Howard A. Peelle

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This paper discusses common mistakes novices make when learning to program in APL. We present several exemplary APL “learning bugs”, describe the context in which they occur, indicate why we believe they are interesting, and speculate about underlying thinking processes. We claim that such learning bugs are worth examining: further study may(More)
In an effort to understand “APL thinking”, we examine a few selected examples of using APL to solve specific problems, namely: compute the median of a numerical vector; simulate the Replicate function; string search; carry forward work-to-be-done in excess of capacity; rotate concentric rectangular rings in a matrix; find column indices of(More)
This paper uses A Programming Language to provide a perspicuous representation of the recurslve algorithm for generating the reflected binary Gray Code. Further, the APt definition is compared with the definition of a recursive function for generating standard binary numbers; a simple expression is proposed for converting a binary to its binary Gray code(More)
This paper describes a curriculum unit in which APL is used to introduce models of neural networks. It begins with a simple model for transmitting impulses among a vector of logical neurons; then a more sophisticated model is developed with thresholds, decay, and inhibition in a matrix of neurons; then a general model is offered for higher order arrays of(More)
Seven alternative representations of Rubik's Cube are presented and compared: a 3-by-3-by-3 array of 3-digit integers; a 6-by-3-by-3 array of literals; a 5-by-12 literal matrix; an ll-by-ll sparse literal matrix; a 54-element vector; a 4-dimension array; and a 3-by-3-by-3 nested array. APL functions are given for orientation moves and quarter-turns plus(More)
Recursion is a powerful idea*—with correspondingly powerful implications for learning and teaching mathematics. Computer scientists have previously pointed out that the use of recursion often permits more lucid and concise descriptions of algorithms [1]; mathematicians know that recursion is a fundamental concept upon which entire systems of(More)
This paper discusses “APL teaching bugs”, in three senses: (1) issues inherent in the teaching of APL that confront the instructor with difficult choices; (2) potential mistakes sometimes made by instructors teaching APL; and (3) problematic aspects of the design of APL that are especially difficult to explain. These teaching bugs are presented(More)