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/syntax/path_depth.ma".
  20 include "delayed_updating/syntax/path_reverse.ma".
  21 include "delayed_updating/notation/relations/black_rightarrow_df_4.ma".
  22
  23 (* DELAYED FOCUSED REDUCTION ************************************************)
  24
  25 definition dfr (p) (q): relation2 prototerm prototerm ≝
  26            λt1,t2. ∃n:pnat.
  27            let r ≝ p●𝗔◗𝗟◗q in
  28            ∧∧ (𝗟◗q)ᴿ = ↳[n](rᴿ) & r◖𝗱n ϵ t1 &
  29               t1[⋔r←𝛕n.(t1⋔(p◖𝗦))] ⇔ t2
  30 .
  31
  32 interpretation
  33   "focused reduction with delayed updating (prototerm)"
  34   'BlackRightArrowDF t1 p q t2 = (dfr p q t1 t2).