diff --git a/src/Pure/raw_simplifier.ML b/src/Pure/raw_simplifier.ML --- a/src/Pure/raw_simplifier.ML +++ b/src/Pure/raw_simplifier.ML @@ -1,1462 +1,1462 @@ (* Title: Pure/raw_simplifier.ML Author: Tobias Nipkow and Stefan Berghofer, TU Muenchen Higher-order Simplification. *) infix 4 addsimps delsimps addsimprocs delsimprocs setloop addloop delloop setSSolver addSSolver setSolver addSolver; signature BASIC_RAW_SIMPLIFIER = sig val simp_depth_limit: int Config.T val simp_trace_depth_limit: int Config.T val simp_debug: bool Config.T val simp_trace: bool Config.T type cong_name = bool * string type rrule val mk_rrules: Proof.context -> thm list -> rrule list val eq_rrule: rrule * rrule -> bool type proc type solver val mk_solver: string -> (Proof.context -> int -> tactic) -> solver type simpset val empty_ss: simpset val merge_ss: simpset * simpset -> simpset val dest_ss: simpset -> {simps: (string * thm) list, procs: (string * term list) list, congs: (cong_name * thm) list, weak_congs: cong_name list, loopers: string list, unsafe_solvers: string list, safe_solvers: string list} type simproc val eq_simproc: simproc * simproc -> bool val cert_simproc: theory -> string -> {lhss: term list, proc: morphism -> Proof.context -> cterm -> thm option} -> simproc val transform_simproc: morphism -> simproc -> simproc val simpset_of: Proof.context -> simpset val put_simpset: simpset -> Proof.context -> Proof.context val simpset_map: Proof.context -> (Proof.context -> Proof.context) -> simpset -> simpset val map_theory_simpset: (Proof.context -> Proof.context) -> theory -> theory val empty_simpset: Proof.context -> Proof.context val clear_simpset: Proof.context -> Proof.context val addsimps: Proof.context * thm list -> Proof.context val delsimps: Proof.context * thm list -> Proof.context val addsimprocs: Proof.context * simproc list -> Proof.context val delsimprocs: Proof.context * simproc list -> Proof.context val setloop: Proof.context * (Proof.context -> int -> tactic) -> Proof.context val addloop: Proof.context * (string * (Proof.context -> int -> tactic)) -> Proof.context val delloop: Proof.context * string -> Proof.context val setSSolver: Proof.context * solver -> Proof.context val addSSolver: Proof.context * solver -> Proof.context val setSolver: Proof.context * solver -> Proof.context val addSolver: Proof.context * solver -> Proof.context val rewrite_rule: Proof.context -> thm list -> thm -> thm val rewrite_goals_rule: Proof.context -> thm list -> thm -> thm val rewrite_goals_tac: Proof.context -> thm list -> tactic val rewrite_goal_tac: Proof.context -> thm list -> int -> tactic val prune_params_tac: Proof.context -> tactic val fold_rule: Proof.context -> thm list -> thm -> thm val fold_goals_tac: Proof.context -> thm list -> tactic val norm_hhf: Proof.context -> thm -> thm val norm_hhf_protect: Proof.context -> thm -> thm end; signature RAW_SIMPLIFIER = sig include BASIC_RAW_SIMPLIFIER exception SIMPLIFIER of string * thm list type trace_ops val set_trace_ops: trace_ops -> theory -> theory val subgoal_tac: Proof.context -> int -> tactic val loop_tac: Proof.context -> int -> tactic val solvers: Proof.context -> solver list * solver list val map_ss: (Proof.context -> Proof.context) -> Context.generic -> Context.generic val prems_of: Proof.context -> thm list val add_simp: thm -> Proof.context -> Proof.context val del_simp: thm -> Proof.context -> Proof.context val flip_simp: thm -> Proof.context -> Proof.context val init_simpset: thm list -> Proof.context -> Proof.context val add_eqcong: thm -> Proof.context -> Proof.context val del_eqcong: thm -> Proof.context -> Proof.context val add_cong: thm -> Proof.context -> Proof.context val del_cong: thm -> Proof.context -> Proof.context val mksimps: Proof.context -> thm -> thm list val set_mksimps: (Proof.context -> thm -> thm list) -> Proof.context -> Proof.context val set_mkcong: (Proof.context -> thm -> thm) -> Proof.context -> Proof.context val set_mksym: (Proof.context -> thm -> thm option) -> Proof.context -> Proof.context val set_mkeqTrue: (Proof.context -> thm -> thm option) -> Proof.context -> Proof.context val set_term_ord: term ord -> Proof.context -> Proof.context val set_subgoaler: (Proof.context -> int -> tactic) -> Proof.context -> Proof.context val solver: Proof.context -> solver -> int -> tactic val default_mk_sym: Proof.context -> thm -> thm option val add_prems: thm list -> Proof.context -> Proof.context val set_reorient: (Proof.context -> term list -> term -> term -> bool) -> Proof.context -> Proof.context val set_solvers: solver list -> Proof.context -> Proof.context val rewrite_cterm: bool * bool * bool -> (Proof.context -> thm -> thm option) -> Proof.context -> conv val rewrite_term: theory -> thm list -> (term -> term option) list -> term -> term val rewrite_thm: bool * bool * bool -> (Proof.context -> thm -> thm option) -> Proof.context -> thm -> thm val generic_rewrite_goal_tac: bool * bool * bool -> (Proof.context -> tactic) -> Proof.context -> int -> tactic val rewrite: Proof.context -> bool -> thm list -> conv end; structure Raw_Simplifier: RAW_SIMPLIFIER = struct (** datatype simpset **) (* congruence rules *) type cong_name = bool * string; fun cong_name (Const (a, _)) = SOME (true, a) | cong_name (Free (a, _)) = SOME (false, a) | cong_name _ = NONE; structure Congtab = Table(type key = cong_name val ord = prod_ord bool_ord fast_string_ord); (* rewrite rules *) type rrule = {thm: thm, (*the rewrite rule*) name: string, (*name of theorem from which rewrite rule was extracted*) lhs: term, (*the left-hand side*) elhs: cterm, (*the eta-contracted lhs*) extra: bool, (*extra variables outside of elhs*) fo: bool, (*use first-order matching*) perm: bool}; (*the rewrite rule is permutative*) fun trim_context_rrule ({thm, name, lhs, elhs, extra, fo, perm}: rrule) = {thm = Thm.trim_context thm, name = name, lhs = lhs, elhs = Thm.trim_context_cterm elhs, extra = extra, fo = fo, perm = perm}; (* Remarks: - elhs is used for matching, lhs only for preservation of bound variable names; - fo is set iff either elhs is first-order (no Var is applied), in which case fo-matching is complete, or elhs is not a pattern, in which case there is nothing better to do; *) fun eq_rrule ({thm = thm1, ...}: rrule, {thm = thm2, ...}: rrule) = Thm.eq_thm_prop (thm1, thm2); (* FIXME: it seems that the conditions on extra variables are too liberal if prems are nonempty: does solving the prems really guarantee instantiation of all its Vars? Better: a dynamic check each time a rule is applied. *) fun rewrite_rule_extra_vars prems elhs erhs = let val elhss = elhs :: prems; val tvars = fold Term.add_tvars elhss []; val vars = fold Term.add_vars elhss []; in erhs |> Term.exists_type (Term.exists_subtype (fn TVar v => not (member (op =) tvars v) | _ => false)) orelse erhs |> Term.exists_subterm (fn Var v => not (member (op =) vars v) | _ => false) end; fun rrule_extra_vars elhs thm = rewrite_rule_extra_vars [] (Thm.term_of elhs) (Thm.full_prop_of thm); fun mk_rrule2 {thm, name, lhs, elhs, perm} = let val t = Thm.term_of elhs; val fo = Pattern.first_order t orelse not (Pattern.pattern t); val extra = rrule_extra_vars elhs thm; in {thm = thm, name = name, lhs = lhs, elhs = elhs, extra = extra, fo = fo, perm = perm} end; (*simple test for looping rewrite rules and stupid orientations*) fun default_reorient ctxt prems lhs rhs = rewrite_rule_extra_vars prems lhs rhs orelse is_Var (head_of lhs) orelse (* turns t = x around, which causes a headache if x is a local variable - usually it is very useful :-( is_Free rhs andalso not(is_Free lhs) andalso not(Logic.occs(rhs,lhs)) andalso not(exists_subterm is_Var lhs) orelse *) exists (fn t => Logic.occs (lhs, t)) (rhs :: prems) orelse null prems andalso Pattern.matches (Proof_Context.theory_of ctxt) (lhs, rhs) (*the condition "null prems" is necessary because conditional rewrites with extra variables in the conditions may terminate although the rhs is an instance of the lhs; example: ?m < ?n \ f ?n \ f ?m *) orelse is_Const lhs andalso not (is_Const rhs); (* simplification procedures *) datatype proc = Proc of {name: string, lhs: term, proc: Proof.context -> cterm -> thm option, stamp: stamp}; fun eq_proc (Proc {stamp = stamp1, ...}, Proc {stamp = stamp2, ...}) = stamp1 = stamp2; (* solvers *) datatype solver = Solver of {name: string, solver: Proof.context -> int -> tactic, id: stamp}; fun mk_solver name solver = Solver {name = name, solver = solver, id = stamp ()}; fun solver_name (Solver {name, ...}) = name; fun solver ctxt (Solver {solver = tac, ...}) = tac ctxt; fun eq_solver (Solver {id = id1, ...}, Solver {id = id2, ...}) = (id1 = id2); (* simplification sets *) (*A simpset contains data required during conversion: rules: discrimination net of rewrite rules; prems: current premises; depth: simp_depth and exceeded flag; congs: association list of congruence rules and a list of `weak' congruence constants. A congruence is `weak' if it avoids normalization of some argument. procs: discrimination net of simplification procedures (functions that prove rewrite rules on the fly); mk_rews: mk: turn simplification thms into rewrite rules; mk_cong: prepare congruence rules; mk_sym: turn \ around; mk_eq_True: turn P into P \ True; term_ord: for ordered rewriting;*) datatype simpset = Simpset of {rules: rrule Net.net, prems: thm list, depth: int * bool Unsynchronized.ref} * {congs: thm Congtab.table * cong_name list, procs: proc Net.net, mk_rews: {mk: Proof.context -> thm -> thm list, mk_cong: Proof.context -> thm -> thm, mk_sym: Proof.context -> thm -> thm option, mk_eq_True: Proof.context -> thm -> thm option, reorient: Proof.context -> term list -> term -> term -> bool}, term_ord: term ord, subgoal_tac: Proof.context -> int -> tactic, loop_tacs: (string * (Proof.context -> int -> tactic)) list, solvers: solver list * solver list}; fun internal_ss (Simpset (_, ss2)) = ss2; fun make_ss1 (rules, prems, depth) = {rules = rules, prems = prems, depth = depth}; fun map_ss1 f {rules, prems, depth} = make_ss1 (f (rules, prems, depth)); fun make_ss2 (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) = {congs = congs, procs = procs, mk_rews = mk_rews, term_ord = term_ord, subgoal_tac = subgoal_tac, loop_tacs = loop_tacs, solvers = solvers}; fun map_ss2 f {congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers} = make_ss2 (f (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers)); fun make_simpset (args1, args2) = Simpset (make_ss1 args1, make_ss2 args2); fun dest_ss (Simpset ({rules, ...}, {congs, procs, loop_tacs, solvers, ...})) = {simps = Net.entries rules |> map (fn {name, thm, ...} => (name, thm)), procs = Net.entries procs |> map (fn Proc {name, lhs, stamp, ...} => ((name, lhs), stamp)) |> partition_eq (eq_snd op =) |> map (fn ps => (fst (fst (hd ps)), map (snd o fst) ps)), congs = congs |> fst |> Congtab.dest, weak_congs = congs |> snd, loopers = map fst loop_tacs, unsafe_solvers = map solver_name (#1 solvers), safe_solvers = map solver_name (#2 solvers)}; (* empty *) fun init_ss depth mk_rews term_ord subgoal_tac solvers = make_simpset ((Net.empty, [], depth), ((Congtab.empty, []), Net.empty, mk_rews, term_ord, subgoal_tac, [], solvers)); fun default_mk_sym _ th = SOME (th RS Drule.symmetric_thm); val empty_ss = init_ss (0, Unsynchronized.ref false) {mk = fn _ => fn th => if can Logic.dest_equals (Thm.concl_of th) then [th] else [], mk_cong = K I, mk_sym = default_mk_sym, mk_eq_True = K (K NONE), reorient = default_reorient} Term_Ord.term_ord (K (K no_tac)) ([], []); (* merge *) (*NOTE: ignores some fields of 2nd simpset*) fun merge_ss (ss1, ss2) = if pointer_eq (ss1, ss2) then ss1 else let val Simpset ({rules = rules1, prems = prems1, depth = depth1}, {congs = (congs1, weak1), procs = procs1, mk_rews, term_ord, subgoal_tac, loop_tacs = loop_tacs1, solvers = (unsafe_solvers1, solvers1)}) = ss1; val Simpset ({rules = rules2, prems = prems2, depth = depth2}, {congs = (congs2, weak2), procs = procs2, mk_rews = _, term_ord = _, subgoal_tac = _, loop_tacs = loop_tacs2, solvers = (unsafe_solvers2, solvers2)}) = ss2; val rules' = Net.merge eq_rrule (rules1, rules2); val prems' = Thm.merge_thms (prems1, prems2); val depth' = if #1 depth1 < #1 depth2 then depth2 else depth1; val congs' = Congtab.merge (K true) (congs1, congs2); val weak' = merge (op =) (weak1, weak2); val procs' = Net.merge eq_proc (procs1, procs2); val loop_tacs' = AList.merge (op =) (K true) (loop_tacs1, loop_tacs2); val unsafe_solvers' = merge eq_solver (unsafe_solvers1, unsafe_solvers2); val solvers' = merge eq_solver (solvers1, solvers2); in make_simpset ((rules', prems', depth'), ((congs', weak'), procs', mk_rews, term_ord, subgoal_tac, loop_tacs', (unsafe_solvers', solvers'))) end; (** context data **) structure Simpset = Generic_Data ( type T = simpset; val empty = empty_ss; val extend = I; val merge = merge_ss; ); val simpset_of = Simpset.get o Context.Proof; fun map_simpset f = Context.proof_map (Simpset.map f); fun map_simpset1 f = map_simpset (fn Simpset (ss1, ss2) => Simpset (map_ss1 f ss1, ss2)); fun map_simpset2 f = map_simpset (fn Simpset (ss1, ss2) => Simpset (ss1, map_ss2 f ss2)); -fun simpset_map ctxt f ss = ctxt |> map_simpset (K ss) |> f |> Context.Proof |> Simpset.get; +fun put_simpset ss = map_simpset (K ss); -fun put_simpset ss = map_simpset (K ss); +fun simpset_map ctxt f ss = ctxt |> put_simpset ss |> f |> simpset_of; val empty_simpset = put_simpset empty_ss; fun map_theory_simpset f thy = let val ctxt' = f (Proof_Context.init_global thy); val thy' = Proof_Context.theory_of ctxt'; in Context.theory_map (Simpset.map (K (simpset_of ctxt'))) thy' end; fun map_ss f = Context.mapping (map_theory_simpset (f o Context_Position.not_really)) f; val clear_simpset = map_simpset (fn Simpset ({depth, ...}, {mk_rews, term_ord, subgoal_tac, solvers, ...}) => init_ss depth mk_rews term_ord subgoal_tac solvers); (* accessors for tactis *) fun subgoal_tac ctxt = (#subgoal_tac o internal_ss o simpset_of) ctxt ctxt; fun loop_tac ctxt = FIRST' (map (fn (_, tac) => tac ctxt) (rev ((#loop_tacs o internal_ss o simpset_of) ctxt))); val solvers = #solvers o internal_ss o simpset_of (* simp depth *) (* The simp_depth_limit is meant to abort infinite recursion of the simplifier early but should not terminate "normal" executions. As of 2017, 25 would suffice; 40 builds in a safety margin. *) val simp_depth_limit = Config.declare_int ("simp_depth_limit", \<^here>) (K 40); val simp_trace_depth_limit = Config.declare_int ("simp_trace_depth_limit", \<^here>) (K 1); fun inc_simp_depth ctxt = ctxt |> map_simpset1 (fn (rules, prems, (depth, exceeded)) => (rules, prems, (depth + 1, if depth = Config.get ctxt simp_trace_depth_limit then Unsynchronized.ref false else exceeded))); fun simp_depth ctxt = let val Simpset ({depth = (depth, _), ...}, _) = simpset_of ctxt in depth end; (* diagnostics *) exception SIMPLIFIER of string * thm list; val simp_debug = Config.declare_bool ("simp_debug", \<^here>) (K false); val simp_trace = Config.declare_bool ("simp_trace", \<^here>) (K false); fun cond_warning ctxt msg = if Context_Position.is_really_visible ctxt then warning (msg ()) else (); fun cond_tracing' ctxt flag msg = if Config.get ctxt flag then let val Simpset ({depth = (depth, exceeded), ...}, _) = simpset_of ctxt; val depth_limit = Config.get ctxt simp_trace_depth_limit; in if depth > depth_limit then if ! exceeded then () else (tracing "simp_trace_depth_limit exceeded!"; exceeded := true) else (tracing (enclose "[" "]" (string_of_int depth) ^ msg ()); exceeded := false) end else (); fun cond_tracing ctxt = cond_tracing' ctxt simp_trace; fun print_term ctxt s t = s ^ "\n" ^ Syntax.string_of_term ctxt t; fun print_thm ctxt s (name, th) = print_term ctxt (if name = "" then s else s ^ " " ^ quote name ^ ":") (Thm.full_prop_of th); (** simpset operations **) (* prems *) fun prems_of ctxt = let val Simpset ({prems, ...}, _) = simpset_of ctxt in prems end; fun add_prems ths = map_simpset1 (fn (rules, prems, depth) => (rules, ths @ prems, depth)); (* maintain simp rules *) fun del_rrule loud (rrule as {thm, elhs, ...}) ctxt = ctxt |> map_simpset1 (fn (rules, prems, depth) => (Net.delete_term eq_rrule (Thm.term_of elhs, rrule) rules, prems, depth)) handle Net.DELETE => (if not loud then () else cond_warning ctxt (fn () => print_thm ctxt "Rewrite rule not in simpset:" ("", thm)); ctxt); fun insert_rrule (rrule as {thm, name, ...}) ctxt = (cond_tracing ctxt (fn () => print_thm ctxt "Adding rewrite rule" (name, thm)); ctxt |> map_simpset1 (fn (rules, prems, depth) => let val rrule2 as {elhs, ...} = mk_rrule2 rrule; val rules' = Net.insert_term eq_rrule (Thm.term_of elhs, trim_context_rrule rrule2) rules; in (rules', prems, depth) end) handle Net.INSERT => (cond_warning ctxt (fn () => print_thm ctxt "Ignoring duplicate rewrite rule:" ("", thm)); ctxt)); local fun vperm (Var _, Var _) = true | vperm (Abs (_, _, s), Abs (_, _, t)) = vperm (s, t) | vperm (t1 $ t2, u1 $ u2) = vperm (t1, u1) andalso vperm (t2, u2) | vperm (t, u) = (t = u); fun var_perm (t, u) = vperm (t, u) andalso eq_set (op =) (Term.add_vars t [], Term.add_vars u []); in fun decomp_simp thm = let val prop = Thm.prop_of thm; val prems = Logic.strip_imp_prems prop; val concl = Drule.strip_imp_concl (Thm.cprop_of thm); val (lhs, rhs) = Thm.dest_equals concl handle TERM _ => raise SIMPLIFIER ("Rewrite rule not a meta-equality", [thm]); val elhs = Thm.dest_arg (Thm.cprop_of (Thm.eta_conversion lhs)); val erhs = Envir.eta_contract (Thm.term_of rhs); val perm = var_perm (Thm.term_of elhs, erhs) andalso not (Thm.term_of elhs aconv erhs) andalso not (is_Var (Thm.term_of elhs)); in (prems, Thm.term_of lhs, elhs, Thm.term_of rhs, perm) end; end; fun decomp_simp' thm = let val (_, lhs, _, rhs, _) = decomp_simp thm in if Thm.nprems_of thm > 0 then raise SIMPLIFIER ("Bad conditional rewrite rule", [thm]) else (lhs, rhs) end; fun mk_eq_True ctxt (thm, name) = let val Simpset (_, {mk_rews = {mk_eq_True, ...}, ...}) = simpset_of ctxt in (case mk_eq_True ctxt thm of NONE => [] | SOME eq_True => let val (_, lhs, elhs, _, _) = decomp_simp eq_True; in [{thm = eq_True, name = name, lhs = lhs, elhs = elhs, perm = false}] end) end; (*create the rewrite rule and possibly also the eq_True variant, in case there are extra vars on the rhs*) fun rrule_eq_True ctxt thm name lhs elhs rhs thm2 = let val rrule = {thm = thm, name = name, lhs = lhs, elhs = elhs, perm = false} in if rewrite_rule_extra_vars [] lhs rhs then mk_eq_True ctxt (thm2, name) @ [rrule] else [rrule] end; fun mk_rrule ctxt (thm, name) = let val (prems, lhs, elhs, rhs, perm) = decomp_simp thm in if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}] else (*weak test for loops*) if rewrite_rule_extra_vars prems lhs rhs orelse is_Var (Thm.term_of elhs) then mk_eq_True ctxt (thm, name) else rrule_eq_True ctxt thm name lhs elhs rhs thm end |> map (fn {thm, name, lhs, elhs, perm} => {thm = Thm.trim_context thm, name = name, lhs = lhs, elhs = Thm.trim_context_cterm elhs, perm = perm}); fun orient_rrule ctxt (thm, name) = let val (prems, lhs, elhs, rhs, perm) = decomp_simp thm; val Simpset (_, {mk_rews = {reorient, mk_sym, ...}, ...}) = simpset_of ctxt; in if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}] else if reorient ctxt prems lhs rhs then if reorient ctxt prems rhs lhs then mk_eq_True ctxt (thm, name) else (case mk_sym ctxt thm of NONE => [] | SOME thm' => let val (_, lhs', elhs', rhs', _) = decomp_simp thm' in rrule_eq_True ctxt thm' name lhs' elhs' rhs' thm end) else rrule_eq_True ctxt thm name lhs elhs rhs thm end; fun extract_rews ctxt sym thms = let val Simpset (_, {mk_rews = {mk, ...}, ...}) = simpset_of ctxt; val mk = if sym then fn ctxt => fn th => (mk ctxt th) RL [Drule.symmetric_thm] else mk in maps (fn thm => map (rpair (Thm.get_name_hint thm)) (mk ctxt thm)) thms end; fun extract_safe_rrules ctxt thm = maps (orient_rrule ctxt) (extract_rews ctxt false [thm]); fun mk_rrules ctxt thms = let val rews = extract_rews ctxt false thms val raw_rrules = flat (map (mk_rrule ctxt) rews) in map mk_rrule2 raw_rrules end (* add/del rules explicitly *) local fun comb_simps ctxt comb mk_rrule sym thms = let val rews = extract_rews ctxt sym (map (Thm.transfer' ctxt) thms); in fold (fold comb o mk_rrule) rews ctxt end; (* This code checks if the symetric version of a rule is already in the simpset. However, the variable names in the two versions of the rule may differ. Thus the current test modulo eq_rrule is too weak to be useful and needs to be refined. fun present ctxt rules (rrule as {thm, elhs, ...}) = (Net.insert_term eq_rrule (Thm.term_of elhs, trim_context_rrule rrule) rules; false) handle Net.INSERT => (cond_warning ctxt (fn () => print_thm ctxt "Symmetric rewrite rule already in simpset:" ("", thm)); true); fun sym_present ctxt thms = let val rews = extract_rews ctxt true (map (Thm.transfer' ctxt) thms); val rrules = map mk_rrule2 (flat(map (mk_rrule ctxt) rews)) val Simpset({rules, ...},_) = simpset_of ctxt in exists (present ctxt rules) rrules end *) in fun ctxt addsimps thms = comb_simps ctxt insert_rrule (mk_rrule ctxt) false thms; fun addsymsimps ctxt thms = comb_simps ctxt insert_rrule (mk_rrule ctxt) true thms; fun ctxt delsimps thms = comb_simps ctxt (del_rrule true) (map mk_rrule2 o mk_rrule ctxt) false thms; fun delsimps_quiet ctxt thms = comb_simps ctxt (del_rrule false) (map mk_rrule2 o mk_rrule ctxt) false thms; fun add_simp thm ctxt = ctxt addsimps [thm]; (* with check for presence of symmetric version: if sym_present ctxt [thm] then (cond_warning ctxt (fn () => print_thm ctxt "Ignoring rewrite rule:" ("", thm)); ctxt) else ctxt addsimps [thm]; *) fun del_simp thm ctxt = ctxt delsimps [thm]; fun flip_simp thm ctxt = addsymsimps (delsimps_quiet ctxt [thm]) [thm]; end; fun init_simpset thms ctxt = ctxt |> Context_Position.set_visible false |> empty_simpset |> fold add_simp thms |> Context_Position.restore_visible ctxt; (* congs *) local fun is_full_cong_prems [] [] = true | is_full_cong_prems [] _ = false | is_full_cong_prems (p :: prems) varpairs = (case Logic.strip_assums_concl p of Const ("Pure.eq", _) $ lhs $ rhs => let val (x, xs) = strip_comb lhs and (y, ys) = strip_comb rhs in is_Var x andalso forall is_Bound xs andalso not (has_duplicates (op =) xs) andalso xs = ys andalso member (op =) varpairs (x, y) andalso is_full_cong_prems prems (remove (op =) (x, y) varpairs) end | _ => false); fun is_full_cong thm = let val prems = Thm.prems_of thm and concl = Thm.concl_of thm; val (lhs, rhs) = Logic.dest_equals concl; val (f, xs) = strip_comb lhs and (g, ys) = strip_comb rhs; in f = g andalso not (has_duplicates (op =) (xs @ ys)) andalso length xs = length ys andalso is_full_cong_prems prems (xs ~~ ys) end; fun mk_cong ctxt = let val Simpset (_, {mk_rews = {mk_cong = f, ...}, ...}) = simpset_of ctxt in f ctxt end; in fun add_eqcong thm ctxt = ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) => let val (lhs, _) = Logic.dest_equals (Thm.concl_of thm) handle TERM _ => raise SIMPLIFIER ("Congruence not a meta-equality", [thm]); (*val lhs = Envir.eta_contract lhs;*) val a = the (cong_name (head_of lhs)) handle Option.Option => raise SIMPLIFIER ("Congruence must start with a constant or free variable", [thm]); val (xs, weak) = congs; val xs' = Congtab.update (a, Thm.trim_context thm) xs; val weak' = if is_full_cong thm then weak else a :: weak; in ((xs', weak'), procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) end); fun del_eqcong thm ctxt = ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) => let val (lhs, _) = Logic.dest_equals (Thm.concl_of thm) handle TERM _ => raise SIMPLIFIER ("Congruence not a meta-equality", [thm]); (*val lhs = Envir.eta_contract lhs;*) val a = the (cong_name (head_of lhs)) handle Option.Option => raise SIMPLIFIER ("Congruence must start with a constant", [thm]); val (xs, _) = congs; val xs' = Congtab.delete_safe a xs; val weak' = Congtab.fold (fn (a, th) => if is_full_cong th then I else insert (op =) a) xs' []; in ((xs', weak'), procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) end); fun add_cong thm ctxt = add_eqcong (mk_cong ctxt thm) ctxt; fun del_cong thm ctxt = del_eqcong (mk_cong ctxt thm) ctxt; end; (* simprocs *) datatype simproc = Simproc of {name: string, lhss: term list, proc: morphism -> Proof.context -> cterm -> thm option, stamp: stamp}; fun eq_simproc (Simproc {stamp = stamp1, ...}, Simproc {stamp = stamp2, ...}) = stamp1 = stamp2; fun cert_simproc thy name {lhss, proc} = Simproc {name = name, lhss = map (Sign.cert_term thy) lhss, proc = proc, stamp = stamp ()}; fun transform_simproc phi (Simproc {name, lhss, proc, stamp}) = Simproc {name = name, lhss = map (Morphism.term phi) lhss, proc = Morphism.transform phi proc, stamp = stamp}; local fun add_proc (proc as Proc {name, lhs, ...}) ctxt = (cond_tracing ctxt (fn () => print_term ctxt ("Adding simplification procedure " ^ quote name ^ " for") lhs); ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) => (congs, Net.insert_term eq_proc (lhs, proc) procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers)) handle Net.INSERT => (cond_warning ctxt (fn () => "Ignoring duplicate simplification procedure " ^ quote name); ctxt)); fun del_proc (proc as Proc {name, lhs, ...}) ctxt = ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) => (congs, Net.delete_term eq_proc (lhs, proc) procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers)) handle Net.DELETE => (cond_warning ctxt (fn () => "Simplification procedure " ^ quote name ^ " not in simpset"); ctxt); fun prep_procs (Simproc {name, lhss, proc, stamp}) = lhss |> map (fn lhs => Proc {name = name, lhs = lhs, proc = Morphism.form proc, stamp = stamp}); in fun ctxt addsimprocs ps = fold (fold add_proc o prep_procs) ps ctxt; fun ctxt delsimprocs ps = fold (fold del_proc o prep_procs) ps ctxt; end; (* mk_rews *) local fun map_mk_rews f = map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) => let val {mk, mk_cong, mk_sym, mk_eq_True, reorient} = mk_rews; val (mk', mk_cong', mk_sym', mk_eq_True', reorient') = f (mk, mk_cong, mk_sym, mk_eq_True, reorient); val mk_rews' = {mk = mk', mk_cong = mk_cong', mk_sym = mk_sym', mk_eq_True = mk_eq_True', reorient = reorient'}; in (congs, procs, mk_rews', term_ord, subgoal_tac, loop_tacs, solvers) end); in fun mksimps ctxt = let val Simpset (_, {mk_rews = {mk, ...}, ...}) = simpset_of ctxt in mk ctxt end; fun set_mksimps mk = map_mk_rews (fn (_, mk_cong, mk_sym, mk_eq_True, reorient) => (mk, mk_cong, mk_sym, mk_eq_True, reorient)); fun set_mkcong mk_cong = map_mk_rews (fn (mk, _, mk_sym, mk_eq_True, reorient) => (mk, mk_cong, mk_sym, mk_eq_True, reorient)); fun set_mksym mk_sym = map_mk_rews (fn (mk, mk_cong, _, mk_eq_True, reorient) => (mk, mk_cong, mk_sym, mk_eq_True, reorient)); fun set_mkeqTrue mk_eq_True = map_mk_rews (fn (mk, mk_cong, mk_sym, _, reorient) => (mk, mk_cong, mk_sym, mk_eq_True, reorient)); fun set_reorient reorient = map_mk_rews (fn (mk, mk_cong, mk_sym, mk_eq_True, _) => (mk, mk_cong, mk_sym, mk_eq_True, reorient)); end; (* term_ord *) fun set_term_ord term_ord = map_simpset2 (fn (congs, procs, mk_rews, _, subgoal_tac, loop_tacs, solvers) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers)); (* tactics *) fun set_subgoaler subgoal_tac = map_simpset2 (fn (congs, procs, mk_rews, term_ord, _, loop_tacs, solvers) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers)); fun ctxt setloop tac = ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, _, solvers) => (congs, procs, mk_rews, term_ord, subgoal_tac, [("", tac)], solvers)); fun ctxt addloop (name, tac) = ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) => (congs, procs, mk_rews, term_ord, subgoal_tac, AList.update (op =) (name, tac) loop_tacs, solvers)); fun ctxt delloop name = ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, solvers) => (congs, procs, mk_rews, term_ord, subgoal_tac, (if AList.defined (op =) loop_tacs name then () else cond_warning ctxt (fn () => "No such looper in simpset: " ^ quote name); AList.delete (op =) name loop_tacs), solvers)); fun ctxt setSSolver solver = ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (unsafe_solvers, _)) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (unsafe_solvers, [solver]))); fun ctxt addSSolver solver = ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (unsafe_solvers, insert eq_solver solver solvers))); fun ctxt setSolver solver = ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (_, solvers)) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, ([solver], solvers))); fun ctxt addSolver solver = ctxt |> map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (insert eq_solver solver unsafe_solvers, solvers))); fun set_solvers solvers = map_simpset2 (fn (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, _) => (congs, procs, mk_rews, term_ord, subgoal_tac, loop_tacs, (solvers, solvers))); (* trace operations *) type trace_ops = {trace_invoke: {depth: int, term: term} -> Proof.context -> Proof.context, trace_apply: {unconditional: bool, term: term, thm: thm, rrule: rrule} -> Proof.context -> (Proof.context -> (thm * term) option) -> (thm * term) option}; structure Trace_Ops = Theory_Data ( type T = trace_ops; val empty: T = {trace_invoke = fn _ => fn ctxt => ctxt, trace_apply = fn _ => fn ctxt => fn cont => cont ctxt}; val extend = I; fun merge (trace_ops, _) = trace_ops; ); val set_trace_ops = Trace_Ops.put; val trace_ops = Trace_Ops.get o Proof_Context.theory_of; fun trace_invoke args ctxt = #trace_invoke (trace_ops ctxt) args ctxt; fun trace_apply args ctxt = #trace_apply (trace_ops ctxt) args ctxt; (** rewriting **) (* Uses conversions, see: L C Paulson, A higher-order implementation of rewriting, Science of Computer Programming 3 (1983), pages 119-149. *) fun check_conv ctxt msg thm thm' = let val thm'' = Thm.transitive thm thm' handle THM _ => let val nthm' = Thm.transitive (Thm.symmetric (Drule.beta_eta_conversion (Thm.lhs_of thm'))) thm' in Thm.transitive thm nthm' handle THM _ => let val nthm = Thm.transitive thm (Drule.beta_eta_conversion (Thm.rhs_of thm)) in Thm.transitive nthm nthm' end end val _ = if msg then cond_tracing ctxt (fn () => print_thm ctxt "SUCCEEDED" ("", thm')) else (); in SOME thm'' end handle THM _ => let val _ $ _ $ prop0 = Thm.prop_of thm; val _ = cond_tracing ctxt (fn () => print_thm ctxt "Proved wrong theorem (bad subgoaler?)" ("", thm') ^ "\n" ^ print_term ctxt "Should have proved:" prop0); in NONE end; (* mk_procrule *) fun mk_procrule ctxt thm = let val (prems, lhs, elhs, rhs, _) = decomp_simp thm val thm' = Thm.close_derivation \<^here> thm; in if rewrite_rule_extra_vars prems lhs rhs then (cond_warning ctxt (fn () => print_thm ctxt "Extra vars on rhs:" ("", thm)); []) else [mk_rrule2 {thm = thm', name = "", lhs = lhs, elhs = elhs, perm = false}] end; (* rewritec: conversion to apply the meta simpset to a term *) (*Since the rewriting strategy is bottom-up, we avoid re-normalizing already normalized terms by carrying around the rhs of the rewrite rule just applied. This is called the `skeleton'. It is decomposed in parallel with the term. Once a Var is encountered, the corresponding term is already in normal form. skel0 is a dummy skeleton that is to enforce complete normalization.*) val skel0 = Bound 0; (*Use rhs as skeleton only if the lhs does not contain unnormalized bits. The latter may happen iff there are weak congruence rules for constants in the lhs.*) fun uncond_skel ((_, weak), (lhs, rhs)) = if null weak then rhs (*optimization*) else if exists_subterm (fn Const (a, _) => member (op =) weak (true, a) | Free (a, _) => member (op =) weak (false, a) | _ => false) lhs then skel0 else rhs; (*Behaves like unconditional rule if rhs does not contain vars not in the lhs. Otherwise those vars may become instantiated with unnormalized terms while the premises are solved.*) fun cond_skel (args as (_, (lhs, rhs))) = if subset (op =) (Term.add_vars rhs [], Term.add_vars lhs []) then uncond_skel args else skel0; (* Rewriting -- we try in order: (1) beta reduction (2) unconditional rewrite rules (3) conditional rewrite rules (4) simplification procedures IMPORTANT: rewrite rules must not introduce new Vars or TVars! *) fun rewritec (prover, maxt) ctxt t = let val thy = Proof_Context.theory_of ctxt; val Simpset ({rules, ...}, {congs, procs, term_ord, ...}) = simpset_of ctxt; val eta_thm = Thm.eta_conversion t; val eta_t' = Thm.rhs_of eta_thm; val eta_t = Thm.term_of eta_t'; fun rew rrule = let val {thm = thm0, name, lhs, elhs = elhs0, extra, fo, perm} = rrule; val thm = Thm.transfer thy thm0; val elhs = Thm.transfer_cterm thy elhs0; val prop = Thm.prop_of thm; val (rthm, elhs') = if maxt = ~1 orelse not extra then (thm, elhs) else (Thm.incr_indexes (maxt + 1) thm, Thm.incr_indexes_cterm (maxt + 1) elhs); val insts = if fo then Thm.first_order_match (elhs', eta_t') else Thm.match (elhs', eta_t'); val thm' = Thm.instantiate insts (Thm.rename_boundvars lhs eta_t rthm); val prop' = Thm.prop_of thm'; val unconditional = (Logic.count_prems prop' = 0); val (lhs', rhs') = Logic.dest_equals (Logic.strip_imp_concl prop'); val trace_args = {unconditional = unconditional, term = eta_t, thm = thm', rrule = rrule}; in if perm andalso is_greater_equal (term_ord (rhs', lhs')) then (cond_tracing ctxt (fn () => print_thm ctxt "Cannot apply permutative rewrite rule" (name, thm) ^ "\n" ^ print_thm ctxt "Term does not become smaller:" ("", thm')); NONE) else (cond_tracing ctxt (fn () => print_thm ctxt "Applying instance of rewrite rule" (name, thm)); if unconditional then (cond_tracing ctxt (fn () => print_thm ctxt "Rewriting:" ("", thm')); trace_apply trace_args ctxt (fn ctxt' => let val lr = Logic.dest_equals prop; val SOME thm'' = check_conv ctxt' false eta_thm thm'; in SOME (thm'', uncond_skel (congs, lr)) end)) else (cond_tracing ctxt (fn () => print_thm ctxt "Trying to rewrite:" ("", thm')); if simp_depth ctxt > Config.get ctxt simp_depth_limit then (cond_tracing ctxt (fn () => "simp_depth_limit exceeded - giving up"); NONE) else trace_apply trace_args ctxt (fn ctxt' => (case prover ctxt' thm' of NONE => (cond_tracing ctxt' (fn () => print_thm ctxt' "FAILED" ("", thm')); NONE) | SOME thm2 => (case check_conv ctxt' true eta_thm thm2 of NONE => NONE | SOME thm2' => let val concl = Logic.strip_imp_concl prop; val lr = Logic.dest_equals concl; in SOME (thm2', cond_skel (congs, lr)) end))))) end; fun rews [] = NONE | rews (rrule :: rrules) = let val opt = rew rrule handle Pattern.MATCH => NONE in (case opt of NONE => rews rrules | some => some) end; fun sort_rrules rrs = let fun is_simple ({thm, ...}: rrule) = (case Thm.prop_of thm of Const ("Pure.eq", _) $ _ $ _ => true | _ => false); fun sort [] (re1, re2) = re1 @ re2 | sort (rr :: rrs) (re1, re2) = if is_simple rr then sort rrs (rr :: re1, re2) else sort rrs (re1, rr :: re2); in sort rrs ([], []) end; fun proc_rews [] = NONE | proc_rews (Proc {name, proc, lhs, ...} :: ps) = if Pattern.matches (Proof_Context.theory_of ctxt) (lhs, Thm.term_of t) then (cond_tracing' ctxt simp_debug (fn () => print_term ctxt ("Trying procedure " ^ quote name ^ " on:") eta_t); (case proc ctxt eta_t' of NONE => (cond_tracing' ctxt simp_debug (fn () => "FAILED"); proc_rews ps) | SOME raw_thm => (cond_tracing ctxt (fn () => print_thm ctxt ("Procedure " ^ quote name ^ " produced rewrite rule:") ("", raw_thm)); (case rews (mk_procrule ctxt raw_thm) of NONE => (cond_tracing ctxt (fn () => print_term ctxt ("IGNORED result of simproc " ^ quote name ^ " -- does not match") (Thm.term_of t)); proc_rews ps) | some => some)))) else proc_rews ps; in (case eta_t of Abs _ $ _ => SOME (Thm.transitive eta_thm (Thm.beta_conversion false eta_t'), skel0) | _ => (case rews (sort_rrules (Net.match_term rules eta_t)) of NONE => proc_rews (Net.match_term procs eta_t) | some => some)) end; (* conversion to apply a congruence rule to a term *) fun congc prover ctxt maxt cong t = let val rthm = Thm.incr_indexes (maxt + 1) cong; val rlhs = fst (Thm.dest_equals (Drule.strip_imp_concl (Thm.cprop_of rthm))); val insts = Thm.match (rlhs, t) (* Thm.match can raise Pattern.MATCH; is handled when congc is called *) val thm' = Thm.instantiate insts (Thm.rename_boundvars (Thm.term_of rlhs) (Thm.term_of t) rthm); val _ = cond_tracing ctxt (fn () => print_thm ctxt "Applying congruence rule:" ("", thm')); fun err (msg, thm) = (cond_tracing ctxt (fn () => print_thm ctxt msg ("", thm)); NONE); in (case prover thm' of NONE => err ("Congruence proof failed. Could not prove", thm') | SOME thm2 => (case check_conv ctxt true (Drule.beta_eta_conversion t) thm2 of NONE => err ("Congruence proof failed. Should not have proved", thm2) | SOME thm2' => if op aconv (apply2 Thm.term_of (Thm.dest_equals (Thm.cprop_of thm2'))) then NONE else SOME thm2')) end; val vA = (("A", 0), propT); val vB = (("B", 0), propT); val vC = (("C", 0), propT); fun transitive1 NONE NONE = NONE | transitive1 (SOME thm1) NONE = SOME thm1 | transitive1 NONE (SOME thm2) = SOME thm2 | transitive1 (SOME thm1) (SOME thm2) = SOME (Thm.transitive thm1 thm2); fun transitive2 thm = transitive1 (SOME thm); fun transitive3 thm = transitive1 thm o SOME; fun bottomc ((simprem, useprem, mutsimp), prover, maxidx) = let fun botc skel ctxt t = if is_Var skel then NONE else (case subc skel ctxt t of some as SOME thm1 => (case rewritec (prover, maxidx) ctxt (Thm.rhs_of thm1) of SOME (thm2, skel2) => transitive2 (Thm.transitive thm1 thm2) (botc skel2 ctxt (Thm.rhs_of thm2)) | NONE => some) | NONE => (case rewritec (prover, maxidx) ctxt t of SOME (thm2, skel2) => transitive2 thm2 (botc skel2 ctxt (Thm.rhs_of thm2)) | NONE => NONE)) and try_botc ctxt t = (case botc skel0 ctxt t of SOME trec1 => trec1 | NONE => Thm.reflexive t) and subc skel ctxt t0 = let val Simpset (_, {congs, ...}) = simpset_of ctxt in (case Thm.term_of t0 of Abs (a, T, _) => let val (v, ctxt') = Variable.next_bound (a, T) ctxt; val b = #1 (Term.dest_Free v); val (v', t') = Thm.dest_abs (SOME b) t0; val b' = #1 (Term.dest_Free (Thm.term_of v')); val _ = if b <> b' then warning ("Bad Simplifier context: renamed bound variable " ^ quote b ^ " to " ^ quote b' ^ Position.here (Position.thread_data ())) else (); val skel' = (case skel of Abs (_, _, sk) => sk | _ => skel0); in (case botc skel' ctxt' t' of SOME thm => SOME (Thm.abstract_rule a v' thm) | NONE => NONE) end | t $ _ => (case t of Const ("Pure.imp", _) $ _ => impc t0 ctxt | Abs _ => let val thm = Thm.beta_conversion false t0 in (case subc skel0 ctxt (Thm.rhs_of thm) of NONE => SOME thm | SOME thm' => SOME (Thm.transitive thm thm')) end | _ => let fun appc () = let val (tskel, uskel) = (case skel of tskel $ uskel => (tskel, uskel) | _ => (skel0, skel0)); val (ct, cu) = Thm.dest_comb t0; in (case botc tskel ctxt ct of SOME thm1 => (case botc uskel ctxt cu of SOME thm2 => SOME (Thm.combination thm1 thm2) | NONE => SOME (Thm.combination thm1 (Thm.reflexive cu))) | NONE => (case botc uskel ctxt cu of SOME thm1 => SOME (Thm.combination (Thm.reflexive ct) thm1) | NONE => NONE)) end; val (h, ts) = strip_comb t; in (case cong_name h of SOME a => (case Congtab.lookup (fst congs) a of NONE => appc () | SOME cong => (*post processing: some partial applications h t1 ... tj, j <= length ts, may be a redex. Example: map (\x. x) = (\xs. xs) wrt map_cong*) (let val thm = congc (prover ctxt) ctxt maxidx cong t0; val t = the_default t0 (Option.map Thm.rhs_of thm); val (cl, cr) = Thm.dest_comb t val dVar = Var(("", 0), dummyT) val skel = list_comb (h, replicate (length ts) dVar) in (case botc skel ctxt cl of NONE => thm | SOME thm' => transitive3 thm (Thm.combination thm' (Thm.reflexive cr))) end handle Pattern.MATCH => appc ())) | _ => appc ()) end) | _ => NONE) end and impc ct ctxt = if mutsimp then mut_impc0 [] ct [] [] ctxt else nonmut_impc ct ctxt and rules_of_prem prem ctxt = if maxidx_of_term (Thm.term_of prem) <> ~1 then (cond_tracing ctxt (fn () => print_term ctxt "Cannot add premise as rewrite rule because it contains (type) unknowns:" (Thm.term_of prem)); (([], NONE), ctxt)) else let val (asm, ctxt') = Thm.assume_hyps prem ctxt in ((extract_safe_rrules ctxt' asm, SOME asm), ctxt') end and add_rrules (rrss, asms) ctxt = (fold o fold) insert_rrule rrss ctxt |> add_prems (map_filter I asms) and disch r prem eq = let val (lhs, rhs) = Thm.dest_equals (Thm.cprop_of eq); val eq' = Thm.implies_elim (Thm.instantiate ([], [(vA, prem), (vB, lhs), (vC, rhs)]) Drule.imp_cong) (Thm.implies_intr prem eq); in if not r then eq' else let val (prem', concl) = Thm.dest_implies lhs; val (prem'', _) = Thm.dest_implies rhs; in Thm.transitive (Thm.transitive (Thm.instantiate ([], [(vA, prem'), (vB, prem), (vC, concl)]) Drule.swap_prems_eq) eq') (Thm.instantiate ([], [(vA, prem), (vB, prem''), (vC, concl)]) Drule.swap_prems_eq) end end and rebuild [] _ _ _ _ eq = eq | rebuild (prem :: prems) concl (_ :: rrss) (_ :: asms) ctxt eq = let val ctxt' = add_rrules (rev rrss, rev asms) ctxt; val concl' = Drule.mk_implies (prem, the_default concl (Option.map Thm.rhs_of eq)); val dprem = Option.map (disch false prem); in (case rewritec (prover, maxidx) ctxt' concl' of NONE => rebuild prems concl' rrss asms ctxt (dprem eq) | SOME (eq', _) => transitive2 (fold (disch false) prems (the (transitive3 (dprem eq) eq'))) (mut_impc0 (rev prems) (Thm.rhs_of eq') (rev rrss) (rev asms) ctxt)) end and mut_impc0 prems concl rrss asms ctxt = let val prems' = strip_imp_prems concl; val ((rrss', asms'), ctxt') = fold_map rules_of_prem prems' ctxt |>> split_list; in mut_impc (prems @ prems') (strip_imp_concl concl) (rrss @ rrss') (asms @ asms') [] [] [] [] ctxt' ~1 ~1 end and mut_impc [] concl [] [] prems' rrss' asms' eqns ctxt changed k = transitive1 (fold (fn (eq1, prem) => fn eq2 => transitive1 eq1 (Option.map (disch false prem) eq2)) (eqns ~~ prems') NONE) (if changed > 0 then mut_impc (rev prems') concl (rev rrss') (rev asms') [] [] [] [] ctxt ~1 changed else rebuild prems' concl rrss' asms' ctxt (botc skel0 (add_rrules (rev rrss', rev asms') ctxt) concl)) | mut_impc (prem :: prems) concl (rrs :: rrss) (asm :: asms) prems' rrss' asms' eqns ctxt changed k = (case (if k = 0 then NONE else botc skel0 (add_rrules (rev rrss' @ rrss, rev asms' @ asms) ctxt) prem) of NONE => mut_impc prems concl rrss asms (prem :: prems') (rrs :: rrss') (asm :: asms') (NONE :: eqns) ctxt changed (if k = 0 then 0 else k - 1) | SOME eqn => let val prem' = Thm.rhs_of eqn; val tprems = map Thm.term_of prems; val i = 1 + fold Integer.max (map (fn p => find_index (fn q => q aconv p) tprems) (Thm.hyps_of eqn)) ~1; val ((rrs', asm'), ctxt') = rules_of_prem prem' ctxt; in mut_impc prems concl rrss asms (prem' :: prems') (rrs' :: rrss') (asm' :: asms') (SOME (fold_rev (disch true) (take i prems) (Drule.imp_cong_rule eqn (Thm.reflexive (Drule.list_implies (drop i prems, concl))))) :: eqns) ctxt' (length prems') ~1 end) (*legacy code -- only for backwards compatibility*) and nonmut_impc ct ctxt = let val (prem, conc) = Thm.dest_implies ct; val thm1 = if simprem then botc skel0 ctxt prem else NONE; val prem1 = the_default prem (Option.map Thm.rhs_of thm1); val ctxt1 = if not useprem then ctxt else let val ((rrs, asm), ctxt') = rules_of_prem prem1 ctxt in add_rrules ([rrs], [asm]) ctxt' end; in (case botc skel0 ctxt1 conc of NONE => (case thm1 of NONE => NONE | SOME thm1' => SOME (Drule.imp_cong_rule thm1' (Thm.reflexive conc))) | SOME thm2 => let val thm2' = disch false prem1 thm2 in (case thm1 of NONE => SOME thm2' | SOME thm1' => SOME (Thm.transitive (Drule.imp_cong_rule thm1' (Thm.reflexive conc)) thm2')) end) end; in try_botc end; (* Meta-rewriting: rewrites t to u and returns the theorem t \ u *) (* Parameters: mode = (simplify A, use A in simplifying B, use prems of B (if B is again a meta-impl.) to simplify A) when simplifying A \ B prover: how to solve premises in conditional rewrites and congruences *) fun rewrite_cterm mode prover raw_ctxt raw_ct = let val thy = Proof_Context.theory_of raw_ctxt; val ct = raw_ct |> Thm.transfer_cterm thy |> Thm.adjust_maxidx_cterm ~1; val maxidx = Thm.maxidx_of_cterm ct; val ctxt = raw_ctxt |> Variable.set_body true |> Context_Position.set_visible false |> inc_simp_depth |> (fn ctxt => trace_invoke {depth = simp_depth ctxt, term = Thm.term_of ct} ctxt); val _ = cond_tracing ctxt (fn () => print_term ctxt "SIMPLIFIER INVOKED ON THE FOLLOWING TERM:" (Thm.term_of ct)); in ct |> bottomc (mode, Option.map (Drule.flexflex_unique (SOME ctxt)) oo prover, maxidx) ctxt |> Thm.solve_constraints end; val simple_prover = SINGLE o (fn ctxt => ALLGOALS (resolve_tac ctxt (prems_of ctxt))); fun rewrite _ _ [] = Thm.reflexive | rewrite ctxt full thms = rewrite_cterm (full, false, false) simple_prover (init_simpset thms ctxt); fun rewrite_rule ctxt = Conv.fconv_rule o rewrite ctxt true; (*simple term rewriting -- no proof*) fun rewrite_term thy rules procs = Pattern.rewrite_term thy (map decomp_simp' rules) procs; fun rewrite_thm mode prover ctxt = Conv.fconv_rule (rewrite_cterm mode prover ctxt); (*Rewrite the subgoals of a proof state (represented by a theorem)*) fun rewrite_goals_rule ctxt thms th = Conv.fconv_rule (Conv.prems_conv ~1 (rewrite_cterm (true, true, true) simple_prover (init_simpset thms ctxt))) th; (** meta-rewriting tactics **) (*Rewrite all subgoals*) fun rewrite_goals_tac ctxt defs = PRIMITIVE (rewrite_goals_rule ctxt defs); (*Rewrite one subgoal*) fun generic_rewrite_goal_tac mode prover_tac ctxt i thm = if 0 < i andalso i <= Thm.nprems_of thm then Seq.single (Conv.gconv_rule (rewrite_cterm mode (SINGLE o prover_tac) ctxt) i thm) else Seq.empty; fun rewrite_goal_tac ctxt thms = generic_rewrite_goal_tac (true, false, false) (K no_tac) (init_simpset thms ctxt); (*Prunes all redundant parameters from the proof state by rewriting.*) fun prune_params_tac ctxt = rewrite_goals_tac ctxt [Drule.triv_forall_equality]; (* for folding definitions, handling critical pairs *) (*The depth of nesting in a term*) fun term_depth (Abs (_, _, t)) = 1 + term_depth t | term_depth (f $ t) = 1 + Int.max (term_depth f, term_depth t) | term_depth _ = 0; val lhs_of_thm = #1 o Logic.dest_equals o Thm.prop_of; (*folding should handle critical pairs! E.g. K \ Inl 0, S \ Inr (Inl 0) Returns longest lhs first to avoid folding its subexpressions.*) fun sort_lhs_depths defs = let val keylist = AList.make (term_depth o lhs_of_thm) defs val keys = sort_distinct (rev_order o int_ord) (map #2 keylist) in map (AList.find (op =) keylist) keys end; val rev_defs = sort_lhs_depths o map Thm.symmetric; fun fold_rule ctxt defs = fold (rewrite_rule ctxt) (rev_defs defs); fun fold_goals_tac ctxt defs = EVERY (map (rewrite_goals_tac ctxt) (rev_defs defs)); (* HHF normal form: \ before \, outermost \ generalized *) local fun gen_norm_hhf ss ctxt0 th0 = let val (ctxt, th) = Thm.join_transfer_context (ctxt0, th0); val th' = if Drule.is_norm_hhf (Thm.prop_of th) then th else Conv.fconv_rule (rewrite_cterm (true, false, false) (K (K NONE)) (put_simpset ss ctxt)) th; in th' |> Thm.adjust_maxidx_thm ~1 |> Variable.gen_all ctxt end; val hhf_ss = Context.the_local_context () |> init_simpset Drule.norm_hhf_eqs |> simpset_of; val hhf_protect_ss = Context.the_local_context () |> init_simpset Drule.norm_hhf_eqs |> add_eqcong Drule.protect_cong |> simpset_of; in val norm_hhf = gen_norm_hhf hhf_ss; val norm_hhf_protect = gen_norm_hhf hhf_protect_ss; end; end; structure Basic_Meta_Simplifier: BASIC_RAW_SIMPLIFIER = Raw_Simplifier; open Basic_Meta_Simplifier;