D. Kesner. Confluence of extensional and non-extensional -calculi with explicit substitutions. Preprint, 1997. Home/Search Document Not in Database Summary Related Articles Check |
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A Left-linear Variant of λσ - Muñoz H. (1997) (Correct)
....substitutions. However, is incompatible with the extensional rule (j) due to the fact that substitutions id and 1 Delta are not convertible. A key point in L is the preservation of this extensional equivalence. The extensional version of L calculus is confluent on ground terms as shown in [18], and we conjecture that it is also on semi open expressions. The L calculus is extended to dependent types in [27] and work is in progress to use this calculus in a formulation of the Calculus of Inductive Constructions with explicit substitutions and open expressions. Acknowledgments Many ....
D. Kesner. Confluence of extensional and non-extensional -calculi with explicit substitutions. Preprint, 1997.
Confluence of Extensional and Non-Extensional λ-calculi.. - Kesner Self-citation (Kesner) (Correct)
....any valid equality as they are just introduced to avoid reduction loops. The result can be obtained by proving that any fij equality can be generated by the reflexive, symmetric and transitive closure of fi b j reduction. We omit here the details of this (standard) proof, which can be found in [Kes97a] (theorem 2.7) As expected, the b j expansion rule enjoys the subject reduction property: Lemma 2.2 (Subject reduction for b j) If Gamma a : A and a Gamma bj b, then Gamma b : A. Proof. If a Gamma bj b is a root expansion step, then A is a functional type B C and b = B: a ....
.... Gamma a : B C B; Gamma a : B C B; Gamma 1 : B B; Gamma (a 1) C Gamma B: a 1) B C If a Gamma bj b is not a root expansion, then one proceeds by induction on terms. A direct proof of confluence of fi [ b j in the calculus a la de Bruijn can be found in [Kes97a], but since we know that the union of fi and b j yields a confluent reduction relation in the typed calculus, and also that the calculus is isomorphic 1 to the calculus a la de Bruijn [Mau85, Cur83, dB72] then we are able to conclude that Theorem 2.3 Gamma fibj is confluent in the ....
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Delia Kesner. Confluence of extensional and non-extensional -calculi with explicit substitutions. Technical Report 1103, LRI, Universit'e Paris-Sud, 1997.
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