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The semantics of assignment and mutual exclusion in concurrent and multi-core/multi-processor systems is presented with attention to low level architectural features in an attempt to make the presentation realistic. Recursive functions on…
Symbolic regression, i.e. predicting a function from the observation of its values, is well-known to be a challenging task. In this paper, we train Transformers to infer the function or recurrence relation underlying sequences of integers…
Decomposition and abstraction is an essential component of computational thinking, yet it is not always emphasized in introductory programming courses. In addition, as generative AI further reduces the focus on syntax and increases the…
The sequent calculus is a formalism for proving validity of statements formulated in First-Order Logic. It is routinely used in computer science modules on mathematical logic. Formal proofs in the sequent calculus are finite trees obtained…
We introduce the Rebound library that supports well-scoped term representations in Haskell and automates the definition of substitution, alpha-equivalence, and other operations that work with binding structures. The key idea of our design…
Automatic differentiation is a key component in deep learning. This topic is well studied and excellent surveys such as Baydin et al. (2018) have been available to clearly describe the basic concepts. Further, sophisticated implementations…
Cognitive Architectures are the forefront of the research into developing an artificial cognition. However, they approach the problem from a separated memory and program model of computation. This model of computation poses a fundamental…
This thesis describes work on two applications of probabilistic programming: the learning of probabilistic program code given specifications, in particular program code of one-dimensional samplers; and the facilitation of sequential Monte…
We propose learning flexible but interpretable functions that aggregate a variable-length set of permutation-invariant feature vectors to predict a label. We use a deep lattice network model so we can architect the model structure to…
In this paper we introduce the Functional Modelling System (FMS). The system introduces the Functional Modelling Language (FML), which is a modelling language for NP-complete search problems based on concepts of functional programming.…
With the rise of machine learning, there is a great deal of interest in treating programs as data to be fed to learning algorithms. However, programs do not start off in a form that is immediately amenable to most off-the-shelf learning…
Recursive definitions of predicates are usually interpreted either inductively or coinductively. Recently, a more powerful approach has been proposed, called flexible coinduction, to express a variety of intermediate interpretations,…
The general translator formalism and computing specific implementations are proposed. The implementation of specific elements necessary to process the source and destination information within the translators are presented. Some common…
Chain-of-thought responses from language models improve performance across most benchmarks. However, it remains unclear to what extent these performance gains can be attributed to human-like task decomposition or simply the greater…
This paper provides a general account of the notion of recursive program schemes, studying both uninterpreted and interpreted solutions. It can be regarded as the category-theoretic version of the classical area of algebraic semantics. The…
We investigate representations of imperative programs as constrained Horn clauses. Starting from operational semantics transition rules, we proceed by writing interpreters as constrained Horn clause programs directly encoding the rules. We…
Hybrid programs combine digital control with differential equations, and naturally appear in a wide range of application domains, from biology and control theory to real-time software engineering. The entanglement of discrete and continuous…
The encoder-decoder models for unsupervised sentence representation learning tend to discard the decoder after being trained on a large unlabelled corpus, since only the encoder is needed to map the input sentence into a vector…
To generalize across tasks, an agent should acquire knowledge from past tasks that facilitate adaptation and exploration in future tasks. We focus on the problem of in-context adaptation and exploration, where an agent only relies on…
Recent work by (Richardson and Kuhn, 2017a,b; Richardson et al., 2018) looks at semantic parser induction and question answering in the domain of source code libraries and APIs. In this brief note, we formalize the representations being…