Comprehending Monads-英文文献.pdf

Comprehending Monads Philip Wadler University of Glasgow Abstract Category theorists invented monads in the s to concisely express certain asp ects of universal algebra Functional programmers invented list comprehensions in the s to concisely express certain programs involving lists This pap er shows how list comprehensions may b e generalised to an arbitrary monad and how the resulting programming feature can concisely express in a pure functional language some programs that manipulate state handle exceptions parse text or invoke con tinuations A new solution to the old problem of destructive array up date is also presented No knowledge of category theory is assumed Intro duction Is there a way to combine the indulgences of impurity with the blessings of purity Impure strict functional languages such as Standard ML Mil HMT and Scheme RC supp ort a wide variety of features such as assigning to state handling exceptions and invoking continuations Pure lazy functional languages such as Haskell HPW or Miranda Tur eschew such features b ecause they are incompatible with the advan tages of lazy evaluation and equational reasoning advantages that have b een describ ed at length elsewhere Hug BW Purity has its regrets and all programmers in pure functional languages will recall some moment when an impure feature has tempted them For instance if a counter is required to generate unique names then an assignable variable seems just the ticket In such cases it is always p ossible to mimic the required impure feature by straightforward though tedious means For instance a counter can b e simulate