# HG changeset patch # User traytel # Date 1380707872 -7200 # Node ID 82d9b2701a036727f05f52313a290f4e540a4820 # Parent 70bc41e7a91e7a24ad3f9111fe0abb6183c5f277 new coinduction method diff -r 70bc41e7a91e -r 82d9b2701a03 src/HOL/BNF/BNF.thy --- 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 diff -r 70bc41e7a91e -r 82d9b2701a03 src/HOL/BNF/Coinduction.thy --- /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 diff -r 70bc41e7a91e -r 82d9b2701a03 src/HOL/BNF/Tools/coinduction.ML --- /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; +