Related papers: Generating collection transformations from proofs
We address the predicate generation problem in the context of loop invariant inference. Motivated by the interpolation-based abstraction refinement technique, we apply the interpolation theorem to synthesize predicates implicitly implied by…
Traces and their extension called combined traces (comtraces) are two formal models used in the analysis and verification of concurrent systems. Both models are based on concepts originating in the theory of formal languages, and they are…
We define a strongly normalising proof-net calculus corresponding to the logic of strongly compact closed categories with biproducts. The calculus is a full and faithful representation of the free strongly compact closed category with…
We develop synthetic notions of oracle computability and Turing reducibility in the Calculus of Inductive Constructions (CIC), the constructive type theory underlying the Coq proof assistant. As usual in synthetic approaches, we employ a…
The Theory of Functional Connections (TFC) is a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The functionals derived from this method, called \emph{constrained expressions},…
Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular, now several type systems based on circular reasoning have…
Search-oriented conversational systems rely on information needs expressed in natural language (NL). We focus here on the understanding of NL expressions for building keyword-based queries. We propose a reinforcement-learning-driven…
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
We address generating theorems from a given set of axioms, without proof goal, aiming at value from a mathematical point of view or as lemmas for automated proving. As benchmark, we convert a fragment of the Metamath database set.mm. Our…
Temporal logic is a framework for representing and reasoning about propositions that evolve over time. It is commonly used for specifying requirements in various domains, including hardware and software systems, as well as robotics.…
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
Large, human-annotated datasets are central to the development of natural language processing models. Collecting these datasets can be the most challenging part of the development process. We address this problem by introducing a general…
Learning effective representations of sentences is one of the core missions of natural language understanding. Existing models either train on a vast amount of text, or require costly, manually curated sentence relation datasets. We show…
Representation choice is of fundamental importance to our ability to communicate and reason effectively. A major unsolved problem, addressed in this paper, is how to devise representational-system (RS) agnostic techniques that drive…
We introduce Transformer Grammars (TGs), a novel class of Transformer language models that combine (i) the expressive power, scalability, and strong performance of Transformers and (ii) recursive syntactic compositions, which here are…
Network Calculus (NC) is an algebraic theory that represents traffic and service guarantees as curves in a Cartesian plane, in order to compute performance guarantees for flows traversing a network. NC uses transformation operations, e.g.,…
We propose a procedure for automated implicit inductive theorem proving for equational specifications made of rewrite rules with conditions and constraints. The constraints are interpreted over constructor terms (representing data values),…
We introduce the \emph{Arrow Language Model}, a neural architecture derived from an intuitionistic-logic interpretation of next-token prediction. Instead of representing tokens as additive embeddings mixed by attention, we encode a prefix…
Nested words are a structured model of execution paths in procedural programs, reflecting their call and return nesting structure. Finite nested words also capture the structure of parse trees and other tree-structured data, such as XML. We…
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…