Programming in Scala”

Chapter notes 8
Parametricity
When we can “follow the type” of a function to derive the only possible implementation, we say
that the definition is given by parametricity. See the Wikipedia article on parametricity²², and Philip
Wadler’s paper Theorems for free!²³
Curry
The idea of Currying²⁴ is named after the mathematician Haskell Curry.²⁵ He also discovered one of
the most important results in computer science, the Curry-Howard isomorphism²⁶ which says that
a program is a logical proof, and the hypothesis that it proves is its type.
Function composition
Function composition in functional programming is closely related to function composition in
mathematics.²⁷
FAQ for chapter 2
Are tail calls optimized if the @annotation.tailrec annotation isn’t there?
They are still optimized, but the compiler won’t warn you if it can’t do the tail call optimization.
Is there a list of other annotation types somewhere?
See the Scaladoc for the Annotation class²⁸, and expand the ‘known subclasses section’.
Is the common style to define loops using local function, rather than a
(private) standalone function?
Yes, this is much more common. There’s no need to pollute the namespace with helper functions
you aren’t expecting to be called by anyone.
Is a || go(x) considered a tail call? What about a && go(x)?
Yes
²²http://en.wikipedia.org/wiki/Parametricity
²³http://homepages.inf.ed.ac.uk/wadler/topics/parametricity.html
²⁴http://en.wikipedia.org/wiki/Currying
²⁵http://en.wikipedia.org/wiki/Haskell_Curry
²⁶http://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
²⁷http://en.wikipedia.org/wiki/Function_composition
²⁸http://www.scala-lang.org/api/current/index.html#scala.annotation.Annotation