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 a99d8ca0633e96180ddcb3cf2220c6d18d6ba880..3c328fcb206fb067dfa1e54ebf809d400a1ee856 100644 (file)
--- a/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
+++ b/matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma
@@ -12,19 +12,26 @@
 (*                                                                        *)
 (**************************************************************************)
 
+include "delayed_updating/unwind1/unwind.ma".
+include "delayed_updating/substitution/fsubst.ma".
+include "delayed_updating/syntax/prototerm_constructors.ma".
+include "delayed_updating/syntax/prototerm_equivalence.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/relations/black_rightarrow_4.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 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. ∃∃b,n.
+           let r ≝ p●𝗔◗b●𝗟◗q in
+           ∧∧ ⊗b ϵ 𝐁 & ↑❘q❘ = (▼[r]𝐢)@❨n❩ & r◖𝗱n ϵ t1 &
+              t1[⋔r←𝛗(n+❘b❘).(t1⋔(p◖𝗦))] ⇔ t2
 .
 
 interpretation
-  "delayed focalized reduction (preterm)"
-  'BlackRightArrow t1 p q t2 = (dfr p q t1 t2).
+  "focused balanced reduction with delayed updating (prototerm)"
+  'BlackRightArrowDF t1 p q t2 = (dfr p q t1 t2).