Related papers: Handling polymorphic algebraic effects
Mathematical concepts emerge through an interplay of processes, including experimentation, efforts at proof, and counterexamples. In this paper, we present a new multi-agent model for computational mathematical discovery based on this…
Type-and-effect systems incorporate information about the computational effects, e.g., state mutation, probabilistic choice, or I/O, a program phrase may invoke alongside its return value. A semantics for type-and-effect systems involves a…
In this paper we present two flavors of a quantum extension to the lambda calculus. The first one, $\lambda_\rho$, follows the approach of classical control/quantum data, where the quantum data is represented by density matrices. We provide…
This paper investigates type isomorphism in a lambda-calculus with intersection and union types. It is known that in lambda-calculus, the isomorphism between two types is realised by a pair of terms inverse one each other. Notably,…
One of the few available complete methods for checking the satisfiability of sets of polynomial constraints over the reals is the cylindrical algebraic covering (CAlC) method. In this paper, we propose an extension for this method to…
In dependent type theory, being able to refer to a type universe as a term itself increases its expressive power, but requires mechanisms in place to prevent Girard's paradox from introducing logical inconsistency in the presence of…
We investigate the interplay between a modality for controlling the behaviour of recursive functional programs on infinite structures which are completely silent in the syntax. The latter means that programs do not contain "marks" showing…
The algebraic lambda calculus and the linear algebraic lambda calculus are two extensions of the classical lambda calculus with linear combinations of terms. They arise independently in distinct contexts: the former is a fragment of the…
The theme of symbolic computation in algebraic categories has become of utmost importance in the last decade since it enables the automatic modeling of modern algebra theories. On this theoretical background, the present paper reveals the…
We introduce two extensions of the $\lambda$-calculus with a probabilistic choice operator, $\Lambda_\oplus^{cbv}$ and $\Lambda_\oplus^{cbn}$, modeling respectively call-by-value and call-by-name probabilistic computation. We prove that…
We present a type system that combines, in a controlled way, first-order polymorphism with intersectiontypes, union types, and subtyping, and prove its safety. We then define a type reconstruction algorithm that issound and terminating.…
Parser combinators are a well-known mechanism used for the compositional construction of parsers, and have shown to be particularly useful in writing parsers for rich grammars with data-dependencies and global state. Verifying applications…
While many robotic tasks, like manipulation and locomotion, are fundamentally based in making and breaking contact with the environment, state-of-the-art control policies struggle to deal with the hybrid nature of multi-contact motion. Such…
Probabilistic behavior is omnipresent in computer controlled systems, in particular, so-called safety-critical hybrid systems, because of various reasons, like uncertain environments, or fundamental properties of nature. In this paper, we…
Loop invariants are properties of a program loop that hold before and after each iteration of the loop. They are often employed to verify programs and ensure that algorithms consistently produce correct results during execution.…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Types-and-effects are type systems, which allow one to express general semantic properties and to statically reason about program's execution. They have been widely exploited to specify static analyses, for example to track computational…
We investigate the implementation of reduced-form allocation probabilities in a two-person bargaining problem without side payments, where the agents have to select one alternative from a finite set of social alternatives. We provide a…
This paper is a compressed summary of some principal definitions and concepts in the approach to the black box algebra being developed by the authors. We suggest that black box algebra could be useful in cryptanalysis of homomorphic…
We consider the call-by-value lambda-calculus extended with a may-convergent non-deterministic choice and a must-convergent parallel composition. Inspired by recent works on the relational semantics of linear logic and non-idempotent…