Static Type Inference for the Q language using Constraint Logic Programming

We describe an application of Prolog: a type inference tool for the Q functional language. Q is a terse vector processing language, a descendant of APL, which is getting more and more popular, especially in financial applications. Q is a dynamically typed language, much like Prolog. Extending Q with static typing improves both the readability of programs and programmer productivity, as type errors are discovered by the tool at compile time, rather than through debugging the program execution. We map the task of type inference onto a constraint satisfaction problem and use constraint logic programming, in particular the Constraint Handling Rules extension of Prolog. We determine the possible type values for each program expression and detect inconsistencies. As most built-in function names of Q are overloaded, i.e. their meaning depends on the argument types, a quite complex system of constraints had to be implemented

A resolution based description logic calculus

We present a resolution based reasoning algorithm called DL calculus that decides concept satisfiability for the SHQ language. Unlike existing resolution based approaches, the DL calculus is defined directly on DL expressions. We argue that working on this high level of abstraction provides an easier to grasp algorithm with less intermediary transformation steps and increased efficiency. We give a proof of the completeness of our algorithm that relies solely on th e ALCHQ tableau method without requiring any further background knowledge

Static Type Checking for the Q Functional Language in Prolog

We describe an application of Prolog: a type checking tool for the Q functional language. Q is a terse vector processing language, a descendant of APL, which is getting more and more popular, especially in financial applications. Q is a dynamically typed language, much like Prolog. Extending Q with static typing improves both the readability of programs and programmer productivity, as type errors are discovered by the tool at compile time, rather than through debugging the program execution. We designed a type description syntax for Q and implemented a parser for both the Q language and its type extension. We then implemented a type checking algorithm using constraints. As most built-in function names of Q are overloaded, i.e. their meaning depends on the argument types, a quite complex system of constraints had to be implemented. Prolog proved to be an ideal implementation language for the task at hand. We used Definite Clause Grammars for parsing and Constraint Handling Rules for the type checking algorithm. In the paper we describe the main problems solved and the experiences gained in the development of the type checking tool

Loop elimination, a sound optimisation technique for PTTP related theorem proving

In this paper we present loop elimination, an important optimisation technique for first-order theorem proving based on Prolog technology, such as the Prolog Technology Theorem Prover or the DLog Description Logic Reasoner. Although several loop checking techniques exist for logic programs, to the best of our knowledge, we are the first to examine the interaction of loop checking with ancestor resolution. Our main contribution is a rigorous proof of the soundness of loop elimination

Gradient Regularization Improves Accuracy of Discriminative Models

Regularizing the gradient norm of the output of a neural network is a powerful technique, rediscovered several times. This paper presents evidence that gradient regularization can consistently improve classification accuracy on vision tasks, using modern deep neural networks, especially when the amount of training data is small. We introduce our regularizers as members of a broader class of Jacobian-based regularizers. We demonstrate empirically on real and synthetic data that the learning process leads to gradients controlled beyond the training points, and results in solutions that generalize well