What

In this paper we show that two features of functional languages in particular, higher-order functions and lazy evaluation, can contribute greatly to modularity. ~ John Hughes

Modular Programming is a key technique in successful software design and all major programming languages have a notion of component based engineering. Functional programming has contributed a lot in enhancing modular software design by providing features such as high order functions and lazy evaluation that have pushed back on the conceptual limits of conventional languages on the ways problems can be modularised.

"Why Functional Programming Matters" is a late 80s paper by John Hughes that portrays the importance of functional programming moreso where modularisation is key:

This paper is an attempt to demonstrate to the “real world” that functional programming is vitally important, and also to help functional programmers exploit its advantages to the full by making it clear what those advantages are.

Why

Such a catalogue of “advantages” is all very well, but one must not be surprised if outsiders don’t take it too seriously. It says a lot about what functional programming is not (it has no assignment, no side effects, no flow of control) but not much about what it is.

Perhaps the biggest motivation for this paper could have been to provide an adequate characterisation of functional programming and argue that it supports the development of reusable software way better than conventional programming paradigms.

Hughes gives a great analogy of functional programming with structured programming, and shows how FP strives beyond structured programming by enabling greater modularity and supporting "programming in the large"

It is helpful to draw an analogy between functional and structured programming. In the past, the characteristics and advantages of structured programming have been summed up more or less as follows. Structured programs contain no goto statements. Blocks in a structured program do not have multiple entries or exits. Structured programs are more tractable mathematically than their unstructured counterparts. These “advantages” of structured programming are very similar in spirit to the “advantages” of functional programming we discussed earlier.

Whom, when, where

Why functional programming matters, was published in 1989 in the Computer Journal by John Hughes as a professor at Chalmers University of Technology. He had however originally written it in 1984 as a post-doc.

I wrote the paper in 1984 as a post-doc, but misjudged its significance completely. I thought it would be unpublishable, because it contained no difficult research results, just a manifesto and some nice programming examples. So I circulated it privately to friends, who passed it on to others, and soon I found it turning up in the most unexpected places. Finally, after five years, I was invited to submit it to the Computer Journal. link

How

As examples of the application of high-order functions and lazy-evaluation, the paper covers several topics:

Lists and Trees manipulation.

Use of high-order functions and recursive patterns is used to illustrate how simple modularizations can be re-used to implement more complex functionality.

Numerical algorithms

The Newton-Raphson Square Roots algorithm is implemented in a modular fashion using lazy evalaution.

This program is indivisible in conventional languages. We will express it in a more modular form using lazy evaluation, and then show some other uses to which the parts may be put.

Numerical differentiation and integration implementations are also illustrated using lazy evaluation.

Alpha-beta heuristic, an AI algorithm

We have argued that functional languages are powerful primarily because they provide two new kinds of glue: higher-order functions and lazy evaluation. In this section we take a larger example from Artificial Intelligence and show how it can be programmed quite simply using these two kinds of glue.

The paper implements the alpha-beta heurisitc, an algorithm for estimating how good a position a game player is in. The algorithm works by looking ahead to see how the game might develop, but avoids pursuing unprofitable plays. It's used to predict favourable positions.

Recap

"Why Functional Programming Matters" argues that modularity is key to successful programming. It illustrates how functional programming eases modularisation and composability way better than conventional languages. To this end, it gives examples of lists and trees manipulation, numerical algorithms and an artificial intelligence algorithm applications.