Related papers: Computational Adequacy for Substructural Lambda Ca…
We propose a new type system for lambda-calculus ensuring that well-typed programs can be executed in polynomial time: Dual light affine logic (DLAL). DLAL has a simple type language with a linear and an intuitionistic type arrow, and one…
We show that the principal types of the closed terms of the affine fragment of $\lambda$-calculus, with respect to a simple type discipline, are structurally isomorphic to their interpretations, as partial involutions, in a natural Geometry…
With a view towards models of quantum computation and/or the interpretation of linear logic, we define a functional language where all functions are linear operators by construction. A small step operational semantic (and hence an…
Ordered, linear, and other substructural type systems allow us to expose deep properties of programs at the syntactic level of types. In this paper, we develop a family of unary logical relations that allow us to prove consequences of…
We introduce a novel architecture and computational framework for formal, automated analysis of systems with a broad set of nonlinearities in the feedback loop, such as neural networks, vision controllers, switched systems, and even simple…
It has become commonplace to use complex computer models to predict outcomes in regions where data does not exist. Typically these models need to be calibrated and validated using some experimental data, which often consists of multiple…
We give a categorical semantics for a call-by-value linear lambda calculus. Such a lambda calculus was used by Selinger and Valiron as the backbone of a functional programming language for quantum computation. One feature of this lambda…
We present an affine-intuitionistic system of types and effects which can be regarded as an extension of Barber-Plotkin Dual Intuitionistic Linear Logic to multi-threaded programs with effects. In the system, dynamically generated values…
We present an affine-intuitionistic system of types and effects which can be regarded as an extension of Barber-Plotkin Dual Intuitionistic Linear Logic to multi-threaded programs with effects. In the system, dynamically generated values…
Identifying control-friendly models of nonlinear systems remains one of the major challenges at the intersection of system identification and control. The Linear Parameter-Varying (LPV) framework offers a promising solution, but existing…
We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…
Dependent types provide a lightweight and modular means to integrate programming and formal program verification. In particular, the types of programs written in dependently typed programming languages (Agda, Idris, F*, etc.) can be used to…
A residual design ${\cal{D}}_B$ with respect to a block $B$ of a given design $\cal{D}$ is defined to be linearly embeddable over $GF(p)$ if the $p$-ranks of the incidence matrices of ${\cal{D}}_B$ and $\cal{D}$ differ by one. A sufficient…
A fragment of second-order lambda calculus (System F) is defined that characterizes the elementary recursive functions. Type quantification is restricted to be non-interleaved and stratified, i.e., the types are assigned levels, and a…
We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…
We completely describe a new domain for abstract interpretation of numerical programs. Fixpoint iteration in this domain is proved to converge to finite precise invariants for (at least) the class of stable linear recursive filters of any…
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…
This book explores an alternative to the current dominant paradigm where a discrete computer model is constructed as an attempt to approximate some continuum theory. We focus on a class of discrete computer models that are based on simple…
Binary matrix codes with restricted row and column weights are a desirable method of coded modulation for power line communication. In this work, we construct such matrix codes that are obtained as products of affine codes - cosets of…
Extending the lambda-calculus with a construct for sharing, such as let expressions, enables a special representation of terms: iterated applications are decomposed by introducing sharing points in between any two of them, reducing to the…