Related papers: Handling Higher-Order Effectful Operations with Ju…
We introduce a new programming language and its categorical semantics in order to design and implement neural networks within the framework of algebraic effects and handlers for arrows. Our language enables us to construct neural networks…
We introduce refutationally complete superposition calculi for intentional and extensional clausal $\lambda$-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a…
We introduce Clerical, a programming language for exact real-number computation that combines first-order imperative-style programming with a limit operator for computation of real numbers as limits of Cauchy sequences. We address the…
We introduce an extension of Hoare logic for call-by-value higher-order functions with ML-like local reference generation. Local references may be generated dynamically and exported outside their scope, may store higher-order functions and…
Algebraic effects and handlers support composable and structured control-flow abstraction. However, existing designs of algebraic effects often require effects to be executed sequentially. This paper studies parallel algebraic effect…
Symbolic Computation algorithms and their implementation in computer algebra systems often contain choices which do not affect the correctness of the output but can significantly impact the resources required: such choices can benefit from…
Reasoning about program equivalence in imperative languages is notoriously challenging, as the presence of states (in the form of variable stores) fundamentally increases the observational power of program terms. The key desideratum for any…
We motivate and study an infinite sequence of binary operations on the ordinal numbers, extending the standard arithmetic on the ordinals to higher degrees of iteration. Connections to the hyperoperations on the natural numbers are…
Abstract clones serve as an algebraic presentation of the syntax of a simple type theory. From the perspective of universal algebra, they define algebraic theories like those of groups, monoids and rings. This link allows one to study the…
Type-preserving translations are effective rigorous tools in the study of core programming calculi. In this paper, we develop a new typed translation that connects sequential and concurrent calculi; it is governed by type systems that…
The present paper gives a mathematical, in particular, syntax-independent, formulation of intensionality and dynamics of computation in terms of games and strategies. Specifically, we give a game semantics for a higher-order programming…
The termination method of weakly monotonic algebras, which has been defined for higher-order rewriting in the HRS formalism, offers a lot of power, but has seen little use in recent years. We adapt and extend this method to the alternative…
In this work, we introduce a framework to study the effect of random operations on the combinatorial list-decodability of a code. The operations we consider correspond to row and column operations on the matrix obtained from the code by…
In previous works, a tableau calculus has been defined, which constitutes a decision procedure for hybrid logic with the converse and global modalities and a restricted use of the binder. This work shows how to extend such a calculus to…
We propose a general framework to allow: (a) specifying the operational semantics of a programming language; and (b) stating and proving properties about program correctness. Our framework is based on a many-sorted system of hybrid modal…
Exception handling is provided by most modern programming languages. It allows to deal with anomalous or exceptional events which require special processing. In computer algebra, exception handling is an efficient way to implement the…
Monads are extensively used nowadays to abstractly model a wide range of computational effects such as nondeterminism, statefulness, and exceptions. It turns out that equipping a monad with a (uniform) iteration operator satisfying a set of…
We study the operad of associative algebras equipped with a derivation. We show that it is determined by polynomials in several variables and substitution. Replacing polynomials by rational functions gives an operad which is isomorphic to…
Processing programs as data is one of the successes of functional and logic programming. Higher-order functions, as program-processing programs are called in functional programming, and meta-programs, as they are called in logic…
A class of models is presented, in the form of continuation monads polymorphic for first-order individuals, that is sound and complete for minimal intuitionistic predicate logic. The proofs of soundness and completeness are constructive and…