Related papers: Induction by Coinduction and Control Operators in …
This work presents a novel systematic methodology to analyse the capabilities and limitations of Large Language Models (LLMs) with feedback from a formal inference engine, on logic theory induction. The analysis is complexity-graded w.r.t.…
Inference algorithms for probabilistic programming are complex imperative programs with many moving parts. Efficient inference often requires customising an algorithm to a particular probabilistic model or problem, sometimes called…
We present a rich type system with subtyping for an extension of System F. Our type constructors include sum and product types, universal and existential quantifiers, inductive and coinductive types. The latter two size annotations allowing…
We investigate a variant of the fuel-based approach to modeling diverging computation in type theories and use it to abstractly capture the essence of oracle Turing machines. The resulting objects we call continuous machines. We prove that…
Some total languages, like Agda and Coq, allow the use of guarded corecursion to construct infinite values and proofs. Guarded corecursion is a form of recursion in which arbitrary recursive calls are allowed, as long as they are guarded by…
Delimited control is a powerful mechanism for programming language extension which has been recently proposed for Prolog (and implemented in SWI-Prolog). By manipulating the control flow of a program from inside the language, it enables the…
Transformer components such as non-linear activations and normalization are inherently non-injective, suggesting that different inputs could map to the same output and prevent exact recovery of the input from a model's representations. In…
Starting from pseudometrics and preorders on sets of integers, we extend the focus to sets of finite sequences of integers, in particular sequences of consecutive integers. We outline existing concepts for deriving centred pseudometrics and…
Recent work has shown that the input-output behavior of some machine learning systems can be captured symbolically using Boolean expressions or tractable Boolean circuits, which facilitates reasoning about the behavior of these systems.…
We describe a type system for the linear-algebraic lambda-calculus. The type system accounts for the part of the language emulating linear operators and vectors, i.e. it is able to statically describe the linear combinations of terms…
A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be…
To ensure decidability and consistency of its type theory, a proof assistant should only accept terminating recursive functions and productive corecursive functions. Most proof assistants enforce this through syntactic conditions, which can…
Mixed-initiative dialogue tasks involve repeated exchanges of information and conversational control. Conversational agents gain control by generating responses that follow particular dialogue intents or strategies, prescribed by a policy…
In this paper, we introduce the concept of two-way coding, which originates in communication theory characterizing coding schemes for two-way channels, into control theory, particularly to facilitate the analysis and design of feedback…
This paper investigates using large language models (LLMs) to generate control actions directly, without requiring control-engineering expertise or hand-tuned algorithms. We implement several variants: (i) prompt-only, (ii) tool-assisted…
Delimited control is a powerful mechanism for programming language extension which has been recently proposed for Prolog (and implemented in SWI-Prolog). By manipulating the control flow of a program from inside the language, it enables the…
Guiding biological systems toward desired states, such as morphogenetic outcomes, remains a fundamental challenge with far-reaching implications for medicine and synthetic biology. While large language models (LLMs) have enabled natural…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
In a functional language, the dominant control-flow mechanism is function call and return. Most higher-order flow analyses, including k-CFA, do not handle call and return well: they remember only a bounded number of pending calls because…
Context-free session types describe structured patterns of communication on heterogeneously-typed channels, allowing the specification of protocols unconstrained by tail recursion. The enhanced expressive power provided by non-regular…