What is "Total Functional Programming"?
functional-programming, programming-languages
Solution
If I understood that correctly, Total Functional Programming means just that: Programming with Total Functions. If I remember my math courses correctly, a Total Function is a function which is defined over its entire domain, a Partial Function is one which has "holes" in its definition.
Now, if you have a function which for some input value `v` goes into an infinite recursion or an infinite loop or in general doesn't terminate in some other fashion, then your function isn't defined for `v`, and thus partial, i.e. not total.
Total Functional Programming doesn't allow you to write such a function. All functions always return a result for all possible inputs; and the type checker ensures that this is the case.
My guess is that this vastly simplifies error handling: there aren't any.
The downside is already mentioned in your quote: it's not Turing-complete. E.g. an Operating System is essentially a giant infinite loop. Indeed, we do not want an Operating System to terminate, we call this behaviour a "crash" and yell at our computers about it!
Problem
Wikipedia has this to say: Total functional programming (also known as strong functional programming, to be contrasted with ordinary, or weak functional programming) is a programming paradigm which restricts the range of programs to those which are provably terminating. and These restrictions mean that total functional programming is not Turing-complete. However, the set of algorithms which can be used is still huge. For example, any algorithm which has had an asymptotic upper bound calculated for it can be trivially transformed into a provably-terminating function by using the upper bound as an extra argument which is decremented upon each iteration or recursion. There is also a Lambda The Ultimate Post about a paper on Total Functional Programming. I hadn't come across that until last week on a mailing list. Are there any more resources, references or any example implementations that you know of?