val (intrs', ctxt2) =
+ ctxt1 |>
+ LocalTheory.notes (map (NameSpace.append rec_name) intr_names ~~ intr_atts ~~
+ map (single o rpair [] o single) (ProofContext.export ctxt1 ctxt intrs)) |>>
+ map (hd o snd); (* FIXME? *)
+ val (((_, (_, elims')), (_, [induct'])), ctxt3) =
+ ctxt2 |>
+ LocalTheory.note ((NameSpace.append rec_name "intros", []), intrs') ||>>
+ LocalTheory.note ((NameSpace.append rec_name "elims",
+ [Attrib.internal (RuleCases.consumes 1)]), elims) ||>>
+ LocalTheory.note ((NameSpace.append rec_name (coind_prefix coind ^ "induct"),
+ map Attrib.internal (#2 induct)), [rulify (#1 induct)])
+ in (ctxt3, rec_name,
+ {preds = preds,
+ defs = fp_def :: rec_preds_defs,
+ mono = singleton (ProofContext.export ctxt1 ctxt) mono,
+ unfold = singleton (ProofContext.export ctxt1 ctxt) unfold,
intrs = intrs',
elims = elims',
mk_cases = mk_cases elims',
@@ -813,55 +731,52 @@
(* external interfaces *)
-fun try_term f msg thy t =
- (case Library.try f t of
- SOME x => x
- | NONE => error (msg ^ Sign.string_of_term thy t));
-
-fun add_inductive_i verbose declare_consts alt_name coind no_elim no_ind cs pre_intros monos thy =
+fun add_inductive_i verbose alt_name coind no_elim no_ind cnames_syn pnames pre_intros monos ctxt =
let
+ val thy = ProofContext.theory_of ctxt;
val _ = Theory.requires thy "Inductive" (coind_prefix coind ^ "inductive definitions");
- (*parameters should agree for all mutually recursive components*)
- val (_, params) = strip_comb (hd cs);
- val paramTs = map (try_term (snd o dest_Free) "Parameter in recursive\
- \ component is not a free variable: " thy) params;
+ val frees = fold (Term.add_frees o snd) pre_intros [];
+ fun type_of s = (case AList.lookup op = frees s of
+ NONE => error ("No such variable: " ^ s) | SOME T => T);
- val cTs = map (try_term (HOLogic.dest_setT o fastype_of)
- "Recursive component not of type set: " thy) cs;
+ val params = map
+ (fn (s, SOME T) => Free (s, T) | (s, NONE) => Free (s, type_of s)) pnames;
+ val cs = map
+ (fn (s, SOME T, _) => Free (s, T) | (s, NONE, _) => Free (s, type_of s)) cnames_syn;
+ val cnames_syn' = map (fn (s, _, mx) => (s, mx)) cnames_syn;
+ val cnames = map (Sign.full_name thy o #1) cnames_syn;
- val cnames = map (try_term (fst o dest_Const o head_of)
- "Recursive set not previously declared as constant: " thy) cs;
+ fun close_rule (x, r) = (x, list_all_free (rev (fold_aterms
+ (fn t as Free (v as (s, _)) =>
+ if Variable.is_fixed ctxt s orelse member op = cs t orelse
+ member op = params t then I else insert op = v
+ | _ => I) r []), r));
- val save_thy = thy
- |> Theory.copy |> cond_declare_consts declare_consts cs paramTs cnames;
- val intros = map (check_rule save_thy cs) pre_intros;
+ val intros = map (close_rule o check_rule thy cs params) pre_intros;
val induct_cases = map (#1 o #1) intros;
- val (thy1, result as {elims, induct, ...}) =
- add_ind_def verbose declare_consts alt_name coind no_elim no_ind cs intros monos
- thy params paramTs cTs cnames induct_cases;
- val thy2 = thy1
- |> put_inductives cnames ({names = cnames, coind = coind}, result)
- |> add_cases_induct no_elim no_ind coind cnames elims induct
- |> Theory.parent_path;
- in (thy2, result) end;
+ val (ctxt1, rec_name, result as {elims, induct, ...}) =
+ add_ind_def verbose alt_name coind no_elim no_ind cs intros monos
+ params cnames_syn' induct_cases ctxt;
+ val ctxt2 = ctxt1
+ |> LocalTheory.declaration
+ (put_inductives cnames ({names = cnames, coind = coind}, result))
+ |> add_cases_induct no_elim no_ind coind rec_name cnames elims induct;
+ in (ctxt2, result) end;
-fun add_inductive verbose coind c_strings intro_srcs raw_monos thy =
+fun add_inductive verbose coind cnames_syn pnames_syn intro_srcs raw_monos ctxt =
let
- val cs = map (Sign.read_term thy) c_strings;
-
- val intr_names = map (fst o fst) intro_srcs;
- fun read_rule s = Thm.read_cterm thy (s, propT)
- handle ERROR msg => cat_error msg ("The error(s) above occurred for " ^ s);
- val intr_ts = map (Thm.term_of o read_rule o snd o fst) intro_srcs;
- val intr_atts = map (map (Attrib.attribute thy) o snd) intro_srcs;
- val (cs', intr_ts') = unify_consts thy cs intr_ts;
-
- val (monos, thy') = thy |> IsarThy.apply_theorems raw_monos;
+ val (_, ctxt') = Specification.read_specification (cnames_syn @ pnames_syn) [] ctxt;
+ val intrs = map (fn spec => apsnd hd (hd (snd (fst
+ (Specification.read_specification [] [apsnd single spec] ctxt'))))) intro_srcs;
+ val pnames = map (fn (s, _, _) =>
+ (s, SOME (ProofContext.infer_type ctxt' s))) pnames_syn;
+ val cnames_syn' = map (fn (s, _, mx) =>
+ (s, SOME (ProofContext.infer_type ctxt' s), mx)) cnames_syn;
+ val (monos, ctxt'') = LocalTheory.theory_result (IsarThy.apply_theorems raw_monos) ctxt;
in
- add_inductive_i verbose false "" coind false false cs'
- ((intr_names ~~ intr_ts') ~~ intr_atts) monos thy'
+ add_inductive_i verbose "" coind false false cnames_syn' pnames intrs monos ctxt''
end;
@@ -872,9 +787,9 @@
val setup =
InductiveData.init #>
- Method.add_methods [("ind_cases", mk_cases_meth oo mk_cases_args,
- "dynamic case analysis on sets")] #>
- Attrib.add_attributes [("mono", Attrib.add_del_args mono_add mono_del,
+ Method.add_methods [("ind_cases2", mk_cases_meth oo mk_cases_args,
+ "dynamic case analysis on predicates")] #>
+ Attrib.add_attributes [("mono2", Attrib.add_del_args mono_add mono_del,
"declaration of monotonicity rule")];
@@ -882,21 +797,23 @@
local structure P = OuterParse and K = OuterKeyword in
-fun mk_ind coind ((sets, intrs), monos) =
- #1 o add_inductive true coind sets (map P.triple_swap intrs) monos;
+fun mk_ind coind ((((loc, preds), params), intrs), monos) =
+ Toplevel.local_theory loc
+ (#1 o add_inductive true coind preds params intrs monos);
fun ind_decl coind =
- Scan.repeat1 P.term --
+ P.opt_locale_target --
+ P.fixes -- Scan.optional (P.$$$ "for" |-- P.fixes) [] --
(P.$$$ "intros" |--
P.!!! (Scan.repeat (P.opt_thm_name ":" -- P.prop))) --
Scan.optional (P.$$$ "monos" |-- P.!!! P.xthms1) []
- >> (Toplevel.theory o mk_ind coind);
+ >> mk_ind coind;
val inductiveP =
- OuterSyntax.command "inductive" "define inductive sets" K.thy_decl (ind_decl false);
+ OuterSyntax.command "inductive2" "define inductive predicates" K.thy_decl (ind_decl false);
val coinductiveP =
- OuterSyntax.command "coinductive" "define coinductive sets" K.thy_decl (ind_decl true);
+ OuterSyntax.command "coinductive2" "define coinductive predicates" K.thy_decl (ind_decl true);
val ind_cases =
@@ -904,7 +821,7 @@
>> (Toplevel.theory o inductive_cases);
val inductive_casesP =
- OuterSyntax.command "inductive_cases"
+ OuterSyntax.command "inductive_cases2"
"create simplified instances of elimination rules (improper)" K.thy_script ind_cases;
val _ = OuterSyntax.add_keywords ["intros", "monos"];