Related papers: Equivalence of eval-readback and eval-apply big-st…
The existing call-by-need lambda calculi describe lazy evaluation via equational logics. A programmer can use these logics to safely ascertain whether one term is behaviorally equivalent to another or to determine the value of a lazy…
Taha and Nielsen have developed a multi-stage calculus {\lambda}{\alpha} with a sound type system using the notion of environment classifiers. They are special identifiers, with which code fragments and variable declarations are annotated,…
Reinforcement Learning with Verifiable Rewards (RLVR) elicits long chain-of-thought reasoning in large language models (LLMs), but outcome-based rewards lead to coarse-grained advantage estimation. While existing approaches improve RLVR via…
In a paper presented at SOS 2010, we developed a framework for big-step semantics for interactive input-output in combination with divergence, based on coinductive and mixed inductive-coinductive notions of resumptions, evaluation and…
In appropriate frameworks, automatic differentiation is transparent to the user at the cost of being a significant computational burden when the number of operations is large. For iterative algorithms, implicit differentiation alleviates…
Checking the semantic equivalence of operations is an important task in software development. For instance, regression testing is a routine task performed when software systems are developed and improved, and software package managers…
Same-style products retrieval plays an important role in e-commerce platforms, aiming to identify the same products which may have different text descriptions or images. It can be used for similar products retrieval from different suppliers…
This paper provides foundations for strong (that is, possibly under abstraction) call-by-value evaluation for the lambda-calculus. Recently, Accattoli et al. proposed a form of call-by-value strong evaluation for the lambda-calculus, the…
We aim to reason about the correctness of behaviour-preserving transformations of Erlang programs. Behaviour preservation is characterised by semantic equivalence. Based upon our existing formal semantics for Core Erlang, we investigate…
In courses that involve programming assignments, giving meaningful feedback to students is an important challenge. Human beings can give useful feedback by manually grading the programs but this is a time-consuming, labor intensive, and…
Using a call-by-value functional language as an example, this article illustrates the use of coinductive definitions and proofs in big-step operational semantics, enabling it to describe diverging evaluations in addition to terminating…
The leaderboard of Large Language Models (LLMs) in mathematical tasks has been continuously updated. However, the majority of evaluations focus solely on the final results, neglecting the quality of the intermediate steps. This oversight…
We propose a one-step procedure to estimate the latent positions in random dot product graphs efficiently. Unlike the classical spectral-based methods such as the adjacency and Laplacian spectral embedding, the proposed one-step procedure…
Despite the remarkable coherence of Large Language Models (LLMs), existing evaluation methods often suffer from fluency bias and rely heavily on multiple-choice formats, making it difficult to assess factual accuracy and complex reasoning…
Large language models (LLMs) achieve strong reasoning performance by allocating substantial computation at inference time, often generating long and verbose reasoning traces. While recent work on efficient reasoning reduces this overhead…
We propose an operationally-based deductive proof method for program equivalence. It is based on encoding the language semantics as logically constrained term rewriting systems (LCTRSs) and the two programs as terms. The main feature of our…
Contextual equivalence is the de facto standard notion of program equivalence. A key theorem is that contextual equivalence is an equational theory. Making contextual equivalence more intensional, for example taking into account the time…
Visual fine-tuning has garnered significant attention with the rise of pre-trained vision models. The current prevailing method, full fine-tuning, suffers from the issue of knowledge forgetting as it focuses solely on fitting the downstream…
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…
In this paper, we introduce a new iterative method which we call one step back approach: the main idea is to anticipate the consequence of the iterative computation per coordinate and to optimize on the choice of the sequence of the…