Related papers: Quantitative Logics for Equivalence of Effectful P…
The paper investigates behavioural equivalence between programs in a call-by-value functional language extended with a signature of (algebraic) effect-triggering operations. Two programs are considered as being behaviourally equivalent if…
This paper studies the quantitative refinements of Abramsky's applicative similarity and bisimilarity in the context of a generalisation of Fuzz, a call-by-value $\lambda$-calculus with a linear type system that can express programs…
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…
A modal logic that is strong enough to fully characterize the behavior of a system is called expressive. Recently, with the growing diversity of systems to be reasoned about (probabilistic, cyber-physical, etc.), the focus shifted to…
Graded modal types systems and coeffects are becoming a standard formalism to deal with context-dependent computations where code usage plays a central role. The theory of program equivalence for modal and coeffectful languages, however, is…
There are several ways to define program equivalence for functional programs with algebraic effects. We consider two complementing ways to specify behavioural equivalence. One way is to specify a set of axiomatic equations, and allow proof…
Applicative bisimulation is a coinductive technique to check program equivalence in higher-order functional languages. It is known to be sound, and sometimes complete, with respect to context equivalence. In this paper we show that…
We demonstrate that behavioral probabilities of human decision makers share many common features with quantum probabilities. This does not imply that humans are some quantum objects, but just shows that the mathematics of quantum theory is…
We formulate a framework for describing behaviour of effectful higher-order recursive programs. Examples of effects are implemented using effect operations, and include: execution cost, nondeterminism, global store and interaction with a…
We define quantum-like probabilistic behaviour as behaviour which is impossible to describe by using the classical probability model. We discuss the conjecture that cognitive behaviour is quantum-like. There is presented the scheme for an…
Substructural logics naturally support a quantitative interpretation of formulas, as they are seen as consumable resources. Distances are the quantitative counterpart of equivalence relations: they measure how much two objects are similar,…
In this paper we show several similarities among logic systems that deal simultaneously with deductive and quantitative inference. We claim it is appropriate to call the tasks those systems perform as Quantitative Logic Reasoning. Analogous…
Quantitative aspects of computation are important and sometimes essential in characterising the behavior and determining the properties of systems. They are related to the use of physical quantities (storage space, time, bandwidth, etc.) as…
We study Abramsky's applicative bisimilarity abstractly, in the context of call-by-value $\lambda$-calculi with algebraic effects. We first of all endow a computational $\lambda$-calculus with a monadic operational semantics. We then show…
We establish a general framework for reasoning about the relationship between call-by-value and call-by-name. In languages with computational effects, call-by-value and call-by-name executions of programs often have different, but related,…
Behavioural metrics provide a quantitative refinement of classical two-valued behavioural equivalences on systems with quantitative data, such as metric or probabilistic transition systems. In analogy to the linear-time/branching-time…
This paper explores the space of (propositional) probabilistic logical languages, ranging from a purely `qualitative' comparative language to a highly `quantitative' language involving arbitrary polynomials over probability terms. While…
According to Strachey, a polymorphic program is parametric if it applies a uniform algorithm independently of the type instantiations at which it is applied. The notion of relational parametricity, introduced by Reynolds, is one possible…
Levy's call-by-push-value is a comprehensive programming paradigm that combines elements from functional and imperative programming, supports computational effects and subsumes both call-by-value and call-by-name evaluation strategies. In…
Quantitative aspects of computation are related to the use of both physical and mathematical quantities, including time, performance metrics, probability, and measures for reliability and security. They are essential in characterizing the…