A. R'ios. Contribution `a l"etude des -calculus avec substitutions explicites. Th`ese de doctorat, Universit'e de Paris VII, 1993. This article was processed using the L A T E X macro package with LLNCS style  Home/Search Document Not in Database Summary Related Articles Check |
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lambda-calculi with explicit substitutions and composition.. - Ferreira, al. (1996) (7 citations) (Correct)
....preserving fi SN and being confluent on closed terms. We study d and dn , two different calculi with explicit substitutions initially defined in [10] these calculi, do have composition, are confluent on closed terms 3 and preserve fi SN. The d calculus is inspired by the calculus from [18], which is in turn inspired by [7] the difference being that the MapEnv rule of , namely #(a) ffi s Gamma (s) ffi #(a[s] is replaced here by the two following rules: 1[#(a) ffi s] Gamma a[s] and ffi(#(a) ffi s) Gamma s. This may seem irrelevant, but it is essential to prove ....
A. R'ios. Contribution `a l"etude des -calculus avec substitutions explicites. Th`ese de doctorat, Universit'e de Paris VII, 1993. This article was processed using the L A T E X macro package with LLNCS style
Lambda-Calculi With Explicit Substitutions And Weak.. - Ferreira, Kesner, Puel (1996) (7 citations) (Correct)
....closed terms. We study two different calculi with explicit substitutions initially defined in [Kes96] these calculi, named d and dn respectively, do have (weak) composition, are confluent on closed terms and preserve fi strong normalization. The d calculus is inspired by the calculus from [R io93], which is in turn inspired by [Ehr88] the difference being that the MapEnv rule of the calculus, namely: #(a) ffi s Gamma (s) ffi #(a[s] is replaced here by the two following rules: 1[#(a) ffi s] Gamma a[s] ffi(#(a) ffi s) Gamma s This may seem superfluous, but it is essential ....
Alejandro R'ios. Contribution `a l"etude des -calculus avec substitutions explicites. Th`ese de doctorat, Universit'e de Paris VII, 1993.
Confluence of Extensional and Non-Extensional λ-calculi.. - Kesner (Correct)
....extensional rules. For that, we keep the classical definition of Beta reduction associated to fi reduction, and define the d Eta expansion rule associated to the classical b j expansion one, this rule being more natural than all the contractive interpretations given before in the literature [Har92, Har94, R io93, Bri95]. We study confluence of the reduction relation associated to the Beta reduction alone as well as that associated to the combination of Beta reduction and d Eta expansion. Since we are interested in many different calculi with explicit substitutions (such as oe [ACCL91] oe [HL89] OE ....
....turning the Eta axiom into a reduction rule some problems arise. If we orient this equation from left to right as the rewriting rule (a[shif t] 1) Gamma a, an infinite set of critical pairs is usually generated. As a consequence, the rule is often expressed by the following conditional rule [Har92, Har94, R io93]: Eta 1 ) a 1) Gamma b if a =W b[shif t] However, the condition a =W b[shif t] depends on the particular definition of the substitution calculus W , and may be difficult (or expensive) to be verified each time that an Eta 1 reduction is performed. There is another unconditional rewriting ....
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Alejandro R'ios. Contribution `a l"etude des -calculus avec substitutions explicites. Th`ese de doctorat, Universit'e de Paris VII, 1993.
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