"On X"

Paul Graham has interesting book called On Lisp. If you are interested to know more about Lisp programming you can download the book for free or read it on on line. The point of this post is not so much to talk about the Lisp programming language as much as talking about why it is call "On Lisp". Here is what author has to say about it:

Bottom-up design is becoming more important as software grows in complexity. Programs today may have to meet specifications which are extremely complex, or even open-ended. Under such circumstances, the traditional top-down method sometimes breaks down. In its place there has evolved a style of programming quite different from what is currently taught in most computer science courses: a bottom-up style in which a program is written as a series of layers, each one acting as a sort of programming language for the one above. X Windows and TeX are examples of programs written in this style.

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The title is intended to stress the importance of bottom-up programming in Lisp. Instead of just writing your program in Lisp, you can write your own language on Lisp, and write your program in that.

and,

Bottom-up design leads naturally to extensible programs. The simplest bottom-up programs consist of two layers: language and program. Complex programs may be written as a series of layers, each one acting as a programming language for the one above. If this philosophy is carried all the way up to the topmost layer, that layer becomes a programming language for the user. Such a program, where extensibility permeates every level, is likely to make a much better programming language than a system which was written as a traditional black box, and then made extensible as an afterthought.

Keep "bottom-up" and more importantly "On XXX" concept in mind as you are trying to understand the functional programming paradigm.