Related papers: A Recipe for State-and-Effect Triangles
Syntactic theory has traditionally adopted a constructivist approach, in which a set of atomic elements are manipulated by combinatory operations to yield derived, complex elements. Syntactic structure is thus seen as the result or discrete…
Category theory provides a collective description of many arrangements in mathematics, such as topological spaces, Banach spaces and game theory. Within this collective description, the perspective from any individual member of the…
Modeling sequential and parallel composition of effectful computations has been investigated in a variety of languages for a long time. In particular, the popular do-notation provides a lightweight effect embedding for any instance of a…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…
We introduce a neural semantic parser that converts natural language utterances to intermediate representations in the form of predicate-argument structures, which are induced with a transition system and subsequently mapped to target…
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…
In the theory of answer set programming, two groups of rules are called strongly equivalent if, informally speaking, they have the same meaning in any context. The relationship between strong equivalence and the propositional logic of…
In previous work, we proposed a logic-based framework in which computation is the execution of actions in an attempt to make reactive rules of the form if antecedent then consequent true in a canonical model of a logic program determined by…
We introduce string diagrams as a formal mathematical, graphical language to represent, compose, program and reason about games. The language is well established in quantum physics, quantum computing and quantum linguistic with the…
It is shown how, given a "probability data table" for a quantum or classical system, the representation of states and measurement outcomes as vectors in a real vector space follows in a natural way. Some properties of the resulting sets of…
The principle behind algebraic language theory for various kinds of structures, such as words or trees, is to use a compositional function from the structures into a finite set. To talk about compositionality, one needs some way of…
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…
In the study of computational effects, it is important to consider the notion of computational effects with parameters. The need of such a notion arises when, for example, statically estimating the range of effects caused by a program, or…
We consider a simple extension of logic programming where variables may range over goals and goals may be arguments of predicates. In this language we can write logic programs which use goals as data. We give practical evidence that, by…
Refinement calculus is a powerful and expressive tool for reasoning about sequential programs in a compositional manner. In this paper we present an extension of refinement calculus for reactive systems. Refinement calculus is based on…
Comprehending procedural text, e.g., a paragraph describing photosynthesis, requires modeling actions and the state changes they produce, so that questions about entities at different timepoints can be answered. Although several recent…
Some aspects of programming education are examined in this work. It is emphasised, based on the entertainment value, the most appropriate examples are chosen to demonstrate the different language constructions and data structures. Such an…
State monads in cartesian closed categories are those defined by the familiar adjunction between product and exponential. We investigate the structure of their algebras, and show that the exponential functor is monadic provided the base…
Stack allocation and first-class functions don't naturally mix together. In this paper we show that a type and effect system can be the detergent that helps these features form a nice emulsion. Our interest in this problem comes from our…
The idea of "summing over all intermediate states" that is central for implementing locality in quantum systems can be realized by coend constructions. In the concrete case of systems of conformal blocks for a certain class of conformal…