Edsger Dijkstra said the following of abstraction:
“The purpose of abstraction is not to be vague, but to create a new semantic level in which one can be absolutely precise.”
Abstraction is a cornerstone of programming a complex software system. Without it, a complex software system is a complicated software system. In this article I will explore an important tool in achieving abstraction in programming: function totality.
Just this morning these two books landed my mailbox:
The Littler Typer and Verified Functional Programming in Agda
The Little Typer is a new book on dependent type theory, written by Daniel P. Friedman, an author of The Little Schemer, and David Thrane Christiansen, an Idris contributor. Verified Functional Programming in Agda is a book by Aaron Stump, on using dependent types in Agda to prove various properties of programs. After having read the Type-driven Development with Idris book by Edwin Brady, I am hoping these two books will significantly expand my knowledge of and improve my skills in type theory, theorem proving and typed functional programming. Looking forward to reading the books! If you haven’t noticed by now, I got hooked on dependent types!
Software testing has been an important, if not prevalent way of checking software correctness. In this article I will tell how have my doctoral dissertation on testing and verification of imperative software as well as my work experience after the studies led me to typed functional programming, which consequently gave me a different perspective on automatic software testing. Furthermore, I’ll explain why functional programming and static type systems are important for software correctness.
You might think it’s only imperative programmers that don’t see value in function totality, but neither do many functional programmers. The ability to abstract in programming is severely impaired when totality is ignored. A programmer should strive to work in a programming language with a compiler that supports totality checking, such as Agda and Idris.