--- a/src/Provers/induct_method.ML Thu Nov 10 20:57:16 2005 +0100
+++ b/src/Provers/induct_method.ML Thu Nov 10 20:57:17 2005 +0100
@@ -22,7 +22,7 @@
val cases_tac: Proof.context -> bool -> term option list list -> thm option ->
thm list -> int -> RuleCases.tactic
val induct_tac: Proof.context -> bool -> term option list list ->
- thm option -> thm list -> int -> RuleCases.tactic
+ thm option -> (string * typ) list -> thm list -> int -> RuleCases.tactic
val setup: (theory -> theory) list
end;
@@ -50,10 +50,10 @@
fun prep_var (x, SOME t) =
let
val cx = cert x;
- val {T = xT, sign, ...} = Thm.rep_cterm cx;
+ val {T = xT, thy, ...} = Thm.rep_cterm cx;
val ct = cert (tune t);
in
- if Sign.typ_instance sign (#T (Thm.rep_cterm ct), xT) then SOME (cx, ct)
+ if Sign.typ_instance thy (#T (Thm.rep_cterm ct), xT) then SOME (cx, ct)
else raise ERROR_MESSAGE (Pretty.string_of (Pretty.block
[Pretty.str "Ill-typed instantiation:", Pretty.fbrk,
Display.pretty_cterm ct, Pretty.str " ::", Pretty.brk 1,
@@ -81,10 +81,9 @@
local
fun resolveq_cases_tac make ruleq i st =
- ruleq |> Seq.map (fn (rule, (cases, facts)) =>
+ ruleq |> Seq.maps (fn (rule, (cases, facts)) =>
(Method.insert_tac facts THEN' Tactic.rtac rule) i st
- |> Seq.map (rpair (make (Thm.sign_of_thm rule, Thm.prop_of rule) cases)))
- |> Seq.flat;
+ |> Seq.map (rpair (make (Thm.theory_of_thm rule, Thm.prop_of rule) cases)));
fun find_casesT ctxt ((SOME t :: _) :: _) = InductAttrib.find_casesT ctxt (fastype_of t)
| find_casesT _ _ = [];
@@ -96,8 +95,8 @@
fun cases_tac ctxt is_open insts opt_rule facts =
let
- val sg = ProofContext.sign_of ctxt;
- val cert = Thm.cterm_of sg;
+ val thy = ProofContext.theory_of ctxt;
+ val cert = Thm.cterm_of thy;
fun inst_rule r =
if null insts then RuleCases.add r
@@ -110,13 +109,13 @@
NONE =>
let val rules = find_casesS ctxt facts @ find_casesT ctxt insts @ [Data.cases_default] in
Method.trace ctxt rules;
- Seq.flat (Seq.map (Seq.try inst_rule) (Seq.of_list rules))
+ Seq.maps (Seq.try inst_rule) (Seq.of_list rules)
end
| SOME r => Seq.single (inst_rule r));
fun prep_rule (th, (cases, n)) = Seq.map (apsnd (rpair (Library.drop (n, facts))) o rpair cases)
(Method.multi_resolves (Library.take (n, facts)) [th]);
- in resolveq_cases_tac (RuleCases.make is_open NONE) (Seq.flat (Seq.map prep_rule ruleq)) end;
+ in resolveq_cases_tac (RuleCases.make is_open NONE) (Seq.maps prep_rule ruleq) end;
val cases_meth = Method.METHOD_CASES o ((Seq.DETERM o HEADGOAL) oo
(fn (ctxt, (is_open, (insts, opt_rule))) => cases_tac ctxt is_open insts opt_rule));
@@ -139,15 +138,15 @@
(* atomize and rulify *)
-fun atomize_term sg =
- ObjectLogic.drop_judgment sg o MetaSimplifier.rewrite_term sg Data.atomize [];
+fun atomize_term thy =
+ ObjectLogic.drop_judgment thy o MetaSimplifier.rewrite_term thy Data.atomize [];
fun rulified_term thm =
- let val sg = Thm.sign_of_thm thm in
+ let val thy = Thm.theory_of_thm thm in
Thm.prop_of thm
- |> MetaSimplifier.rewrite_term sg Data.rulify1 []
- |> MetaSimplifier.rewrite_term sg Data.rulify2 []
- |> pair sg
+ |> MetaSimplifier.rewrite_term thy Data.rulify1 []
+ |> MetaSimplifier.rewrite_term thy Data.rulify2 []
+ |> pair thy
end;
val atomize_tac = Tactic.rewrite_goal_tac Data.atomize;
@@ -160,16 +159,53 @@
val localize = Goal.norm_hhf o Tactic.simplify false Data.localize;
-(* imp_intr --- limited to atomic prems *)
+(* fix_tac *)
+
+local
+
+val meta_spec = PureThy.get_thm Pure.thy (Name "meta_spec");
+
+fun meta_spec_tac ctxt (x, T) i st = SUBGOAL (fn (goal, _) =>
+ let
+ val thy = Thm.theory_of_thm st;
+ val cert = Thm.cterm_of thy;
+ val certT = Thm.ctyp_of thy;
+
+ val v = Free (x, T);
+ val _ = Term.exists_subterm (fn t => t aconv v) goal orelse
+ error ("No occurrence of " ^ ProofContext.string_of_term ctxt v ^ " in subgoal");
+ val P = Term.absfree (x, T, goal);
+ val rule = meta_spec
+ |> Drule.instantiate' [SOME (certT T)] [SOME (cert P), SOME (cert v)]
+ |> Thm.rename_params_rule ([x], 1);
+ in compose_tac (false, rule, 1) end i) i st;
+
+in
+
+fun fix_tac ctxt fixes = EVERY' (map (meta_spec_tac ctxt) (rev fixes));
+
+end;
+
+
+(* internalize implications -- limited to atomic prems *)
+
+local
fun imp_intr i raw_th =
let
val th = Thm.permute_prems (i - 1) 1 raw_th;
+ val {thy, maxidx, ...} = Thm.rep_thm th;
val cprems = Drule.cprems_of th;
val As = Library.take (length cprems - 1, cprems);
- val C = Thm.cterm_of (Thm.sign_of_thm th) (Var (("C", #maxidx (Thm.rep_thm th) + 1), propT));
+ val C = Thm.cterm_of thy (Var (("C", maxidx + 1), propT));
in th COMP Thm.lift_rule (Drule.list_implies (As, C)) Data.local_impI end;
+in
+
+fun internalize k th = if k > 0 then internalize (k - 1) (imp_intr k th) else th;
+
+end;
+
(* join multi-rules *)
@@ -195,86 +231,87 @@
(* divinate rule instantiation (cannot handle pending goal parameters) *)
-fun dest_env sign (env as Envir.Envir {iTs, ...}) =
+fun dest_env thy (env as Envir.Envir {iTs, ...}) =
let
+ val cert = Thm.cterm_of thy;
+ val certT = Thm.ctyp_of thy;
val pairs = Envir.alist_of env;
- val ts = map (Thm.cterm_of sign o Envir.norm_term env o #2 o #2) pairs;
- val xs = map2 (Thm.cterm_of sign o Var) (map #1 pairs, map (#T o Thm.rep_cterm) ts);
- val cert = Thm.ctyp_of sign;
- in (map (fn (ixn, (S, T)) => (cert (TVar (ixn, S)), cert T)) (Vartab.dest iTs), xs ~~ ts) end;
+ val ts = map (cert o Envir.norm_term env o #2 o #2) pairs;
+ val xs = map2 (cert o Var) (map #1 pairs, map (#T o Thm.rep_cterm) ts);
+ in (map (fn (xi, (S, T)) => (certT (TVar (xi, S)), certT T)) (Vartab.dest iTs), xs ~~ ts) end;
fun divinate_inst rule i st =
let
- val {sign, maxidx, ...} = Thm.rep_thm st;
- val goal = List.nth (Thm.prems_of st, i - 1); (*exception Subscript*)
+ val {thy, maxidx, ...} = Thm.rep_thm st;
+ val goal = Thm.term_of (Thm.cprem_of st i); (*exception Subscript*)
val params = rev (rename_wrt_term goal (Logic.strip_params goal)); (*as they are printed :-*)
in
if not (null params) then
(warning ("Cannot determine rule instantiation due to pending parameter(s): " ^
- commas (map (Sign.string_of_term sign o Syntax.mark_boundT) params));
+ commas (map (Sign.string_of_term thy o Syntax.mark_boundT) params));
Seq.single rule)
else
let
val rule' = Thm.incr_indexes (maxidx + 1) rule;
val concl = Logic.strip_assums_concl goal;
in
- Unify.smash_unifiers (sign, Envir.empty (#maxidx (Thm.rep_thm rule')),
+ Unify.smash_unifiers (thy, Envir.empty (#maxidx (Thm.rep_thm rule')),
[(Thm.concl_of rule', concl)])
- |> Seq.map (fn env => Drule.instantiate (dest_env sign env) rule')
+ |> Seq.map (fn env => Drule.instantiate (dest_env thy env) rule')
end
end handle Subscript => Seq.empty;
(* compose tactics with cases *)
-fun internalize k th = if k > 0 then internalize (k - 1) (imp_intr k th) else th;
-
-fun resolveq_cases_tac' make is_open ruleq i st =
- ruleq |> Seq.map (fn (rule, (cases, k, more_facts)) => st
- |> (Method.insert_tac more_facts THEN' atomize_tac) i
- |> Seq.map (fn st' => divinate_inst (internalize k rule) i st' |> Seq.map (fn rule' =>
- st' |> Tactic.rtac rule' i
- |> Seq.map (rpair (make is_open (SOME (Thm.prop_of rule')) (rulified_term rule') cases)))
- |> Seq.flat)
- |> Seq.flat)
- |> Seq.flat;
+fun resolveq_cases_tac' ctxt make is_open ruleq fixes i st =
+ ruleq |> Seq.maps (fn (rule, (cases, k, more_facts)) =>
+ (Method.insert_tac more_facts THEN' fix_tac ctxt fixes THEN' atomize_tac) i st
+ |> Seq.maps (fn st' =>
+ divinate_inst (internalize k rule) i st'
+ |> Seq.maps (fn rule' =>
+ Tactic.rtac rule' i st'
+ |> Seq.map (rpair (make is_open (SOME (Thm.prop_of rule')) (rulified_term rule') cases)))));
infix 1 THEN_ALL_NEW_CASES;
fun (tac1 THEN_ALL_NEW_CASES tac2) i st =
- st |> Seq.THEN (tac1 i, (fn (st', cases) =>
- Seq.map (rpair cases) (Seq.INTERVAL tac2 i (i + nprems_of st' - nprems_of st) st')));
+ st |> tac1 i |> Seq.maps (fn (st', cases) =>
+ Seq.map (rpair cases) (Seq.INTERVAL tac2 i (i + nprems_of st' - nprems_of st) st'));
(* find rules *)
-(* rename all outermost !!-bound vars of type T in all premises of thm to x,
- possibly indexed to avoid clashes *)
-fun rename [[SOME(Free(x,Type(T,_)))]] thm =
- let
- fun index i [] = []
- | index i (y::ys) = if x=y then x^string_of_int i :: index (i+1) ys
- else y :: index i ys;
- fun rename_params [] = []
- | rename_params ((y,Type(U,_))::ys) =
- (if U=T then x else y)::rename_params ys
- | rename_params ((y,_)::ys) = y::rename_params ys;
- fun rename_asm (A:term):term =
- let val xs = rename_params (Logic.strip_params A)
- val xs' = case List.filter (equal x) xs of
- [] => xs | [_] => xs | _ => index 1 xs
- in Logic.list_rename_params (xs',A) end;
- fun rename_prop (p:term) =
- let val (As,C) = Logic.strip_horn p
- in Logic.list_implies(map rename_asm As, C) end;
- val cp' = cterm_fun rename_prop (cprop_of thm);
- val thm' = equal_elim (reflexive cp') thm
- in Thm.put_name_tags (Thm.get_name_tags thm) thm' end
+(*rename all outermost !!-bound vars of type T in all premises of thm to x,
+ possibly indexed to avoid clashes*)
+fun rename [[SOME (Free (x, Type (T, _)))]] thm =
+ let
+ fun index i [] = []
+ | index i (y :: ys) =
+ if x = y then x ^ string_of_int i :: index (i + 1) ys
+ else y :: index i ys;
+ fun rename_params [] = []
+ | rename_params ((y, Type (U, _)) :: ys) =
+ (if U = T then x else y) :: rename_params ys
+ | rename_params ((y, _) :: ys) = y :: rename_params ys;
+ fun rename_asm A =
+ let
+ val xs = rename_params (Logic.strip_params A);
+ val xs' =
+ (case List.filter (equal x) xs of
+ [] => xs | [_] => xs | _ => index 1 xs);
+ in Logic.list_rename_params (xs', A) end;
+ fun rename_prop p =
+ let val (As, C) = Logic.strip_horn p
+ in Logic.list_implies (map rename_asm As, C) end;
+ val cp' = cterm_fun rename_prop (Thm.cprop_of thm);
+ val thm' = Thm.equal_elim (Thm.reflexive cp') thm;
+ in Thm.put_name_tags (Thm.get_name_tags thm) thm' end
| rename _ thm = thm;
fun find_inductT ctxt insts =
- foldr multiply [[]] (insts |> List.mapPartial (fn [] => NONE | ts => List.last ts)
- |> map (InductAttrib.find_inductT ctxt o fastype_of))
+ fold_rev multiply (insts |> List.mapPartial (fn [] => NONE | ts => List.last ts)
+ |> map (InductAttrib.find_inductT ctxt o fastype_of)) [[]]
|> map join_rules |> List.concat |> map (rename insts);
fun find_inductS ctxt (fact :: _) = InductAttrib.find_inductS ctxt fact
@@ -282,12 +319,13 @@
in
+
(* main tactic *)
-fun induct_tac ctxt is_open insts opt_rule facts =
+fun induct_tac ctxt is_open insts opt_rule fixes facts =
let
- val sg = ProofContext.sign_of ctxt;
- val cert = Thm.cterm_of sg;
+ val thy = ProofContext.theory_of ctxt;
+ val cert = Thm.cterm_of thy;
fun rule_versions r = Seq.cons (r, Seq.filter (not o curry Thm.eq_thm r)
(Seq.make (fn () => SOME (localize r, Seq.empty))))
@@ -297,7 +335,7 @@
if null insts then r
else (align_right "Rule has fewer conclusions than arguments given"
(Data.dest_concls (Thm.concl_of r)) insts
- |> (List.concat o map (prep_inst align_right cert (atomize_term sg)))
+ |> (List.concat o map (prep_inst align_right cert (atomize_term thy)))
|> Drule.cterm_instantiate) r);
val ruleq =
@@ -306,18 +344,19 @@
let val rules = find_inductS ctxt facts @ find_inductT ctxt insts in
conditional (null rules) (fn () => error "Unable to figure out induct rule");
Method.trace ctxt rules;
- rules |> Seq.THEN (Seq.of_list, Seq.THEN (rule_versions, Seq.try inst_rule))
+ rules |> Seq.of_list |> Seq.maps rule_versions |> Seq.maps (Seq.try inst_rule)
end
- | SOME r => r |> Seq.THEN (rule_versions, Seq.single o inst_rule));
+ | SOME r => r |> rule_versions |> Seq.map inst_rule);
fun prep_rule (th, (cases, n)) =
Seq.map (rpair (cases, n - length facts, Library.drop (n, facts)))
(Method.multi_resolves (Library.take (n, facts)) [th]);
- val tac = resolveq_cases_tac' RuleCases.make is_open (Seq.flat (Seq.map prep_rule ruleq));
+ val tac = resolveq_cases_tac' ctxt RuleCases.make is_open (Seq.maps prep_rule ruleq) fixes;
in tac THEN_ALL_NEW_CASES rulify_tac end;
val induct_meth = Method.RAW_METHOD_CASES o ((Seq.DETERM o HEADGOAL) oo
- (fn (ctxt, (is_open, (insts, opt_rule))) => induct_tac ctxt is_open insts opt_rule));
+ (fn (ctxt, (is_open, (insts, (opt_rule, fixes)))) =>
+ induct_tac ctxt is_open insts opt_rule fixes));
end;
@@ -328,6 +367,7 @@
val openN = "open";
val ruleN = "rule";
val ofN = "of";
+val fixingN = "fixing";
local
@@ -344,19 +384,26 @@
val cases_rule = rule InductAttrib.lookup_casesT InductAttrib.lookup_casesS;
val induct_rule = rule InductAttrib.lookup_inductT InductAttrib.lookup_inductS;
-val kind_inst =
- (Args.$$$ InductAttrib.typeN || Args.$$$ InductAttrib.setN || Args.$$$ ruleN || Args.$$$ ofN)
- -- Args.colon;
-val term = Scan.unless (Scan.lift kind_inst) Args.local_term;
-val term_dummy = Scan.unless (Scan.lift kind_inst)
+val more_args =
+ (Args.$$$ InductAttrib.typeN || Args.$$$ InductAttrib.setN || Args.$$$ ruleN ||
+ Args.$$$ ofN || Args.$$$ fixingN) -- Args.colon;
+
+val term = Scan.unless (Scan.lift more_args) Args.local_term;
+val term_dummy = Scan.unless (Scan.lift more_args)
(Scan.lift (Args.$$$ "_") >> K NONE || Args.local_term >> SOME);
val instss = Args.and_list (Scan.repeat term_dummy);
+val free = Scan.state -- Args.local_term >> (fn (_, Free v) => v | (ctxt, t) =>
+ error ("Bad free variable: " ^ ProofContext.string_of_term ctxt t));
+val fixing = Scan.optional (Scan.lift (Args.$$$ fixingN -- Args.colon) |-- Scan.repeat1 free) [];
+
in
-val cases_args = Method.syntax (Args.mode openN -- (instss -- Scan.option cases_rule));
-val induct_args = Method.syntax (Args.mode openN -- (instss -- Scan.option induct_rule));
+val cases_args =
+ Method.syntax (Args.mode openN -- (instss -- Scan.option cases_rule));
+val induct_args =
+ Method.syntax (Args.mode openN -- (instss -- (Scan.option induct_rule -- fixing)));
end;
@@ -370,4 +417,3 @@
(InductAttrib.inductN, induct_meth oo induct_args, "induction on types or sets")]];
end;
-