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- W2088508256 abstract "It is well known that for each λ-term there is a corresponding combinatory term formed using the combinators K and S instead of the λ-operator. Similarly for every combinatory term there is a λ-term. For weaker sets of combinators such as B , C and K or B , B′ , I and W we show how such a correspondence or “translation” can be formulated and we determine in the case of several such sets of combinators the sets of λ-terms that can be translated using them. As combinators can represent Hilbert-style proofs of theorems of implicational logic and λ-terms natural deduction style proofs, this work allows us to formulate natural deduction systems equivalent to the Hilbert-style systems for various implicational logics and can form a basis for proof generating programs for these logics." @default.
- W2088508256 created "2016-06-24" @default.
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- W2088508256 date "1996-11-01" @default.
- W2088508256 modified "2023-10-17" @default.
- W2088508256 title "Lambda terms definable as combinators" @default.
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- W2088508256 doi "https://doi.org/10.1016/s0304-3975(96)00111-9" @default.
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