Pattern matching is an important feature of programming languages for data abstraction. Many pattern-matching extensions have been proposed and implemented for extending the range of data types to which pattern matching is applicable. Among them, the pattern-matching system proposed by Egi and Nishiwaki features practical pattern matching for non-free data types by providing an extensible non-linear pattern-matching facility with backtracking [20]. However, they implemented their proposal only in an interpreter of the Egison programming language, and a method for compiling pattern-matching expressions of Egison was not discussed. This paper proposes a method for translating a program that contains patternmatching expressions of Egison to a program that contains only the existing syntax constructs of functional programming languages. This method is based on the three key ideas: (i) transformation of a matcher to a function that takes a pattern and a target, and returns lists of triples of a pattern, a matcher, and a target; (ii) compilation of match-all to application of the map function; (iii) transformation of a value pattern to a function that takes an intermediate pattern-matching result and returns a value. This paper shows the proposed method works by showing Scheme macros that provide the users the patternmatching facility of Egison. This paper also presents benchmark results that show Egison pattern-matching embedded in Gauche Scheme is faster than the original Egison interpreter.

In this paper, we propose a method for importing tensor index notation, including Einstein summation notation, into functional programming. This method involves introducing two types of parameters, i.e, scalar and tensor parameters, and simplified tensor index rules that do not handle expressions that are valid only for the Cartesian coordinate system, in which the index can move up and down freely. An example of such an expression is "c = AiBi". As an ordinary function, when a tensor parameter obtains a tensor as an argument, the function treats the tensor argument as a whole. In contrast, when a scalar parameter obtains a tensor as an argument, the function is applied to each component of the tensor. In this paper, we show that introducing these two types of parameters and our simplified index rules enables us to apply arbitrary user-defined functions to tensor arguments using index notation including Einstein summation notation without requiring an additional description to enable each function to handle tensors.

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Throughout the history of functional programming, recursion has emerged as a natural method for describing loops in programs. However, there does often exist a substantial cognitive distance between the recursive definition and the simplest explanation of an algorithm even for the basic list processing functions such as map, concat, or unique; when we explain these functions, we seldom use recursion explicitly as we do in functional programming. For example, map is often explained as follows: the map function takes a function and a list and returns a list of the results of applying the function to all the elements of the list.This paper advocates a new programming paradigm called pattern-match-oriented programming for filling this gap. An essential ingredient of our method is utilizing pattern matching for non-free data types. Pattern matching for non-free data types features non-linear pattern matching with backtracking and extensibility of pattern-matching algorithms. Several non-standard pattern constructs, such as not-patterns, loop patterns, and sequential patterns, are derived from this pattern-matching facility. Based on that result, this paper introduces many programming techniques that replace explicit recursions with an intuitive pattern by confining recursions inside patterns. We classify these techniques as pattern-match-oriented programming design patterns.These programming techniques allow us to redefine not only the most basic functions for list processing such as map, concat, or unique more elegantly than the traditional functional programming style, but also more practical mathematical algorithms and software such as a SAT solver, computer algebra system, and database query language that we had not been able to implement concisely. ACM CCS 2012Software and its engineering → General programming languages;

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