matita/matita/contribs/lambdadelta/delayed_updating/reduction/dfr.ma

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  14
  15 include "delayed_updating/substitution/fsubst.ma".
  16 include "delayed_updating/syntax/prototerm_constructors.ma".
  17 include "delayed_updating/syntax/prototerm_eq.ma".
  18 include "delayed_updating/syntax/path_head.ma".
  19 include "delayed_updating/notation/relations/black_rightarrow_df_3.ma".
  20 include "ground/xoa/ex_4_3.ma".
  21
  22 (* DELAYED FOCUSED REDUCTION ************************************************)
  23
  24 (**) (* explicit ninj because we cannot declare the expectd type of k *)
  25 definition dfr (r): relation2 prototerm prototerm ≝
  26            λt1,t2.
  27            ∃∃p,q,k. p●𝗔◗𝗟◗q = r &
  28            (𝗟◗q) = ↳[ninj k](𝗟◗q) & r◖𝗱k ϵ t1 &
  29            t1[⋔r←𝛕k.(t1⋔(p◖𝗦))] ⇔ t2
  30 .
  31
  32 interpretation
  33   "focused reduction with delayed updating (prototerm)"
  34   'BlackRightArrowDF t1 r t2 = (dfr r t1 t2).