We present a graded modal type theory, a dependent type theory with grades that can be
used to enforce various properties of the code. The theory has Π-types, weak and strong Σ …

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 …

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 …

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 …

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 …

Ownership and borrowing systems, designed to enforce safe memory management without
the need for garbage collection, have been brought to the fore by the Rust programming …

In quantitative reasoning one compares objects by distances, instead of equivalence
relations, so that one can measure how much they are similar, rather than just saying …

Effect and coeffect tracking integrate many types of compile-time analysis, such as cost,
liveness, or dataflow, directly into a language's type system. In this paper, we investigate the …

Mechanisation of programming language research is of growing interest, and the act of
mechanising type systems and their metatheory is generally becoming easier as new …