move constant 'Respects' into Lifting.thy;
add quantifier transfer rules for quotients
(* Title: Pure/raw_simplifier.ML
Author: Tobias Nipkow and Stefan Berghofer, TU Muenchen
Higher-order Simplification.
*)
infix 4
addsimps delsimps addsimprocs delsimprocs
setloop' setloop addloop 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 rrule
val eq_rrule: rrule * rrule -> bool
type simpset
type proc
type solver
val mk_solver: string -> (simpset -> 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 transform_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 addsimps: simpset * thm list -> simpset
val delsimps: simpset * thm list -> simpset
val addsimprocs: simpset * simproc list -> simpset
val delsimprocs: simpset * simproc list -> 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 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 RAW_SIMPLIFIER =
sig
include BASIC_RAW_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 prems_of: simpset -> thm list
val add_simp: thm -> simpset -> simpset
val del_simp: thm -> simpset -> simpset
val add_eqcong: thm -> simpset -> simpset
val del_eqcong: thm -> simpset -> simpset
val add_cong: thm -> simpset -> simpset
val del_cong: thm -> simpset -> simpset
val mksimps: simpset -> thm -> thm list
val set_mksimps: (simpset -> thm -> thm list) -> simpset -> simpset
val set_mkcong: (simpset -> thm -> thm) -> simpset -> simpset
val set_mksym: (simpset -> thm -> thm option) -> simpset -> simpset
val set_mkeqTrue: (simpset -> thm -> thm option) -> simpset -> simpset
val set_termless: (term * term -> bool) -> simpset -> simpset
val set_subgoaler: (simpset -> int -> tactic) -> simpset -> simpset
val solver: simpset -> solver -> int -> tactic
val simp_depth_limit_raw: Config.raw
val clear_ss: simpset -> simpset
val default_mk_sym: simpset -> thm -> thm option
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 simp_trace_depth_limit_raw: Config.raw
val simp_trace_depth_limit_default: int Unsynchronized.ref
val simp_trace_default: bool Unsynchronized.ref
val simp_trace_raw: Config.raw
val simp_debug_raw: Config.raw
val add_prems: thm list -> simpset -> simpset
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 generic_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 Raw_Simplifier: RAW_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 (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 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 => Context_Position.if_visible ctxt f x
| 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 (fold_map Name.variant (rev (map #2 bs)) names));
fun subst (((b, T), _), x') = (Free (b, T), Syntax_Trans.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 (Proof_Context.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 Proof_Context.init_global;
fun activate_context thy ss =
let
val ctxt = the_context ss;
val ctxt' = ctxt
|> Context.raw_transfer (Theory.merge (thy, Proof_Context.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 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 = 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 (ss as Simpset (_, {mk_rews = {mk_cong = f, ...}, ...})) = f ss;
in
fun add_eqcong thm ss = 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 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_eqcong thm ss = 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 add_cong thm ss = add_eqcong (mk_cong ss thm) ss;
fun del_cong thm ss = del_eqcong (mk_cong ss thm) ss;
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 transform_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 (Proof_Context.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 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;
(* termless *)
fun set_termless termless =
map_simpset2 (fn (congs, procs, mk_rews, _, subgoal_tac, loop_tacs, solvers) =>
(congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers));
(* tactics *)
fun set_subgoaler subgoal_tac =
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;
fun default_mk_sym _ th = SOME (th RS Drule.symmetric_thm);
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 = default_mk_sym,
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) (Thm.hyps_of 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)));
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;
(** meta-rewriting tactics **)
(*Rewrite all subgoals*)
fun rewrite_goals_tac defs = PRIMITIVE (rewrite_goals_rule defs);
(*Rewrite one subgoal*)
fun generic_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 => generic_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.*)
val prune_params_tac = rewrite_goals_tac [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 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 |> add_eqcong Drule.protect_cong);
end;
end;
structure Basic_Meta_Simplifier: BASIC_RAW_SIMPLIFIER = Raw_Simplifier;
open Basic_Meta_Simplifier;