(* Title: Pure/meta_simplifier.ML
ID: $Id$
Author: Tobias Nipkow and Stefan Berghofer
Meta-level Simplification.
*)
infix 4
addsimps delsimps addeqcongs deleqcongs addcongs delcongs addsimprocs delsimprocs
setmksimps setmkcong setmksym setmkeqTrue settermless setsubgoaler
setloop addloop delloop setSSolver addSSolver setSolver addSolver;
signature BASIC_META_SIMPLIFIER =
sig
val debug_simp: bool ref
val trace_simp: bool ref
val simp_depth_limit: int ref
val trace_simp_depth_limit: int ref
type rrule
type cong
type solver
val mk_solver: string -> (thm list -> int -> tactic) -> solver
type simpset
type proc
val rep_ss: simpset ->
{rules: rrule Net.net,
prems: thm list,
bounds: int} *
{congs: (string * cong) list * string list,
procs: proc Net.net,
mk_rews:
{mk: thm -> thm list,
mk_cong: thm -> thm,
mk_sym: thm -> thm option,
mk_eq_True: thm -> thm option},
termless: term * term -> bool,
subgoal_tac: simpset -> int -> tactic,
loop_tacs: (string * (int -> tactic)) list,
solvers: solver list * solver list}
val print_ss: simpset -> unit
val empty_ss: simpset
val merge_ss: simpset * simpset -> simpset
type simproc
val mk_simproc: string -> cterm list ->
(Sign.sg -> 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 setmksimps: simpset * (thm -> thm list) -> simpset
val setmkcong: simpset * (thm -> thm) -> simpset
val setmksym: simpset * (thm -> thm option) -> simpset
val setmkeqTrue: simpset * (thm -> thm option) -> simpset
val settermless: simpset * (term * term -> bool) -> simpset
val setsubgoaler: simpset * (simpset -> int -> tactic) -> simpset
val setloop: 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 generic_simp_tac: bool -> bool * bool * bool -> simpset -> int -> tactic
end;
signature META_SIMPLIFIER =
sig
include BASIC_META_SIMPLIFIER
exception SIMPLIFIER of string * thm
val clear_ss: simpset -> simpset
exception SIMPROC_FAIL of string * exn
val simproc_i: Sign.sg -> string -> term list
-> (Sign.sg -> simpset -> term -> thm option) -> simproc
val simproc: Sign.sg -> string -> string list
-> (Sign.sg -> simpset -> term -> thm option) -> simproc
val rewrite_cterm: bool * bool * bool ->
(simpset -> thm -> thm option) -> simpset -> cterm -> thm
val rewrite_aux: (simpset -> thm -> thm option) -> bool -> thm list -> cterm -> thm
val simplify_aux: (simpset -> thm -> thm option) -> bool -> thm list -> thm -> thm
val rewrite_term: Sign.sg -> thm list -> (term -> term option) list -> term -> term
val rewrite_thm: bool * bool * bool ->
(simpset -> thm -> thm option) -> simpset -> thm -> thm
val rewrite_goals_rule_aux: (simpset -> thm -> thm option) -> thm list -> 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 simp_thm: bool * bool * bool -> simpset -> thm -> thm
val simp_cterm: bool * bool * bool -> simpset -> cterm -> thm
end;
structure MetaSimplifier: META_SIMPLIFIER =
struct
(** diagnostics **)
exception SIMPLIFIER of string * thm;
val debug_simp = ref false;
val trace_simp = ref false;
val simp_depth = ref 0;
val simp_depth_limit = ref 1000;
val trace_simp_depth_limit = ref 1000;
local
fun println a =
if !simp_depth > !trace_simp_depth_limit then ()
else tracing (enclose "[" "]" (string_of_int(!simp_depth)) ^ a);
fun prnt warn a = if warn then warning a else println a;
fun prtm warn a sg t = prnt warn (a ^ "\n" ^ Sign.string_of_term sg t);
fun prctm warn a t = prnt warn (a ^ "\n" ^ Display.string_of_cterm t);
in
fun debug warn a = if ! debug_simp then prnt warn a else ();
fun trace warn a = if ! trace_simp then prnt warn a else ();
fun debug_term warn a sign t = if ! debug_simp then prtm warn a sign t else ();
fun trace_term warn a sign t = if ! trace_simp then prtm warn a sign t else ();
fun trace_cterm warn a ct = if ! trace_simp then prctm warn a ct else ();
fun trace_thm a th = if ! trace_simp then prctm false a (Thm.cprop_of th) else ();
fun trace_named_thm a (thm, name) =
if ! trace_simp then
prctm false (if name = "" then a else a ^ " " ^ quote name ^ ":") (Thm.cprop_of thm)
else ();
fun warn_thm a = prctm true a o Thm.cprop_of;
end;
(** datatype simpset **)
(* rewrite rules *)
type rrule = {thm: thm, name: string, lhs: term, elhs: cterm, fo: bool, perm: bool};
(*thm: the rewrite rule;
name: name of theorem from which rewrite rule was extracted;
lhs: the left-hand side;
elhs: the etac-contracted lhs;
fo: use first-order matching;
perm: 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) =
Drule.eq_thm_prop (thm1, thm2);
(* congruences *)
type cong = {thm: thm, lhs: cterm};
fun eq_cong ({thm = thm1, ...}: cong, {thm = thm2, ...}: cong) =
Drule.eq_thm_prop (thm1, thm2);
(* solvers *)
datatype solver =
Solver of
{name: string,
solver: thm list -> int -> tactic,
id: stamp};
fun mk_solver name solver = Solver {name = name, solver = solver, id = stamp ()};
fun solver_name (Solver {name, ...}) = name;
fun solver ths (Solver {solver = tacf, ...}) = tacf ths;
fun eq_solver (Solver {id = id1, ...}, Solver {id = id2, ...}) = (id1 = id2);
val merge_solvers = gen_merge_lists eq_solver;
(* simplification sets and procedures *)
(*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);
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;*)
type mk_rews =
{mk: thm -> thm list,
mk_cong: thm -> thm,
mk_sym: thm -> thm option,
mk_eq_True: thm -> thm option};
datatype simpset =
Simpset of
{rules: rrule Net.net,
prems: thm list,
bounds: int} *
{congs: (string * cong) list * string list,
procs: proc Net.net,
mk_rews: mk_rews,
termless: term * term -> bool,
subgoal_tac: simpset -> int -> tactic,
loop_tacs: (string * (int -> tactic)) list,
solvers: solver list * solver list}
and proc =
Proc of
{name: string,
lhs: cterm,
proc: Sign.sg -> simpset -> term -> thm option,
id: stamp};
fun eq_proc (Proc {id = id1, ...}, Proc {id = id2, ...}) = (id1 = id2);
fun rep_ss (Simpset args) = args;
fun make_ss1 (rules, prems, bounds) =
{rules = rules, prems = prems, bounds = bounds};
fun map_ss1 f {rules, prems, bounds} =
make_ss1 (f (rules, prems, bounds));
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_simpset f (Simpset ({rules, prems, bounds},
{congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers})) =
make_simpset (f ((rules, prems, bounds),
(congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers)));
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);
(* print simpsets *)
fun print_ss ss =
let
val pretty_thms = map Display.pretty_thm;
fun pretty_cong (name, th) =
Pretty.block [Pretty.str (name ^ ":"), Pretty.brk 1, Display.pretty_thm th];
fun pretty_proc (name, lhss) =
Pretty.big_list (name ^ ":") (map Display.pretty_cterm lhss);
val Simpset ({rules, ...}, {congs, procs, loop_tacs, solvers, ...}) = ss;
val smps = map (#thm o #2) (Net.dest rules);
val cngs = map (fn (name, {thm, ...}) => (name, thm)) (#1 congs);
val prcs = Net.dest procs |>
map (fn (_, Proc {name, lhs, id, ...}) => ((name, lhs), id))
|> partition_eq eq_snd
|> map (fn ps => (#1 (#1 (hd ps)), map (#2 o #1) ps))
|> Library.sort_wrt #1;
in
[Pretty.big_list "simplification rules:" (pretty_thms smps),
Pretty.big_list "simplification procedures:" (map pretty_proc prcs),
Pretty.big_list "congruences:" (map pretty_cong cngs),
Pretty.strs ("loopers:" :: map (quote o #1) loop_tacs),
Pretty.strs ("unsafe solvers:" :: map (quote o solver_name) (#1 solvers)),
Pretty.strs ("safe solvers:" :: map (quote o solver_name) (#2 solvers))]
|> Pretty.chunks |> Pretty.writeln
end;
(* empty simpsets *)
local
fun init_ss mk_rews termless subgoal_tac solvers =
make_simpset ((Net.empty, [], 0),
(([], []), Net.empty, mk_rews, termless, subgoal_tac, [], solvers));
val basic_mk_rews: mk_rews =
{mk = fn th => if can Logic.dest_equals (Thm.concl_of th) then [th] else [],
mk_cong = I,
mk_sym = SOME o Drule.symmetric_fun,
mk_eq_True = K NONE};
in
val empty_ss = init_ss basic_mk_rews Term.termless (K (K no_tac)) ([], []);
fun clear_ss (Simpset (_, {mk_rews, termless, subgoal_tac, solvers, ...})) =
init_ss mk_rews termless subgoal_tac solvers;
end;
(* merge simpsets *) (*NOTE: ignores some fields of 2nd simpset*)
fun merge_ss (ss1, ss2) =
let
val Simpset ({rules = rules1, prems = prems1, bounds = bounds1},
{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},
{congs = (congs2, weak2), procs = procs2, mk_rews = _, termless = _, subgoal_tac = _,
loop_tacs = loop_tacs2, solvers = (unsafe_solvers2, solvers2)}) = ss2;
val rules' = Net.merge (rules1, rules2, eq_rrule);
val prems' = gen_merge_lists Drule.eq_thm_prop prems1 prems2;
val bounds' = Int.max (bounds1, bounds2);
val congs' = gen_merge_lists (eq_cong o pairself #2) congs1 congs2;
val weak' = merge_lists weak1 weak2;
val procs' = Net.merge (procs1, procs2, eq_proc);
val loop_tacs' = merge_alists loop_tacs1 loop_tacs2;
val unsafe_solvers' = merge_solvers unsafe_solvers1 unsafe_solvers2;
val solvers' = merge_solvers solvers1 solvers2;
in
make_simpset ((rules', prems', bounds'), ((congs', weak'), procs',
mk_rews, termless, subgoal_tac, loop_tacs', (unsafe_solvers', solvers')))
end;
(* simprocs *)
exception SIMPROC_FAIL of string * exn;
datatype simproc = Simproc of proc list;
fun mk_simproc name lhss proc =
let val id = stamp () in
Simproc (lhss |> map (fn lhs =>
Proc {name = name, lhs = lhs, proc = proc, id = id}))
end;
fun simproc_i sg name = mk_simproc name o map (Thm.cterm_of sg o Logic.varify);
fun simproc sg name = simproc_i sg name o map (Sign.simple_read_term sg TypeInfer.logicT);
(** simpset operations **)
(* bounds and prems *)
val incr_bounds = map_simpset1 (fn (rules, prems, bounds) =>
(rules, prems, bounds + 1));
fun add_prems ths = map_simpset1 (fn (rules, prems, bounds) =>
(rules, ths @ prems, bounds));
fun prems_of_ss (Simpset ({prems, ...}, _)) = prems;
(* addsimps *)
fun mk_rrule2 {thm, name, lhs, elhs, perm} =
let
val fo = Pattern.first_order (term_of elhs) orelse not (Pattern.pattern (term_of elhs))
in {thm = thm, name = name, lhs = lhs, elhs = elhs, fo = fo, perm = perm} end;
fun insert_rrule quiet (ss, rrule as {thm, name, lhs, elhs, perm}) =
(trace_named_thm "Adding rewrite rule" (thm, name);
ss |> map_simpset1 (fn (rules, prems, bounds) =>
let
val rrule2 as {elhs, ...} = mk_rrule2 rrule;
val rules' = Net.insert_term ((term_of elhs, rrule2), rules, eq_rrule);
in (rules', prems, bounds) end)
handle Net.INSERT =>
(if quiet then () else warn_thm "Ignoring duplicate rewrite rule:" 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 (term_varnames t, term_varnames u);
(* 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 =
not (term_varnames erhs subset Library.foldl add_term_varnames (term_varnames elhs, prems))
orelse
not (term_tvars erhs subset (term_tvars elhs union List.concat (map term_tvars prems)));
(*simple test for looping rewrite rules and stupid orientations*)
fun reorient sign prems lhs rhs =
rewrite_rule_extra_vars prems lhs rhs
orelse
is_Var (head_of lhs)
orelse
exists (apl (lhs, Logic.occs)) (rhs :: prems)
orelse
null prems andalso Pattern.matches (Sign.tsig_of sign) (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 {sign, prop, ...} = Thm.rep_thm thm;
val prems = Logic.strip_imp_prems prop;
val concl = Drule.strip_imp_concl (Thm.cprop_of thm);
val (lhs, rhs) = Drule.dest_equals concl handle TERM _ =>
raise SIMPLIFIER ("Rewrite rule not a meta-equality", thm);
val (_, elhs) = Drule.dest_equals (Thm.cprop_of (Thm.eta_conversion lhs));
val elhs = if elhs = lhs then lhs else elhs; (*share identical copies*)
val erhs = Pattern.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 (sign, 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 (Simpset (_, {mk_rews = {mk_eq_True, ...}, ...})) (thm, name) =
(case mk_eq_True 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 term_varnames rhs subset term_varnames lhs andalso
term_tvars rhs subset term_tvars lhs then [rrule]
else mk_eq_True ss (thm2, name) @ [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 (sign, prems, lhs, elhs, rhs, perm) = decomp_simp thm in
if perm then [{thm = thm, name = name, lhs = lhs, elhs = elhs, perm = true}]
else if reorient sign prems lhs rhs then
if reorient sign prems rhs lhs
then mk_eq_True ss (thm, name)
else
let val Simpset (_, {mk_rews = {mk_sym, ...}, ...}) = ss in
(case mk_sym 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)
end
else rrule_eq_True (thm, name, lhs, elhs, rhs, ss, thm)
end;
fun extract_rews (Simpset (_, {mk_rews = {mk, ...}, ...}), thms) =
List.concat (map (fn thm => map (rpair (Thm.name_of_thm thm)) (mk thm)) thms);
fun orient_comb_simps comb mk_rrule (ss, thms) =
let
val rews = extract_rews (ss, thms);
val rrules = List.concat (map mk_rrule rews);
in Library.foldl comb (ss, rrules) end;
fun extract_safe_rrules (ss, thm) =
List.concat (map (orient_rrule ss) (extract_rews (ss, [thm])));
(*add rewrite rules explicitly; do not reorient!*)
fun ss addsimps thms =
orient_comb_simps (insert_rrule false) (mk_rrule ss) (ss, thms);
(* delsimps *)
fun del_rrule (ss, rrule as {thm, elhs, ...}) =
ss |> map_simpset1 (fn (rules, prems, bounds) =>
(Net.delete_term ((term_of elhs, rrule), rules, eq_rrule), prems, bounds))
handle Net.DELETE => (warn_thm "Rewrite rule not in simpset:" thm; ss);
fun ss delsimps thms =
orient_comb_simps del_rrule (map mk_rrule2 o mk_rrule ss) (ss, thms);
(* 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
null (findrep xs) andalso xs = ys andalso
(x, y) mem varpairs andalso
is_full_cong_prems prems (varpairs \ (x, y))
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 null (findrep (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, _) = Drule.dest_equals (Drule.strip_imp_concl (Thm.cprop_of thm))
handle TERM _ => raise SIMPLIFIER ("Congruence not a meta-equality", thm);
(*val lhs = Pattern.eta_contract lhs;*)
val a = valOf (cong_name (head_of (term_of lhs))) handle Option =>
raise SIMPLIFIER ("Congruence must start with a constant or free variable", thm);
val (alist, weak) = congs;
val alist2 = overwrite_warn (alist, (a, {lhs = lhs, thm = thm}))
("Overwriting congruence rule for " ^ quote a);
val weak2 = if is_full_cong thm then weak else a :: weak;
in ((alist2, weak2), 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 = Pattern.eta_contract lhs;*)
val a = valOf (cong_name (head_of lhs)) handle Option =>
raise SIMPLIFIER ("Congruence must start with a constant", thm);
val (alist, _) = congs;
val alist2 = List.filter (fn (x, _) => x <> a) alist;
val weak2 = alist2 |> List.mapPartial (fn (a, {thm, ...}) =>
if is_full_cong thm then NONE else SOME a);
in ((alist2, weak2), procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) end);
fun mk_cong (Simpset (_, {mk_rews = {mk_cong = f, ...}, ...})) = f;
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 *)
local
fun add_proc (ss, proc as Proc {name, lhs, ...}) =
(trace_cterm false ("Adding simplification procedure " ^ quote name ^ " for") lhs;
map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
(congs, Net.insert_term ((term_of lhs, proc), procs, eq_proc),
mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
handle Net.INSERT =>
(warning ("Ignoring duplicate simplification procedure " ^ quote name); ss));
fun del_proc (ss, proc as Proc {name, lhs, ...}) =
map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
(congs, Net.delete_term ((term_of lhs, proc), procs, eq_proc),
mk_rews, termless, subgoal_tac, loop_tacs, solvers)) ss
handle Net.DELETE =>
(warning ("Simplification procedure " ^ quote name ^ " not in simpset"); ss);
in
val (op addsimprocs) = Library.foldl (fn (ss, Simproc procs) => Library.foldl add_proc (ss, procs));
val (op delsimprocs) = Library.foldl (fn (ss, Simproc procs) => Library.foldl del_proc (ss, procs));
end;
(* mk_rews *)
local
fun map_mk_rews f = map_simpset2 (fn (congs, procs, {mk, mk_cong, mk_sym, mk_eq_True},
termless, subgoal_tac, loop_tacs, solvers) =>
let val (mk', mk_cong', mk_sym', mk_eq_True') = f (mk, mk_cong, mk_sym, mk_eq_True) in
(congs, procs, {mk = mk', mk_cong = mk_cong', mk_sym = mk_sym', mk_eq_True = mk_eq_True'},
termless, subgoal_tac, loop_tacs, solvers)
end);
in
fun ss setmksimps mk = ss |> map_mk_rews (fn (_, mk_cong, mk_sym, mk_eq_True) =>
(mk, mk_cong, mk_sym, mk_eq_True));
fun ss setmkcong mk_cong = ss |> map_mk_rews (fn (mk, _, mk_sym, mk_eq_True) =>
(mk, mk_cong, mk_sym, mk_eq_True));
fun ss setmksym mk_sym = ss |> map_mk_rews (fn (mk, mk_cong, _, mk_eq_True) =>
(mk, mk_cong, mk_sym, mk_eq_True));
fun ss setmkeqTrue mk_eq_True = ss |> map_mk_rews (fn (mk, mk_cong, mk_sym, _) =>
(mk, mk_cong, mk_sym, mk_eq_True));
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 addloop (name, tac) = ss |>
map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
(congs, procs, mk_rews, termless, subgoal_tac,
overwrite_warn (loop_tacs, (name, tac)) ("Overwriting looper " ^ quote name),
solvers));
fun ss delloop name = ss |>
map_simpset2 (fn (congs, procs, mk_rews, termless, subgoal_tac, loop_tacs, solvers) =>
let val loop_tacs' = filter_out (equal name o #1) loop_tacs in
if length loop_tacs <> length loop_tacs' then ()
else warning ("No such looper in simpset: " ^ quote name);
(congs, procs, mk_rews, termless, subgoal_tac, loop_tacs', solvers)
end);
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, merge_solvers solvers [solver])));
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, (merge_solvers unsafe_solvers [solver], 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)));
(** rewriting **)
(*
Uses conversions, see:
L C Paulson, A higher-order implementation of rewriting,
Science of Computer Programming 3 (1983), pages 119-149.
*)
val dest_eq = Drule.dest_equals o Thm.cprop_of;
val lhs_of = #1 o dest_eq;
val rhs_of = #2 o dest_eq;
fun check_conv msg thm thm' =
let
val thm'' = transitive thm (transitive
(symmetric (Drule.beta_eta_conversion (lhs_of thm'))) thm')
in if msg then trace_thm "SUCCEEDED" thm' else (); SOME thm'' end
handle THM _ =>
let val {sign, prop = _ $ _ $ prop0, ...} = Thm.rep_thm thm in
trace_thm "Proved wrong thm (Check subgoaler?)" thm';
trace_term false "Should have proved:" sign prop0;
NONE
end;
(* mk_procrule *)
fun mk_procrule thm =
let val (_, prems, lhs, elhs, rhs, _) = decomp_simp thm in
if rewrite_rule_extra_vars prems lhs rhs
then (warn_thm "Extra vars on rhs:" thm; [])
else [mk_rrule2 {thm = thm, name = "", lhs = lhs, elhs = elhs, perm = false}]
end;
(* rewritec: conversion to apply the meta simpset to a term *)
(*Since the rewriting strategy is bottom-up, we avoid re-normalizing already
normalized terms by carrying around the rhs of the rewrite rule just
applied. This is called the `skeleton'. It is decomposed in parallel
with the term. Once a Var is encountered, the corresponding term is
already in normal form.
skel0 is a dummy skeleton that is to enforce complete normalization.*)
val skel0 = Bound 0;
(*Use rhs as skeleton only if the lhs does not contain unnormalized bits.
The latter may happen iff there are weak congruence rules for constants
in the lhs.*)
fun uncond_skel ((_, weak), (lhs, rhs)) =
if null weak then rhs (*optimization*)
else if exists_Const (fn (c, _) => c mem weak) 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 (congs, (lhs, rhs))) =
if term_varnames rhs subset term_varnames 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, signt, maxt) ss t =
let
val Simpset ({rules, ...}, {congs, procs, termless, ...}) = ss;
val eta_thm = Thm.eta_conversion t;
val eta_t' = rhs_of eta_thm;
val eta_t = term_of eta_t';
val tsigt = Sign.tsig_of signt;
fun rew {thm, name, lhs, elhs, fo, perm} =
let
val {sign, prop, maxidx, ...} = rep_thm thm;
val (rthm, elhs') = if maxt = ~1 then (thm, elhs)
else (Thm.incr_indexes (maxt+1) thm, Thm.cterm_incr_indexes (maxt+1) elhs);
val insts = if fo then Thm.cterm_first_order_match (elhs', eta_t')
else Thm.cterm_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) = 0);
val (lhs', rhs') = Logic.dest_equals (Logic.strip_imp_concl prop')
in
if perm andalso not (termless (rhs', lhs'))
then (trace_named_thm "Cannot apply permutative rewrite rule" (thm, name);
trace_thm "Term does not become smaller:" thm'; NONE)
else (trace_named_thm "Applying instance of rewrite rule" (thm, name);
if unconditional
then
(trace_thm "Rewriting:" thm';
let val lr = Logic.dest_equals prop;
val SOME thm'' = check_conv false eta_thm thm'
in SOME (thm'', uncond_skel (congs, lr)) end)
else
(trace_thm "Trying to rewrite:" thm';
if !simp_depth > !simp_depth_limit
then let val s = "simp_depth_limit exceeded - giving up"
in trace false s; warning s; NONE end
else
case prover ss thm' of
NONE => (trace_thm "FAILED" thm'; NONE)
| SOME thm2 =>
(case check_conv true eta_thm thm2 of
NONE => NONE |
SOME thm2' =>
let val concl = Logic.strip_imp_concl prop
val lr = Logic.dest_equals concl
in SOME (thm2', cond_skel (congs, lr)) end)))
end
fun rews [] = NONE
| rews (rrule :: rrules) =
let val opt = rew rrule handle Pattern.MATCH => NONE
in case opt of NONE => rews rrules | some => some end;
fun sort_rrules rrs = let
fun is_simple({thm, ...}:rrule) = case Thm.prop_of thm of
Const("==",_) $ _ $ _ => 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 tsigt (Thm.term_of lhs, Thm.term_of t) then
(debug_term false ("Trying procedure " ^ quote name ^ " on:") signt eta_t;
case transform_failure (curry SIMPROC_FAIL name)
(fn () => proc signt ss eta_t) () of
NONE => (debug false "FAILED"; proc_rews ps)
| SOME raw_thm =>
(trace_thm ("Procedure " ^ quote name ^ " produced rewrite rule:") raw_thm;
(case rews (mk_procrule raw_thm) of
NONE => (trace_cterm true ("IGNORED result of simproc " ^ quote name ^
" -- does not match") t; proc_rews ps)
| some => some)))
else proc_rews ps;
in case eta_t of
Abs _ $ _ => SOME (transitive eta_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,signt,maxt) {thm=cong,lhs=lhs} t =
let val sign = Thm.sign_of_thm cong
val rthm = if maxt = ~1 then cong else Thm.incr_indexes (maxt+1) cong;
val rlhs = fst (Drule.dest_equals (Drule.strip_imp_concl (cprop_of rthm)));
val insts = Thm.cterm_match (rlhs, t)
(* Pattern.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 unit = trace_thm "Applying congruence rule:" thm';
fun err (msg, thm) = (trace_thm msg thm; NONE)
in case prover thm' of
NONE => err ("Congruence proof failed. Could not prove", thm')
| SOME thm2 => (case check_conv true (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 (dest_equals (cprop_of thm2')))
then NONE else SOME thm2')
end;
val (cA, (cB, cC)) =
apsnd dest_equals (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 (transitive thm1 thm2)
fun transitive2 thm = transitive1 (SOME thm);
fun transitive3 thm = transitive1 thm o SOME;
fun bottomc ((simprem, useprem, mutsimp), prover, sign, 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, sign, maxidx) ss (rhs_of thm1) of
SOME (thm2, skel2) =>
transitive2 (transitive thm1 thm2)
(botc skel2 ss (rhs_of thm2))
| NONE => some)
| NONE =>
(case rewritec (prover, sign, maxidx) ss t of
SOME (thm2, skel2) => transitive2 thm2
(botc skel2 ss (rhs_of thm2))
| NONE => NONE))
and try_botc ss t =
(case botc skel0 ss t of
SOME trec1 => trec1 | NONE => (reflexive t))
and subc skel (ss as Simpset ({bounds, ...}, {congs, ...})) t0 =
(case term_of t0 of
Abs (a, T, t) =>
let
val (v, t') = Thm.dest_abs (SOME ("." ^ a ^ "." ^ string_of_int bounds)) t0;
val ss' = incr_bounds ss;
val skel' = case skel of Abs (_, _, sk) => sk | _ => skel0;
in case botc skel' ss' t' of
SOME thm => SOME (abstract_rule a v thm)
| NONE => NONE
end
| t $ _ => (case t of
Const ("==>", _) $ _ => impc t0 ss
| Abs _ =>
let val thm = beta_conversion false t0
in case subc skel0 ss (rhs_of thm) of
NONE => SOME thm
| SOME thm' => SOME (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 (combination thm1 thm2)
| NONE => SOME (combination thm1 (reflexive cu)))
| NONE =>
(case botc uskel ss cu of
SOME thm1 => SOME (combination (reflexive ct) thm1)
| NONE => NONE))
end
val (h, ts) = strip_comb t
in case cong_name h of
SOME a =>
(case assoc_string (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, sign, maxidx) cong t0;
val t = getOpt (Option.map rhs_of thm, t0);
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
(combination thm' (reflexive cr))
end handle TERM _ => error "congc result"
| 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
"Cannot add premise as rewrite rule because it contains (type) unknowns:" prem; ([], NONE))
else
let val asm = assume prem
in (extract_safe_rrules (ss, asm), SOME asm) end
and add_rrules (rrss, asms) ss =
Library.foldl (insert_rrule true) (ss, List.concat rrss) |> add_prems (List.mapPartial I asms)
and disch r (prem, eq) =
let
val (lhs, rhs) = dest_eq eq;
val eq' = implies_elim (Thm.instantiate
([], [(cA, prem), (cB, lhs), (cC, rhs)]) Drule.imp_cong)
(implies_intr prem eq)
in if not r then eq' else
let
val (prem', concl) = dest_implies lhs;
val (prem'', _) = dest_implies rhs
in transitive (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 (rrs :: rrss) (asm :: asms) ss eq =
let
val ss' = add_rrules (rev rrss, rev asms) ss;
val concl' =
Drule.mk_implies (prem, getOpt (Option.map rhs_of eq, concl));
val dprem = Option.map (curry (disch false) prem)
in case rewritec (prover, sign, maxidx) ss' concl' of
NONE => rebuild prems concl' rrss asms ss (dprem eq)
| SOME (eq', _) => transitive2 (Library.foldl (disch false o swap)
(valOf (transitive3 (dprem eq) eq'), prems))
(mut_impc0 (rev prems) (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 (Library.foldl (fn (eq2, (eq1, prem)) => transitive1 eq1
(Option.map (curry (disch false) prem) eq2)) (NONE, eqns ~~ prems'))
(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' = rhs_of eqn;
val tprems = map term_of prems;
val i = 1 + Library.foldl Int.max (~1, map (fn p =>
find_index_eq p tprems) (#hyps (rep_thm eqn)));
val (rrs', asm') = rules_of_prem ss prem'
in mut_impc prems concl rrss asms (prem' :: prems')
(rrs' :: rrss') (asm' :: asms') (SOME (foldr (disch true)
(Drule.imp_cong' eqn (reflexive (Drule.list_implies
(Library.drop (i, prems), concl)))) (Library.take (i, prems))) :: eqns) ss (length prems') ~1
end
(*legacy code - only for backwards compatibility*)
and nonmut_impc ct ss =
let val (prem, conc) = dest_implies ct;
val thm1 = if simprem then botc skel0 ss prem else NONE;
val prem1 = getOpt (Option.map rhs_of thm1, prem);
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' thm1' (reflexive conc)))
| SOME thm2 =>
let val thm2' = disch false (prem1, thm2)
in (case thm1 of
NONE => SOME thm2'
| SOME thm1' =>
SOME (transitive (Drule.imp_cong' thm1' (reflexive conc)) thm2'))
end)
end
in try_botc end;
(* Meta-rewriting: rewrites t to u and returns the theorem t==u *)
(*
Parameters:
mode = (simplify A,
use A in simplifying B,
use prems of B (if B is again a meta-impl.) to simplify A)
when simplifying A ==> B
prover: how to solve premises in conditional rewrites and congruences
*)
fun rewrite_cterm mode prover ss ct =
(simp_depth := !simp_depth + 1;
if !simp_depth mod 10 = 0
then warning ("Simplification depth " ^ string_of_int (!simp_depth))
else ();
trace_cterm false "SIMPLIFIER INVOKED ON THE FOLLOWING TERM:" ct;
let val {sign, t, maxidx, ...} = Thm.rep_cterm ct
val res = bottomc (mode, prover, sign, maxidx) ss ct
handle THM (s, _, thms) =>
error ("Exception THM was raised in simplifier:\n" ^ s ^ "\n" ^
Pretty.string_of (Display.pretty_thms thms))
in simp_depth := !simp_depth - 1; res end
) handle exn => (simp_depth := 0; raise exn);
(*Rewrite a cterm*)
fun rewrite_aux _ _ [] = (fn ct => Thm.reflexive ct)
| rewrite_aux prover full thms =
rewrite_cterm (full, false, false) prover (empty_ss addsimps thms);
(*Rewrite a theorem*)
fun simplify_aux _ _ [] = (fn th => th)
| simplify_aux prover full thms =
Drule.fconv_rule (rewrite_cterm (full, false, false) prover (empty_ss addsimps thms));
(*simple term rewriting -- no proof*)
fun rewrite_term sg rules procs =
Pattern.rewrite_term (Sign.tsig_of sg) (map decomp_simp' rules) procs;
fun rewrite_thm mode prover ss = Drule.fconv_rule (rewrite_cterm mode prover ss);
(*Rewrite the subgoals of a proof state (represented by a theorem) *)
fun rewrite_goals_rule_aux _ [] th = th
| rewrite_goals_rule_aux prover thms th =
Drule.fconv_rule (Drule.goals_conv (K true) (rewrite_cterm (true, true, false) prover
(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 <= nprems_of thm
then Drule.fconv_rule (Drule.goals_conv (fn j => j=i) (rewrite_cterm mode prover ss)) thm
else raise THM("rewrite_goal_rule",i,[thm]);
(*Rewrite subgoal i only. SELECT_GOAL avoids inefficiencies in goals_conv.*)
fun asm_rewrite_goal_tac mode prover_tac ss =
SELECT_GOAL
(PRIMITIVE (rewrite_goal_rule mode (SINGLE o prover_tac) ss 1));
(** simplification tactics and rules **)
fun solve_all_tac solvers ss =
let
val Simpset (_, {subgoal_tac, ...}) = ss;
val solve_tac = subgoal_tac (set_solvers solvers ss) THEN_ALL_NEW (K no_tac);
in DEPTH_SOLVE (solve_tac 1) end;
(*NOTE: may instantiate unknowns that appear also in other subgoals*)
fun generic_simp_tac safe mode ss =
let
val Simpset ({prems, ...}, {loop_tacs, solvers = (unsafe_solvers, solvers), ...}) = ss;
val loop_tac = FIRST' (map #2 loop_tacs);
val solve_tac = FIRST' (map (solver prems) (if safe then solvers else unsafe_solvers));
fun simp_loop_tac i =
asm_rewrite_goal_tac mode (solve_all_tac unsafe_solvers) ss i THEN
(solve_tac i ORELSE TRY ((loop_tac THEN_ALL_NEW simp_loop_tac) i));
in simp_loop_tac end;
fun simp rew mode ss thm =
let
val Simpset (_, {solvers = (unsafe_solvers, _), ...}) = ss;
val tacf = solve_all_tac unsafe_solvers;
fun prover s th = Option.map #1 (Seq.pull (tacf s th));
in rew mode prover ss thm end;
val simp_thm = simp rewrite_thm;
val simp_cterm = simp rewrite_cterm;
end;
structure BasicMetaSimplifier: BASIC_META_SIMPLIFIER = MetaSimplifier;
open BasicMetaSimplifier;