(* *)
(**************************************************************************)
-include "delayed_updating/syntax/path_depth.ma".
-include "delayed_updating/syntax/path_structure.ma".
-include "delayed_updating/syntax/path_balanced.ma".
include "delayed_updating/substitution/fsubst.ma".
-include "delayed_updating/substitution/lift_preterm.ma".
-include "delayed_updating/notation/relations/black_rightarrow_f_4.ma".
+include "delayed_updating/substitution/lift_prototerm.ma".
+include "delayed_updating/syntax/prototerm_eq.ma".
+include "delayed_updating/syntax/path_head.ma".
+include "delayed_updating/notation/relations/black_rightarrow_if_3.ma".
+include "ground/relocation/tr_uni.ma".
+include "ground/xoa/ex_4_3.ma".
(* IMMEDIATE FOCUSED REDUCTION ************************************************)
-inductive ifr (p) (q) (t): predicate preterm โ
-| ifr_beta (b):
- let r โ pโ๐โbโ๐โq in
- rโ๐ฑ(โโqโ) ฯต t โ โ(โb) โ ifr p q t (t[โrโโ[๐ฎโจโโqโโฉ]tโ(pโ๐ฆ)])
+(**) (* explicit ninj because we cannot declare the expectd type of k *)
+definition ifr (r): relation2 prototerm prototerm โ
+ ฮปt1,t2.
+ โโp,q,k. pโ๐โ๐โq = r &
+ (๐โq) = โณ[ninj k](๐โq) & rโ๐ฑk ฯต t1 &
+ t1[โrโโ[๐ฎโจninj kโฉ](t1โ(pโ๐ฆ))] โ t2
.
interpretation
- "focused balanced reduction with immediate updating (preterm)"
- 'BlackRightArrowF t1 p q t2 = (ifr p q t1 t2).
+ "focused reduction with immediate updating (prototerm)"
+ 'BlackRightArrowIF t1 r t2 = (ifr r t1 t2).