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.
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Hamana, M. (2004). Free Σ-Monoids: A Higher-Order Syntax with Metavariables. In: Chin, WN. (eds) Programming Languages and Systems. APLAS 2004. Lecture Notes in Computer Science, vol 3302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30477-7_23
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DOI: https://doi.org/10.1007/978-3-540-30477-7_23
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