Related papers: Refinement Types as Higher Order Dependency Pairs
In functional programming languages, generalized algebraic data types (GADTs) are very useful as the unnecessary pattern matching over them can be ruled out by the failure of unification of type arguments. In dependent type systems, this is…
Iterative self-refinement is a simple inference-time strategy for machine translation: an LLM revises its own translation over multiple inference-time passes. Yet document-scale refinement remains poorly understood: 1) which pipelines work…
Event-B is a formal approach oriented to system modeling and analysis. It supports refinement mechanism that enables stepwise modeling and verification of a system. By using refinement, the complexity of verification can be spread and…
Sequential dependencies present a fundamental bottleneck in deploying large-scale autoregressive models, particularly for real-time applications. While traditional optimization approaches like pruning and quantization often compromise model…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
Recommendations Systems allow users to identify trending items among a community while being timely and relevant to the user's expectations. When the purpose of various Recommendation Systems differs, the required type of recommendations…
We investigate a growing body of work that seeks to improve recommender systems through the use of review text. Generally, these papers argue that since reviews 'explain' users' opinions, they ought to be useful to infer the underlying…
Recommender systems are significant to help people deal with the world of information explosion and overload. In this Letter, we develop a general framework named self-consistent refinement and implement it be embedding two representative…
Refinement is one of the cornerstones of a formal approach to software engineering. Refinement is the process of developing a more detailed design or implementation from an abstract specification through a sequence of mathematically-based…
Revision programming is a formalism to describe and enforce updates of belief sets and databases. That formalism was extended by Fitting who assigned annotations to revision atoms. Annotations provide a way to quantify the confidence…
Sized types are a modular and theoretically well-understood tool for checking termination of recursive and productivity of corecursive definitions. The essential idea is to track structural descent and guardedness in the type system to make…
We extend the higher-order termination method of dynamic dependency pairs to Algebraic Functional Systems (AFSs). In this setting, simply typed lambda-terms with algebraic reduction and separate {\beta}-steps are considered. For left-linear…
Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language…
This article presents resource-guided synthesis, a technique for synthesizing recursive programs that satisfy both a functional specification and a symbolic resource bound. The technique is type-directed and rests upon a novel type system…
We introduce a new two-sided type system for verifying the correctness and incorrectness of functional programs with atoms and pattern matching. A key idea in the work is that types should range over sets of normal forms, rather than sets…
Validation is a major challenge in differentiable programming. The state of the art is based on algorithmic differentiation. Consistency of first-order tangent and adjoint programs is defined by a well-known first-order differential…
As recommendation is essentially a comparative (or ranking) process, a good explanation should illustrate to users why an item is believed to be better than another, i.e., comparative explanations about the recommended items. Ideally, after…
Refinement based formal methods allow the modelling of systems through incremental steps via abstraction. Discovering the right levels of abstraction, formulating correct and meaningful invariants, and analysing faulty models are some of…
Software bugs have caused enormous economic and human loss in recent years. Certified programming seeks to solve this problem by developing languages where we can make demonstrations that guarantee that our programs work properly. However,…
Type inference methods based on deep learning are becoming increasingly popular as they aim to compensate for the drawbacks of static and dynamic analysis approaches, such as high uncertainty. However, their practical application is still…