Related papers: Separated and Shared Effects in Higher-Order Langu…
Prompting techniques such as chain-of-thought have established themselves as a popular vehicle for improving the outputs of large language models (LLMs). For code generation, however, their exact mechanics and efficacy are under-explored.…
Theories for reasoning about programs with effects initially focused on basic manipulation of lists and other mutable data. The next challenge was to consider higher-order programming, adding functions as first class objects to mutable…
We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…
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.…
With the rapid development of deep learning, most of current state-of-the-art techniques in natural langauge processing are based on deep learning models trained with argescaled static textual corpora. However, we human beings learn and…
Relational program verification is a variant of program verification where one can reason about two programs and as a special case about two executions of a single program on different inputs. Relational program verification can be used for…
This perspective paper explores the bidirectional influence between language emergence and the relational structure of subjective experiences, termed qualia structure, and lays out a constructive approach to the intricate dependency between…
Logic Programming is a Turing complete language. As a consequence, designing algorithms that decide termination and non-termination of programs or decide inductive/coinductive soundness of formulae is a challenging task. For example, the…
This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is…
Large language models excel on static benchmarks, but their ability as self-learning agents in dynamic environments remains unclear. We evaluate three prompting strategies: self-reflection, heuristic mutation, and planning across dynamic…
Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving…
Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in…
Game semantics extends the Curry-Howard isomorphism to a three-way correspondence: proofs, programs, strategies. But the universe of strategies goes beyond intuitionistic logics and lambda calculus, to capture stateful programs. In this…
We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…
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…
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…
We characterise non-distributive positive logic as the fragment of a single-sorted first-order language that is preserved by a new notion of simulation called a meet-simulation. Meet-simulations distinguish themselves from simulations…
Recent years have witnessed the rise of compositional semantics as a foundation for formal verification of complex systems. In particular, interaction trees have emerged as a popular denotational semantics. Interaction trees achieve…
Theoretical foundations of compositional reasoning about heaps in imperative programming languages are investigated. We introduce a novel concept of compositional symbolic memory and its relevant properties. We utilize these formal…
We develop local reasoning techniques for message passing concurrent programs based on ideas from separation logics and resource usage analysis. We extend processes with permission- resources and define a reduction semantics for this…