include "delayed_updating/syntax/path_depth.ma".
include "delayed_updating/syntax/path_structure.ma".
include "delayed_updating/syntax/path_balanced.ma".
+include "delayed_updating/syntax/prototerm_constructors.ma".
+include "delayed_updating/syntax/prototerm_equivalence.ma".
include "delayed_updating/substitution/fsubst.ma".
include "delayed_updating/notation/relations/black_rightarrow_df_4.ma".
(* DELAYED FOCUSED REDUCTION ************************************************)
-inductive dfr (p) (q) (t): predicate preterm โ
-| dfr_beta (b):
- let r โ pโ๐โbโ๐โqโ๐ฑ(โโqโ) in
- r ฯต t โ โ(โb) โ dfr p q t (t[โrโtโ(pโ๐ฆ)])
+definition dfr (p) (q): relation2 prototerm prototerm โ
+ ฮปt1,t2. โb.
+ let r โ pโ๐โbโ๐โq in
+ โงโง โ(โb) & rโ๐ฑ(โโqโ) ฯต t1 &
+ t2 โ t1[โrโ๐(โโqโ).t1โ(pโ๐ฆ)]
.
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).