Related papers: The Category Theoretic Solution of Recursive Progr…
Recursive calls over recursive data are useful for generating probability distributions, and probabilistic programming allows computations over these distributions to be expressed in a modular and intuitive way. Exact inference is also…
Predictive models are fundamental to engineering reliable software systems. However, designing conservative, computable approximations for the behavior of programs (static analyses) remains a difficult and error-prone process for modern…
Substructural type systems, such as affine (and linear) type systems, are type systems which impose restrictions on copying (and discarding) of variables, and they have found many applications in computer science, including quantum…
Term rewriting systems have a simple syntax and semantics and facilitate proofs of correctness. However, they are not as popular in industry or academia as imperative languages. We define a term rewriting based abstract programming language…
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with…
We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
Most modern (classical) programming languages support recursion. Recursion has also been successfully applied to the design of several quantum algorithms and introduced in a couple of quantum programming languages. So, it can be expected…
Dependent pattern matching is a key feature in dependently typed programming. However, there is a theory-practice disconnect: while many proof assistants implement pattern matching as primitive, theoretical presentations give semantics to…
This paper introduces a category theory-based framework to redefine physical computing in light of advancements in quantum computing and non-standard computing systems. By integrating classical definitions within this broader perspective,…
We propose a presentation of classical propositional tableaux elaborated by application of methods that are noteworthy in program design, namely program derivation with separation of concerns. We start by deriving from a straightforward…
We design various logics for proving hyper properties of iterative programs by application of abstract interpretation principles. In part I, we design a generic, structural, fixpoint abstract interpreter parameterized by an algebraic…
Coherence theorems for covariant structures carried by a category have traditionally relied on the underlying term rewriting system of the structure being terminating and confluent. While this holds in a variety of cases, it is not a…
The rather unintuitive nature of quantum theory has led numerous people to develop sets of (physically motivated) principles that can be used to derive quantum mechanics from the ground up, in order to better understand where the structure…
Tree ensembles are very popular machine learning models, known for their effectiveness in supervised classification and regression tasks. Their performance derives from aggregating predictions of multiple decision trees, which are renowned…
This paper presents a novel approach to automatically solving arithmetic word problems. This is the first algorithmic approach that can handle arithmetic problems with multiple steps and operations, without depending on additional…
A novel model of reversible computing, the $\aleph$-calculus, is introduced. It is declarative, reversible-Turing complete, and has a local term-rewriting semantics. Unlike previously demonstrated reversible term-rewriting systems, it does…
An abstract machine is a theoretical model designed to perform a rigorous study of computation. Such a model usually consists of configurations, instructions, programs, inputs and outputs for the machine. In this paper we formalize these…
We study transformational program logics for correctness and incorrectness that we extend to explicitly handle both termination and nontermination. We show that the logics are abstract interpretations of the right image transformer for a…
The program Reverse Mathematics (RM for short) seeks to identify the axioms necessary to prove theorems of ordinary mathematics, usually working in the language of second-order arithmetic $L_{2}$. A major theme in RM is therefore the study…