Related papers: Recursive Definitions of Monadic Functions
Let No be Conway's class of surreal numbers. I will make explicit the notion of a function f on No recursively defined over some family of functions. Under some "tameness" and uniformity condition, f must satisfy some interesting…
We propose to use Tarski's least fixpoint theorem as a basis to define recursive functions in the calculus of inductive constructions. This widens the class of functions that can be modeled in type-theory based theorem proving tool to…
We study concrete sheaf models for a call-by-value higher-order language with recursion. Our family of sheaf models is a generalization of many examples from the literature, such as models for probabilistic and differentiable programming,…
Category theory is famous for its innovative way of thinking of concepts by their descriptions, in particular by establishing universal properties. Concepts that can be characterized in a universal way receive a certain quality seal, which…
In this functional pearl, we examine the use of definitional interpreters as a basis for abstract interpretation of higher-order programming languages. As it turns out, definitional interpreters, especially those written in monadic style,…
There are many scientific problems generated by the multiple and conflicting alternative definitions of linguistic recursion and human recursive processing that exist in the literature. The purpose of this article is to make available to…
Godel's theory T can be understood as a theory of the simply-typed lambda calculus that is extended to include the constant 0, the successor function S, and the operator R_tau for primitive recursion on objects of type tau. It is known that…
We show that verification of object-oriented programs by means of the assertional method can be achieved in a simple way by exploiting a syntax-directed transformation from object-oriented programs to recursive programs. This transformation…
Extending G\"odel's \emph{Dialectica} interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite…
We argue that verification of recursive programs by means of the assertional method of C.A.R. Hoare can be conceptually simplified using a modular reasoning. In this approach some properties of the program are established first and…
Initial semantics aims to model inductive structures and their properties, and to provide them with recursion principles respecting these properties. An ubiquitous example is the fold operator for lists. We are concerned with initial…
Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…
The most common methods in explainable artificial intelligence are post-hoc techniques which identify the most relevant features used by pretrained opaque models. Some of the most advanced post hoc methods can generate explanations that…
Natural language processing has greatly benefited from the introduction of the attention mechanism. However, standard attention models are of limited interpretability for tasks that involve a series of inference steps. We describe an…
We propose an extension of Poole's independent choice logic based on a relaxation of the underlying independence assumptions. A credal semantics involving multiple joint probability mass functions over the possible worlds is adopted. This…
We define a fragment of monadic infinitary second-order logic corresponding to an abstract separation property. We use this to define the concept of a separation subclass. We use model theoretic techniques and games to show that separation…
Relational properties describe multiple runs of one or more programs. They characterize many useful notions of security, program refinement, and equivalence for programs with diverse computational effects, and they have received much…
In imperative programming, the Domain-Driven Design methodology helps in coping with the complexity of software development by materializing in code the invariants of a domain of interest. Code is cleaner and more secure because any…
Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…
We introduce an operational rewriting-based semantics for strictly positive nested higher-order (co)inductive types. The semantics takes into account the "limits" of infinite reduction sequences. This may be seen as a refinement and…