Related papers: Free Monads, Intrinsic Scoping, and Higher-Order P…
We propose a novel method for inferring refinement types of higher-order functional programs. The main advantage of the proposed method is that it can infer maximally preferred (i.e., Pareto optimal) refinement types with respect to a…
We define a logical framework with singleton types and one universe of small types. We give the semantics using a PER model; it is used for constructing a normalisation-by-evaluation algorithm. We prove completeness and soundness of the…
The bisimulation proof method can be enhanced by employing `bisimulations up-to' techniques. A comprehensive theory of such enhancements has been developed for first-order (i.e., CCS-like) labelled transition systems (LTSs) and…
We examine the class of languages that can be defined entirely in terms of provability in an extension of the sorted type theory (Ty_n) by embedding the logic of phonologies, without introduction of special types for syntactic entities.…
We present Tores, a core language for encoding metatheoretic proofs. The novel features we introduce are well-founded Mendler-style (co)recursion over indexed data types and a form of recursion over objects in the index language to build…
Uncertainty is unavoidable in modeling dynamical systems and it may be represented mathematically by differential inclusions. In the past, we proposed an algorithm to compute validated solutions of differential inclusions; here we provide…
This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three ingredients: a powerful type system for size analysis and a sound type inference procedure for it, a ticking…
This paper introduces a new methodology for the complexity analysis of higher-order functional programs, which is based on three components: a powerful type system for size analysis and a sound type inference procedure for it, a ticking…
An inductive inference system for proving validity of formulas in the initial algebra $T_{\mathcal{E}}$ of an order-sorted equational theory $\mathcal{E}$ is presented. It has 20 inference rules, but only 9 of them require user interaction;…
For Martin-Lof type theory with a hierarchy U(0): U(1): U(2): ... of univalent universes, we show that U(n) is not an n-type. Our construction also solves the problem of finding a type that strictly has some high truncation level without…
Human value detection from single sentences is a sparse, imbalanced multi-label task. We study whether Schwartz higher-order (HO) categories help this setting on ValueEval'24 / ValuesML (74K English sentences) under a compute-frugal budget.…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…
To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary…
There are two kinds of higher-order extensions of model checking: HORS model checking and HFL model checking. Whilst the former has been applied to automated verification of higher-order functional programs, applications of the latter have…
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,…
Our approach to higher order Fourier analysis is to study the ultra product of finite (or compact) Abelian groups on which a new algebraic theory appears. This theory has consequences on finite (or compact) groups usually in the form of…
We give an algorithm for the class of second order unification problems in which second order variables have at most one occurrence.
We define the pattern fragment for higher-order unification problems in linear and affine type theory and give a deterministic unification algorithm that computes most general unifiers.
Large language models (LLMs) have shown promise in formal theorem proving, but their token-level processing often fails to capture the inherent hierarchical nature of mathematical proofs. We introduce \textbf{Hierarchical Attention}, a…
A key feature of inductive logic programming (ILP) is its ability to learn first-order programs, which are intrinsically more expressive than propositional programs. In this paper, we introduce techniques to learn higher-order programs.…