Related papers: Tracing monadic computations and representing effe…
In type-and-coeffect systems, contexts are enriched by coeffects modeling how they are actually used, typically through annotations on single variables. Coeffects are computed bottom-up, combining, for each term, the coeffects of its…
This report specifies an observational semantics and gives an original presentation of the Byrd's box model. The approach accounts for the semantics of Prolog tracers independently of a particular implementation. Traces are, in general,…
Two very basic constructions involving experimental procedures are the formation of coarse-grained versions of experiments, and the formation of branching sequential experiments. The latter allow for the conditioning of states on the…
We define a notion of grading of a monoid T in a monoidal category C, relative to a class of morphisms M (which provide a notion of M-subobject). We show that, under reasonable conditions (including that M forms a factorization system),…
This paper describes a categorical interpretation of the Wolfram Language and introduces a simple implementation of monadic types and the "do" notation. The monadic style of programming combined with the many built in functions of the…
Canonical functions are a powerful concept with numerous applications in the study of groups, monoids, and clones on countable structures with Ramsey-type properties. In this short note, we present a proof of the existence of canonical…
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
We propose a new class of generative diffusion models, called functional diffusion. In contrast to previous work, functional diffusion works on samples that are represented by functions with a continuous domain. Functional diffusion can be…
Modern software projects include automated tests written to check the programs' functionality. The set of functions invoked by a test is called the trace of the test, and the action of obtaining a trace is called tracing. There are many…
Capture calculus has recently been proposed as a solution to effect checking, achieved by tracking the captured references of terms in the types. Boxes, along with the box and unbox operations, are a crucial construct in capture calculus,…
Transformers pretrained via next token prediction learn to factor their world into parts, representing these factors in orthogonal subspaces of the residual stream. We formalize two representational hypotheses: (1) a representation in the…
Effect handlers are a powerful abstraction for defining, customising, and composing computational effects. Statically ensuring that all effect operations are handled requires some form of effect system, but using a traditional effect system…
In this paper we use topological techniques to construct generalized trace and modified dimension functions on ideals in certain ribbon categories. Examples of such ribbon categories naturally arise in representation theory where the usual…
Using standard domain-theoretic fixed-points, we present an approach for defining recursive functions that are formulated in monadic style. The method works both in the simple option monad and the state-exception monad of Isabelle/HOL's…
We present a new approach to termination analysis of numerical computations in logic programs. Traditional approaches fail to analyse them due to non well-foundedness of the integers. We present a technique that allows overcoming these…
Even though computational reproducibility is widely accepted as necessary for research validation and reuse, it is often not considered during the research process. This is because reproducibility tools are typically stand-alone and require…
In purely functional programming languages imperative features, more generally computational effects are prohibited. However, non-functional lan- guages do involve effects. The theory of decorated logic provides a rigorous for- malism (with…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
In the quest to give a formal compositional semantics to natural languages, semanticists have started turning their attention to phenomena that have been also considered as parts of pragmatics (e.g., discourse anaphora and presupposition…
Machine-specific optimizations command the machine to behave in a specific way. As current programming models largely leave machine details unexposed, they cannot accommodate direct encoding of such commands. In previous work we have…