(* Title: Pure/meta_simplifier.ML
ID: $Id$
Author: Tobias Nipkow and Stefan Berghofer
Meta-level Simplification.
*)
signature BASIC_META_SIMPLIFIER =
sig
val trace_simp: bool ref
val debug_simp: bool ref
val simp_depth_limit: int ref
end;
signature META_SIMPLIFIER =
sig
include BASIC_META_SIMPLIFIER
exception SIMPLIFIER of string * thm
exception SIMPROC_FAIL of string * exn
type meta_simpset
val dest_mss : meta_simpset ->
{simps: thm list, congs: thm list, procs: (string * cterm list) list}
val empty_mss : meta_simpset
val clear_mss : meta_simpset -> meta_simpset
val merge_mss : meta_simpset * meta_simpset -> meta_simpset
val add_simps : meta_simpset * thm list -> meta_simpset
val del_simps : meta_simpset * thm list -> meta_simpset
val mss_of : thm list -> meta_simpset
val add_congs : meta_simpset * thm list -> meta_simpset
val del_congs : meta_simpset * thm list -> meta_simpset
val add_simprocs : meta_simpset *
(string * cterm list * (Sign.sg -> thm list -> term -> thm option) * stamp) list
-> meta_simpset
val del_simprocs : meta_simpset *
(string * cterm list * (Sign.sg -> thm list -> term -> thm option) * stamp) list
-> meta_simpset
val add_prems : meta_simpset * thm list -> meta_simpset
val prems_of_mss : meta_simpset -> thm list
val set_mk_rews : meta_simpset * (thm -> thm list) -> meta_simpset
val set_mk_sym : meta_simpset * (thm -> thm option) -> meta_simpset
val set_mk_eq_True : meta_simpset * (thm -> thm option) -> meta_simpset
val get_mk_rews : meta_simpset -> thm -> thm list
val get_mk_sym : meta_simpset -> thm -> thm option
val get_mk_eq_True : meta_simpset -> thm -> thm option
val set_termless : meta_simpset * (term * term -> bool) -> meta_simpset
val beta_eta_conversion: cterm -> thm
val rewrite_cterm: bool * bool * bool ->
(meta_simpset -> thm -> thm option) -> meta_simpset -> cterm -> thm
val goals_conv : (int -> bool) -> (cterm -> thm) -> cterm -> thm
val forall_conv : (cterm -> thm) -> cterm -> thm
val fconv_rule : (cterm -> thm) -> thm -> thm
val rewrite_aux : (meta_simpset -> thm -> thm option) -> bool -> thm list -> cterm -> thm
val simplify_aux : (meta_simpset -> thm -> thm option) -> bool -> thm list -> thm -> thm
val rewrite_thm : bool * bool * bool
-> (meta_simpset -> thm -> thm option)
-> meta_simpset -> thm -> thm
val rewrite_goals_rule_aux: (meta_simpset -> thm -> thm option) -> thm list -> thm -> thm
val rewrite_goal_rule : bool* bool * bool
-> (meta_simpset -> thm -> thm option)
-> meta_simpset -> int -> thm -> thm
val rewrite_term: Sign.sg -> thm list -> (term -> term option) list -> term -> term
end;
structure MetaSimplifier : META_SIMPLIFIER =
struct
(** diagnostics **)
exception SIMPLIFIER of string * thm;
exception SIMPROC_FAIL of string * exn;
val simp_depth = ref 0;
val simp_depth_limit = ref 1000;
local
fun println a =
tracing ((case ! simp_depth of 0 => "" | n => "[" ^ string_of_int n ^ "]") ^ a);
fun prnt warn a = if warn then warning a else println a;
fun prtm warn a sign t = prnt warn (a ^ "\n" ^ Sign.string_of_term sign t);
fun prctm warn a t = prnt warn (a ^ "\n" ^ Display.string_of_cterm t);
in
fun prthm warn a = prctm warn a o Thm.cprop_of;
val trace_simp = ref false;
val debug_simp = ref false;
fun trace warn a = if !trace_simp then prnt warn a else ();
fun debug warn a = if !debug_simp then prnt warn a else ();
fun trace_term warn a sign t = if !trace_simp then prtm warn a sign t else ();
fun trace_cterm warn a t = if !trace_simp then prctm warn a t else ();
fun debug_term warn a sign t = if !debug_simp then prtm warn a sign t else ();
fun trace_thm a thm =
let val {sign, prop, ...} = rep_thm thm
in trace_term false a sign prop end;
fun trace_named_thm a (thm, name) =
trace_thm (a ^ (if name = "" then "" else " " ^ quote name) ^ ":") thm;
end;
(** meta simp sets **)
(* basic components *)
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.
*)
type cong = {thm: thm, lhs: cterm};
type simproc =
{name: string, proc: Sign.sg -> thm list -> term -> thm option, lhs: cterm, id: stamp};
fun eq_rrule ({thm = thm1, ...}: rrule, {thm = thm2, ...}: rrule) =
#prop (rep_thm thm1) aconv #prop (rep_thm thm2);
fun eq_cong ({thm = thm1, ...}: cong, {thm = thm2, ...}: cong) =
#prop (rep_thm thm1) aconv #prop (rep_thm thm2);
fun eq_prem (thm1, thm2) =
#prop (rep_thm thm1) aconv #prop (rep_thm thm2);
fun eq_simproc ({id = s1, ...}:simproc, {id = s2, ...}:simproc) = (s1 = s2);
fun mk_simproc (name, proc, lhs, id) =
{name = name, proc = proc, lhs = lhs, id = id};
(* datatype mss *)
(*
A "mss" contains data needed during conversion:
rules: discrimination net of rewrite rules;
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);
bounds: names of bound variables already used
(for generating new names when rewriting under lambda abstractions);
prems: current premises;
mk_rews: mk: turns simplification thms into rewrite rules;
mk_sym: turns == around; (needs Drule!)
mk_eq_True: turns P into P == True - logic specific;
termless: relation for ordered rewriting;
depth: depth of conditional rewriting;
*)
datatype meta_simpset =
Mss of {
rules: rrule Net.net,
congs: (string * cong) list * string list,
procs: simproc Net.net,
bounds: string list,
prems: thm list,
mk_rews: {mk: thm -> thm list,
mk_sym: thm -> thm option,
mk_eq_True: thm -> thm option},
termless: term * term -> bool,
depth: int};
fun mk_mss (rules, congs, procs, bounds, prems, mk_rews, termless, depth) =
Mss {rules = rules, congs = congs, procs = procs, bounds = bounds,
prems=prems, mk_rews=mk_rews, termless=termless, depth=depth};
fun upd_rules(Mss{rules,congs,procs,bounds,prems,mk_rews,termless,depth}, rules') =
mk_mss(rules',congs,procs,bounds,prems,mk_rews,termless,depth);
val empty_mss =
let val mk_rews = {mk = K [], mk_sym = K None, mk_eq_True = K None}
in mk_mss (Net.empty, ([], []), Net.empty, [], [], mk_rews, Term.termless, 0) end;
fun clear_mss (Mss {mk_rews, termless, ...}) =
mk_mss (Net.empty, ([], []), Net.empty, [], [], mk_rews, termless,0);
fun incr_depth(Mss{rules,congs,procs,bounds,prems,mk_rews,termless,depth}) =
let val depth1 = depth+1
in if depth1 > !simp_depth_limit
then (warning "simp_depth_limit exceeded - giving up"; None)
else (if depth1 mod 10 = 0
then warning("Simplification depth " ^ string_of_int depth1)
else ();
Some(mk_mss(rules,congs,procs,bounds,prems,mk_rews,termless,depth1))
)
end;
(** simpset operations **)
(* term variables *)
val add_term_varnames = foldl_aterms (fn (xs, Var (x, _)) => ins_ix (x, xs) | (xs, _) => xs);
fun term_varnames t = add_term_varnames ([], t);
(* dest_mss *)
fun dest_mss (Mss {rules, congs, procs, ...}) =
{simps = map (fn (_, {thm, ...}) => thm) (Net.dest rules),
congs = map (fn (_, {thm, ...}) => thm) (fst congs),
procs =
map (fn (_, {name, lhs, id, ...}) => ((name, lhs), id)) (Net.dest procs)
|> partition_eq eq_snd
|> map (fn ps => (#1 (#1 (hd ps)), map (#2 o #1) ps))
|> Library.sort_wrt #1};
(* merge_mss *) (*NOTE: ignores mk_rews, termless and depth of 2nd mss*)
fun merge_mss
(Mss {rules = rules1, congs = (congs1,weak1), procs = procs1,
bounds = bounds1, prems = prems1, mk_rews, termless, depth},
Mss {rules = rules2, congs = (congs2,weak2), procs = procs2,
bounds = bounds2, prems = prems2, ...}) =
mk_mss
(Net.merge (rules1, rules2, eq_rrule),
(gen_merge_lists (eq_cong o pairself snd) congs1 congs2,
merge_lists weak1 weak2),
Net.merge (procs1, procs2, eq_simproc),
merge_lists bounds1 bounds2,
gen_merge_lists eq_prem prems1 prems2,
mk_rews, termless, depth);
(* add_simps *)
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 (mss as Mss {rules,...},
rrule as {thm,name,lhs,elhs,perm}) =
(trace_named_thm "Adding rewrite rule" (thm, name);
let val rrule2 as {elhs,...} = mk_rrule2 rrule
val rules' = Net.insert_term ((term_of elhs, rrule2), rules, eq_rrule)
in upd_rules(mss,rules') end
handle Net.INSERT => if quiet then mss else
(prthm true "Ignoring duplicate rewrite rule:" thm; mss));
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 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, ...} = rep_thm thm;
val prems = Logic.strip_imp_prems prop;
val concl = Drule.strip_imp_concl (cprop_of thm);
val (lhs, rhs) = Drule.dest_equals concl handle TERM _ =>
raise SIMPLIFIER ("Rewrite rule not a meta-equality", thm)
val elhs = snd (Drule.dest_equals (cprop_of (Thm.eta_conversion lhs)));
val elhs = if elhs=lhs then lhs else elhs (* try to share *)
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 (Mss{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 ==True variant,
in case there are extra vars on the rhs *)
fun rrule_eq_True(thm,name,lhs,elhs,rhs,mss,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 mss (thm2, name) @ [rrule]
end;
fun mk_rrule mss (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 mss (thm, name)
else rrule_eq_True(thm,name,lhs,elhs,rhs,mss,thm)
end;
fun orient_rrule mss (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 mss (thm, name)
else let val Mss{mk_rews={mk_sym,...},...} = mss
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',mss,thm) end
end
else rrule_eq_True(thm,name,lhs,elhs,rhs,mss,thm)
end;
fun extract_rews(Mss{mk_rews = {mk,...},...},thms) =
flat (map (fn thm => map (rpair (Thm.name_of_thm thm)) (mk thm)) thms);
fun orient_comb_simps comb mk_rrule (mss,thms) =
let val rews = extract_rews(mss,thms)
val rrules = flat (map mk_rrule rews)
in foldl comb (mss,rrules) end
(* Add rewrite rules explicitly; do not reorient! *)
fun add_simps(mss,thms) =
orient_comb_simps (insert_rrule false) (mk_rrule mss) (mss,thms);
fun mss_of thms = foldl (insert_rrule false) (empty_mss, flat
(map (fn thm => mk_rrule empty_mss (thm, Thm.name_of_thm thm)) thms));
fun extract_safe_rrules(mss,thm) =
flat (map (orient_rrule mss) (extract_rews(mss,[thm])));
(* del_simps *)
fun del_rrule(mss as Mss {rules,...},
rrule as {thm, elhs, ...}) =
(upd_rules(mss, Net.delete_term ((term_of elhs, rrule), rules, eq_rrule))
handle Net.DELETE =>
(prthm true "Rewrite rule not in simpset:" thm; mss));
fun del_simps(mss,thms) =
orient_comb_simps del_rrule (map mk_rrule2 o mk_rrule mss) (mss,thms);
(* add_congs *)
fun is_full_cong_prems [] varpairs = null varpairs
| 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 cong_name (Const (a, _)) = Some a
| cong_name (Free (a, _)) = Some ("Free: " ^ a)
| cong_name _ = None;
fun add_cong (Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, thm) =
let
val (lhs, _) = Drule.dest_equals (Drule.strip_imp_concl (cprop_of thm)) handle TERM _ =>
raise SIMPLIFIER ("Congruence not a meta-equality", thm);
(* val lhs = Pattern.eta_contract lhs; *)
val a = (case cong_name (head_of (term_of lhs)) of
Some a => a
| None =>
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
mk_mss (rules,(alist2,weak2),procs,bounds,prems,mk_rews,termless,depth)
end;
val (op add_congs) = foldl add_cong;
(* del_congs *)
fun del_cong (Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, thm) =
let
val (lhs, _) = Logic.dest_equals (concl_of thm) handle TERM _ =>
raise SIMPLIFIER ("Congruence not a meta-equality", thm);
(* val lhs = Pattern.eta_contract lhs; *)
val a = (case cong_name (head_of lhs) of
Some a => a
| None =>
raise SIMPLIFIER ("Congruence must start with a constant", thm));
val (alist,_) = congs
val alist2 = filter (fn (x,_)=> x<>a) alist
val weak2 = mapfilter (fn(a,{thm,...}) => if is_full_cong thm then None
else Some a)
alist2
in
mk_mss (rules,(alist2,weak2),procs,bounds,prems,mk_rews,termless,depth)
end;
val (op del_congs) = foldl del_cong;
(* add_simprocs *)
fun add_proc (mss as Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth},
(name, lhs, proc, id)) =
let val {sign, t, ...} = rep_cterm lhs
in (trace_term false ("Adding simplification procedure " ^ quote name ^ " for")
sign t;
mk_mss (rules, congs,
Net.insert_term ((t, mk_simproc (name, proc, lhs, id)), procs, eq_simproc)
handle Net.INSERT =>
(warning ("Ignoring duplicate simplification procedure \""
^ name ^ "\"");
procs),
bounds, prems, mk_rews, termless,depth))
end;
fun add_simproc (mss, (name, lhss, proc, id)) =
foldl add_proc (mss, map (fn lhs => (name, lhs, proc, id)) lhss);
val add_simprocs = foldl add_simproc;
(* del_simprocs *)
fun del_proc (mss as Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth},
(name, lhs, proc, id)) =
mk_mss (rules, congs,
Net.delete_term ((term_of lhs, mk_simproc (name, proc, lhs, id)), procs, eq_simproc)
handle Net.DELETE =>
(warning ("Simplification procedure \"" ^ name ^
"\" not in simpset"); procs),
bounds, prems, mk_rews, termless, depth);
fun del_simproc (mss, (name, lhss, proc, id)) =
foldl del_proc (mss, map (fn lhs => (name, lhs, proc, id)) lhss);
val del_simprocs = foldl del_simproc;
(* prems *)
fun add_prems (Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, thms) =
mk_mss (rules, congs, procs, bounds, thms @ prems, mk_rews, termless, depth);
fun prems_of_mss (Mss {prems, ...}) = prems;
(* mk_rews *)
fun set_mk_rews
(Mss {rules, congs, procs, bounds, prems, mk_rews, termless, depth}, mk) =
mk_mss (rules, congs, procs, bounds, prems,
{mk=mk, mk_sym= #mk_sym mk_rews, mk_eq_True= #mk_eq_True mk_rews},
termless, depth);
fun set_mk_sym
(Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, mk_sym) =
mk_mss (rules, congs, procs, bounds, prems,
{mk= #mk mk_rews, mk_sym= mk_sym, mk_eq_True= #mk_eq_True mk_rews},
termless,depth);
fun set_mk_eq_True
(Mss {rules,congs,procs,bounds,prems,mk_rews,termless,depth}, mk_eq_True) =
mk_mss (rules, congs, procs, bounds, prems,
{mk= #mk mk_rews, mk_sym= #mk_sym mk_rews, mk_eq_True= mk_eq_True},
termless,depth);
fun get_mk_rews (Mss {mk_rews,...}) = #mk mk_rews
fun get_mk_sym (Mss {mk_rews,...}) = #mk_sym mk_rews
fun get_mk_eq_True (Mss {mk_rews,...}) = #mk_eq_True mk_rews
(* termless *)
fun set_termless
(Mss {rules, congs, procs, bounds, prems, mk_rews, depth, ...}, termless) =
mk_mss (rules, congs, procs, bounds, prems, mk_rews, termless, depth);
(** 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 cprop_of;
val lhs_of = fst o dest_eq;
val rhs_of = snd o dest_eq;
fun beta_eta_conversion t =
let val thm = beta_conversion true t;
in transitive thm (eta_conversion (rhs_of thm)) end;
fun check_conv msg thm thm' =
let
val thm'' = transitive thm (transitive
(symmetric (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, ...} = 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 (prthm true "Extra vars on rhs:" thm; [])
else [mk_rrule2{thm=thm, name="", lhs=lhs, elhs=elhs, perm=false}]
end;
(* 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;
(*
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)
(mss as Mss{rules, procs, termless, prems, congs, depth,...}) t =
let
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 _ = if Sign.subsig (sign, signt) then ()
else (prthm true "Ignoring rewrite rule from different theory:" thm;
raise Pattern.MATCH);
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';
case incr_depth mss of
None => (trace_thm "FAILED - reached depth limit" thm'; None)
| Some mss =>
(case prover mss 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 ([]:simproc list) = None
| proc_rews ({name, proc, lhs, ...} :: ps) =
if Pattern.matches tsigt (term_of lhs, 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 prems 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 _ = if Sign.subsig (sign, signt) then ()
else error("Congruence rule from different theory")
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 (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 imp_cong' e = combination (combination refl_implies e);
fun bottomc ((simprem,useprem,mutsimp), prover, sign, maxidx) =
let
fun botc skel mss t =
if is_Var skel then None
else
(case subc skel mss t of
some as Some thm1 =>
(case rewritec (prover, sign, maxidx) mss (rhs_of thm1) of
Some (thm2, skel2) =>
transitive2 (transitive thm1 thm2)
(botc skel2 mss (rhs_of thm2))
| None => some)
| None =>
(case rewritec (prover, sign, maxidx) mss t of
Some (thm2, skel2) => transitive2 thm2
(botc skel2 mss (rhs_of thm2))
| None => None))
and try_botc mss t =
(case botc skel0 mss t of
Some trec1 => trec1 | None => (reflexive t))
and subc skel
(mss as Mss{rules,congs,procs,bounds,prems,mk_rews,termless,depth}) t0 =
(case term_of t0 of
Abs (a, T, t) =>
let val b = variant bounds a
val (v, t') = Thm.dest_abs (Some ("." ^ b)) t0
val mss' = mk_mss (rules, congs, procs, b :: bounds, prems, mk_rews, termless,depth)
val skel' = case skel of Abs (_, _, sk) => sk | _ => skel0
in case botc skel' mss' t' of
Some thm => Some (abstract_rule a v thm)
| None => None
end
| t $ _ => (case t of
Const ("==>", _) $ _ => impc t0 mss
| Abs _ =>
let val thm = beta_conversion false t0
in case subc skel0 mss (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 mss ct of
Some thm1 =>
(case botc uskel mss cu of
Some thm2 => Some (combination thm1 thm2)
| None => Some (combination thm1 (reflexive cu)))
| None =>
(case botc uskel mss 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 mss, sign, maxidx) cong t0;
val t = if_none (apsome 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 mss 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 mss =
if mutsimp then mut_impc0 [] ct [] [] mss else nonmut_impc ct mss
and rules_of_prem mss 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 (mss, asm), Some asm) end
and add_rrules (rrss, asms) mss =
add_prems (foldl (insert_rrule true) (mss, flat rrss), mapfilter 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) mss eq =
let
val mss' = add_rrules (rev rrss, rev asms) mss;
val concl' =
Drule.mk_implies (prem, if_none (apsome rhs_of eq) concl);
val dprem = apsome (curry (disch false) prem)
in case rewritec (prover, sign, maxidx) mss' concl' of
None => rebuild prems concl' rrss asms mss (dprem eq)
| Some (eq', _) => transitive2 (foldl (disch false o swap)
(the (transitive3 (dprem eq) eq'), prems))
(mut_impc0 (rev prems) (rhs_of eq') (rev rrss) (rev asms) mss)
end
and mut_impc0 prems concl rrss asms mss =
let
val prems' = strip_imp_prems concl;
val (rrss', asms') = split_list (map (rules_of_prem mss) prems')
in mut_impc (prems @ prems') (strip_imp_concl concl) (rrss @ rrss')
(asms @ asms') [] [] [] [] mss ~1 ~1
end
and mut_impc [] concl [] [] prems' rrss' asms' eqns mss changed k =
transitive1 (foldl (fn (eq2, (eq1, prem)) => transitive1 eq1
(apsome (curry (disch false) prem) eq2)) (None, eqns ~~ prems'))
(if changed > 0 then
mut_impc (rev prems') concl (rev rrss') (rev asms')
[] [] [] [] mss ~1 changed
else rebuild prems' concl rrss' asms' mss
(botc skel0 (add_rrules (rev rrss', rev asms') mss) concl))
| mut_impc (prem :: prems) concl (rrs :: rrss) (asm :: asms)
prems' rrss' asms' eqns mss changed k =
case (if k = 0 then None else botc skel0 (add_rrules
(rev rrss' @ rrss, rev asms' @ asms) mss) prem) of
None => mut_impc prems concl rrss asms (prem :: prems')
(rrs :: rrss') (asm :: asms') (None :: eqns) mss 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 + foldl Int.max (~1, map (fn p =>
find_index_eq p tprems) (#hyps (rep_thm eqn)));
val (rrs', asm') = rules_of_prem mss prem'
in mut_impc prems concl rrss asms (prem' :: prems')
(rrs' :: rrss') (asm' :: asms') (Some (foldr (disch true)
(take (i, prems), imp_cong' eqn (reflexive (Drule.list_implies
(drop (i, prems), concl))))) :: eqns) mss (length prems') ~1
end
(* legacy code - only for backwards compatibility *)
and nonmut_impc ct mss =
let val (prem, conc) = dest_implies ct;
val thm1 = if simprem then botc skel0 mss prem else None;
val prem1 = if_none (apsome rhs_of thm1) prem;
val mss1 = if not useprem then mss else add_rrules
(apsnd single (apfst single (rules_of_prem mss prem1))) mss
in (case botc skel0 mss1 conc of
None => (case thm1 of
None => None
| Some thm1' => Some (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 (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
mss: contains equality theorems of the form [|p1,...|] ==> t==u
prover: how to solve premises in conditional rewrites and congruences
*)
fun rewrite_cterm mode prover mss ct =
let val {sign, t, maxidx, ...} = rep_cterm ct
val Mss{depth, ...} = mss
in trace_cterm false "SIMPLIFIER INVOKED ON THE FOLLOWING TERM:" ct;
simp_depth := depth;
bottomc (mode, prover, sign, maxidx) mss ct
end
handle THM (s, _, thms) =>
error ("Exception THM was raised in simplifier:\n" ^ s ^ "\n" ^
Pretty.string_of (Display.pretty_thms thms));
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
fun goals_conv pred cv =
let fun gconv i ct =
let val (A,B) = Drule.dest_implies ct
in imp_cong' (if pred i then cv A else reflexive A) (gconv (i+1) B) end
handle TERM _ => reflexive ct
in gconv 1 end;
(* Rewrite A in !!x1,...,xn. A *)
fun forall_conv cv ct =
let val p as (ct1, ct2) = Thm.dest_comb ct
in (case pairself term_of p of
(Const ("all", _), Abs (s, _, _)) =>
let val (v, ct') = Thm.dest_abs (Some "@") ct2;
in Thm.combination (Thm.reflexive ct1)
(Thm.abstract_rule s v (forall_conv cv ct'))
end
| _ => cv ct)
end handle TERM _ => cv ct;
(*Use a conversion to transform a theorem*)
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
(*Rewrite a cterm*)
fun rewrite_aux _ _ [] = (fn ct => Thm.reflexive ct)
| rewrite_aux prover full thms = rewrite_cterm (full, false, false) prover (mss_of thms);
(*Rewrite a theorem*)
fun simplify_aux _ _ [] = (fn th => th)
| simplify_aux prover full thms =
fconv_rule (rewrite_cterm (full, false, false) prover (mss_of thms));
fun rewrite_thm mode prover mss = fconv_rule (rewrite_cterm mode prover mss);
(*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 =
fconv_rule (goals_conv (K true) (rewrite_cterm (true, true, false) prover
(mss_of thms))) th;
(*Rewrite the subgoal of a proof state (represented by a theorem) *)
fun rewrite_goal_rule mode prover mss i thm =
if 0 < i andalso i <= nprems_of thm
then fconv_rule (goals_conv (fn j => j=i) (rewrite_cterm mode prover mss)) thm
else raise THM("rewrite_goal_rule",i,[thm]);
(*simple term rewriting -- without proofs*)
fun rewrite_term sg rules procs =
Pattern.rewrite_term (Sign.tsig_of sg) (map decomp_simp' rules) procs;
end;
structure BasicMetaSimplifier: BASIC_META_SIMPLIFIER = MetaSimplifier;
open BasicMetaSimplifier;