Related papers: The Best of Both Worlds: Linear Functional Program…

Computational interpretations of linear logic allow static control of memory resources: the data produced by the program are endowed through its type with attributes that determine its life cycle, and guarantee safe deallocation. The use of…

We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an…

We present an optimization framework for learning a fair classifier in the presence of noisy perturbations in the protected attributes. Compared to prior work, our framework can be employed with a very general class of linear and…

We present a marriage of functional and structured imperative programming that embeds in pure lambda calculus. We describe how we implement the core of this language in a monadic DSL which is structurally equivalent to our intended source…

The categorical models of the differential lambda-calculus are additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential…

Program equivalence in linear contexts, where programs are used or executed exactly once, is an important issue in programming languages. However, existing techniques like those based on bisimulations and logical relations only target at…

Linear algebra computations are foundational for neural networks and machine learning, often handled through arrays. While many functional programming languages feature lists and recursion, arrays in linear algebra demand constant-time…

We consider Continuous Linear Programs over a continuous finite time horizon $T$, with linear cost coefficient functions, linear right hand side functions, and a constant coefficient matrix, as well as their symmetric dual. We search for…

We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…

Linear Temporal Logic (LTL) is the standard specification language for reactive systems and is successfully applied in industrial settings. However, many shortcomings of LTL have been identified in the literature, among them the limited…

Throughout the history of functional programming, recursion has emerged as a natural method for describing loops in programs. However, there does often exist a substantial cognitive distance between the recursive definition and the simplest…

We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type…

Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…

Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…

We study functional and concurrent calculi with non-determinism, along with type systems to control resources based on linearity. The interplay between non-determinism and linearity is delicate: careless handling of branches can discard…

Machine learning is a thriving part of computer science. There are many efficient approaches to machine learning that do not provide strong theoretical guarantees, and a beautiful general learning theory. Unfortunately, machine learning…

A coverage type generalizes refinement types found in many functional languages with support for must-style underapproximate reasoning. Property-based testing frameworks are one particularly useful domain where such capabilities are useful…

Regular cost functions have been introduced recently as an extension to the notion of regular languages with counting capabilities, which retains strong closure, equivalence, and decidability properties. The specificity of cost functions is…

Semantic theories of natural language associate meanings with utterances by providing meanings for lexical items and rules for determining the meaning of larger units given the meanings of their parts. Meanings are often assumed to combine…

Bounded linear types have proved to be useful for automated resource analysis and control in functional programming languages. In this paper we introduce an affine bounded linear typing discipline on a general notion of resource which can…