--- a/src/Pure/meta_simplifier.ML Fri Dec 17 18:32:40 2010 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1379 +0,0 @@
-(* Title: Pure/meta_simplifier.ML
- Author: Tobias Nipkow and Stefan Berghofer, TU Muenchen
-
-Meta-level Simplification.
-*)
-
-infix 4
- addsimps delsimps addeqcongs deleqcongs addcongs delcongs addsimprocs delsimprocs
- setmksimps setmkcong setmksym setmkeqTrue settermless setsubgoaler
- setloop' setloop addloop addloop' delloop setSSolver addSSolver setSolver addSolver;
-
-signature BASIC_META_SIMPLIFIER =
-sig
- val simp_debug: bool Config.T
- val simp_debug_raw: Config.raw
- val simp_trace: bool Config.T
- val simp_trace_raw: Config.raw
- val simp_trace_default: bool Unsynchronized.ref
- val simp_trace_depth_limit: int Config.T
- val simp_trace_depth_limit_raw: Config.raw
- val simp_trace_depth_limit_default: int Unsynchronized.ref
- type rrule
- val eq_rrule: rrule * rrule -> bool
- type simpset
- type proc
- type solver
- val mk_solver': string -> (simpset -> int -> tactic) -> solver
- val mk_solver: string -> (thm list -> int -> tactic) -> solver
- val empty_ss: simpset
- val merge_ss: simpset * simpset -> simpset
- val dest_ss: simpset ->
- {simps: (string * thm) list,
- procs: (string * cterm list) list,
- congs: (string * thm) list,
- weak_congs: string list,
- loopers: string list,
- unsafe_solvers: string list,
- safe_solvers: string list}
- type simproc
- val eq_simproc: simproc * simproc -> bool
- val morph_simproc: morphism -> simproc -> simproc
- val make_simproc: {name: string, lhss: cterm list,
- proc: morphism -> simpset -> cterm -> thm option, identifier: thm list} -> simproc
- val mk_simproc: string -> cterm list -> (theory -> simpset -> term -> thm option) -> simproc
- val add_prems: thm list -> simpset -> simpset
- val prems_of_ss: simpset -> thm list
- val addsimps: simpset * thm list -> simpset
- val delsimps: simpset * thm list -> simpset
- val addeqcongs: simpset * thm list -> simpset
- val deleqcongs: simpset * thm list -> simpset
- val addcongs: simpset * thm list -> simpset
- val delcongs: simpset * thm list -> simpset
- val addsimprocs: simpset * simproc list -> simpset
- val delsimprocs: simpset * simproc list -> simpset
- val mksimps: simpset -> thm -> thm list
- val setmksimps: simpset * (simpset -> thm -> thm list) -> simpset
- val setmkcong: simpset * (simpset -> thm -> thm) -> simpset
- val setmksym: simpset * (simpset -> thm -> thm option) -> simpset
- val setmkeqTrue: simpset * (simpset -> thm -> thm option) -> simpset
- val settermless: simpset * (term * term -> bool) -> simpset
- val setsubgoaler: simpset * (simpset -> int -> tactic) -> simpset
- val setloop': simpset * (simpset -> int -> tactic) -> simpset
- val setloop: simpset * (int -> tactic) -> simpset
- val addloop': simpset * (string * (simpset -> int -> tactic)) -> simpset
- val addloop: simpset * (string * (int -> tactic)) -> simpset
- val delloop: simpset * string -> simpset
- val setSSolver: simpset * solver -> simpset
- val addSSolver: simpset * solver -> simpset
- val setSolver: simpset * solver -> simpset
- val addSolver: simpset * solver -> simpset
-
- val rewrite_rule: thm list -> thm -> thm
- val rewrite_goals_rule: thm list -> thm -> thm
- val rewrite_goals_tac: thm list -> tactic
- val rewrite_goal_tac: thm list -> int -> tactic
- val rewtac: thm -> tactic
- val prune_params_tac: tactic
- val fold_rule: thm list -> thm -> thm
- val fold_goals_tac: thm list -> tactic
- val norm_hhf: thm -> thm
- val norm_hhf_protect: thm -> thm
-end;
-
-signature META_SIMPLIFIER =
-sig
- include BASIC_META_SIMPLIFIER
- exception SIMPLIFIER of string * thm
- val internal_ss: simpset ->
- {rules: rrule Net.net,
- prems: thm list,
- bounds: int * ((string * typ) * string) list,
- depth: int * bool Unsynchronized.ref,
- context: Proof.context option} *
- {congs: (string * thm) list * string list,
- procs: proc Net.net,
- mk_rews:
- {mk: simpset -> thm -> thm list,
- mk_cong: simpset -> thm -> thm,
- mk_sym: simpset -> thm -> thm option,
- mk_eq_True: simpset -> thm -> thm option,
- reorient: theory -> term list -> term -> term -> bool},
- termless: term * term -> bool,
- subgoal_tac: simpset -> int -> tactic,
- loop_tacs: (string * (simpset -> int -> tactic)) list,
- solvers: solver list * solver list}
- val add_simp: thm -> simpset -> simpset
- val del_simp: thm -> simpset -> simpset
- val solver: simpset -> solver -> int -> tactic
- val simp_depth_limit_raw: Config.raw
- val simp_depth_limit: int Config.T
- val clear_ss: simpset -> simpset
- val simproc_global_i: theory -> string -> term list
- -> (theory -> simpset -> term -> thm option) -> simproc
- val simproc_global: theory -> string -> string list
- -> (theory -> simpset -> term -> thm option) -> simproc
- val inherit_context: simpset -> simpset -> simpset
- val the_context: simpset -> Proof.context
- val context: Proof.context -> simpset -> simpset
- val global_context: theory -> simpset -> simpset
- val with_context: Proof.context -> (simpset -> simpset) -> simpset -> simpset
- val debug_bounds: bool Unsynchronized.ref
- val set_reorient: (theory -> term list -> term -> term -> bool) -> simpset -> simpset
- val set_solvers: solver list -> simpset -> simpset
- val rewrite_cterm: bool * bool * bool -> (simpset -> thm -> thm option) -> simpset -> conv
- val rewrite_term: theory -> thm list -> (term -> term option) list -> term -> term
- val rewrite_thm: bool * bool * bool ->
- (simpset -> thm -> thm option) -> simpset -> thm -> thm
- val rewrite_goal_rule: bool * bool * bool ->
- (simpset -> thm -> thm option) -> simpset -> int -> thm -> thm
- val asm_rewrite_goal_tac: bool * bool * bool ->
- (simpset -> tactic) -> simpset -> int -> tactic
- val rewrite: bool -> thm list -> conv
- val simplify: bool -> thm list -> thm -> thm
-end;
-
-structure MetaSimplifier: META_SIMPLIFIER =
-struct
-
-(** datatype simpset **)
-
-(* 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 etac-contracted lhs*)
- extra: bool, (*extra variables outside of elhs*)
- fo: bool, (*use first-order matching*)
- perm: bool}; (*the rewrite rule is permutative*)
-
-(*
-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);
-
-
-(* simplification sets, procedures, and solvers *)
-
-(*A simpset contains data required during conversion:
- rules: discrimination net of rewrite rules;
- prems: current premises;
- bounds: maximal index of bound variables already used
- (for generating new names when rewriting under lambda abstractions);
- 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;
- termless: relation for ordered rewriting;*)
-
-datatype simpset =
- Simpset of
- {rules: rrule Net.net,
- prems: thm list,
- bounds: int * ((string * typ) * string) list,
- depth: int * bool Unsynchronized.ref,
- context: Proof.context option} *
- {congs: (string * thm) list * string list,
- procs: proc Net.net,
- mk_rews:
- {mk: simpset -> thm -> thm list,
- mk_cong: simpset -> thm -> thm,
- mk_sym: simpset -> thm -> thm option,
- mk_eq_True: simpset -> thm -> thm option,
- reorient: theory -> term list -> term -> term -> bool},
- termless: term * term -> bool,
- subgoal_tac: simpset -> int -> tactic,
- loop_tacs: (string * (simpset -> int -> tactic)) list,
- solvers: solver list * solver list}
-and proc =
- Proc of
- {name: string,
- lhs: cterm,
- proc: simpset -> cterm -> thm option,
- id: stamp * thm list}
-and solver =
- Solver of
- {name: string,
- solver: simpset -> int -> tactic,
- id: stamp};
-
-
-fun internal_ss (Simpset args) = args;
-
-fun make_ss1 (rules, prems, bounds, depth, context) =
- {rules = rules, prems = prems, bounds = bounds, depth = depth, context = context};
-
-fun map_ss1 f {rules, prems, bounds, depth, context} =
- make_ss1 (f (rules, prems, bounds, depth, context));
-
-fun make_ss2 (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =
- {congs = congs, procs = procs, mk_rews = mk_rews, termless = termless,
- subgoal_tac = subgoal_tac, loop_tacs = loop_tacs, solvers = solvers};
-
-fun map_ss2 f {congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers} =
- make_ss2 (f (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
-
-fun make_simpset (args1, args2) = Simpset (make_ss1 args1, make_ss2 args2);
-
-fun map_simpset1 f (Simpset (r1, r2)) = Simpset (map_ss1 f r1, r2);
-fun map_simpset2 f (Simpset (r1, r2)) = Simpset (r1, map_ss2 f r2);
-
-fun prems_of_ss (Simpset ({prems, ...}, _)) = prems;
-
-fun eq_procid ((s1: stamp, ths1: thm list), (s2, ths2)) =
- s1 = s2 andalso eq_list Thm.eq_thm (ths1, ths2);
-fun eq_proc (Proc {id = id1, ...}, Proc {id = id2, ...}) = eq_procid (id1, id2);
-
-fun mk_solver' name solver = Solver {name = name, solver = solver, id = stamp ()};
-fun mk_solver name solver = mk_solver' name (solver o prems_of_ss);
-
-fun solver_name (Solver {name, ...}) = name;
-fun solver ss (Solver {solver = tac, ...}) = tac ss;
-fun eq_solver (Solver {id = id1, ...}, Solver {id = id2, ...}) = (id1 = id2);
-
-
-(* simp depth *)
-
-val simp_depth_limit_raw = Config.declare "simp_depth_limit" (K (Config.Int 100));
-val simp_depth_limit = Config.int simp_depth_limit_raw;
-
-val simp_trace_depth_limit_default = Unsynchronized.ref 1;
-val simp_trace_depth_limit_raw = Config.declare "simp_trace_depth_limit"
- (fn _ => Config.Int (! simp_trace_depth_limit_default));
-val simp_trace_depth_limit = Config.int simp_trace_depth_limit_raw;
-
-fun simp_trace_depth_limit_of NONE = ! simp_trace_depth_limit_default
- | simp_trace_depth_limit_of (SOME ctxt) = Config.get ctxt simp_trace_depth_limit;
-
-fun trace_depth (Simpset ({depth = (depth, exceeded), context, ...}, _)) msg =
- if depth > simp_trace_depth_limit_of context then
- if ! exceeded then () else (tracing "simp_trace_depth_limit exceeded!"; exceeded := true)
- else
- (tracing (enclose "[" "]" (string_of_int depth) ^ msg); exceeded := false);
-
-val inc_simp_depth = map_simpset1 (fn (rules, prems, bounds, (depth, exceeded), context) =>
- (rules, prems, bounds,
- (depth + 1,
- if depth = simp_trace_depth_limit_of context then Unsynchronized.ref false else exceeded), context));
-
-fun simp_depth (Simpset ({depth = (depth, _), ...}, _)) = depth;
-
-
-(* diagnostics *)
-
-exception SIMPLIFIER of string * thm;
-
-val simp_debug_raw = Config.declare "simp_debug" (K (Config.Bool false));
-val simp_debug = Config.bool simp_debug_raw;
-
-val simp_trace_default = Unsynchronized.ref false;
-val simp_trace_raw = Config.declare "simp_trace" (fn _ => Config.Bool (! simp_trace_default));
-val simp_trace = Config.bool simp_trace_raw;
-
-fun if_enabled (Simpset ({context, ...}, _)) flag f =
- (case context of
- SOME ctxt => if Config.get ctxt flag then f ctxt else ()
- | NONE => ())
-
-fun if_visible (Simpset ({context, ...}, _)) f x =
- (case context of
- SOME ctxt => if Context_Position.is_visible ctxt then f x else ()
- | NONE => ());
-
-local
-
-fun prnt ss warn a = if warn then warning a else trace_depth ss a;
-
-fun show_bounds (Simpset ({bounds = (_, bs), ...}, _)) t =
- let
- val names = Term.declare_term_names t Name.context;
- val xs = rev (#1 (Name.variants (rev (map #2 bs)) names));
- fun subst (((b, T), _), x') = (Free (b, T), Syntax.mark_boundT (x', T));
- in Term.subst_atomic (ListPair.map subst (bs, xs)) t end;
-
-fun print_term ss warn a t ctxt = prnt ss warn (a () ^ "\n" ^
- Syntax.string_of_term ctxt
- (if Config.get ctxt simp_debug then t else show_bounds ss t));
-
-in
-
-fun print_term_global ss warn a thy t =
- print_term ss warn (K a) t (ProofContext.init_global thy);
-
-fun debug warn a ss = if_enabled ss simp_debug (fn _ => prnt ss warn (a ()));
-fun trace warn a ss = if_enabled ss simp_trace (fn _ => prnt ss warn (a ()));
-
-fun debug_term warn a ss t = if_enabled ss simp_debug (print_term ss warn a t);
-fun trace_term warn a ss t = if_enabled ss simp_trace (print_term ss warn a t);
-
-fun trace_cterm warn a ss ct =
- if_enabled ss simp_trace (print_term ss warn a (Thm.term_of ct));
-
-fun trace_thm a ss th =
- if_enabled ss simp_trace (print_term ss false a (Thm.full_prop_of th));
-
-fun trace_named_thm a ss (th, name) =
- if_enabled ss simp_trace (print_term ss false
- (fn () => if name = "" then a () else a () ^ " " ^ quote name ^ ":")
- (Thm.full_prop_of th));
-
-fun warn_thm a ss th =
- print_term_global ss true a (Thm.theory_of_thm th) (Thm.full_prop_of th);
-
-fun cond_warn_thm a ss th = if_visible ss (fn () => warn_thm a ss th) ();
-
-end;
-
-
-
-(** simpset operations **)
-
-(* context *)
-
-fun eq_bound (x: string, (y, _)) = x = y;
-
-fun add_bound bound = map_simpset1 (fn (rules, prems, (count, bounds), depth, context) =>
- (rules, prems, (count + 1, bound :: bounds), depth, context));
-
-fun add_prems ths = map_simpset1 (fn (rules, prems, bounds, depth, context) =>
- (rules, ths @ prems, bounds, depth, context));
-
-fun inherit_context (Simpset ({bounds, depth, context, ...}, _)) =
- map_simpset1 (fn (rules, prems, _, _, _) => (rules, prems, bounds, depth, context));
-
-fun the_context (Simpset ({context = SOME ctxt, ...}, _)) = ctxt
- | the_context _ = raise Fail "Simplifier: no proof context in simpset";
-
-fun context ctxt =
- map_simpset1 (fn (rules, prems, bounds, depth, _) => (rules, prems, bounds, depth, SOME ctxt));
-
-val global_context = context o ProofContext.init_global;
-
-fun activate_context thy ss =
- let
- val ctxt = the_context ss;
- val ctxt' = ctxt
- |> Context.raw_transfer (Theory.merge (thy, ProofContext.theory_of ctxt))
- |> Context_Position.set_visible false;
- in context ctxt' ss end;
-
-fun with_context ctxt f ss = inherit_context ss (f (context ctxt ss));
-
-
-(* maintain simp rules *)
-
-(* 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 [] (term_of elhs) (Thm.full_prop_of thm);
-
-fun mk_rrule2 {thm, name, lhs, elhs, perm} =
- let
- val t = 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;
-
-fun del_rrule (rrule as {thm, elhs, ...}) ss =
- ss |> map_simpset1 (fn (rules, prems, bounds, depth, context) =>
- (Net.delete_term eq_rrule (term_of elhs, rrule) rules, prems, bounds, depth, context))
- handle Net.DELETE => (cond_warn_thm "Rewrite rule not in simpset:" ss thm; ss);
-
-fun insert_rrule (rrule as {thm, name, ...}) ss =
- (trace_named_thm (fn () => "Adding rewrite rule") ss (thm, name);
- ss |> map_simpset1 (fn (rules, prems, bounds, depth, context) =>
- let
- val rrule2 as {elhs, ...} = mk_rrule2 rrule;
- val rules' = Net.insert_term eq_rrule (term_of elhs, rrule2) rules;
- in (rules', prems, bounds, depth, context) end)
- handle Net.INSERT => (cond_warn_thm "Ignoring duplicate rewrite rule:" ss thm; ss));
-
-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 []);
-
-(*simple test for looping rewrite rules and stupid orientations*)
-fun default_reorient thy 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 thy (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);
-
-fun decomp_simp thm =
- let
- val thy = Thm.theory_of_thm thm;
- 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 elhs = if term_of elhs aconv term_of lhs then lhs else elhs; (*share identical copies*)
- val erhs = Envir.eta_contract (term_of rhs);
- val perm =
- var_perm (term_of elhs, erhs) andalso
- not (term_of elhs aconv erhs) andalso
- not (is_Var (term_of elhs));
- in (thy, prems, term_of lhs, elhs, term_of rhs, perm) 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 (ss as Simpset (_, {mk_rews = {mk_eq_True, ...}, ...})) (thm, name) =
- (case mk_eq_True ss 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);
-
-(*create the rewrite rule and possibly also the eq_True variant,
- in case there are extra vars on the rhs*)
-fun rrule_eq_True (thm, name, lhs, elhs, rhs, ss, 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 ss (thm2, name) @ [rrule]
- else [rrule]
- end;
-
-fun mk_rrule ss (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 (term_of elhs)
- then mk_eq_True ss (thm, name)
- else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)
- end;
-
-fun orient_rrule ss (thm, name) =
- let
- val (thy, prems, lhs, elhs, rhs, perm) = decomp_simp thm;
- val Simpset (_, {mk_rews = {reorient, mk_sym, ...}, ...}) = ss;
- in
- if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]
- else if reorient thy prems lhs rhs then
- if reorient thy prems rhs lhs
- then mk_eq_True ss (thm, name)
- else
- (case mk_sym ss thm of
- NONE => []
- | SOME thm' =>
- let val (_, _, lhs', elhs', rhs', _) = decomp_simp thm'
- in rrule_eq_True (thm', name, lhs', elhs', rhs', ss, thm) end)
- else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)
- end;
-
-fun extract_rews (ss as Simpset (_, {mk_rews = {mk, ...}, ...}), thms) =
- maps (fn thm => map (rpair (Thm.get_name_hint thm)) (mk ss thm)) thms;
-
-fun extract_safe_rrules (ss, thm) =
- maps (orient_rrule ss) (extract_rews (ss, [thm]));
-
-
-(* add/del rules explicitly *)
-
-fun comb_simps comb mk_rrule (ss, thms) =
- let
- val rews = extract_rews (ss, thms);
- in fold (fold comb o mk_rrule) rews ss end;
-
-fun ss addsimps thms =
- comb_simps insert_rrule (mk_rrule ss) (ss, thms);
-
-fun ss delsimps thms =
- comb_simps del_rrule (map mk_rrule2 o mk_rrule ss) (ss, thms);
-
-fun add_simp thm ss = ss addsimps [thm];
-fun del_simp thm ss = ss delsimps [thm];
-
-
-(* congs *)
-
-fun cong_name (Const (a, _)) = SOME a
- | cong_name (Free (a, _)) = SOME ("Free: " ^ a)
- | cong_name _ = NONE;
-
-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 ("==", _) $ 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 = prems_of thm and concl = 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 add_cong (ss, thm) = ss |>
- map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
- let
- val (lhs, _) = Thm.dest_equals (Drule.strip_imp_concl (Thm.cprop_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 (term_of lhs))) handle Option.Option =>
- raise SIMPLIFIER ("Congruence must start with a constant or free variable", thm);
- val (xs, weak) = congs;
- val _ =
- if AList.defined (op =) xs a
- then if_visible ss warning ("Overwriting congruence rule for " ^ quote a)
- else ();
- val xs' = AList.update (op =) (a, thm) xs;
- val weak' = if is_full_cong thm then weak else a :: weak;
- in ((xs', weak'), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);
-
-fun del_cong (ss, thm) = ss |>
- map_simpset2 (fn (congs, procs, mk_rews, termless, 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' = filter_out (fn (x : string, _) => x = a) xs;
- val weak' = xs' |> map_filter (fn (a, thm) =>
- if is_full_cong thm then NONE else SOME a);
- in ((xs', weak'), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);
-
-fun mk_cong (ss as Simpset (_, {mk_rews = {mk_cong = f, ...}, ...})) = f ss;
-
-in
-
-val (op addeqcongs) = Library.foldl add_cong;
-val (op deleqcongs) = Library.foldl del_cong;
-
-fun ss addcongs congs = ss addeqcongs map (mk_cong ss) congs;
-fun ss delcongs congs = ss deleqcongs map (mk_cong ss) congs;
-
-end;
-
-
-(* simprocs *)
-
-datatype simproc =
- Simproc of
- {name: string,
- lhss: cterm list,
- proc: morphism -> simpset -> cterm -> thm option,
- id: stamp * thm list};
-
-fun eq_simproc (Simproc {id = id1, ...}, Simproc {id = id2, ...}) = eq_procid (id1, id2);
-
-fun morph_simproc phi (Simproc {name, lhss, proc, id = (s, ths)}) =
- Simproc
- {name = name,
- lhss = map (Morphism.cterm phi) lhss,
- proc = Morphism.transform phi proc,
- id = (s, Morphism.fact phi ths)};
-
-fun make_simproc {name, lhss, proc, identifier} =
- Simproc {name = name, lhss = lhss, proc = proc, id = (stamp (), identifier)};
-
-fun mk_simproc name lhss proc =
- make_simproc {name = name, lhss = lhss, proc = fn _ => fn ss => fn ct =>
- proc (ProofContext.theory_of (the_context ss)) ss (Thm.term_of ct), identifier = []};
-
-(* FIXME avoid global thy and Logic.varify_global *)
-fun simproc_global_i thy name = mk_simproc name o map (Thm.cterm_of thy o Logic.varify_global);
-fun simproc_global thy name = simproc_global_i thy name o map (Syntax.read_term_global thy);
-
-
-local
-
-fun add_proc (proc as Proc {name, lhs, ...}) ss =
- (trace_cterm false (fn () => "Adding simplification procedure " ^ quote name ^ " for") ss lhs;
- map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
- (congs, Net.insert_term eq_proc (term_of lhs, proc) procs,
- mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
- handle Net.INSERT =>
- (if_visible ss warning ("Ignoring duplicate simplification procedure " ^ quote name); ss));
-
-fun del_proc (proc as Proc {name, lhs, ...}) ss =
- map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
- (congs, Net.delete_term eq_proc (term_of lhs, proc) procs,
- mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
- handle Net.DELETE =>
- (if_visible ss warning ("Simplification procedure " ^ quote name ^ " not in simpset"); ss);
-
-fun prep_procs (Simproc {name, lhss, proc, id}) =
- lhss |> map (fn lhs => Proc {name = name, lhs = lhs, proc = Morphism.form proc, id = id});
-
-in
-
-fun ss addsimprocs ps = fold (fold add_proc o prep_procs) ps ss;
-fun ss delsimprocs ps = fold (fold del_proc o prep_procs) ps ss;
-
-end;
-
-
-(* mk_rews *)
-
-local
-
-fun map_mk_rews f = map_simpset2 (fn (congs, procs, {mk, mk_cong, mk_sym, mk_eq_True, reorient},
- termless, subgoal_tac, loop_tacs, solvers) =>
- let
- 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', termless, subgoal_tac, loop_tacs, solvers) end);
-
-in
-
-fun mksimps (ss as Simpset (_, {mk_rews = {mk, ...}, ...})) = mk ss;
-
-fun ss setmksimps mk = ss |> map_mk_rews (fn (_, mk_cong, mk_sym, mk_eq_True, reorient) =>
- (mk, mk_cong, mk_sym, mk_eq_True, reorient));
-
-fun ss setmkcong mk_cong = ss |> map_mk_rews (fn (mk, _, mk_sym, mk_eq_True, reorient) =>
- (mk, mk_cong, mk_sym, mk_eq_True, reorient));
-
-fun ss setmksym mk_sym = ss |> map_mk_rews (fn (mk, mk_cong, _, mk_eq_True, reorient) =>
- (mk, mk_cong, mk_sym, mk_eq_True, reorient));
-
-fun ss setmkeqTrue mk_eq_True = ss |> 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;
-
-
-(* termless *)
-
-fun ss settermless termless = ss |>
- map_simpset2 (fn (congs, procs, mk_rews, _, subgoal_tac, loop_tacs, solvers) =>
- (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
-
-
-(* tactics *)
-
-fun ss setsubgoaler subgoal_tac = ss |>
- map_simpset2 (fn (congs, procs, mk_rews, termless, _, loop_tacs, solvers) =>
- (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
-
-fun ss setloop' tac = ss |>
- map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, _, solvers) =>
- (congs, procs, mk_rews, termless, subgoal_tac, [("", tac)], solvers));
-
-fun ss setloop tac = ss setloop' (K tac);
-
-fun ss addloop' (name, tac) = ss |>
- map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
- (congs, procs, mk_rews, termless, subgoal_tac,
- (if AList.defined (op =) loop_tacs name
- then if_visible ss warning ("Overwriting looper " ^ quote name)
- else (); AList.update (op =) (name, tac) loop_tacs), solvers));
-
-fun ss addloop (name, tac) = ss addloop' (name, K tac);
-
-fun ss delloop name = ss |>
- map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
- (congs, procs, mk_rews, termless, subgoal_tac,
- (if AList.defined (op =) loop_tacs name then ()
- else if_visible ss warning ("No such looper in simpset: " ^ quote name);
- AList.delete (op =) name loop_tacs), solvers));
-
-fun ss setSSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
- subgoal_tac, loop_tacs, (unsafe_solvers, _)) =>
- (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, (unsafe_solvers, [solver])));
-
-fun ss addSSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
- subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, termless,
- subgoal_tac, loop_tacs, (unsafe_solvers, insert eq_solver solver solvers)));
-
-fun ss setSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
- subgoal_tac, loop_tacs, (_, solvers)) => (congs, procs, mk_rews, termless,
- subgoal_tac, loop_tacs, ([solver], solvers)));
-
-fun ss addSolver solver = ss |> map_simpset2 (fn (congs, procs, mk_rews, termless,
- subgoal_tac, loop_tacs, (unsafe_solvers, solvers)) => (congs, procs, mk_rews, termless,
- subgoal_tac, loop_tacs, (insert eq_solver solver unsafe_solvers, solvers)));
-
-fun set_solvers solvers = map_simpset2 (fn (congs, procs, mk_rews, termless,
- subgoal_tac, loop_tacs, _) => (congs, procs, mk_rews, termless,
- subgoal_tac, loop_tacs, (solvers, solvers)));
-
-
-(* empty *)
-
-fun init_ss mk_rews termless subgoal_tac solvers =
- make_simpset ((Net.empty, [], (0, []), (0, Unsynchronized.ref false), NONE),
- (([], []), Net.empty, mk_rews, termless, subgoal_tac, [], solvers));
-
-fun clear_ss (ss as Simpset (_, {mk_rews, termless, subgoal_tac, solvers, ...})) =
- init_ss mk_rews termless subgoal_tac solvers
- |> inherit_context ss;
-
-val empty_ss =
- init_ss
- {mk = fn _ => fn th => if can Logic.dest_equals (Thm.concl_of th) then [th] else [],
- mk_cong = K I,
- mk_sym = K (SOME o Drule.symmetric_fun),
- mk_eq_True = K (K NONE),
- reorient = default_reorient}
- Term_Ord.termless (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, bounds = bounds1, depth = depth1, context = _},
- {congs = (congs1, weak1), procs = procs1, mk_rews, termless, subgoal_tac,
- loop_tacs = loop_tacs1, solvers = (unsafe_solvers1, solvers1)}) = ss1;
- val Simpset ({rules = rules2, prems = prems2, bounds = bounds2, depth = depth2, context = _},
- {congs = (congs2, weak2), procs = procs2, mk_rews = _, termless = _, 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 bounds' = if #1 bounds1 < #1 bounds2 then bounds2 else bounds1;
- val depth' = if #1 depth1 < #1 depth2 then depth2 else depth1;
- val congs' = merge (Thm.eq_thm_prop o pairself #2) (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', bounds', depth', NONE), ((congs', weak'), procs',
- mk_rews, termless, subgoal_tac, loop_tacs', (unsafe_solvers', solvers')))
- end;
-
-
-(* dest_ss *)
-
-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, id, ...} => ((name, lhs), id))
- |> partition_eq (eq_snd eq_procid)
- |> map (fn ps => (fst (fst (hd ps)), map (snd o fst) ps)),
- congs = #1 congs,
- weak_congs = #2 congs,
- loopers = map fst loop_tacs,
- unsafe_solvers = map solver_name (#1 solvers),
- safe_solvers = map solver_name (#2 solvers)};
-
-
-
-(** 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 msg ss thm thm' =
- let
- val thm'' = Thm.transitive thm thm' handle THM _ =>
- Thm.transitive thm (Thm.transitive
- (Thm.symmetric (Drule.beta_eta_conversion (Thm.lhs_of thm'))) thm')
- in if msg then trace_thm (fn () => "SUCCEEDED") ss thm' else (); SOME thm'' end
- handle THM _ =>
- let
- val _ $ _ $ prop0 = Thm.prop_of thm;
- in
- trace_thm (fn () => "Proved wrong thm (Check subgoaler?)") ss thm';
- trace_term false (fn () => "Should have proved:") ss prop0;
- NONE
- end;
-
-
-(* mk_procrule *)
-
-fun mk_procrule ss thm =
- let val (_, prems, lhs, elhs, rhs, _) = decomp_simp thm in
- if rewrite_rule_extra_vars prems lhs rhs
- then (cond_warn_thm "Extra vars on rhs:" ss 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_Const (member (op =) weak o #1) 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, thyt, maxt) ss t =
- let
- val ctxt = the_context ss;
- val Simpset ({rules, ...}, {congs, procs, termless, ...}) = ss;
- val eta_thm = Thm.eta_conversion t;
- val eta_t' = Thm.rhs_of eta_thm;
- val eta_t = term_of eta_t';
- fun rew {thm, name, lhs, elhs, extra, fo, perm} =
- let
- 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')
- in
- if perm andalso not (termless (rhs', lhs'))
- then (trace_named_thm (fn () => "Cannot apply permutative rewrite rule") ss (thm, name);
- trace_thm (fn () => "Term does not become smaller:") ss thm'; NONE)
- else (trace_named_thm (fn () => "Applying instance of rewrite rule") ss (thm, name);
- if unconditional
- then
- (trace_thm (fn () => "Rewriting:") ss thm';
- let
- val lr = Logic.dest_equals prop;
- val SOME thm'' = check_conv false ss eta_thm thm';
- in SOME (thm'', uncond_skel (congs, lr)) end)
- else
- (trace_thm (fn () => "Trying to rewrite:") ss thm';
- if simp_depth ss > Config.get ctxt simp_depth_limit
- then
- let
- val s = "simp_depth_limit exceeded - giving up";
- val _ = trace false (fn () => s) ss;
- val _ = if_visible ss warning s;
- in NONE end
- else
- case prover ss thm' of
- NONE => (trace_thm (fn () => "FAILED") ss thm'; NONE)
- | SOME thm2 =>
- (case check_conv true ss 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 ("==", _) $ _ $ _ => 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 thyt (Thm.term_of lhs, Thm.term_of t) then
- (debug_term false (fn () => "Trying procedure " ^ quote name ^ " on:") ss eta_t;
- case proc ss eta_t' of
- NONE => (debug false (fn () => "FAILED") ss; proc_rews ps)
- | SOME raw_thm =>
- (trace_thm (fn () => "Procedure " ^ quote name ^ " produced rewrite rule:")
- ss raw_thm;
- (case rews (mk_procrule ss raw_thm) of
- NONE => (trace_cterm true (fn () => "IGNORED result of simproc " ^ quote name ^
- " -- does not match") ss 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 ss maxt cong t =
- let val rthm = Thm.incr_indexes (maxt + 1) cong;
- val rlhs = fst (Thm.dest_equals (Drule.strip_imp_concl (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 (term_of rlhs) (term_of t) rthm);
- val _ = trace_thm (fn () => "Applying congruence rule:") ss thm';
- fun err (msg, thm) = (trace_thm (fn () => msg) ss thm; NONE)
- in
- (case prover thm' of
- NONE => err ("Congruence proof failed. Could not prove", thm')
- | SOME thm2 =>
- (case check_conv true ss (Drule.beta_eta_conversion t) thm2 of
- NONE => err ("Congruence proof failed. Should not have proved", thm2)
- | SOME thm2' =>
- if op aconv (pairself term_of (Thm.dest_equals (cprop_of thm2')))
- then NONE else SOME thm2'))
- end;
-
-val (cA, (cB, cC)) =
- apsnd Thm.dest_equals (Thm.dest_implies (hd (cprems_of Drule.imp_cong)));
-
-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, thy, maxidx) =
- let
- fun botc skel ss t =
- if is_Var skel then NONE
- else
- (case subc skel ss t of
- some as SOME thm1 =>
- (case rewritec (prover, thy, maxidx) ss (Thm.rhs_of thm1) of
- SOME (thm2, skel2) =>
- transitive2 (Thm.transitive thm1 thm2)
- (botc skel2 ss (Thm.rhs_of thm2))
- | NONE => some)
- | NONE =>
- (case rewritec (prover, thy, maxidx) ss t of
- SOME (thm2, skel2) => transitive2 thm2
- (botc skel2 ss (Thm.rhs_of thm2))
- | NONE => NONE))
-
- and try_botc ss t =
- (case botc skel0 ss t of
- SOME trec1 => trec1 | NONE => (Thm.reflexive t))
-
- and subc skel (ss as Simpset ({bounds, ...}, {congs, ...})) t0 =
- (case term_of t0 of
- Abs (a, T, _) =>
- let
- val b = Name.bound (#1 bounds);
- 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 ("Simplifier: renamed bound variable " ^
- quote b ^ " to " ^ quote b' ^ Position.str_of (Position.thread_data ()))
- else ();
- val ss' = add_bound ((b', T), a) ss;
- val skel' = case skel of Abs (_, _, sk) => sk | _ => skel0;
- in case botc skel' ss' t' of
- SOME thm => SOME (Thm.abstract_rule a v thm)
- | NONE => NONE
- end
- | t $ _ => (case t of
- Const ("==>", _) $ _ => impc t0 ss
- | Abs _ =>
- let val thm = Thm.beta_conversion false t0
- in case subc skel0 ss (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 ss ct of
- SOME thm1 =>
- (case botc uskel ss cu of
- SOME thm2 => SOME (Thm.combination thm1 thm2)
- | NONE => SOME (Thm.combination thm1 (Thm.reflexive cu)))
- | NONE =>
- (case botc uskel ss 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 AList.lookup (op =) (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 ss) ss 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 ss cl of
- NONE => thm
- | SOME thm' => transitive3 thm
- (Thm.combination thm' (Thm.reflexive cr))
- end handle Pattern.MATCH => appc ()))
- | _ => appc ()
- end)
- | _ => NONE)
-
- and impc ct ss =
- if mutsimp then mut_impc0 [] ct [] [] ss else nonmut_impc ct ss
-
- and rules_of_prem ss prem =
- if maxidx_of_term (term_of prem) <> ~1
- then (trace_cterm true
- (fn () => "Cannot add premise as rewrite rule because it contains (type) unknowns:")
- ss prem; ([], NONE))
- else
- let val asm = Thm.assume prem
- in (extract_safe_rrules (ss, asm), SOME asm) end
-
- and add_rrules (rrss, asms) ss =
- (fold o fold) insert_rrule rrss ss |> 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
- ([], [(cA, prem), (cB, lhs), (cC, 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 ([], [(cA, prem'), (cB, prem), (cC, concl)])
- Drule.swap_prems_eq) eq')
- (Thm.instantiate ([], [(cA, prem), (cB, prem''), (cC, concl)])
- Drule.swap_prems_eq)
- end
- end
-
- and rebuild [] _ _ _ _ eq = eq
- | rebuild (prem :: prems) concl (_ :: rrss) (_ :: asms) ss eq =
- let
- val ss' = add_rrules (rev rrss, rev asms) ss;
- 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, thy, maxidx) ss' concl' of
- NONE => rebuild prems concl' rrss asms ss (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) ss))
- end
-
- and mut_impc0 prems concl rrss asms ss =
- let
- val prems' = strip_imp_prems concl;
- val (rrss', asms') = split_list (map (rules_of_prem ss) prems')
- in
- mut_impc (prems @ prems') (strip_imp_concl concl) (rrss @ rrss')
- (asms @ asms') [] [] [] [] ss ~1 ~1
- end
-
- and mut_impc [] concl [] [] prems' rrss' asms' eqns ss 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')
- [] [] [] [] ss ~1 changed
- else rebuild prems' concl rrss' asms' ss
- (botc skel0 (add_rrules (rev rrss', rev asms') ss) concl))
-
- | mut_impc (prem :: prems) concl (rrs :: rrss) (asm :: asms)
- prems' rrss' asms' eqns ss changed k =
- case (if k = 0 then NONE else botc skel0 (add_rrules
- (rev rrss' @ rrss, rev asms' @ asms) ss) prem) of
- NONE => mut_impc prems concl rrss asms (prem :: prems')
- (rrs :: rrss') (asm :: asms') (NONE :: eqns) ss changed
- (if k = 0 then 0 else k - 1)
- | SOME eqn =>
- let
- val prem' = Thm.rhs_of eqn;
- val tprems = map term_of prems;
- val i = 1 + fold Integer.max (map (fn p =>
- find_index (fn q => q aconv p) tprems) (#hyps (rep_thm eqn))) ~1;
- val (rrs', asm') = rules_of_prem ss prem'
- 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)
- ss (length prems') ~1
- end
-
- (*legacy code - only for backwards compatibility*)
- and nonmut_impc ct ss =
- let
- val (prem, conc) = Thm.dest_implies ct;
- val thm1 = if simprem then botc skel0 ss prem else NONE;
- val prem1 = the_default prem (Option.map Thm.rhs_of thm1);
- val ss1 =
- if not useprem then ss
- else add_rrules (apsnd single (apfst single (rules_of_prem ss prem1))) ss
- in
- (case botc skel0 ss1 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
-*)
-
-val debug_bounds = Unsynchronized.ref false;
-
-fun check_bounds ss ct =
- if ! debug_bounds then
- let
- val Simpset ({bounds = (_, bounds), ...}, _) = ss;
- val bs = fold_aterms (fn Free (x, _) =>
- if Name.is_bound x andalso not (AList.defined eq_bound bounds x)
- then insert (op =) x else I
- | _ => I) (term_of ct) [];
- in
- if null bs then ()
- else print_term_global ss true ("Simplifier: term contains loose bounds: " ^ commas_quote bs)
- (Thm.theory_of_cterm ct) (Thm.term_of ct)
- end
- else ();
-
-fun rewrite_cterm mode prover raw_ss raw_ct =
- let
- val thy = Thm.theory_of_cterm raw_ct;
- val ct = Thm.adjust_maxidx_cterm ~1 raw_ct;
- val {maxidx, ...} = Thm.rep_cterm ct;
- val ss = inc_simp_depth (activate_context thy raw_ss);
- val depth = simp_depth ss;
- val _ =
- if depth mod 20 = 0 then
- if_visible ss warning ("Simplification depth " ^ string_of_int depth)
- else ();
- val _ = trace_cterm false (fn () => "SIMPLIFIER INVOKED ON THE FOLLOWING TERM:") ss ct;
- val _ = check_bounds ss ct;
- in bottomc (mode, Option.map Drule.flexflex_unique oo prover, thy, maxidx) ss ct end;
-
-val simple_prover =
- SINGLE o (fn ss => ALLGOALS (resolve_tac (prems_of_ss ss)));
-
-fun rewrite _ [] ct = Thm.reflexive ct
- | rewrite full thms ct = rewrite_cterm (full, false, false) simple_prover
- (global_context (Thm.theory_of_cterm ct) empty_ss addsimps thms) ct;
-
-fun simplify full thms = Conv.fconv_rule (rewrite full thms);
-val rewrite_rule = simplify 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 ss = Conv.fconv_rule (rewrite_cterm mode prover ss);
-
-(*Rewrite the subgoals of a proof state (represented by a theorem)*)
-fun rewrite_goals_rule thms th =
- Conv.fconv_rule (Conv.prems_conv ~1 (rewrite_cterm (true, true, true) simple_prover
- (global_context (Thm.theory_of_thm th) empty_ss addsimps thms))) th;
-
-(*Rewrite the subgoal of a proof state (represented by a theorem)*)
-fun rewrite_goal_rule mode prover ss i thm =
- if 0 < i andalso i <= Thm.nprems_of thm
- then Conv.gconv_rule (rewrite_cterm mode prover ss) i thm
- else raise THM ("rewrite_goal_rule", i, [thm]);
-
-
-(** meta-rewriting tactics **)
-
-(*Rewrite all subgoals*)
-fun rewrite_goals_tac defs = PRIMITIVE (rewrite_goals_rule defs);
-fun rewtac def = rewrite_goals_tac [def];
-
-(*Rewrite one subgoal*)
-fun asm_rewrite_goal_tac mode prover_tac ss i thm =
- if 0 < i andalso i <= Thm.nprems_of thm then
- Seq.single (Conv.gconv_rule (rewrite_cterm mode (SINGLE o prover_tac) ss) i thm)
- else Seq.empty;
-
-fun rewrite_goal_tac rews =
- let val ss = empty_ss addsimps rews in
- fn i => fn st => asm_rewrite_goal_tac (true, false, false) (K no_tac)
- (global_context (Thm.theory_of_thm st) ss) i st
- end;
-
-(*Prunes all redundant parameters from the proof state by rewriting.
- DOES NOT rewrite main goal, where quantification over an unused bound
- variable is sometimes done to avoid the need for cut_facts_tac.*)
-val prune_params_tac = rewrite_goals_tac [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 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 defs = fold rewrite_rule (rev_defs defs);
-fun fold_goals_tac defs = EVERY (map rewrite_goals_tac (rev_defs defs));
-
-
-(* HHF normal form: !! before ==>, outermost !! generalized *)
-
-local
-
-fun gen_norm_hhf ss th =
- (if Drule.is_norm_hhf (Thm.prop_of th) then th
- else Conv.fconv_rule
- (rewrite_cterm (true, false, false) (K (K NONE)) (global_context (Thm.theory_of_thm th) ss)) th)
- |> Thm.adjust_maxidx_thm ~1
- |> Drule.gen_all;
-
-val hhf_ss = empty_ss addsimps Drule.norm_hhf_eqs;
-
-in
-
-val norm_hhf = gen_norm_hhf hhf_ss;
-val norm_hhf_protect = gen_norm_hhf (hhf_ss addeqcongs [Drule.protect_cong]);
-
-end;
-
-end;
-
-structure Basic_Meta_Simplifier: BASIC_META_SIMPLIFIER = MetaSimplifier;
-open Basic_Meta_Simplifier;