Addressed Term Rewriting Systems
Texte intégral
(2) Laboratoire de l’Informatique du Parallélisme. SPI. École Normale Supérieure de Lyon Unité Mixte de Recherche CNRS-INRIA-ENS LYON no 5668.
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(5) . École Normale Supérieure de Lyon 46 Allée d’Italie, 69364 Lyon Cedex 07, France Téléphone : +33(0)4.72.72.80.37 Télécopieur : +33(0)4.72.72.80.80 Adresse électronique :
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(728)
(729) t%. • t = x% Γ t ∅ + % • t = •b %
(730) a ∈ / Γ b = a% Γ •b {b → •b } + " Γ, a •b {b → •b } = {b → (a)(•b )}. • t = F b (t1 , . . . , tm )%
(731) #
(732) %. % b = a% . (a)(t) = •a
(733) . Γ, a. (a)(t) {a → •a} = (a) ◦ {a → t} ⊆ (a) ◦ ∆. .
(734) 9% b = a% . . (a)(t) = F b (a)(t1), . . . , (a)(tm ). C" ! ∆=. m . .. ( (t) ◦ ∆i ) ∪ {b → t}.. i=1. C" *%F%. Γ, a. (a)(ti ) ∆i ⊆ (a) ◦ ∆i.. F
(735) Γ, a. (a)(t) ( (a)(t)) ◦ ∆i ∪ {b → (a)(t)} ⊆. m . ( ( (a)(t)) ◦ (a) ◦ ∆i ) ∪ ( (a) ◦ {b → t}). i=1. = (a) ◦. m . ( (t) ◦ ∆i ) ∪ {b → t}. . i=1. = (a) ◦ ∆.
(736). 8 4 1 Γ, a t ∆" Γ s Φ ( (s) ◦ ∆) ∪ Φ Γ. 2. (s)(t) ∆ ∆ ⊆ ( (s) ◦ ∆) ∪ Φ.. C"
(737)
(738) t%. • t = x% ∆ = ∅ = ∆ ⊆ (s) ◦ ∅ = ∅% • t = •a % ∆ = {a → •a }%. : * (s) = a ∆ = ∆ = (s) ◦ ∆ ⊆ ( (s) ◦ ∆) ∪ Φ% : * (s) = a ∆ = Φ ⊆ ( (s) ◦ ∆) ∪ Φ% . . • t = F b (t1 , . . . , tm )%. : b = a% (s)(t) = s Γ s Φ ⊆ ( (s) ◦ ∆) ∪ Φ% : b = a% . (s)(t) = F b ( (b)(s))(t1), . . . , ( (b)(s))(tm) C" !
(739) ti . Γ, a, b ti ∆i .. C" 3 # + Γ, b. (b)(s) Φ ⊆ (b) ◦ Φ. :. ..
(740) . . ( (s) ◦ ∆) ∪ Φ !
(741) i ( (s) ◦ ∆i) ∪ Φ !% F
(742) *%F% ti Γ, b ( (b)(s))(ti ) ∆i ⊆ ( ( (b)(s)) ◦ ∆i ) ∪ ( (b) ◦ Φ).
(743) . . ∆ = ⊆. m . ( ( (s)(t)) ◦ ∆i ) ∪ {b → (s)(t)}. i=1 m . . ( (s)(t)) ◦ ( ( (b)(s)) ◦ ∆i) ∪ ( (b) ◦ Φ). i=1.
(744) ∆ =. m. . ∪ {b → (s)(t)}. i=1 (. (t) ◦ ∆i) ∪ {b → t} (t) ◦ ∆i ⊆ ∆. " 3 . ∆i ⊆ (b) ◦ ∆.. F
(745) ∆ ⊆ ( (s)(t)) ◦ ( ( (b)(s)) ◦ (b) ◦ ∆) ∪ ( (b) ◦ Φ) ∪ {b → (s)(t)} = ( (s)(t)) ◦ (b) ◦ ( (s) ◦ ∆) ∪ Φ ∪ {b → (s)(t)} = ( (s) ◦ ∆) ∪ Φ ∪ {b → (s)(t)} " 3 # = ( (s) ◦ ∆) ∪ Φ
(746) {b → t} ⊆ ∆. 3 L ! "
(747) &. ∗ @ " ( (s) ◦ ∆) ∪ Φ
(748) ! b , % ∗ ∆(b) = t
(749) ( (s) ◦ ∆) ∪ Φ (b) = (s)(t)%
(750).
(751)
(752)
(753) + " # " ! # %. " 4 1 Γ t ∆" a ∈ (t)" Γ ∆(a) Φ Φ ⊆ ∆ 2. C"
(754)
(755) t%. • t + %
(756) a ) . (t) #
(757) "%. ;.
(758) • t = •b % a = b ∆(a) = •b + " " % • t = F b (t1 , . . . , tm )% +
(759) #
(760) &. % b = a% ∆(a) = t + " " %. 9% b = a% ) i
(761) a ∈ (ti )%
(762) Γ, b ti ∆i #. + " *%F% Γ, b ∆i (a) Φi ⊆ ∆i . m
(763) ∆ = i=1 ( (t) ◦ ∆i ) ∪ {b → t} (∆) ∆(a) = (t)(∆i (a))..
(764) Φi ⊆ ∆i
(765) ∆ =. m. i=1 (. (t) ◦ Φi ⊆ (t) ◦ ∆i.. (t) ◦ ∆i) ∪ {b → t} . (t) ◦ Φi ⊆ ∆. F
(766)
(767) (∆) ! 3 9 +. . ( (t) ◦ Φi ) ∪ ∆). . Γ ∆(a) = (t)(∆i (a)) Φ ⊆ (t) ◦ Φi ⊆ ∆..
(768). # ! )
(769) +
(770) )
(771)
(772)
(773)
(774) " "
(775)
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