Related papers: Cocon: Computation in Contextual Type Theory
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…
Pretrained language models have shown strong effectiveness in code-related tasks, such as code retrieval, code generation, code summarization, and code completion tasks. In this paper, we propose COde assistaNt viA retrieval-augmeNted…
There are multiple ways to formalise the metatheory of type theory. For some purposes, it is enough to consider specific models of a type theory, but sometimes it is necessary to refer to the syntax, for example in proofs of canonicity and…
Nakano's "later" modality, inspired by G\"{o}del-L\"{o}b provability logic, has been applied in type systems and program logics to capture guarded recursion. Birkedal et al modelled this modality via the internal logic of the topos of…
Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits…
We accommodate the Integrated Connectionist/Symbolic Architecture (ICS) of [32] within the categorical compositional semantics (CatCo) of [13], forming a model of categorical compositional cognition (CatCog). This resolves intrinsic…
We need much better understanding of information processing and computation as its primary form. Future progress of new computational devices capable of dealing with problems of big data, internet of things, semantic web, cognitive robotics…
Pure type systems arise as a generalisation of simply typed lambda calculus. The contemporary development of mathematics has renewed the interest in type theories, as they are not just the object of mere historical research, but have an…
In this paper, we present a formalization of Kozen's propositional modal $\mu$-calculus, in the Calculus of Inductive Constructions. We address several problematic issues, such as the use of higher-order abstract syntax in inductive sets in…
Chain-of-Thought (CoT) prompting helps Large Language Models (LLMs) tackle complex reasoning by eliciting explicit step-by-step rationales. However, CoT's verbosity increases latency and memory usage and may propagate early errors across…
Chain-of-Thought (CoT) reasoning successfully enhances the reasoning capabilities of Large Language Models (LLMs), yet it incurs substantial computational overhead for inference. Existing CoT compression methods often suffer from a critical…
A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and…
Context-Oriented Programming (COP) is a programming paradigm to encourage modularization of context-dependent software. Key features of COP are layers---modules to describe context-dependent behavioral variations of a software system---and…
Data profilers play a crucial role in the preprocessing phase of data analysis by identifying quality issues such as missing, extreme, or erroneous values. Traditionally, profilers have relied solely on statistical methods, which lead to…
Real world programming languages crucially depend on the availability of computational effects to achieve programming convenience and expressive power as well as program efficiency. Logical frameworks rely on predicates, or dependent types,…
Proof assistants are getting more widespread use in research and industry to provide certified and independently checkable guarantees about theories, designs, systems and implementations. However, proof assistant implementations themselves…
We construct an internal language for cartesian closed bicategories. Precisely, we introduce a type theory modelling the structure of a cartesian closed bicategory and show that its syntactic model satisfies an appropriate universal…
Long chain-of-thought (CoT) prompting helps Large Language Models (LLMs) solve difficult problems, but very long traces often slow or even degrade performance on fast, intuitive "System-1" tasks. We introduce Connector-Aware Compact CoT…
Latent or continuous chain-of-thought methods replace explicit textual rationales with a number of internal latent steps, but these intermediate computations are difficult to evaluate beyond correlation-based probes. In this paper, we view…
For the past several decades, programmers have been modeling things in the world with trees using hierarchies of classes and object-oriented programming (OOP) languages. In this paper, we describe a novel approach to programming, called…