--- a/src/HOL/BNF/BNF.thy Wed Oct 02 10:53:15 2013 +0200
+++ b/src/HOL/BNF/BNF.thy Wed Oct 02 11:57:52 2013 +0200
@@ -10,7 +10,7 @@
header {* Bounded Natural Functors for (Co)datatypes *}
theory BNF
-imports More_BNFs BNF_LFP BNF_GFP
+imports More_BNFs BNF_LFP BNF_GFP Coinduction
begin
hide_const (open) image2 image2p vimage2p Gr Grp collect fsts snds setl setr
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/BNF/Coinduction.thy Wed Oct 02 11:57:52 2013 +0200
@@ -0,0 +1,19 @@
+(* Title: HOL/BNF/Coinduction.thy
+ Author: Johannes Hölzl, TU Muenchen
+ Author: Dmitriy Traytel, TU Muenchen
+ Copyright 2013
+
+Coinduction method that avoids some boilerplate compared to coinduct.
+*)
+
+header {* Coinduction Method *}
+
+theory Coinduction
+imports BNF_Util
+begin
+
+ML_file "Tools/coinduction.ML"
+
+setup Coinduction.setup
+
+end
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/BNF/Tools/coinduction.ML Wed Oct 02 11:57:52 2013 +0200
@@ -0,0 +1,159 @@
+(* Title: HOL/BNF/Tools/coinduction.ML
+ Author: Johannes Hölzl, TU Muenchen
+ Author: Dmitriy Traytel, TU Muenchen
+ Copyright 2013
+
+Coinduction method that avoids some boilerplate compared to coinduct.
+*)
+
+signature COINDUCTION =
+sig
+ val coinduction_tac: Proof.context -> term list -> thm option -> thm list -> cases_tactic
+ val setup: theory -> theory
+end;
+
+structure Coinduction : COINDUCTION =
+struct
+
+open BNF_Util
+open BNF_Tactics
+
+fun filter_in_out _ [] = ([], [])
+ | filter_in_out P (x :: xs) = (let
+ val (ins, outs) = filter_in_out P xs;
+ in
+ if P x then (x :: ins, outs) else (ins, x :: outs)
+ end);
+
+fun ALLGOALS_SKIP skip tac st =
+ let fun doall n = if n = skip then all_tac else tac n THEN doall (n - 1)
+ in doall (nprems_of st) st end;
+
+fun THEN_ALL_NEW_SKIP skip tac1 tac2 i st =
+ st |> (tac1 i THEN (fn st' =>
+ Seq.INTERVAL tac2 (i + skip) (i + nprems_of st' - nprems_of st) st'));
+
+fun DELETE_PREMS_AFTER skip tac i st =
+ let
+ val n = nth (prems_of st) (i - 1) |> Logic.strip_assums_hyp |> length;
+ in
+ (THEN_ALL_NEW_SKIP skip tac (REPEAT_DETERM_N n o etac thin_rl)) i st
+ end;
+
+fun coinduction_tac ctxt raw_vars opt_raw_thm prems st =
+ let
+ val lhs_of_eq = HOLogic.dest_Trueprop #> HOLogic.dest_eq #> fst;
+ fun find_coinduct t =
+ Induct.find_coinductP ctxt t @
+ (try (Induct.find_coinductT ctxt o fastype_of o lhs_of_eq) t |> the_default [])
+ val raw_thm = case opt_raw_thm
+ of SOME raw_thm => raw_thm
+ | NONE => st |> prems_of |> hd |> Logic.strip_assums_concl |> find_coinduct |> hd;
+ val skip = Integer.max 1 (Rule_Cases.get_consumes raw_thm) - 1
+ val cases = Rule_Cases.get raw_thm |> fst
+ in
+ NO_CASES (HEADGOAL (
+ Object_Logic.rulify_tac THEN'
+ Method.insert_tac prems THEN'
+ Object_Logic.atomize_prems_tac THEN'
+ DELETE_PREMS_AFTER skip (Subgoal.FOCUS (fn {concl, context = ctxt, params, prems, ...} =>
+ let
+ val vars = raw_vars @ map (term_of o snd) params;
+ val names_ctxt = ctxt
+ |> fold Variable.declare_names vars
+ |> fold Variable.declare_thm (raw_thm :: prems);
+ val thm_concl = Thm.cprop_of raw_thm |> strip_imp_concl;
+ val (rhoTs, rhots) = Thm.match (thm_concl, concl)
+ |>> map (pairself typ_of)
+ ||> map (pairself term_of);
+ val xs = hd (Thm.prems_of raw_thm) |> HOLogic.dest_Trueprop |> strip_comb |> snd
+ |> map (subst_atomic_types rhoTs);
+ val raw_eqs = map (fn x => (x, AList.lookup op aconv rhots x |> the)) xs;
+ val ((names, ctxt), Ts) = map_split (apfst fst o dest_Var o fst) raw_eqs
+ |>> (fn names => Variable.variant_fixes names names_ctxt) ;
+ val eqs =
+ map3 (fn name => fn T => fn (_, rhs) =>
+ HOLogic.mk_eq (Free (name, T), rhs))
+ names Ts raw_eqs;
+ val phi = map (HOLogic.dest_Trueprop o prop_of) prems @ eqs
+ |> try (Library.foldr1 HOLogic.mk_conj)
+ |> the_default @{term True}
+ |> list_exists_free vars
+ |> Term.map_abs_vars (Variable.revert_fixed ctxt)
+ |> fold_rev Term.absfree (names ~~ Ts)
+ |> certify ctxt;
+ val thm = cterm_instantiate_pos [SOME phi] raw_thm;
+ val e = length eqs;
+ val p = length prems;
+ in
+ HEADGOAL (EVERY' [rtac thm,
+ EVERY' (map (fn var =>
+ rtac (cterm_instantiate_pos [NONE, SOME (certify ctxt var)] exI)) vars),
+ EVERY' (map (fn prem => rtac conjI THEN' rtac prem) prems),
+ CONJ_WRAP' (K (rtac refl)) eqs,
+ K (ALLGOALS_SKIP skip
+ (REPEAT_DETERM_N (length vars) o (etac exE THEN' rotate_tac ~1) THEN'
+ DELETE_PREMS_AFTER 0 (Subgoal.FOCUS (fn {prems, params, context = ctxt, ...} =>
+ (case prems of
+ [] => all_tac
+ | inv::case_prems =>
+ let
+ val (init, last) = funpow_yield (p + e - 1) HOLogic.conj_elim inv;
+ val inv_thms = init @ [last];
+ val eqs = drop p inv_thms;
+ fun is_local_var t =
+ member (fn (t, (_, t')) => t aconv (term_of t')) params t;
+ val (eqs, assms') = filter_in_out (is_local_var o lhs_of_eq o prop_of) eqs;
+ val assms = assms' @ take p inv_thms
+ in
+ HEADGOAL (Method.insert_tac (assms @ case_prems)) THEN
+ unfold_thms_tac ctxt eqs
+ end)) ctxt)))])
+ end) ctxt) THEN'
+ K (prune_params_tac))) st
+ |> Seq.maps (fn (_, st) =>
+ CASES (Rule_Cases.make_common (Proof_Context.theory_of ctxt, prop_of st) cases) all_tac st)
+ end;
+
+local
+
+val ruleN = "rule"
+val arbitraryN = "arbitrary"
+fun single_rule [rule] = rule
+ | single_rule _ = error "Single rule expected";
+
+fun named_rule k arg get =
+ Scan.lift (Args.$$$ k -- Args.colon) |-- Scan.repeat arg :|--
+ (fn names => Scan.peek (fn context => Scan.succeed (names |> map (fn name =>
+ (case get (Context.proof_of context) name of SOME x => x
+ | NONE => error ("No rule for " ^ k ^ " " ^ quote name))))));
+
+fun rule get_type get_pred =
+ named_rule Induct.typeN (Args.type_name false) get_type ||
+ named_rule Induct.predN (Args.const false) get_pred ||
+ named_rule Induct.setN (Args.const false) get_pred ||
+ Scan.lift (Args.$$$ ruleN -- Args.colon) |-- Attrib.thms;
+
+val coinduct_rule = rule Induct.lookup_coinductT Induct.lookup_coinductP >> single_rule;
+
+fun unless_more_args scan = Scan.unless (Scan.lift
+ ((Args.$$$ arbitraryN || Args.$$$ Induct.typeN ||
+ Args.$$$ Induct.predN || Args.$$$ Induct.setN || Args.$$$ ruleN) -- Args.colon)) scan;
+
+val arbitrary = Scan.optional (Scan.lift (Args.$$$ arbitraryN -- Args.colon) |--
+ Scan.repeat1 (unless_more_args Args.term)) [];
+
+in
+
+val setup =
+ Method.setup @{binding coinduction}
+ (arbitrary -- Scan.option coinduct_rule >>
+ (fn (arbitrary, opt_rule) => fn ctxt =>
+ RAW_METHOD_CASES (fn facts =>
+ Seq.DETERM (coinduction_tac ctxt arbitrary opt_rule facts))))
+ "coinduction on types or predicates/sets";
+
+end;
+
+end;
+