In this paper, we show how to integrate linear types with type dependency, by extending the
linear/non-linear calculus of Benton to support type dependency. Next, we give an …

We show how to define forward-and reverse-mode automatic differentiation source-code
transformations or on a standard higher-order functional language. The transformations …

We study a simple form of standardization, here called factorization, for explicit substitutions
calculi, ie lambda-calculi where beta-reduction is decomposed in various rules. These …

We introduce Combinatory Homomorphic Automatic Differentiation (CHAD), a principled,
pure, provably correct define-then-run method for performing forward and reverse mode …

Strong monads are important for several applications, in particular, in the denotational
semantics of effectful languages, where strength is needed to sequence computations that …

This article introduces the enriched effect calculus, which extends established type theories
for computational effects with primitives from linear logic. The new calculus provides a …

We give a denotational model for graphical user interface (GUI) programming using the
Cartesian closed category of ultrametric spaces. The ultrametric structure enforces causality …

The Functional Machine Calculus (FMC) was recently introduced as a generalization of the
lambda-calculus to include higher-order global state, probabilistic and non-deterministic …

We study the reduction in a-calculus derived from Moggi's computational one, which we call
the computational core. The reduction relation consists of rules obtained by orienting three …

We investigate the phenomenon that" every monad is a linear state monad". We do this by
studying a fully-complete state-passing translation from an impure call-by-value language to …