Related papers: Subtyping in DHOL -- Extended preprint
We present a new model of Guarded Dependent Type Theory (GDTT), a type theory with guarded recursion and multiple clocks in which one can program with, and reason about coinductive types. Productivity of recursively defined coinductive…
Differential linear logic (DiLL) provides a fine analysis of resource consumption in cut-elimination. We investigate the subsystem of DiLL without promotion in a deep inference formalism, where cuts are at an atomic level. In our system…
Just like any other branch of mathematics, denotational semantics of programming languages should be formalised in type theory, but adapting traditional domain theoretic semantics, as originally formulated in classical set theory to type…
We present a generic framework that facilitates object level reasoning with logics that are encoded within the Higher Order Logic theorem proving environment of HOL Light. This involves proving statements in any logic using intuitive…
Dependently typed lambda calculi such as the Logical Framework (LF) are capable of representing relationships between terms through types. By exploiting the "formulas-as-types" notion, such calculi can also encode the correspondence between…
Deep Learning architectures, and in particular Transformers, are conventionally viewed as a composition of layers. These layers are actually often obtained as the sum of two contributions: a residual path that copies the input and the…
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…
As quantum computers become real, it is high time we come up with effective techniques that help programmers write correct quantum programs. In classical computing, formal verification and sound static type systems prevent several classes…
First-order resolution has been used for type inference for many years, including in Hindley- Milner type inference, type-classes, and constrained data types. Dependent types are a new trend in functional languages. In this paper, we show…
This paper provides an in-depth examination of the concept of semantic diffusion as a complementary instrument to large language models (LLMs) for design applications. Conventional LLMs and diffusion models fail to induce a convergent,…
I propose a system for Automated Theorem Proving in higher order logic using deep learning and eschewing hand-constructed features. Holophrasm exploits the formalism of the Metamath language and explores partial proof trees using a…
Although deep reinforcement learning has become a promising machine learning approach for sequential decision-making problems, it is still not mature enough for high-stake domains such as autonomous driving or medical applications. In such…
Many proof assistants allow the use of features and axioms that increase their expressive power. However, these extensions must be used with care, as some combinations are known to lead to logical inconsistencies. Therefore, proof…
Session types statically prescribe bidirectional communication protocols for message-passing processes. However, simple session types cannot specify properties beyond the type of exchanged messages. In this paper we extend the type system…
Formal theorem proving with TLA+ provides rigorous guarantees for system specifications, but constructing proofs requires substantial expertise and effort. While large language models have shown promise in automating proofs for tactic-based…
In this brief, we discuss the implementation of a third order semi-implicit differentiator as a complement of the recent work by the author that proposes an interconnected semi-implicit Euler double differentiators algorithm through Taylor…
We present a tool for modelling and reasoning with knowledge from various diverse (and possibly conflicting) viewpoints. The theoretical underpinnings are provided by enhancing base logics by standpoints according to a recently introduced…
Dynamic HoTT (DHoTT) is a conservative extension of Homotopy Type Theory designed for evolving texts in conversational AI. In a chat system, a large language model (LLM) is queried with a growing prefix: at turn tau the input is C(tau), the…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
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…