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 6890031062b55e008868119ea09cb6021a5f172e..89c9599079d4f71cc7be1045566f22b014420356 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
@@ -12,20 +12,26 @@
 (*                                                                        *)
 (**************************************************************************)
 
-include "delayed_updating/syntax/path_depth.ma".
+include "delayed_updating/syntax/prototerm_constructors.ma".
+include "delayed_updating/syntax/prototerm_equivalence.ma".
+include "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/substitution/lift.ma".
 include "delayed_updating/syntax/path_structure.ma".
 include "delayed_updating/syntax/path_balanced.ma".
-include "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/syntax/path_depth.ma".
 include "delayed_updating/notation/relations/black_rightarrow_df_4.ma".
+include "ground/xoa/ex_1_2.ma".
+include "ground/xoa/and_4.ma".
 
 (* DELAYED FOCUSED REDUCTION ************************************************)
 
-inductive dfr (p) (q) (t): predicate preterm ≝
-| dfr_beta (b):
-  let r ≝ p●𝗔◗b●𝗟◗q◖𝗱❨↑❘q❘❩ in
-  r ϵ t → ⊓⊗b → dfr p q t (t[⋔r←t⋔(p◖𝗦)])
+definition dfr (p) (q): relation2 prototerm prototerm ≝
+           λt1,t2. ∃∃b,n.
+           let r ≝ p●𝗔◗b●𝗟◗q in
+           ∧∧ ⊗b ϵ 𝐁 & ∀f. ↑❘q❘ = (↑[q]⫯f)@❨n❩ & r◖𝗱n ϵ t1 &
+              t1[⋔r←𝛗(n+❘b❘).(t1⋔(p◖𝗦))] ⇔ t2
 .
 
 interpretation
-  "focused balanced reduction with delayed updating (preterm)"
+  "focused balanced reduction with delayed updating (prototerm)"
   'BlackRightArrowDF t1 p q t2 = (dfr p q t1 t2).