Well, I’m not terribly satisfied with the answers given so far, but I think the comments attached to them are a bit more compelling. So I’ll summarize here: I think there’s only one sensible Functor instance that follows from Applicative: fmap f fa = pure f <*> fa Assuming that’s unique, it makes sense that … Read more
Tying the knot is a solution to the problem of circular data structures. In imperative languages you construct a circular structure by first creating a non-circular structure, and then going back and fixing up the pointers to add the circularity. Say you wanted a two-element circular list with the elements “0” and “1”. It would … Read more
: is the “prepend” operator: x : xs Returns a list which has x as first element, followed by all elements in xs. In other functional languages, this is usually called cons, because it “cons”tructs a list recursively by repeated application from an empty list: 1 : 2 : 3 : 4 : [] is … Read more
In a pure functional language, you can’t do anything that has a side effect. A side effect would mean that evaluating an expression changes some internal state that would later cause evaluating the same expression to have a different result. In a pure functional language you can evaluate the same expression as often as you … Read more
I’m with @Rhymoid on this one, I believe all Monads have two (!!) transformers. My construction is a bit different, and far less complete. I’d like to be able to take this sketch into a proof, but I think I’m either missing the skills/intuition and/or it may be quite involved. Due to Kleisli, every monad … Read more
read can parse a string into float and int: Prelude> :set +t Prelude> read “123.456” :: Float 123.456 it :: Float Prelude> read “123456” :: Int 123456 it :: Int But the problem (1) is in your pattern: createGroceryItem (a:b:c) = … Here : is a (right-associative) binary operator which prepends an element to a … Read more
The easiest way to understand foldr is to rewrite the list you’re folding over without the sugar. [1,2,3,4,5] => 1:(2:(3:(4:(5:[])))) now what foldr f x does is that it replaces each : with f in infix form and [] with x and evaluates the result. For example: sum [1,2,3] = foldr (+) 0 [1,2,3] [1,2,3] … Read more
how to find out why this solution is so slow. Are there any commands that tell me where most of the computation-time is spend so I know which part of my haskell-program is slow? Precisely! GHC provides many excellent tools, including: runtime statistics time profiling heap profiling thread analysis core analysis. comparative benchmarking GC tuning … Read more
These links may be helpful: Evaluating cellular automata is comonadic. In particular, “whenever you see large datastructures pieced together from lots of small but similar computations there’s a good chance that we’re dealing with a comonad”. Sequences, streams, and segments Comonads in everyday life
In the 2009-2012 period, the following things have happened: 2012: From 2012, the parallel Haskell status updates began appearing in the Parallel Haskell Digest. 2011: Parallel and Concurrent Programming in Haskell, a tutorial. version 1.1 released by Simon Marlow Haskell and parallelism, mentioned in an article in the Economist magazine, Jun 2nd 2011. Parallel tree … Read more