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Free Σ-Monoids: A Higher-Order Syntax with Metavariables

  • Makoto Hamana
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3302)

Abstract

The notion of Σ-monoids is proposed by Fiore, Plotkin and Turi, to give abstract algebraic model of languages with variable binding and substitutions. In this paper, we give a free construction of Σ-monoids. The free Σ-monoid over a given presheaf serves a well-structured term language involving binding and substitutions. Moreover, the free Σ-monoid naturally contains interesting syntactic objects which can be viewed as “metavariables” and “environments”. We analyse the term language of the free Σ-monoid by relating it with several concrete systems, especially the λ-calculus extended with contexts.

Keywords

Function Symbol Monoidal Category Object Variable Binding Signature Construction Rule 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Makoto Hamana
    • 1
  1. 1.Department of Computer ScienceGunma UniversityJapan

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