User:Devon McCormick/FunctionalJ

Introduction

J: A Dynamic, Functional Language

J is a radically innovative, dynamic, functional, interpreted, interactive, array-based, multi-platform, open-source, mind-blowing notation that also happens to be implemented as a powerful, productivity-enhancing programming language.

The Entire J Language

The entire language fits on one page.

What is notation and why should we care?

Chunking – another reason notation is important

By grouping concepts and subsuming them into “chunks”, we overcome the limitations of short-term memory. A notation is often an effective way to do this. Another technique for accomplishing this is the development of a specialized vocabulary.

An example of a technical term which encapsulates a lot of meaning into a short phrase is “Hello, World” example. Keep an eye out for this example in the following expositions in which we demonstrate various features of J. We’ll start by learning some specialized J terms.

J Terms: noun, verb, monadic, dyadic, boxed

…Cognitive Tidbit

Resuming… (Definition of "Boxed")

Arrays

Precedence – Order of Operations

J Terms: adverb, conjunction

Calling them higher-order functions just isn't good enough - we need to be able to talk about them precisely.

…Cognitive Tidbit : Great Big Numbers

Someone else appreciating the power of notation.

Resuming… (Definition of "Conjunction")

J Terms: hook, fork

J Term: rank

(the last two) J Terms: explicit, tacit

Converting Between Explicit and Tacit: a Crutch "13 : "

Summary of J Terms

Example of a User-defined Adverb: a Newton Solver

Functional Programming: Procedural Contrasted with Array-based

Paul Hudak, one of the early promoters of functional programming in general and Haskell in particular, wrote a paper titled "Conception, Evolution, and Application of Functional Programming Languages" (ACM Computing Surveys, Vol. 21, No. 3, September 1989) in which he mentions APL as one of the early functional languages. However, he says little about it other than giving it as an example of a functional language that doesn't rely on lambda expressions.

He also notes how it differs from other functional programming languages like Backus's FP because "...FP's fundamental data structure is the sequence, whereas APL's is the array." However, he seems unaware of how significant this is which is understandable given the traditional blind spot of Computer Science toward the importance and utility of array notation.

Since one example is worth a hundred abstract definitions, we'll look at how a procedural - or sequence-based - implementation of an algorithm might differ from an array-based one by implementing the same simulation in the two different fashions.

Procedural Simulation of "Red or Black" Game

Array-based Simulation of "Red or Black" Game

J’s Numeric Tower

Though J has only three types - numeric, character, and boxed - there are numerous different kinds of numbers. The character type also supports Unicode as well as single-byte characters. The "tower" here builds from a base of the simplest to the (arguably) most complex numeric sub-types supported by J.

complex               2j32 186j413 3798j94357 627j3 1440j6
floating point       2.3218 641.3379 89.4357 62731.44060134
extended integer    232186413379894357 627314406013472791111
rational           23r218641 3r37 989r4357 627r314 40r601 3r4
integer           2321 86 4133798 94357 6273 1440 601 34 72 79
boolean          0 1 0 1 0 0 0 1 1 1 1 1 0 1 0 1 1 1 0 0 1 1 1 0

There are a few other numeric notations within J not shown here, including notations for numbers based on pi and on radians.

J Resources

Join the J Forums (mailing lists) –

programming - the main forum, covering J programming from beginner to expert, and announcements
beta - current beta (bugs, problems, suggestions)
chat - all other discussions on computer languages and J - messages welcomed from both J and non-J programmers
general - installation, support, website and other infrastructure topics
source - J engine source

The J Meetup - http://www.meetup.com/J-Dynamic-Functional-Programming, also http://www.jsoftware.com/jwiki/NYCJUG

J Software - http://www.jsoftware.com/

J Wiki - http://www.jsoftware.com/jwiki/FrontPage

Notation as a Tool of Thought - http://www.jsoftware.com/papers/tot.htm

The Joy of Functional Calculation - http://archive.vector.org.uk/art10500630

Bowling scores in J and other languages - http://xprogramming.com/articles/dbcbowlingvector/

Criticisms of J for beginners - http://www.jsoftware.com/jwiki/JforBeginnersCriticisms

Functional programming example - Simplex method - http://www.jsoftware.com/jwiki/Stories/RichardBrown

Fractals, Visualization and J by Cliff Reiter - available on Lulu.com

Cliff's animated Sierpinski pyramid - http://webbox.lafayette.edu/~reiterc/misc_frac/swaa.html

Cliff's gallery of fractals - http://webbox.lafayette.edu/~reiterc/gallery_wfrac.html

Complete gallery - http://webbox.lafayette.edu/~reiterc/gallery.html

Vector magazine of the British APL Association - https://sites.google.com/site/baavector/home

J in a Day - http://www.jsoftware.com/jwiki/IanClark/JinaDay

Oleg's J page - http://olegykj.sourceforge.net/

Books on J - http://www.jsoftware.com/jwiki/Books

This presentation - http://www.jsoftware.com/jwiki/DevonMcCormick/FunctionalJ

Attachments

Here's the handout for the talk.

File:JFunctionalMeetupIntro.pdf

Here's an example I added at the end of the talk - it contrasts an example of functional programming in a more conventional, procedural style against an array-based version which looks and performs considerably better.

File:The Red or Black Game Simulated Functionally by both procedure and array.pdf

Here are the slides from my PowerPoint presentation...