Category theorists invented monads in the 1960's to concisely express certain aspects of universal algebra. Functional programmers invented list comprehensions in the 1970's to concisely express certain programs involving lists. This paper shows how list comprehensions may be 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 continuations. A new solution to the old problem of destructive array update is also presented. No knowledge of category theory is assumed.

An algorithm that transforms programs to eliminate intermediate trees is presented. The algorithm applies to any term containing only functions with definitions in a given syntactic form, and is suitable for incorporation in an optimising compiler. Intermediate lists---and, more generally, intermediate trees---are both the basis and the bane of a certain style of programming in functional languages. For example, to compute the sum of the squares of the numbers from 1 to n, one could write the following program: sum (map square (upto 1 n)) (1) A key feature of this style is the use of functions (upto, map, sum) to encapsulate common patterns of computation ("consider the numbers from 1 to n ", "apply a function to each element", "sum a collection of elements"). Intermediate lists are the basis of this style---they are the glue that holds the functions together. In this case, the list [1; 2; : : : ; n] connects upto to map, and the list [1; 4; : : : ; n 2 ] connects map to sum. B...

. We give two categorical programming languages with variable arrows and associated abstraction/reduction mechanisms, which extend the possibility of categorical programming [Hag87, CF92] in practice. These languages are complementary to each other -- one of them provides a first-order programming style whereas the other does higherorder -- and are "children" of the simply typed lambda calculus in the sense that we can decompose typed lambda calculus into them and, conversely, the combination of them is equivalent to typed lambda calculus. This decomposition is a consequence of a semantic analysis on typed lambda calculus due to C. Hermida and B. Jacobs [HJ94]. 1 Introduction There have been several attempts applying category theory to designing programming languages directly, especially to typed functional programming languages, since category theory itself has been a typed functional language for various mathematics. If one (possibly a programmer or a mathematician) can regard a cat...

We give a logical reconstruction of all-solution predicates in terms of list comprehensions in Prolog's and we describe a variety of logic programming constructs in terms of monads and monad morphisms. Novel monad structures are described for lazy function lists, clause unfoldings and a monad morphism based embedding of Prolog in Prolog is given. Keywords: computing paradigms, logic programming, monads, list comprehensions, all solution predicates, Prolog, higher-order unification, lazy function lists. 1 Introduction Monads and comprehensions, have been successfully used in functional programming as a convenient generalization of various structurally similar programming constructs starting with simple ones like list processing and ending with intricate ones like CPS transformations and state transformers. We refer to the work of Philip Wadler [16, 17] for a long list of powerful examples and to Moggi [10] for the categorist sources of the concept of monad. All-solution predic...