improved tracing of permutative rules.
(* Title: Pure/meta_simplifier.ML
ID: $Id$
Author: Tobias Nipkow
Copyright 1994 University of Cambridge
Meta Simplification
*)
signature META_SIMPLIFIER =
sig
exception SIMPLIFIER of string * thm
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 set_termless : meta_simpset * (term * term -> bool) -> meta_simpset
val trace_simp : bool ref
val debug_simp : bool ref
val rewrite_cterm : bool * bool * bool
-> (meta_simpset -> thm -> thm option)
-> meta_simpset -> cterm -> thm
val rewrite_rule_aux : (meta_simpset -> thm -> thm option) -> 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
end;
structure MetaSimplifier : META_SIMPLIFIER =
struct
(** diagnostics **)
exception SIMPLIFIER of string * thm;
fun prnt warn a = if warn then warning a else writeln a;
fun prtm warn a sign t =
(prnt warn a; prnt warn (Sign.string_of_term sign t));
fun prctm warn a t =
(prnt warn a; prnt warn (Display.string_of_cterm t));
fun prthm warn a thm =
let val {sign, prop, ...} = rep_thm thm
in prtm warn a sign prop end;
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 warn a thm =
let val {sign, prop, ...} = rep_thm thm
in trace_term warn a sign prop end;
(** meta simp sets **)
(* basic components *)
type rrule = {thm: thm, lhs: term, elhs: cterm, fo: bool, perm: bool};
(* thm: the rewrite rule
lhs: the left-hand side
elhs: the etac-contracted lhs.
fo: use first-order matching
perm: the rewrite rule is permutative
Reamrks:
- 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;
*)
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};
fun mk_mss (rules, congs, procs, bounds, prems, mk_rews, termless) =
Mss {rules = rules, congs = congs, procs = procs, bounds = bounds,
prems=prems, mk_rews=mk_rews, termless=termless};
fun upd_rules(Mss{rules,congs,procs,bounds,prems,mk_rews,termless}, rules') =
mk_mss(rules',congs,procs,bounds,prems,mk_rews,termless);
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) end;
fun clear_mss (Mss {mk_rews, termless, ...}) =
mk_mss (Net.empty, ([], []), Net.empty, [], [], mk_rews, termless);
(** 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 and termless of 2nd mss*)
fun merge_mss
(Mss {rules = rules1, congs = (congs1,weak1), procs = procs1,
bounds = bounds1, prems = prems1, mk_rews, termless},
Mss {rules = rules2, congs = (congs2,weak2), procs = procs2,
bounds = bounds2, prems = prems2, ...}) =
mk_mss
(Net.merge (rules1, rules2, eq_rrule),
(generic_merge (eq_cong o pairself snd) I I congs1 congs2,
merge_lists weak1 weak2),
Net.merge (procs1, procs2, eq_simproc),
merge_lists bounds1 bounds2,
generic_merge eq_prem I I prems1 prems2,
mk_rews, termless);
(* add_simps *)
fun mk_rrule2{thm,lhs,elhs,perm} =
let val fo = Pattern.first_order (term_of elhs) orelse not(Pattern.pattern (term_of elhs))
in {thm=thm,lhs=lhs,elhs=elhs,fo=fo,perm=perm} end
fun insert_rrule(mss as Mss {rules,...},
rrule as {thm,lhs,elhs,perm}) =
(trace_thm false "Adding rewrite rule:" thm;
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 =>
(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 (#tsig (Sign.rep_sg 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 mk_eq_True (Mss{mk_rews={mk_eq_True,...},...}) thm =
case mk_eq_True thm of
None => []
| Some eq_True => let val (_,_,lhs,elhs,_,_) = decomp_simp eq_True
in [{thm=eq_True, 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,lhs,elhs,rhs,mss,thm2) =
let val rrule = {thm=thm, 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 @ [rrule]
end;
fun mk_rrule mss thm =
let val (_,prems,lhs,elhs,rhs,perm) = decomp_simp thm
in if perm then [{thm=thm, 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
else rrule_eq_True(thm,lhs,elhs,rhs,mss,thm)
end;
fun orient_rrule mss thm =
let val (sign,prems,lhs,elhs,rhs,perm) = decomp_simp thm
in if perm then [{thm=thm,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
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',lhs',elhs',rhs',mss,thm) end
end
else rrule_eq_True(thm,lhs,elhs,rhs,mss,thm)
end;
fun extract_rews(Mss{mk_rews = {mk,...},...},thms) = flat(map mk 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 (mk_rrule mss) (mss,thms);
fun mss_of thms =
foldl insert_rrule (empty_mss, flat(map (mk_rrule empty_mss) thms));
fun extract_safe_rrules(mss,thm) =
flat (map (orient_rrule mss) (extract_rews(mss,[thm])));
fun add_safe_simp(mss,thm) =
foldl insert_rrule (mss, extract_safe_rrules(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 add_cong (Mss {rules,congs,procs,bounds,prems,mk_rews,termless}, 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, _) = dest_Const (head_of (term_of lhs)) handle TERM _ =>
raise SIMPLIFIER ("Congruence must start with a constant", 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)
end;
val (op add_congs) = foldl add_cong;
(* del_congs *)
fun del_cong (Mss {rules,congs,procs,bounds,prems,mk_rews,termless}, 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, _) = dest_Const (head_of lhs) handle TERM _ =>
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)
end;
val (op del_congs) = foldl del_cong;
(* add_simprocs *)
fun add_proc (mss as Mss {rules,congs,procs,bounds,prems,mk_rews,termless},
(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))
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},
(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);
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}, thms) =
mk_mss (rules, congs, procs, bounds, thms @ prems, mk_rews, termless);
fun prems_of_mss (Mss {prems, ...}) = prems;
(* mk_rews *)
fun set_mk_rews
(Mss {rules, congs, procs, bounds, prems, mk_rews, termless}, 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);
fun set_mk_sym
(Mss {rules, congs, procs, bounds, prems, mk_rews, termless}, 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);
fun set_mk_eq_True
(Mss {rules, congs, procs, bounds, prems, mk_rews, termless}, 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);
(* termless *)
fun set_termless
(Mss {rules, congs, procs, bounds, prems, mk_rews, termless = _}, termless) =
mk_mss (rules, congs, procs, bounds, prems, mk_rews, termless);
(** rewriting **)
(*
Uses conversions, see:
L C Paulson, A higher-order implementation of rewriting,
Science of Computer Programming 3 (1983), pages 119-149.
*)
type prover = meta_simpset -> thm -> thm option;
type termrec = (Sign.sg_ref * term list) * term;
type conv = meta_simpset -> termrec -> termrec;
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 false "SUCCEEDED" thm' else (); Some thm'') end
handle THM _ =>
let val {sign, prop = _ $ _ $ prop0, ...} = rep_thm thm;
in
(trace_thm false "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, 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, ...}) 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, 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' = #prop (rep_thm 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_thm false "Cannot apply permutative rewrite rule:" thm;
trace_thm false "Term does not become smaller:" thm'; None)
else
(trace_thm false "Applying instance of rewrite rule:" thm;
if unconditional
then
(trace_thm false "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 false "Trying to rewrite:" thm';
case prover mss thm' of
None => (trace_thm false "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 #prop (rep_thm 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 proc signt prems eta_t of
None => (debug false "FAILED"; proc_rews ps)
| Some raw_thm =>
(trace_thm false ("Procedure " ^ quote name ^ " produced rewrite rule:") raw_thm;
(case rews (mk_procrule raw_thm) of
None => (trace_cterm false "IGNORED - 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 (rhs_of eta_thm)), 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, ...} = rep_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 false "Applying congruence rule:" thm';
fun err (msg, thm) = (prthm false msg thm; error "Failed congruence proof!")
in case prover thm' of
None => err ("Could not prove", thm')
| Some thm2 => (case check_conv true (beta_eta_conversion t) thm2 of
None => err ("Should not have proved", thm2)
| Some thm2' => thm2')
end;
val (cA, (cB, cC)) =
apsnd dest_equals (dest_implies (hd (cprems_of Drule.imp_cong)));
fun transitive' thm1 None = Some thm1
| transitive' thm1 (Some thm2) = Some (transitive thm1 thm2);
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) =>
transitive' (transitive thm1 thm2)
(botc skel2 mss (rhs_of thm2))
| None => some)
| None =>
(case rewritec (prover, sign, maxidx) mss t of
Some (thm2, skel2) => transitive' 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}) 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)
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 ("==>", _) $ _ =>
let val (s, u) = Drule.dest_implies t0
in impc (s, u, mss) end
| 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 h of
Const(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 = 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 mss cl of
None => Some thm
| Some thm' => Some (transitive thm
(combination thm' (reflexive cr)))
end handle TERM _ => error "congc result"
| Pattern.MATCH => appc ()))
| _ => appc ()
end)
| _ => None)
and impc args =
if mutsimp
then let val (prem, conc, mss) = args
in apsome snd (mut_impc ([], prem, conc, mss)) end
else nonmut_impc args
and mut_impc (prems, prem, conc, mss) = (case botc skel0 mss prem of
None => mut_impc1 (prems, prem, conc, mss)
| Some thm1 =>
let val prem1 = rhs_of thm1
in (case mut_impc1 (prems, prem1, conc, mss) of
None => Some (None,
combination (combination refl_implies thm1) (reflexive conc))
| Some (x, thm2) => Some (x, transitive (combination (combination
refl_implies thm1) (reflexive conc)) thm2))
end)
and mut_impc1 (prems, prem1, conc, mss) =
let
fun uncond ({thm, lhs, elhs, perm}) =
if Thm.no_prems thm then Some lhs else None
val (lhss1, mss1) =
if maxidx_of_term (term_of prem1) <> ~1
then (trace_cterm true
"Cannot add premise as rewrite rule because it contains (type) unknowns:" prem1;
([],mss))
else let val thm = assume prem1
val rrules1 = extract_safe_rrules (mss, thm)
val lhss1 = mapfilter uncond rrules1
val mss1 = foldl insert_rrule (add_prems (mss, [thm]), rrules1)
in (lhss1, mss1) end
fun disch1 thm =
let val (cB', cC') = dest_eq thm
in
implies_elim (Thm.instantiate
([], [(cA, prem1), (cB, cB'), (cC, cC')]) Drule.imp_cong)
(implies_intr prem1 thm)
end
fun rebuild None = (case rewritec (prover, sign, maxidx) mss
(mk_implies (prem1, conc)) of
None => None
| Some (thm, _) => Some (None, thm))
| rebuild (Some thm2) =
let val thm = disch1 thm2
in (case rewritec (prover, sign, maxidx) mss (rhs_of thm) of
None => Some (None, thm)
| Some (thm', _) =>
let val (prem, conc) = Drule.dest_implies (rhs_of thm')
in (case mut_impc (prems, prem, conc, mss) of
None => Some (None, transitive thm thm')
| Some (x, thm'') =>
Some (x, transitive (transitive thm thm') thm''))
end handle TERM _ => Some (None, transitive thm thm'))
end
fun simpconc () =
let val (s, t) = Drule.dest_implies conc
in case mut_impc (prems @ [prem1], s, t, mss1) of
None => rebuild None
| Some (Some i, thm2) =>
let
val (prem, cC') = Drule.dest_implies (rhs_of thm2);
val thm2' = transitive (disch1 thm2) (Thm.instantiate
([], [(cA, prem1), (cB, prem), (cC, cC')])
Drule.swap_prems_eq)
in if i=0 then apsome (apsnd (transitive thm2'))
(mut_impc1 (prems, prem, mk_implies (prem1, cC'), mss))
else Some (Some (i-1), thm2')
end
| Some (None, thm) => rebuild (Some thm)
end handle TERM _ => rebuild (botc skel0 mss1 conc)
in
let
val tsig = Sign.tsig_of sign
fun reducible t =
exists (fn lhs => Pattern.matches_subterm tsig (lhs, term_of t)) lhss1;
in case dropwhile (not o reducible) prems of
[] => simpconc ()
| red::rest => (trace_cterm false "Can now reduce premise:" red;
Some (Some (length rest), reflexive (mk_implies (prem1, conc))))
end
end
(* legacy code - only for backwards compatibility *)
and nonmut_impc (prem, conc, mss) =
let val thm1 = if simprem then botc skel0 mss prem else None;
val prem1 = if_none (apsome rhs_of thm1) prem;
val maxidx1 = maxidx_of_term (term_of prem1)
val mss1 =
if not useprem then mss else
if maxidx1 <> ~1
then (trace_cterm true
"Cannot add premise as rewrite rule because it contains (type) unknowns:" prem1;
mss)
else let val thm = assume prem1
in add_safe_simp (add_prems (mss, [thm]), thm) end
in (case botc skel0 mss1 conc of
None => (case thm1 of
None => None
| Some thm1' => Some (combination
(combination refl_implies thm1') (reflexive conc)))
| Some thm2 =>
let
val conc2 = rhs_of thm2;
val thm2' = implies_elim (Thm.instantiate
([], [(cA, prem1), (cB, conc), (cC, conc2)]) Drule.imp_cong)
(implies_intr prem1 thm2)
in (case thm1 of
None => Some thm2'
| Some thm1' => Some (transitive (combination
(combination refl_implies 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
*)
(* FIXME: check that #bounds(mss) does not "occur" in ct already *)
fun rewrite_cterm mode prover mss ct =
let val {sign, t, maxidx, ...} = rep_cterm ct
in 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 (pretty_thms thms));
(*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*)
(*Do not rewrite flex-flex pairs*)
fun goals_conv pred cv =
let fun gconv i ct =
let val (A,B) = Drule.dest_implies ct
val (thA,j) = case term_of A of
Const("=?=",_)$_$_ => (reflexive A, i)
| _ => (if pred i then cv A else reflexive A, i+1)
in combination (combination refl_implies thA) (gconv j B) end
handle TERM _ => reflexive ct
in gconv 1 end;
(*Use a conversion to transform a theorem*)
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th;
(*Rewrite a theorem*)
fun rewrite_rule_aux _ [] = (fn th => th)
| rewrite_rule_aux prover thms =
fconv_rule (rewrite_cterm (true,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]);
end;
open MetaSimplifier;