Haskell

ihaskell install
jupyter console –kernel haskell

do e → e
do { e; stmts } → e >> do { stmts }
do { v <- e; stmts } → e >>= \v -> do { stmts }
do { let decls; stmts} → let decls in do { stmts }

This is not quite the whole story, since v might be a pattern instead of a variable. For example, one can write

do (x:xs) <- foo
bar x
but what happens if foo produces an empty list? Well, remember that ugly fail function in the Monad type class declaration? That’s what happens.

Monad transformers exist only because monads do not compose in general.
MaybeT : provides the construction for (f of Maybe) for any Monad f.

data Compose f g x = Compose (f (g x))

instance (Functor f, Functor g) => Functor (Compose f g) where
      fmap f (Compose z) = Compose (fmap (fmap f) z)

instance (Monad f, Monad g) => Monad (Compose f g) where
      bind :: Compose f g a -> (a -> Compose f g b) -> Compose f g b
      bind (f (g x)) ff =
      bind = ???
      no way!

f a -> (a -> f b) -> f b
g c -> (c -> g d) -> g d

Looks like @iokasimov can write good #haskell jokes 😏

https://twitter.com/ChShersh/status/1002393643288686592

• State "DONE" from [2019-04-22]
  

https://github.com/krispo/awesome-haskell

• stack ghci
  
• Debug.Trace.traceShowM within do block
  
• pandoc –metadata
  

https://www.gwern.net/Resilient-Haskell-Software

stack ghci (module loaded automatically)
:set args rebuild
main
:break 222

stack build --profile
stack exec -- site rebuild +RTS -xc 

https://twitter.com/hdevalence/status/1088649294746275840

• regular functor
  

  class Functor f where
    fmap :: (a -> b) -> f a -> f b
  

Laws:

fmap id = id                                 -- Identity
fmap (p . q) = (fmap p) . (fmap q)           -- Homomorphism

• applicative
  

  class (Functor f) => Applicative f where
      pure  :: a -> f a
      (<*>) :: f (a -> b) -> f a -> f b
  

Laws:

pure id <*> v = v                            -- Identity
pure (.) <*> u <*> v <*> w = u <*> (v <*> w) -- Composition
pure f <*> pure x = pure (f x)               -- Homomorphism
u <*> pure y = pure ($ y) <*> u              -- Interchange
fmap f x = pure f <*> x                      -- Fmap

The mapping between Haskell functors is a family of functions parameterized by types. For instance, a mapping between the [] functor and the Maybe functor will map a list of a, [a] into Maybe a.
Here's an example of such a family of functions called safeHead:

safeHead :: [a] -> Maybe a
safeHead []     = Nothing
safeHead (x:xs) = Just x

https://wiki.haskell.org/Typeclassopedia#Intuition_3

Let’s look more closely at the type of (>>=). The basic intuition is that it combines two computations into one larger computation. The first argument, m a, is the first computation.
However, it would be boring if the second argument were just an m b; then there would be no way for the computations to interact with one another (actually, this is exactly the situation with Applicative).
So, the second argument to (>>=) has type a -> m b: a function of this type, given a result of the first computation, can produce a second computation to be run.
In other words, x >>= k is a computation which runs x, and then uses the result(s) of x to decide what computation to run second, using the output of the second computation as the result of the entire computation.

Actually, because Haskell allows general recursion, one can recursively construct infinite grammars, and hence Applicative (together with Alternative) is enough to parse any context-sensitive language with a finite alphabet.

http://byorgey.wordpress.com/2012/01/05/parsing-context-sensitive-languages-with-applicative

Here’s the key insight: normally, grammars are defined as finite objects: a finite set of terminals, a finite set of nonterminals, and a finite set of productions.
However, Haskell’s general recursion means that we can write down a "grammar" with an infinite set of production rules. This is what lets us get away with parsing context-sensitive languages with Applicative: we just make a different production rule for every possible input!