Related papers: Deriving monadic quicksort (Declarative Pearl)
We extend to natural deduction the approach of Linear Nested Sequents and of 2-sequents. Formulas are decorated with a spatial coordinate, which allows a formulation of formal systems in the original spirit of natural deduction -- only one…
Functional logic languages are a high-level approach to programming by combining the most important declarative features. They abstract from small-step operational details so that programmers can concentrate on the logical aspects of an…
Backpropagation is a classic automatic differentiation algorithm computing the gradient of functions specified by a certain class of simple, first-order programs, called computational graphs. It is a fundamental tool in several fields, most…
Logic program transformation by the unfold/fold method ad- vocates the writing of correct logic programs via the application of some rules to a naive program. This work focuses on how to overcome subgoal- introduction difficulties in…
We present a system for generating parsers based directly on the metaphor of parsing as deduction. Parsing algorithms can be represented directly as deduction systems, and a single deduction engine can interpret such deduction systems so as…
We derive multiple program logics, including correctness, incorrectness, and relational Hoare logic, from the axioms of imperative categories: uniformly traced distributive copy-discard categories. We introduce an internal language for…
We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of…
We give a construction that identifies the collection of pure processes (i.e. those which are deterministic, or without randomness) within a theory containing both pure and mixed processes. Working in the framework of symmetric monoidal…
Monadic second order logic is the expansion of first order logic by quantifiers ranging over unary relations. We study the shared monadic second order theory of finite linear orders, i.e. the pseudofinite monadic second order theory of…
Using non-linear difference equations, combined with symbolic computations, we make a detailed study of the running times of numerous variants of the celebrated Quicksort algorithms, where we consider the variants of single-pivot and…
This paper studies the design of programming languages with handlers of higher-order effectful operations -- effectful operations that may take in computations as arguments or return computations as output. We present and analyse a core…
The short note describes the chart parser for multimodal type-logical grammars which has been developed in conjunction with the type-logical treebank for French. The chart parser presents an incomplete but fast implementation of proof…
We define a broad class of deterministic stream functions and show they can be implemented as homomorphisms into a "state" monoid. The homomorphism laws are simpler than the conditions of previous semantic frameworks for stream program…
To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new…
We provide full certifications of two versions of merge sort of arrays in the verification-aware programming language Dafny. We start by considering schemas for applying the divide-and-conquer or partition method of solution to…
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…
Defeasible reasoning is a simple but efficient approach to nonmonotonic reasoning that has recently attracted considerable interest and that has found various applications. Defeasible logic and its variants are an important family of…
The key assumption underlying linear Markov Decision Processes (MDPs) is that the learner has access to a known feature map $\phi(x, a)$ that maps state-action pairs to $d$-dimensional vectors, and that the rewards and transitions are…
We study the question of whether, for a given class of finite graphs, one can define, for each graph of the class, a linear ordering in monadic second-order logic, possibly with the help of monadic parameters. We consider two variants of…
We introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the…