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1 results

  • 2 - Terms, Formulas, and Sequents

  • Dale Miller, INRIA Saclay-Île-de-France
  • Book:
    Proof Theory and Logic Programming
    Published online:
    01 December 2025
    Print publication:
    18 December 2025, pp 9-19

  • Summary

    This chapter lays the syntactic foundations for the book, covering topics in both first-order and higher-order logic. It introduces untyped lambda-terms and their properties, including beta-conversion and beta-normal forms. The chapter then defines types, signatures, and typed terms, restricting the typing judgment to beta-normal formulas. Finally, it introduces the concept of formulas and sequents, which are central to the proof-theoretic approach discussed in the book. Bibliographic notes provide references for further reading on these foundational concepts.