(* *)
(**************************************************************************)
-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_closed.ma".
+include "delayed_updating/notation/relations/black_rightarrow_df_3.ma".
+include "ground/xoa/ex_4_3.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 (r): relation2 prototerm prototerm ≝
+ λt1,t2.
+ ∃∃p,q,n. p●𝗔◗𝗟◗q = r &
+ q ϵ 𝐂❨n❩ & r◖𝗱↑n ϵ t1 &
+ t1[⋔r←𝛕↑n.(t1⋔(p◖𝗦))] ⇔ t2
.
-(*
+
interpretation
- "focalized substitution (preterm)"
- 'PitchforkLeftArrow t p u = (fsubst p u t).
-*)
+ "focused reduction with delayed updating (prototerm)"
+ 'BlackRightArrowDF t1 r t2 = (dfr r t1 t2).