Related papers: A graded dependent type system with a usage-aware …
We present a type theory combining both linearity and dependency by stratifying typing rules into a level for logics and a level for programs. The distinction between logics and programs decouples their semantics, allowing the type system…
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 $\Pi$-types, weak and strong $\Sigma$-types, natural numbers, an empty type, and a…
We extend the semantics and type system of a lambda calculus equipped with common constructs to be "resource-aware". That is, the semantics keeps track of the usage of resources, and is stuck, besides in case of type errors, if either a…
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 many such theories in recent years which equip a type theory with…
We present a compositional framework for certifying resource bounds in typed programs. Terms are typed with synthesized bounds drawn from an abstract resource lattice, enabling uniform treatment of time, memory, gas, and domain-specific…
Typed operational semantics is a method developed by H. Goguen to prove meta-theoretic properties of type systems. This paper studies the metatheory of a type system with dependent record types, using the approach of typed operational…
We present a soundness theorem for a dependent type theory with context constants with respect to an indexed category of (finite, abstract) simplical complexes. The point of interest for computer science is that this category can be seen to…
Resource-aware type systems statically approximate not only the expected result type of a program, but also the way external resources are used, e.g., how many times the value of a variable is needed. We extend the type system of…
We propose two new dependent type systems. The first, is a dependent graded/linear type system where a graded dependent type system is connected via modal operators to a linear type system in the style of Linear/Non-linear logic. We then…
We propose a type-based resource usage analysis for the π-calculus extended with resource creation/access primitives. The goal of the resource usage analysis is to statically check that a program accesses resources such as files and…
Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…
We present a novel dependent linear type theory in which the multiplicity of some variable-i.e., the number of times the variable can be used in a program-can depend on other variables. This allows us to give precise resource annotations to…
This work proposes a dependent type theory that combines functions and session-typed processes (with value dependencies) through a contextual monad, internalising typed processes in a dependently-typed lambda-calculus. The proposed…
Nakano's later modality can be used to specify and define recursive functions which are causal or synchronous; in concert with a notion of clock variable, it is possible to also capture the broader class of productive (co)programs. Until…
A type system is introduced for a generic Object Oriented programming language in order to infer resource upper bounds. A sound andcomplete characterization of the set of polynomial time computable functions is obtained. As a consequence,…
Gradually typed programming languages, which allow for soundly mixing static and dynamically typed programming styles, present a strong challenge for metatheorists. Even the simplest sound gradually typed languages feature at least…
Static resource analysis determines the resource consumption (e.g., time complexity) of a program without executing it. Among the numerous existing approaches for resource analysis, affine type systems have been one dominant approach.…
Many formal languages of contemporary mathematical music theory -- particularly those employing category theory -- are powerful but cumbersome: ideas that are conceptually simple frequently require expression through elaborate categorical…
Types in logic programming have focused on conservative approximations of program semantics by regular types, on one hand, and on type systems based on a prescriptive semantics defined for typed programs, on the other. In this paper, we…
Type systems which account for resource sensitive computations can generally be split into two styles: First, substructural logics such as Linear Logic which seek to restrict weakening and contraction and reintroduce them in a controlled…