We introduce MTT, a dependent type theory which supports multiple modalities. MTT is
parametrized by a mode theory which specifies a collection of modes, modalities, and …

In programming, some data acts as a resource (eg, file handles, channels) subject to usage
constraints. This poses a challenge to software correctness as most languages are agnostic …

We propose to unify the treatment of a broad range of modalities in typed lambda calculi. We
do so by defining a generic structure of modalities, and show that this structure arises …

Reasoning about the use of external resources is an important aspect of many practical
applications. Effect systems enable tracking such information in types, but at the cost of …

Graded Type Theory provides a mechanism to track and reason about resource usage in
type systems. In this paper, we develop GraD, a novel version of such a graded dependent …

Graded modal types systems and coeffects are becoming a standard formalism to deal with
context-dependent, usage-sensitive computations, especially when combined with …

We introduce a general theory of quantitative and metric rewriting systems, namely systems
with a rewriting relation enriched over quantales modelling abstract quantities. We develop …

Combinatorial games are widely used in finite model theory, constraint satisfaction, modal
logic and concurrency theory to characterize logical equivalences between structures. In …

Graded type theories are an emerging paradigm for augmenting the reasoning power of
types with parameterizable, fine-grained analyses of program properties. There have been …

Programmers can often improve the performance of their programs by reducing heap
allocations: either by allocating on the stack or reusing existing memory in-place. However …