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_closed.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 definition dfr (r): relation2 prototerm prototerm ≝
  25            λt1,t2.
  26            ∃∃p,q,n. p●𝗔◗𝗟◗q = r &
  27            q ϵ 𝐂❨n❩ & r◖𝗱↑n ϵ t1 &
  28            t1[⋔r←𝛕↑n.(t1⋔(p◖𝗦))] ⇔ t2
  29 .
  30
  31 interpretation
  32   "focused reduction with delayed updating (prototerm)"
  33   'BlackRightArrowDF t1 r t2 = (dfr r t1 t2).