Related papers: Reflections on Monadic Lenses
Lenses are programs that can be run both "front to back" and "back to front," allowing updates to either their source or their target data to be transferred in both directions. Lenses have been extensively studied, extended, and applied.…
The modern theory of functional programming languages uses monads for encoding computational side-effects and side-contexts, beyond bare-bone program logic. Even though quantum computing is intrinsically side-effectful (as in quantum…
Monads have become a powerful tool for structuring effectful computations in functional programming, because they make the order of effects explicit. When translating pure code to a monadic version, we need to specify evaluation order…
Wadler and Thiemann unified type-and-effect systems with monadic semantics via a syntactic correspondence and soundness results with respect to an operational semantics. They conjecture that a general, "coherent" denotational semantics can…
Transformation optics offers an unconventional approach to the control of electromagnetic fields. A transformation optical structure is designed by first applying a form-invariant coordinate transform to Maxwell's equations, in which part…
Traditional approaches to modelling parallelism and algebraic structure in lambda calculi often rely on monads$\unicode{x2013}$as in Moggi's framework$\unicode{x2013}$or on rich categorical structures such as biproducts$\unicode{x2013}$as…
Strong gravitational lensing by galaxies in MOdified Newtonian Dynamics (MOND) has until now been restricted to spherically symmetric models. These models were able to account for the size of the Einstein ring of observed lenses, but were…
Monads can be interpreted as encoding formal expressions, or formal operations in the sense of universal algebra. We give a construction which formalizes the idea of "evaluating an expression partially": for example, "2+3" can be obtained…
Strong bisimulation for labelled transition systems is one of the most fundamental equivalences in process algebra, and has been generalised to numerous classes of systems that exhibit richer transition behaviour. Nearly all of the ensuing…
Bidirectional transformations between different data representations occur frequently in modern software systems. They appear as serializers and deserializers, as database views and view updaters, and more. Manually building bidirectional…
Monads govern computational side-effects in programming semantics. They can be combined in a ''bottom-up'' way to handle several instances of such effects. Indexed monads and graded monads do this in a modular way. Here, instead, we equip…
Large vision-language models (VLMs) often benefit from intermediate visual cues, either injected via external tools or generated as latent visual tokens during reasoning, but these mechanisms still overlook fine-grained visual evidence…
Modified Newtonian dynamics (MOND) is an alternative theory of gravity that aims to explain large-scale dynamics without recourse to any form of dark matter. However the theory is incomplete, lacking a relativistic counterpart, and so makes…
Graded monads refine traditional monads using effect annotations in order to describe quantitatively the computational effects that a program can generate. They have been successfully applied to a variety of formal systems for reasoning…
Partial Combinatory Algebras (PCAs) provide a foundational model of the untyped $\lambda$-calculus and serve as the basis for many notions of computability, such as realizability theory. However, PCAs support a very limited notion of…
Bilingual word embeddings, which representlexicons of different languages in a shared em-bedding space, are essential for supporting se-mantic and knowledge transfers in a variety ofcross-lingual NLP tasks. Existing approachesto training…
Over the past two decades the notion of a strong monad has found wide applicability in computing. Arising out of a need to interpret products in computational and semantic settings, different approaches to this concept have arisen. In this…
Polyhedral convex set optimization problems are the simplest optimization problems with set-valued objective function. Their role in set optimization is comparable to the role of linear programs in scalar optimization. Vector linear…
Multiple (more than 2) model synchronization is ubiquitous and important for model driven engineering, but its theoretical underpinning gained much less attention than the binary case. Specifically, the latter was extensively studied by the…
Bokeh effect is an optical phenomenon that offers a pleasant visual experience, typically generated by high-end cameras with wide aperture lenses. The task of bokeh effect transformation aims to produce a desired effect in one set of lenses…