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