lucas - fixed bug with name capture variables bound outside redex could (previously)conflict with scheme variables that occur in the conditions of an equation, and which were renamed to avoid conflict with another instantiation. This has now been fixed.
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(* Title: sys/rw_inst.ML
Author: Lucas Dixon, University of Edinburgh
lucas.dixon@ed.ac.uk
Created: 25 Aug 2004
*)
(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- *)
(* DESCRIPTION:
rewriting using a conditional meta-equality theorem which supports
schematic variable instantiation.
*)
(* -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=- *)
signature RW_INST =
sig
(* Rewrite: give it instantiation infromation, a rule, and the
target thm, and it will return the rewritten target thm *)
val rw :
((Term.indexname * Term.typ) list * (* type var instantiations *)
(Term.indexname * Term.term) list) (* schematic var instantiations *)
* (string * Term.typ) list * (* bound types *)
Term.term -> (* outer term for instantiation *)
Thm.thm -> (* rule with indexies lifted *)
Thm.thm -> (* target thm *)
Thm.thm (* rewritten theorem possibly
with additional premises for
rule conditions *)
(* used tools *)
val mk_abstractedrule :
(string * Term.typ) list -> Thm.thm -> Thm.cterm list * Thm.thm
val mk_fixtvar_tyinsts :
Term.indexname list ->
Term.term list -> ((string * int) * Term.typ) list * string list
val mk_renamings :
Term.term -> Thm.thm -> (((string * int) * Term.typ) * Term.term) list
val new_tfree :
((string * int) * Term.sort) *
(((string * int) * Term.typ) list * string list) ->
((string * int) * Term.typ) list * string list
val cross_inst : (Term.indexname * Term.term) list
-> (Term.indexname * Term.term) list
val beta_contract_tac : Thm.thm -> Thm.thm
val beta_eta_contract_tac : Thm.thm -> Thm.thm
end;
structure RWInst : RW_INST=
struct
(* beta contract the theorem *)
fun beta_contract_tac thm =
equal_elim (Thm.beta_conversion true (Thm.cprop_of thm)) thm;
(* beta-eta contract the theorem *)
fun beta_eta_contract_tac thm =
let
val thm2 = equal_elim (Thm.beta_conversion true (Thm.cprop_of thm)) thm
val thm3 = equal_elim (Thm.eta_conversion (Thm.cprop_of thm2)) thm2
in thm3 end;
(* Given a list of variables that were bound, and a that has been
instantiated with free variable placeholders for the bound vars, it
creates an abstracted version of the theorem, with local bound vars as
lambda-params:
Ts:
("x", ty)
rule::
C :x ==> P :x = Q :x
results in:
("!! x. C x", (%x. p x = %y. p y) [!! x. C x])
note: assumes rule is instantiated
*)
(* Note, we take abstraction in the order of last abstraction first *)
fun mk_abstractedrule Ts rule =
let
val ctermify = Thm.cterm_of (Thm.sign_of_thm rule);
(* now we change the names the temporary free vars that represent
bound vars with binders outside the redex *)
val prop = Thm.prop_of rule;
val names = Term.add_term_names (prop, []);
val (fromnames,tonames,names2,Ts') =
foldl (fn ((rnf,rnt,names, Ts'),(n,ty)) =>
let val n2 = Term.variant names n in
(ctermify (Free(RWTools.mk_fake_bound_name n,
ty)) :: rnf,
ctermify (Free(n2,ty)) :: rnt,
n2 :: names,
(n2,ty) :: Ts')
end)
(([],[],names, []), Ts);
val rule' = rule |> Drule.forall_intr_list fromnames
|> Drule.forall_elim_list tonames;
(* make unconditional rule and prems *)
val (uncond_rule, cprems) = IsaND.allify_conditions ctermify (rev Ts')
rule';
(* using these names create lambda-abstracted version of the rule *)
val abstractions = rev (Ts' ~~ tonames);
val abstract_rule = foldl (fn (th,((n,ty),ct)) =>
Thm.abstract_rule n ct th)
(uncond_rule, abstractions);
in (cprems, abstract_rule) end;
(* given names to avoid, and vars that need to be fixed, it gives
unique new names to the vars so that they can be fixed as free
variables *)
(* make fixed unique free variable instantiations for non-ground vars *)
(* Create a table of vars to be renamed after instantiation - ie
other uninstantiated vars in the hyps of the rule
ie ?z in C ?z ?x ==> A ?x ?y = B ?x ?y *)
fun mk_renamings tgt rule_inst =
let
val rule_conds = Thm.prems_of rule_inst
val names = foldr Term.add_term_names (tgt :: rule_conds, []);
val (conds_tyvs,cond_vs) =
foldl (fn ((tyvs, vs), t) =>
(Library.union
(Term.term_tvars t, tyvs),
Library.union
(map Term.dest_Var (Term.term_vars t), vs)))
(([],[]), rule_conds);
val termvars = map Term.dest_Var (Term.term_vars tgt);
val vars_to_fix = Library.union (termvars, cond_vs);
val (renamings, names2) =
foldr (fn (((n,i),ty), (vs, names')) =>
let val n' = Term.variant names' n in
((((n,i),ty), Free (n', ty)) :: vs, n'::names')
end)
(vars_to_fix, ([], names));
in renamings end;
(* make a new fresh typefree instantiation for the given tvar *)
fun new_tfree (tv as (ix,sort), (pairs,used)) =
let val v = variant used (string_of_indexname ix)
in ((ix,TFree(v,sort))::pairs, v::used) end;
(* make instantiations to fix type variables that are not
already instantiated (in ignore_ixs) from the list of terms. *)
fun mk_fixtvar_tyinsts ignore_ixs ts =
let val (tvars, tfreenames) =
foldr (fn (t, (varixs, tfreenames)) =>
(Term.add_term_tvars (t,varixs),
Term.add_term_tfree_names (t,tfreenames)))
(ts, ([],[]));
val unfixed_tvars = filter (fn (ix,s) => not (ix mem ignore_ixs)) tvars;
val (fixtyinsts, _) = foldr new_tfree (unfixed_tvars, ([], tfreenames))
in (fixtyinsts, tfreenames) end;
(* cross-instantiate the instantiations - ie for each instantiation
replace all occurances in other instantiations - no loops are possible
and thus only one-parsing of the instantiations is necessary. *)
fun cross_inst insts =
let
fun instL (ix, t) =
map (fn (ix2,t2) => (ix2, Term.subst_vars ([], [(ix, t)]) t2));
fun cross_instL ([], l) = rev l
| cross_instL ((ix, t) :: insts, l) =
cross_instL (instL (ix, t) insts, (ix, t) :: (instL (ix, t) l));
in cross_instL (insts, []) end;
(* as above but for types -- I don't know if this is needed, will we ever incur mixed up types? *)
fun cross_inst_typs insts =
let
fun instL (ix, ty) =
map (fn (ix2,ty2) => (ix2, Term.typ_subst_TVars [(ix, ty)] ty2));
fun cross_instL ([], l) = rev l
| cross_instL ((ix, t) :: insts, l) =
cross_instL (instL (ix, t) insts, (ix, t) :: (instL (ix, t) l));
in cross_instL (insts, []) end;
(* assume that rule and target_thm have distinct var names *)
(* THINK: efficient version with tables for vars for: target vars,
introduced vars, and rule vars, for quicker instantiation? *)
(* The outerterm defines which part of the target_thm was modified *)
(* Note: we take Ts in the upterm order, ie last abstraction first.,
and with an outeterm where the abstracted subterm has the arguments in
the revered order, ie first abstraction first. *)
fun rw ((nonfixed_typinsts, unprepinsts), Ts, outerterm) rule target_thm =
let
(* general signature info *)
val target_sign = (Thm.sign_of_thm target_thm);
val ctermify = Thm.cterm_of target_sign;
val ctypeify = Thm.ctyp_of target_sign;
(* fix all non-instantiated tvars *)
val (fixtyinsts, othertfrees) =
mk_fixtvar_tyinsts (map fst nonfixed_typinsts)
[Thm.prop_of rule, Thm.prop_of target_thm];
val typinsts = cross_inst_typs (nonfixed_typinsts @ fixtyinsts);
(* certified instantiations for types *)
val ctyp_insts = map (apsnd ctypeify) typinsts;
(* type instantiated versions *)
val tgt_th_tyinst =
Thm.instantiate (ctyp_insts, []) target_thm;
val rule_tyinst =
Thm.instantiate (ctyp_insts, []) rule;
(* type instanitated outer term *)
val outerterm_tyinst =
Term.subst_vars (typinsts,[]) outerterm;
(* type-instantiate the var instantiations *)
val insts_tyinst = foldr (fn ((ix,t),insts_tyinst) =>
(ix, Term.subst_vars (typinsts,[]) t)
:: insts_tyinst)
(unprepinsts,[]);
(* cross-instantiate *)
val insts_tyinst_inst = cross_inst insts_tyinst;
(* create certms of instantiations *)
val cinsts_tyinst =
map (fn (ix,t) => (ctermify (Var (ix, Term.type_of t)),
ctermify t)) insts_tyinst_inst;
(* The instantiated rule *)
val rule_inst = rule_tyinst |> Thm.instantiate ([], cinsts_tyinst);
(* Create a table of vars to be renamed after instantiation - ie
other uninstantiated vars in the hyps the *instantiated* rule
ie ?z in C ?z ?x ==> A ?x ?y = B ?x ?y *)
val renamings = mk_renamings (Thm.prop_of tgt_th_tyinst)
rule_inst;
val cterm_renamings =
map (fn (x,y) => (ctermify (Var x), ctermify y)) renamings;
(* Create the specific version of the rule for this target application *)
val outerterm_inst =
outerterm_tyinst
|> Term.subst_vars ([], insts_tyinst_inst)
|> Term.subst_vars ([], map (fn ((ix,ty),t) => (ix,t))
renamings);
val couter_inst = Thm.reflexive (ctermify outerterm_inst);
val (cprems, abstract_rule_inst) =
rule_inst |> Thm.instantiate ([], cterm_renamings)
|> mk_abstractedrule Ts;
val specific_tgt_rule =
beta_eta_contract_tac
(Thm.combination couter_inst abstract_rule_inst);
(* create an instantiated version of the target thm *)
val tgt_th_inst =
tgt_th_tyinst |> Thm.instantiate ([], cinsts_tyinst)
|> Thm.instantiate ([], cterm_renamings);
val (vars,frees_of_fixed_vars) = Library.split_list cterm_renamings;
in
(beta_eta_contract_tac tgt_th_inst)
|> Thm.equal_elim specific_tgt_rule
|> Drule.implies_intr_list cprems
|> Drule.forall_intr_list frees_of_fixed_vars
|> Drule.forall_elim_list vars
|> fst o Thm.varifyT' othertfrees
|> Drule.zero_var_indexes
end;
end; (* struct *)