Related papers: Python Type Hints are Turing Complete

This paper describes a reduction from the halting problem of Turing machines to subtype checking in Java. It follows that subtype checking in Java is undecidable, which answers a question posed by Kennedy and Pierce in 2007. It also follows…

Python's dynamic typing system offers flexibility and expressiveness but can lead to type-related errors, prompting the need for automated type inference to enhance type hinting. While existing learning-based approaches show promising…

Gradual typing enables programmers to combine static and dynamic typing in the same language. However, ensuring a sound interaction between the static and dynamic parts can incur significant runtime cost. In this paper, we perform a…

We prove that Cypher 25, the graph query language of Neo4j, is Turing-complete. The proof shows that a single RETURN statement using reduce(), CASE expressions, and list comprehensions can simulate any 2-counter machine (Minsky 1967). We…

We present a type system to guarantee termination of pi-calculus processes that exploits input/output capabilities and subtyping, as originally introduced by Pierce and Sangiorgi, in order to analyse the usage of channels. We show that our…

Automated tutoring systems offer the flexibility and scalability necessary to facilitate the provision of high quality and universally accessible programming education. In order to realise the full potential of these systems, recent work…

Generative AI and large language models hold great promise in enhancing programming education by automatically generating individualized feedback for students. We investigate the role of generative AI models in providing human tutor-style…

Session types, types for structuring communication between endpoints in distributed systems, are recently being integrated into mainstream programming languages. In practice, a very important notion for dealing with such types is that of…

The Unix command \texttt{find} is among the first commands taught to beginners, yet remains indispensable for experienced engineers. In this paper, we demonstrate that \texttt{find} possesses unexpected computational power, establishing…

With the recent advances in AI programming assistants such as GitHub Copilot, programming is not limited to classical programming languages anymore--programming tasks can also be expressed and solved by end-users in natural text. Despite…

We show that 2-tag systems efficiently simulate Turing machines. As a corollary we find that the small universal Turing machines of Rogozhin, Minsky and others simulate Turing machines in polynomial time. This is an exponential improvement…

We introduce a new type of generalized Turing machines (GTMs), which are intended as a tool for the mathematician who studies computability in Analysis. In a single tape cell a GTM can store a symbol, a real number, a continuous real…

Extending a given language with new dedicated features is a general and quite used approach to make the programming language more adapted to problems. Being closer to the application, this leads to less programming flaws and easier…

Python is a popular dynamic programming language, evidenced by its ranking as the second most commonly used language on GitHub. However, its dynamic type system can lead to potential type errors, leading researchers to explore automatic…

This paper provides a new and more direct proof of the assertion that a Turing computable function of the natural numbers is primitive recursive if and only if the time complexity of the corresponding Turing machine is bounded by a…

We consider type inference for guarded recursive data types (GRDTs) -- a recent generalization of algebraic data types. We reduce type inference for GRDTs to unification under a mixed prefix. Thus, we obtain efficient type inference.…

The pseudoinverse of a matrix, a generalized notion of the inverse, is of fundamental importance in linear algebra and, thereby, in many different fields. Despite its proven existence, an algorithmic approach is typically necessary to…

Python's typing system has evolved pragmatically into a powerful but theoretically fragmented system, with scattered specifications. This paper proposes a formalization to address this fragmentation. The central contribution is a formal…

The Turing machine, as it was presented by Turing himself, models the calculations done by a person. This means that we can compute whatever any Turing machine can compute, and therefore we are Turing complete. The question addressed here…

Java's type system mostly relies on type checking augmented with local type inference to improve programmer convenience. We study global type inference for Featherweight Generic Java (FGJ), a functional Java core language. Given generic…