Introduction to higher order categorical logic
Introduction to higher order categorical logic
The Category Theoretic Understanding of Universal Algebra: Lawvere Theories and Monads
Electronic Notes in Theoretical Computer Science (ENTCS)
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Any interpretation of the lambda calculus determines a composition monoid and this monoid can be equipped with structure from which the interpretation can be recovered. That is the essence of Dana Scott's account of the lambda calculus in terms of its category of retracts. This paper presents a new approach to the needed structure on the monoid deriving from a recent analysis of the lambda calculus in terms of algebraic theory.