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- W2049764522 abstract "Abstract We are considering here two linked questions about the representation of λ -terms from combinators (i.e., from closed λ -terms). The first one was raised by R. Statman ( see [6]) and deals with simply typed λ -calculus: can we find for a given type A a finite set of typed combinators generating through applications every closed λ -term of the type A up to βη -equivalence? We will show (Section 1) that this cannot be done for the type: L =(o→o)→o , ( o 2 → o )→ o . The second question is about pure λ -calculus: how far from a pure λ -term t is any of its combinatoric representation M , the distance between them being measured by the length of the reduction: M →→ t ? We will prove (Section 2) that given any integer k and any finite set C of pure combinators there is a closed normal λ -term t such that the β -normalization of any of its combinatoric representation from C requires more than k complete developments." @default.
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- W2049764522 date "2000-10-01" @default.
- W2049764522 modified "2023-10-18" @default.
- W2049764522 title "Non finitely generated types and λ-terms combinatoric representation cost" @default.
- W2049764522 doi "https://doi.org/10.1016/s0764-4442(00)01686-4" @default.
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