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**A proof-theoretic treatment of \(\lambda \)-reduction with cut-elimination: \(\lambda \)-calculus as a logic programming language.**
*(English)*
Zbl 1223.03038

Summary: We build on an existing a term-sequent logic for the \(\lambda \)-calculus. We formulate a general sequent system that fully integrates \(\alpha \beta \eta \)-reductions between untyped \(\lambda \)-terms into first-order logic.

We prove a cut-elimination result and then offer an application of cut-elimination by giving a notion of uniform proof for \(\lambda \)-terms. We suggest how this allows us to view the calculus of untyped \(\alpha \beta \)-reductions as a logic programming language (as well as a functional programming language, as it is traditionally seen).

We prove a cut-elimination result and then offer an application of cut-elimination by giving a notion of uniform proof for \(\lambda \)-terms. We suggest how this allows us to view the calculus of untyped \(\alpha \beta \)-reductions as a logic programming language (as well as a functional programming language, as it is traditionally seen).

### MSC:

03F05 | Cut-elimination and normal-form theorems |

03B40 | Combinatory logic and lambda calculus |

68N17 | Logic programming |

68N18 | Functional programming and lambda calculus |

Full Text:
DOI

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