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Algebraic characterizations of the computational aspects of functions defined over the real numbers provide very effective tool to understand what computability and complexity over the reals, and generally over continuous spaces, mean. This…
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…
Database schema elements such as tables, views, triggers and functions are typically defined with many interrelationships. In order to support database users in understanding a given schema, a rule-based approach for analyzing the…
Large language models (LLMs) have achieved notable success in code generation. However, they still frequently produce uncompilable output because their next-token inference procedure does not model formal aspects of code. Although…
Advancing the frontier of subquadratic architectures for Language Models (LMs) is crucial in the rapidly evolving field of natural language processing. Current innovations, including State Space Models, were initially celebrated for…
Large language models (LLMs) represent a new paradigm for processing unstructured data, with applications across an unprecedented range of domains. In this paper, we address, through two arguments, whether the development and application of…
We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two…
In this paper we demonstrate an approach to model structure and behavior of distributed systems, to map those models to a lightweight execution engine by using a functional programming language and to systematically define and execute tests…
This work proposes a dependent type theory that combines functions and session-typed processes (with value dependencies) through a contextual monad, internalising typed processes in a dependently-typed lambda-calculus. The proposed…
We describe the foundation of the metaprogramming language, Moebius, which supports the generation of polymorphic code and, more importantly the analysis of polymorphic code via pattern matching. Moebius has two main ingredients: 1) we…
Certainly, the success of the Unified Modeling Language (UML) as the de facto standard for modeling software systems does not imply closing the door on scientific exploration or experimentation with modeling in the field. Continuing studies…
Supervised training of abstractive language generation models results in learning conditional probabilities over language sequences based on the supervised training signal. When the training signal contains a variety of writing styles, such…
Language models (LMs) are said to be exhibiting reasoning, but what does this entail? We assess definitions of reasoning and how key papers in the field of natural language processing (NLP) use the notion and argue that the definitions…
While modern software development heavily uses versioned packages, programming languages rarely support the concept of versions in their semantics, which makes software updates more bulky and unsafe. This paper proposes a programming…
Large language models (LLMs) have shown impressive capabilities across a wide range of language tasks. However, their reasoning process is primarily guided by statistical patterns in training data, which limits their ability to handle novel…
Type analyses of logic programs which aim at inferring the types of the program being analyzed are presented in a unified abstract interpretation-based framework. This covers most classical abstract interpretation-based type analyzers for…
Context Oriented Programming (COP) concerns the ability of programs to adapt to changes in their running environment. A number of programming languages endowed with COP constructs and features have been developed. However, some foundational…
Results in interpretability suggest that large vision and language models learn implicit linear encodings when models are biased by in-context prompting. However, the existence of similar linear representations in more general adaptation…
When trained on language data, do transformers learn some arbitrary computation that utilizes the full capacity of the architecture or do they learn a simpler, tree-like computation, hypothesized to underlie compositional meaning systems…
Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…