arXiv subjects

Joachim Tilsted Kristensen

Publications and source records attributed to Joachim Tilsted Kristensen.

5 recordsLinked to original sources

arXiv2025

OnlineProver: Experience with a Visualisation Tool for Teaching Formal Proofs

OnlineProver is an interactive proof assistant tailored for the educational setting. Its main features include a user-friendly interface for editing and checking proofs. The user interface provides feedback directly within the derivation, based on error messages from a proof-checking web service. A basic philosophy of the tool is that it should aid the student while still ensuring that the students construct the proofs as if they were working on paper. We gathered feedback on the tool through a questionnaire, and we conducted an intervention to assess its effectiveness for students in a classroom setting, alongside an evaluation of technical aspects. The initial intervention showed that students were satisfied with using OnlineProver as part of their coursework, providing initial confirmation of the learning approach behind it. This gives clear directions for future developments, with the potential to find and evaluate how OnlineProver can improve the teaching of natural deduction.

cs.LO↗

arXiv2023

pun: Fun with Properties; Towards a Programming Language With Built-in Facilities for Program Validation

Property-based testing is a powerful method to validate program correctness. It is, however, not widely use in industry as the barrier of entry can be very high. One of the hindrances is to write the generators that are needed to generate randomised input data. Program properties often take complicated data structures as inputs and, it requires a significant amount of effort to write generators for such structures in a invariant preserving way. In this paper, we suggest and formalise a new programming language \textsf{pun}; a simple functional programming with properties as a built-in mechanism for program validation. We show how to generate input for \textsf{pun} properties automatically, thus, providing the programmer with a low barrier of entry for using property-based testing. We evaluate our work a on library for binary search trees and compare the test results to a similar library in Haskell.

cs.PL↗

arXiv2023

Tail recursion transformation for invertible functions

Tail recursive functions allow for a wider range of optimisations than general recursive functions. For this reason, much research has gone into the transformation and optimisation of this family of functions, in particular those written in continuation passing style (CPS). Though the CPS transformation, capable of transforming any recursive function to an equivalent tail recursive one, is deeply problematic in the context of reversible programming (as it relies on troublesome features such as higher-order functions), we argue that relaxing (local) reversibility to (global) invertibility drastically improves the situation. On this basis, we present an algorithm for tail recursion conversion specifically for invertible functions. The key insight is that functions introduced by program transformations that preserve invertibility, need only be invertible in the context in which the functions subject of transformation calls them. We show how a bespoke data type, corresponding to such a context, can be used to transform invertible recursive functions into a pair of tail recursive function acting on this context, in a way where calls are highlighted, and from which a tail recursive inverse can be straightforwardly extracted.

cs.PL↗

arXiv2022

Jeopardy: An Invertible Functional Programming Language

Algorithms are ways of mapping problems to solutions. An algorithm is invertible precisely when this mapping is injective, such that the initial problem can be uniquely inferred from its solution. While invertible algorithms can be described in general-purpose languages, no guarantees are generally made by such languages as regards invertibility, so ensuring invertibility requires additional (and often non-trivial) proof. On the other hand, while reversible programming languages guarantee that their programs are invertible by restricting the permissible operations to those which are locally invertible, writing programs in the reversible style can be cumbersome, and may differ significantly from conventional implementations even when the implemented algorithm is, in fact, invertible. In this paper we introduce Jeopardy, a functional programming language that guarantees program invertibility without imposing local reversibility. In particular, Jeopardy allows the limited use of uninvertible -- and even nondeterministic! -- operations, provided that they are used in a way that can be statically determined to be invertible. To this end, we outline an \emph{implicitly available arguments analysis} and three further approaches that can give a partial static guarantee to the (generally difficult) problem of guaranteeing invertibility.

cs.PL↗

arXiv2022

Branching execution symmetry in Jeopardy by available implicit arguments analysis

When the inverse of an algorithm is well-defined -- that is, when its output can be deterministically transformed into the input producing it -- we say that the algorithm is invertible. While one can describe an invertible algorithm using a general-purpose programming language, it is generally not possible to guarantee that its inverse is well-defined without additional argument. Reversible languages enforce deterministic inverse interpretation at the cost of expressibility, by restricting the building blocks from which an algorithm may be constructed. Jeopardy is a functional programming language designed for writing invertible algorithms \emph{without} the syntactic restrictions of reversible programming. In particular, Jeopardy allows the limited use of locally non-invertible operations, provided that they are used in a way that can be statically determined to be globally invertible. However, guaranteeing invertibility in Jeopardy is not obvious. One of the central problems in guaranteeing invertibility is that of deciding whether a program is symmetric in the face of branching control flow. In this paper, we show how Jeopardy can solve this problem, using a program analysis called available implicit arguments analysis, to approximate branching symmetries.

cs.PL↗