John Hughes and Mary Sheeran in Why Functional Programming Matters [0] list “algebra as a litmus test” as one of the four salient features of functional programming, and Ken Iverson in Notation as a Tool of Thought [1] lists “amenability to formal proof” as one of the five important characteristics of notation. Using the language APL, we prove the correctness of some programs, derive simplifications, and illustrate design validation and program test techniques for functional programs.

[0] Hughes, John, and Mary Sheeran, Why Functional Programming Matters, Code Mesh, London, 2015-11-02 to -04.

[1] Iverson, Kenneth E., Notation as a Tool of Thought, Communications of the ACM, volume 23, number 8, 1980-08.

Dyalog is a modern, array-first, multi-paradigm programming language, which supports functional, object-oriented and imperative programming based on an APL language kernel. During the morning and early afternoon, we will explore the fundamentals of functional programming in APL. At the end of the day, Dyalog CXO Morten Kromberg will round off with an application development session, showing how a simple application with a HTML5/JS front-end and a RESTful web service can be used to deliver the power of APL to end users, or as embeddable components for other application tools. The "hands on" sections of the workshop can be followed under Mac OS X, Linux, or Microsoft Windows.

APL will be 50 years old in November 2016 (50 years from 1966-11-27 15.53.58, to be exact), and it remains unsurpassed in manifesting Kenneth E. Iverson’s five important characteristics of notation: 

• ease of expression
• suggestivity
• subordination of detail
• economy
• amenability to proof

These characteristics are demonstrated by working through 16 APL expressions. The material is approachable for beginners and yet thought-provoking for experts.

One of the 16 expressions is a fast computation of the partition function without use of the Hardy-Ramanujan (1918) results.