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

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  14
  15 include "delayed_updating/syntax/prototerm_constructors.ma".
  16 include "delayed_updating/syntax/prototerm_equivalence.ma".
  17 include "delayed_updating/substitution/fsubst.ma".
  18 include "delayed_updating/substitution/lift.ma".
  19 include "delayed_updating/syntax/path_structure.ma".
  20 include "delayed_updating/syntax/path_balanced.ma".
  21 include "delayed_updating/syntax/path_depth.ma".
  22 include "delayed_updating/notation/relations/black_rightarrow_df_4.ma".
  23 include "ground/arith/nat_rplus.ma".
  24 include "ground/xoa/ex_1_2.ma".
  25 include "ground/xoa/and_4.ma".
  26
  27 (* DELAYED FOCUSED REDUCTION ************************************************)
  28
  29 definition dfr (p) (q): relation2 prototerm prototerm ≝
  30            λt1,t2. ∃∃b,n.
  31            let r ≝ p●𝗔◗b●𝗟◗q in
  32            ∧∧ ⊗b ϵ 𝐁 & ∀f. ↑❘q❘ = (↑[q]⫯f)@❨n❩ & r◖𝗱n ϵ t1 &
  33               t1[⋔r←𝛗(n+❘b❘).(t1⋔(p◖𝗦))] ⇔ t2
  34 .
  35
  36 interpretation
  37   "focused balanced reduction with delayed updating (prototerm)"
  38   'BlackRightArrowDF t1 p q t2 = (dfr p q t1 t2).