Under Consideration for Publication in J. Functional Programming the Arrow Calculus
Under Consideration for Publication in J. Functional Programming the Arrow Calculus
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正在考虑在《J.函数式编程》中发表《箭头微积分》
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通讯作者：
J. Yallop
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作者：
Sam Lindley;P. Wadler;J. Yallop
我们介绍了箭头演算，这是一种用密切关系来操纵休斯的箭头的金属语言，既可以与Moggi的Monads for Monads和Paterson的箭头表示法。箭头是通过扩展lambda微积分的三个结构来满足九个（某些特质）定律的经典定义的；相比之下，箭头微积分添加了满足五个定律的四个构造（符合两个众所周知的模式）。以前众所周知，这五个法律是合理的。我们证明它们也很完整，因此五个法律可以取代九个。
We introduce the arrow calculus, a metalanguage for manipulating Hughes's arrows with close relations both to Moggi's metalanguage for monads and to Paterson's arrow notation. Arrows are classically defined by extending lambda calculus with three constructs satisfying nine (somewhat idiosyncratic) laws; in contrast, the arrow calculus adds four constructs satisfying five laws (which fit two well-known patterns). The five laws were previously known to be sound; we show that they are also complete, and hence that the five laws may replace the nine.