Introduction to higher order categorical logic
Introduction to higher order categorical logic
Proofs and types
Computational lambda-calculus and monads
Proceedings of the Fourth Annual Symposium on Logic in computer science
The formal semantics of programming languages: an introduction
The formal semantics of programming languages: an introduction
Handbook of logic in computer science
Locus Solum: From the rules of logic to the logic of rules
Mathematical Structures in Computer Science
Call-by-push-value: Decomposing call-by-value and call-by-name
Higher-Order and Symbolic Computation
Focusing and polarization in linear, intuitionistic, and classical logics
Theoretical Computer Science
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We make an argument that, for any study involving computational effects such as divergence or continuations, the traditional syntax of simply typed lambda-calculus cannot be regarded as canonical, because standard arguments for canonicity rely on isomorphisms that may not exist in an effectful setting. To remedy this, we define a “jumbo lambda-calculus” that fuses the traditional connectives together into more general ones, so-called “jumbo connectives”. We provide two pieces of evidence for our thesis that the jumbo formulation is advantageous Firstly, we show that the jumbo lambda-calculus provides a “complete” range of connectives, in the sense of including every possible connective that, within the beta-eta theory, possesses a reversible rule Secondly, in the presence of effects, we show that there is no decomposition of jumbo connectives into non-jumbo ones that is valid in both call-by-value and call-by-name