Related papers: A Calculus for Scoped Effects & Handlers
Probabilistic operational semantics for a nondeterministic extension of pure lambda calculus is studied. In this semantics, a term evaluates to a (finite or infinite) distribution of values. Small-step and big-step semantics are both…
This document introduces a generalization of calculus that treats both continuous and discrete variables on an equal footing. This generalization of calculus was developed independently of the "Calculus on Time Scales" literature but may be…
In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex…
We explore the design and implementation of Frank, a strict functional programming language with a bidirectional effect type system designed from the ground up around a novel variant of Plotkin and Pretnar's effect handler abstraction.…
Runners of algebraic effects, also known as comodels, provide a mathematical model of resource management. We show that they also give rise to a programming concept that models top-level external resources, as well as allows programmers to…
The sequent calculus is a proof system which was designed as a more symmetric alternative to natural deduction. The {\lambda}{\mu}{\mu}-calculus is a term assignment system for the sequent calculus and a great foundation for compiler…
The goal of the present paper is to introduce and study noncommutative Hardy spaces associated with the regular $\Lambda$-polyball, to develop a functional calculus on noncommutative Hardy spaces for the completely non-coisometric (c.n.c.)…
Our basic structure is a finite-dimensional complex Hilbert space $H$. We point out that the set of effects on $H$ form a convex effect algebra. Although the set of operators on $H$ also form a convex effect algebra, they have a more…
The lambda calculus is a universal programming language. It can represent the computable functions, and such offers a formal counterpart to the point of view of functions as rules. Terms represent functions and this allows for the…
We show how an effect algebra $\mathcal{X}$ can be regarded as a category, where the morphisms $x \rightarrow y$ are the elements $f$ such that $x \leq f \leq y$. This gives an embedding $\mathbf{EA} \rightarrow \mathbf{Cat}$. The interval…
The development of programming languages can be quite complicated and costly. Hence, much effort has been devoted to the modular definition of language features that can be reused in various combinations to define new languages and…
We present a modification of the superposition calculus that is meant to generate consequences of sets of first-order axioms. This approach is proven to be sound and deductive-complete in the presence of redundancy elimination rules,…
This dissertation is concerned with the study of program equivalence and algebraic effects as they arise in the theory of programming languages. Algebraic effects represent impure behaviour in a functional programming language, such as…
Probabilistic programming languages (PPLs) allow programmers to construct statistical models and then simulate data or perform inference over them. Many PPLs restrict models to a particular instance of simulation or inference, limiting…
Let $f$ be a real polynomial of $x = (x_1,\dots,x_n)$ and $\varphi$ be a locally integrable function of $x$ which satisfies a holonomic system of linear differential equations. We study the distribution $f_+^\lambda\varphi$ with a…
One can perform equational reasoning about computational effects with a purely functional programming language thanks to monads. Even though equational reasoning for effectful programs is desirable, it is not yet mainstream. This is partly…
This article begins with a study of convex effect-state spaces. We point out that such spaces are equivalent to interval effect algebras that generate an ordered linear space and possess an order-determining set of states. We then discuss…
In this paper we invite the reader to a journey through three lambda calculi with resource control: the lambda calculus, the sequent lambda calculus, and the lambda calculus with explicit substitution. All three calculi enable explicit…
The substitution lemma is a renowned theorem within the realm of lambda-calculus theory and concerns the interactional behaviour of the metasubstitution operation. In this work, we augment the lambda-calculus's grammar with an uninterpreted…
Extended versions of the Lambek Calculus currently used in computational linguistics rely on unary modalities to allow for the controlled application of structural rules affecting word order and phrase structure. These controlled structural…