- Aug 2020
Now it is much clearer that id is really a family of infinitely many functions. It is fair to say that it is an abstract function (as opposed to a concrete one), because its type abstracts over the type variable a. The common and proper mathematical wording is that the type is universally quantified (or often just quantified) over a.
This was very neatly put, and
forallabove is also spot on.
My main issue with this book is that the difficulty is exponentially increasing, and by "keeping it simple" (i.e., trying to use simple terms) it is even harder to do a proper research.
1. The name of this chapter
This chapter should have been called Explicitly quantified type or Explicit universal quantification as it is too general as is, and doing a search to get to know more when someone has no formal/previous functional programming background, makes very hard.
Most importantly though, even if Haskell not mentioned, the word "explicit" would have been important.
It is also more about generic parameters than about quantification itself, and
forallis kind of introduced but it is totally misleading.
The post “forall” is the type-level “lambda” (saved) is the best, most succinct explanation of
forallthat I ever found. Unfortunately not before going down the rabbit hole.. (See links below.) One still needs to know about
- generic parameters
- what pragmas are but after that, it is straightforward.
(Jordan's Reference section on
forallalso doesn't help much.)
forallis also mandatory in PureScript (which is also not mentioned when introducing it), and I believe a comparison (the way the above post did) with Haskell is important, but at the right time. At least Jordan's Reference tries to put it off until later, but still before explaining concepts required to understand it.
3. The "rabbit hole" links
These are all good resources, but not for uninitiated mortals, and at a lower level (such as where I am now) they raise more questions than answers.
(Started here initially, but the single sentence there prompted a search for scoped type variables and rank-n types (or Rank N types).)