Related papers: Formalizing Box Inference for Capture Calculus
Refinement types enable lightweight verification of functional programs. Algorithms for statically inferring refinement types typically work by reduction to solving systems of constrained Horn clauses extracted from typing derivations. An…
We propose a type-based analysis to infer the session protocols of channels in an ML-like concurrent functional language. Combining and extending well-known techniques, we develop a type-checking system that separates the underlying ML type…
The introduction of first-class type classes in the Coq system calls for re-examination of the basic interfaces used for mathematical formalization in type theory. We present a new set of type classes for mathematics and take full advantage…
Incremental computation aims to compute more efficiently on changed input by reusing previously computed results. We give a high-level overview of works on incremental computation, and highlight the essence underlying all of them, which we…
We develop a conformal inference method to construct a joint confidence region for a given group of missing entries within a sparsely observed matrix, focusing primarily on entries from the same column. Our method is model-agnostic and can…
Compact closed categories provide a foundational formalism for a variety of important domains, including quantum computation. These categories have a natural visualisation as a form of graphs. We present a formalism for equational reasoning…
Type theory plays an important role in foundations of mathematics as a framework for formalizing mathematics and a base for proof assistants providing semi-automatic proof checking and construction. Derivation of each theorem in type theory…
Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…
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…
Causal inference, a critical tool for informing business decisions, traditionally relies heavily on structured data. However, in many real-world scenarios, such data can be incomplete or unavailable. This paper presents a framework that…
Programs with control are usually modeled using lambda calculus extended with control operators. Instead of modifying lambda calculus, we consider a different model of computation. We introduce continuation calculus, or CC, a deterministic…
Precondition inference is a non-trivial problem with important applications in program analysis and verification. We present a novel iterative method for automatically deriving preconditions for the safety and unsafety of programs. Each…
The Functional Machine Calculus (FMC), recently introduced by the authors, is a generalization of the lambda-calculus which may faithfully encode the effects of higher-order mutable store, I/O and probabilistic/non-deterministic input.…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda calculus for the classical control model, following the first author's work on quantum flow-charts. We define a…
Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also…
Alias analysis, which determines whether two expressions in a program may reference to the same object, has many potential applications in program construction and verification. We have developed a theory for alias analysis, the "alias…
Testing has become an indispensable activity of software development, yet writing good and relevant tests remains a quite challenging task. One well-known problem is that it often is impossible or unrealistic to test for every outcome, as…
As popularity of algebraic effects and handlers increases, so does a demand for their efficient execution. Eff, an ML-like language with native support for handlers, has a subtyping-based effect system on which an effect-aware optimizing…
The Functional Machine Calculus (FMC) was recently introduced as a generalization of the lambda-calculus to include higher-order global state, probabilistic and non-deterministic choice, and input and output, while retaining confluence. The…