Related papers: Coinductive subtyping for abstract compilation of …
Coinduction is a widely used technique for establishing behavioural equivalence of programs in higher-order languages. In recent years, the rise of languages with quantitative (e.g.~probabilistic) features has led to extensions of…
Here we define a new unification algorithm for terms interpreted in semantic domains denoted by a subclass of regular types here called deterministic regular types. This reflects our intention not to handle the semantic universe as a…
Session-types specify communication protocols for communicating processes, and session-typed languages are often specified using substructural operational semantics given by multiset rewriting systems. We give an observed communication…
Verification problems of programs written in various paradigms (such as imperative, logic, concurrent, functional, and object-oriented ones) can be reduced to problems of solving Horn clause constraints on predicate variables that represent…
Inducing semantic representations directly from speech signals is a highly challenging task but has many useful applications in speech mining and spoken language understanding. This study tackles the unsupervised learning of semantic…
The expression problem describes a fundamental tradeoff between two types of extensibility: extending a type with new operations, such as by pattern matching on an algebraic data type in functional programming, and extending a type with new…
Continuous prompts have become widely adopted for augmenting performance across a wide range of natural language tasks. However, the underlying mechanism of this enhancement remains obscure. Previous studies rely on individual words for…
We define the syntax and reduction relation of a recursively typed lambda calculus with a parallel case-function (a parallel conditional). The reduction is shown to be confluent. We interpret the recursive types as information systems in a…
Similar to a tree grammar, a Horn theory can be used to describe an infinite set of terms. In this paper, we present a class of Horn theories such that the set of definable predicates is closed wrt. conjunction and such that the…
Based on a new coinductive characterization of continuous functions we extract certified programs for exact real number computation from constructive proofs. The extracted programs construct and combine exact real number algorithms with…
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
A theory of recursive and corecursive definitions has been developed in higher-order logic (HOL) and mechanized using Isabelle. Least fixedpoints express inductive data types such as strict lists; greatest fixedpoints express coinductive…
We present a type system and inference algorithm for a rich subset of JavaScript equipped with objects, structural subtyping, prototype inheritance, and first-class methods. The type system supports abstract and recursive objects, and is…
We propose a framework for reasoning about programs that manipulate coinductive data as well as inductive data. Our approach is based on using equational programs, which support a seamless combination of computation and reasoning, and using…
As robots become more ubiquitous and capable, it becomes ever more important to enable untrained users to easily interact with them. Recently, this has led to study of the language grounding problem, where the goal is to extract…
The last decade has seen huge progress in the development of advanced machine learning models; however, those models are powerless unless human users can interpret them. Here we show how the mind's construction of concepts and meaning can…
We present the guarded lambda-calculus, an extension of the simply typed lambda-calculus with guarded recursive and coinductive types. The use of guarded recursive types ensures the productivity of well-typed programs. Guarded recursive…
Foundation models like chatGPT have demonstrated remarkable performance on various tasks. However, for many questions, they may produce false answers that look accurate. How do we train the model to precisely understand the concepts? In…
Brouwer's constructivist foundations of mathematics is based on an intuitively meaningful notion of computation shared by all mathematicians. Martin-L\"of's meaning explanations for constructive type theory define the concept of a type in…
Induction is the process by which we obtain predictive laws or theories or models of the world. We consider the structural aspect of induction. We answer the question as to whether we can find a finite and minmalistic set of operations on…