update in delayed_updating

[helm.git] / matita / matita / contribs / lambdadelta / delayed_updating / reduction / dfr.ma

diff --git a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
index f0b3f5f319c56b603e94593c0355d2e8347df5ad..e0d17a691bfd09951f10149d0705ced65853e1be 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
@@ -12,23 +12,23 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "ground/xoa/ex_3_1.ma".
-include "delayed_updating/syntax/path_structure.ma".
-include "delayed_updating/syntax/path_balanced.ma".
 include "delayed_updating/substitution/fsubst.ma".
-(*
-include "delayed_updating/notation/functions/pitchforkleftarrow_3.ma".
-*)
+include "delayed_updating/syntax/prototerm_constructors.ma".
+include "delayed_updating/syntax/prototerm_eq.ma".
+include "delayed_updating/syntax/path_head.ma".
+include "delayed_updating/syntax/path_depth.ma".
+include "delayed_updating/syntax/path_reverse.ma".
+include "delayed_updating/notation/relations/black_rightarrow_df_4.ma".
 
-(* DELAYED FOCALIZED REDUCTION **********************************************)
+(* DELAYED FOCUSED REDUCTION ************************************************)
 
-inductive dfr (p) (q) (t): predicate preterm ≝
-| dfr_beta (b) (n):
-  let r ≝ p;;(𝗔;b;;(𝗟;q,𝗱❨n❩)) in
-  r ϵ t → ⊓⊗b → dfr p q t (t[⋔r←t⋔p,𝗦])
+definition dfr (p) (q): relation2 prototerm prototerm ≝
+           λt1,t2. ∃n:pnat.
+           let r ≝ p●𝗔◗𝗟◗q in
+           ∧∧ (𝗟◗q)ᴿ = ↳[n](𝗟◗q)ᴿ & r◖𝗱n ϵ t1 &
+              t1[⋔r←𝛕n.(t1⋔(p◖𝗦))] ⇔ t2
 .
-(*
+
 interpretation
-  "focalized substitution (preterm)"
-  'PitchforkLeftArrow t p u = (fsubst p u t).
-*)
+  "focused reduction with delayed updating (prototerm)"
+  'BlackRightArrowDF t1 p q t2 = (dfr p q t1 t2).