Programming Examples Needing Polymorphic Recursion

Inferring types for polymorphic recursive function definitions (abbreviated to polymorphic recursion) is a recurring topic on the mailing lists of popular typed programming languages. This is despite the fact that type inference for polymorphic recursion using for all-types has been proved undecidable. This report presents several programming examples involving polymorphic recursion and determines their typability under various type systems, including the Hindley-Milner system, an intersection-type system, and extensions of these two. The goal of this report is to show that many of these examples are typable using a system of intersection types as an alternative form of polymorphism. By accomplishing this, we hope to lay the foundation for future research into a decidable intersection-type inference algorithm. We do not provide a comprehensive survey of type systems appropriate for polymorphic recursion, with or without type annotations inserted in the source language. Rather, we focus on examples for which types may be inferred without type annotations.

Lightweight Formal Verification in Classroom Instruction of Reasoning about Functional Code

In college courses dealing with material that requires mathematical rigor, the adoption of a machine-readable representation for formal arguments can be advantageous. Students can focus on a specific collection of constructs that are represented consistently. Examples and counterexamples can be evaluated. Assignments can be assembled and checked with the help of an automated formal reasoning system. However, usability and accessibility do not have a high priority and are not addressed sufficiently well in the design of many existing machine-readable representations and corresponding formal reasoning systems. In earlier work [Lap09], we attempt to address this broad problem by proposing several specific design criteria organized around the notion of a natural context: the sphere of awareness a working human user maintains of the relevant constructs, arguments, experiences, and background materials necessary to accomplish the task at hand. We report on our attempt to evaluate our proposed design criteria by deploying within the classroom a lightweight formal verification system designed according to these criteria. The lightweight formal verification system was used within the instruction of a common application of formal reasoning: proving by induction formal propositions about functional code. We present all of the formal reasoning examples and assignments considered during this deployment, most of which are drawn directly from an introductory text on functional programming. We demonstrate how the design of the system improves the effectiveness and understandability of the examples, and how it aids in the instruction of basic formal reasoning techniques. We make brief remarks about the practical and administrative implications of the system’s design from the perspectives of the student, the instructor, and the grader.

Extending snBench to Support a Graphical Programming Interface for a Sensor Network Tasking Language (STEP)

The purpose of this project is the creation of a graphical "programming" interface for a sensor network tasking language called STEP. The graphical interface allows the user to specify a program execution graphically from an extensible pallet of functionalities and save the results as a properly formatted STEP file. Moreover, the software is able to load a file in STEP format and convert it into the corresponding graphical representation. During both phases a type-checker is running on the background to ensure that both the graphical representation and the STEP file are syntactically correct. This project has been motivated by the Sensorium project at Boston University. In this technical report we present the basic features of the software, the process that has been followed during the design and implementation. Finally, we describe the approach used to test and validate our software.

Dynamic Programming for Optimal Control of Set-Up Scheduling with Neural Network Modifications

This paper demonstrates an optimal control solution to change of machine set-up scheduling based on dynamic programming average cost per stage value iteration as set forth by Cararnanis et. al. [2] for the 2D case. The difficulty with the optimal approach lies in the explosive computational growth of the resulting solution. A method of reducing the computational complexity is developed using ideas from biology and neural networks. A real time controller is described that uses a linear-log representation of state space with neural networks employed to fit cost surfaces.