Semantic Component Composition

Building complex software systems necessitates the use of component-based architectures. In theory, of the set of components needed for a design, only some small portion of them are "custom"; the rest are reused or refactored existing pieces of software. Unfortunately, this is an idealized situation. Just because two components should work together does not mean that they will work together. The "glue" that holds components together is not just technology. The contracts that bind complex systems together implicitly define more than their explicit type. These "conceptual contracts" describe essential aspects of extra-system semantics: e.g., object models, type systems, data representation, interface action semantics, legal and contractual obligations, and more. Designers and developers spend inordinate amounts of time technologically duct-taping systems to fulfill these conceptual contracts because system-wide semantics have not been rigorously characterized or codified. This paper describes a formal characterization of the problem and discusses an initial implementation of the resulting theoretical system.Comment: 9 pages, submitted to GCSE/SAIG '0

Dual-Context Calculi for Modal Logic

We present natural deduction systems and associated modal lambda calculi for the necessity fragments of the normal modal logics K, T, K4, GL and S4. These systems are in the dual-context style: they feature two distinct zones of assumptions, one of which can be thought as modal, and the other as intuitionistic. We show that these calculi have their roots in in sequent calculi. We then investigate their metatheory, equip them with a confluent and strongly normalizing notion of reduction, and show that they coincide with the usual Hilbert systems up to provability. Finally, we investigate a categorical semantics which interprets the modality as a product-preserving functor.Comment: Full version of article previously presented at LICS 2017 (see arXiv:1602.04860v4 or doi: 10.1109/LICS.2017.8005089

An Editor for Helping Novices to Learn Standard ML

This paper describes a novel editor intended as an aid in the learning of the functional programming language Standard ML. A common technique used by novices is programming by analogy whereby students refer to similar programs that they have written before or have seen in the course literature and use these programs as a basis to write a new program. We present a novel editor for ML which supports programming by analogy by providing a collection of editing commands that transform old programs into new ones. Each command makes changes to an isolated part of the program. These changes are propagated to the rest of the program using analogical techniques. We observed a group of novice ML students to determine the most common programming errors in learning ML and restrict our editor such that it is impossible to commit these errors. In this way, students encounter fewer bugs and so their rate of learning increases. Our editor, C Y NTHIA, has been implemented and is due to be tested on st..

Type classes for efficient exact real arithmetic in Coq

Floating point operations are fast, but require continuous effort on the part of the user in order to ensure that the results are correct. This burden can be shifted away from the user by providing a library of exact analysis in which the computer handles the error estimates. Previously, we [Krebbers/Spitters 2011] provided a fast implementation of the exact real numbers in the Coq proof assistant. Our implementation improved on an earlier implementation by O'Connor by using type classes to describe an abstract specification of the underlying dense set from which the real numbers are built. In particular, we used dyadic rationals built from Coq's machine integers to obtain a 100 times speed up of the basic operations already. This article is a substantially expanded version of [Krebbers/Spitters 2011] in which the implementation is extended in the various ways. First, we implement and verify the sine and cosine function. Secondly, we create an additional implementation of the dense set based on Coq's fast rational numbers. Thirdly, we extend the hierarchy to capture order on undecidable structures, while it was limited to decidable structures before. This hierarchy, based on type classes, allows us to share theory on the naturals, integers, rationals, dyadics, and reals in a convenient way. Finally, we obtain another dramatic speed-up by avoiding evaluation of termination proofs at runtime.Comment: arXiv admin note: text overlap with arXiv:1105.275