Haskell is an advanced purely-functional programming language.

Features:

• Statically typed: Every expression in Haskell has a type which is determined at compile time. Static type checking is the process of verifying the type safety of a program based on analysis of a program's text (source code). If a program passes a static type checker, then the program is guaranteed to satisfy some set of type safety properties for all possible inputs.
• Purely functional: Every function in Haskell is a function in the mathematical sense. There are no statements or instructions, only expressions which cannot mutate variables (local or global) nor access state like time or random numbers.
• Concurrent: Its flagship compiler, GHC, comes with a high-performance parallel garbage collector and light-weight concurrency library containing a number of useful concurrency primitives and abstractions.
• Lazy evaluation: Functions don't evaluate their arguments. Delays the evaluation of an expression until its value is needed.
• General-purpose: Haskell is built to be used in all contexts and environments.
• Packages: Open source contribution to Haskell is very active with a wide range of packages available on the public package servers.

The latest standard of Haskell is Haskell 2010. As of May 2016, a group is working on the next version, Haskell 2020.

The official Haskell documentation is also a comprehensive and useful resource. Great place to find books, courses, tutorials, manuals, guides, etc.

Integer Literals

is a numeral without a decimal point

for example 0, 1, 42, ...

is implicitly applied to fromInteger which is part of the Num type class so it indeed has type Num a => a - that is it can have any type that is an instance of Num

Fractional Literals

is a numeral with a decimal point

for example 0.0, -0.1111, ...

is implicitly applied to fromRational which is part of the Fractional type class so it indeed has type a => a - that is it can have any type that is an instance of Fractional

String Literals

If you add the language extension OverloadedStrings to GHC you can have the same for String-literals which then are applied to fromString from the Data.String.IsString type class

This is often used to replace String with Text or ByteString.

List Literals

Lists can defined with the [1, 2, 3] literal syntax. In GHC 7.8 and beyond, this can also be used to define other list-like structures with the OverloadedLists extension.

By default, the type of [] is:

> :t []
[] :: [t]

With OverloadedLists, this becomes:

[] :: GHC.Exts.IsList l => l

What is a Lens?

Lenses (and other optics) allow us to separate describing how we want to access some data from what we want to do with it. It is important to distinguish between the abstract notion of a lens and the concrete implementation. Understanding abstractly makes programming with lens much easier in the long run. There are many isomorphic representations of lenses so for this discussion we will avoid any concrete implementation discussion and instead give a high-level overview of the concepts.

Focusing

An important concept in understanding abstractly is the notion of focusing. Important optics focus on a specific part of a larger data structure without forgetting about the larger context. For example, the lens _1 focuses on the first element of a tuple but doesn't forget about what was in the second field.

Once we have focus, we can then talk about which operations we are allowed to perform with a lens. Given a Lens s a which when given a datatype of type s focuses on a specific a, we can either

1. Extract the a by forgetting about the additional context or
2. Replace the a by providing a new value

These correspond to the well-known get and set operations which are usually used to characterise a lens.

Other Optics

We can talk about other optics in a similar fashion.

Each optic focuses in a different way, as such, depending on which type of optic we have we can perform different operations.

Composition

What's more, we can compose any of the two optics we have so-far discussed in order to specify complex data accesses. The four types of optics we have discussed form a lattice, the result of composing two optics together is their upper bound.

For example, if we compose together a lens and a prism, we get a traversal. The reason for this is that by their (vertical) composition, we first focus on one part of a product and then on one part of a sum. The result being an optic which focuses on precisely zero or one parts of our data which is a special case of a traversal. (This is also sometimes called an affine traversal).

In Haskell

The reason for the popularity in Haskell is that there is a very succinct representation of optics. All optics are just functions of a certain form which can be composed together using function composition. This leads to a very light-weight embedding which makes it easy to integrate optics into your programs. Further to this, due to the particulars of the encoding, function composition also automatically computes the upper bound of two optics we compose. This means that we can reuse the same combinators for different optics without explicit casting.

These language extensions are typically available when using the Glasgow Haskell Compiler (GHC) as they are not part of the approved Haskell 2010 language Report. To use these extensions, one must either inform the compiler using a flag or place a LANGUAGE programa before the module keyword in a file. The official documentation can be found in section 7 of the GCH users guide.

The format of the LANGUAGE programa is {-# LANGUAGE ExtensionOne, ExtensionTwo ... #-}. That is the literal {-# followed by LANGUAGE followed by a comma separated list of extensions, and finally the closing #-}. Multiple LANGUAGE programas may be placed in one file.

The following diagram taken from the Typeclassopedia article shows the relationship between the various typeclasses in Haskell.

Functions mentioned here in examples are defined with varying degrees of abstraction in several packages, for example, data-fix and recursion-schemes (more functions here). You can view a more complete list by searching on Hayoo.

Text is a more efficient alternative to Haskell's standard String type. String is defined as a linked list of characters in the standard Prelude, per the Haskell Report:

type String = [Char]

Text is represented as a packed array of Unicode characters. This is similar to how most other high-level languages represent strings, and gives much better time and space efficiency than the list version.

Text should be preferred over String for all production usage. A notable exception is depending on a library which has a String API, but even in that case there may be a benefit of using Text internally and converting to a String just before interfacing with the library.

All of the examples in this topic use the OverloadedStrings language extension.

A Functor can be thought of as a container for some value, or a computation context. Examples are Maybe a or [a]. The Typeclassopedia article has a good write-up of the concepts behind Functors.

To be considered a real Functor, an instance has to respect the 2 following laws:

Identity

fmap id == id

Composition

fmap (f . g) = (fmap f) . (fmap g)

• Parallel and Concurrent Programming in Haskell

• the Haskell Wiki

(.) :: (b -> c) -> (a -> b) ->  (a -> c)
(.)       f           g          x =  f (g x)     -- or, equivalently,  

(.)       f           g     =   \x -> f (g x)     
(.)       f     =    \g     ->  \x -> f (g x)      
(.) =    \f     ->   \g     ->  \x -> f (g x)      
(.) =    \f     ->  (\g     -> (\x -> f (g x) ) ) 

 f g x y z ...    ==    (((f g) x) y) z ...

(.)       f           g          x =  r
                                      where r = f (g x)  
-- g :: a -> b
-- f ::      b -> c
-- x :: a      
-- r ::           c   

(.)       f           g     =    q
                                 where q = \x -> f (g x) 
-- g :: a -> b
-- f ::      b -> c
-- q :: a      -> c

....

(.) f g x  =  (f . g) x  =  (f .) g x  =  (. g) f x 

which is easy to grasp as the "three rules of operator sections", where the "missing argument" just goes into the empty slot near the operator:

(.) f g    =  (f . g)    =  (f .) g    =  (. g) f   
--         1             2             3  

The x, being present on both sides of the equation, can be omitted. This is known as eta-contraction. Thus, the simple way to write down the definition for function composition is just

(f . g) x   =   f (g x)

This of course refers to the "argument" x; whenever we write just (f . g) without the x it is known as point-free style.

infixl 6 +
infixl 6 -
infixl 7 *
infixr 8 ^

More details in section 4.4.2 of the Haskell 98 report.

The Haskell Wiki has these recommendations:

In general:

• End users should use Data.Vector.Unboxed for most cases
• If you need to store more complex structures, use Data.Vector
• If you need to pass to C, use Data.Vector.Storable

For library writers;

• Use the generic interface, to ensure your library is maximally flexible: Data.Vector.Generic

For an in-depth explanation of typed holes, as well as a discussion of the design of typed holes, see the Haskell wiki.

Section of the GHC user guide on typed holes.

The Data.Time module from time package provides support for retrieving & manipulating date & time values:

1. Clone the project from Github
2. Use Stack to build and install

You should now find the hprotoc executable in $HOME/.local/bin/.

What is Template Haskell?

Template Haskell refers to the template meta-programming facilities built into GHC Haskell. The paper describing the original implementation can be found here.

What are stages? (Or, what is the stage restriction?)

Stages refer to when code is executed. Normally, code is exectued only at runtime, but with Template Haskell, code can be executed at compile time. "Normal" code is stage 0 and compile-time code is stage 1.

The stage restriction refers to the fact that a stage 0 program may not be executed at stage 1 - this would be equivalent to being able to run any regular program (not just meta-program) at compile time.

By convention (and for the sake of implementation simplicity), code in the current module is always stage 0 and code imported from all other modules is stage 1. For this reason, only expressions from other modules may be spliced.

Note that a stage 1 program is a stage 0 expression of type Q Exp, Q Type, etc; but the converse is not true - not every value (stage 0 program) of type Q Exp is a stage 1 program,

Futhermore, since splices can be nested, identifiers can have stages greater than 1. The stage restriction can then be generalized - a stage n program may not be executed in any stage m>n. For example, one can see references to such stages greater than 1 in certain error messages:

>:t [| \x -> $x |]

<interactive>:1:10: error:
    * Stage error: `x' is bound at stage 2 but used at stage 1
    * In the untyped splice: $x
      In the Template Haskell quotation [| \ x -> $x |]

Using Template Haskell causes not-in-scope errors from unrelated identifiers?

Normally, all the declarations in a single Haskell module can be thought of as all being mutually recursive. In other words, every top-level declaration is in the scope of every other in a single module. When Template Haskell is enabled, the scoping rules change - the module is instead broken into groups of code seperated by TH splices, and each group is mutually recursive, and each group in the scope of all further groups.

haskell.org has a great chapter on module definition.

As the hackage page describes:

pipes is a clean and powerful stream processing library that lets you build and connect reusable streaming components

Programs implemented through streaming can often be succinct and composable, with simple, short functions allowing you to "slot in or out" features easily with the backing of the Haskell type system.

await :: Monad m => Consumer' a m a

Pulls a value from upstream, where a is our input type.

yield :: Monad m => a -> Producer' a m ()

Produce a value, where a is the output type.

It's highly recommended you read through the embedded Pipes.Tutorial package which gives an excellent overview of the core concepts of Pipes and how Producer, Consumer and Effect interact.

Simon Marlow's book, Concurrent and Parallel Programming in Haskell, is outstanding and covers a multitude of concepts. It is also very much accessible for even the newest Haskell programmer. It is highly recommended and available in PDF or online for free.

Parallel vs Concurrent

Simon Marlow puts it best:

A parallel program is one that uses a multiplicity of computational hardware (e.g., several processor cores) to perform a computation more quickly. The aim is to arrive at the answer earlier, by delegating different parts of the computation to different processors that execute at the same time.

By contrast, concurrency is a program-structuring technique in which there are multiple threads of control. Conceptually, the threads of control execute “at the same time”; that is, the user sees their effects interleaved. Whether they actually execute at the same time or not is an implementation detail; a concurrent program can execute on a single processor through interleaved execution or on multiple physical processors.

Weak Head Normal Form

It's important to be aware of how lazy-evaluation works. The first section of this chapter will give a strong introduction into WHNF and how this relates to parallel and concurrent programming.

While cabal has support for including a C and C++ libraries in a Haskell package, there are a few bugs. First, if you have data (rather than a function) defined in b.o that is used in a.o, and list the C-sources: a.c, b.c, then cabal will be unable to find the data. This is documented in #12152. A workaround when using cabal is to reorder the C-sources list to be C-sources: b.c, a.c. This may not work when using stack, because stack always links the C-sources alphabetically, regardless of the order in which you list them.

Another issues is that you must surround any C++ code in header (.h) files with #ifdef __cplusplus guards. This is because GHC doesn't understand C++ code in header files. You can still write C++ code in header files, but you must surround it with guards.

ccall refers to the calling convention; currently ccall and stdcall (Pascal convention) are supported. The unsafe keyword is optional; this reduces overhead for simple functions but may cause deadlocks if the foreign function blocks indefinitely or has insufficient permission to execute1.

Definition

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

Note the Functor constraint on f. The pure function returns its argument embedded in the Applicative structure. The infix function <*> (pronounced "apply") is very similar to fmap except with the function embedded in the Applicative structure.

A correct instance of Applicative should satisfy the applicative laws, though these are not enforced by the compiler:

pure id <*> a = a                              -- identity
pure (.) <*> a <*> b <*> c = a <*> (b <*> c)   -- composition
pure f <*> pure a = pure (f a)                 -- homomorphism
a <*> pure b = pure ($ b) <*> a                -- interchange

The numeric typeclass hierarchy

Num sits at the root of the numeric typeclass hierarchy. Its characteristic operations and some common instances are shown below (the ones loaded by default with Prelude plus those of Data.Complex):

λ> :i Num
class Num a where
  (+) :: a -> a -> a
  (-) :: a -> a -> a
  (*) :: a -> a -> a
  negate :: a -> a
  abs :: a -> a
  signum :: a -> a
  fromInteger :: Integer -> a
  {-# MINIMAL (+), (*), abs, signum, fromInteger, (negate | (-)) #-}
      -- Defined in ‘GHC.Num’
instance RealFloat a => Num (Complex a) -- Defined in ‘Data.Complex’
instance Num Word -- Defined in ‘GHC.Num’
instance Num Integer -- Defined in ‘GHC.Num’
instance Num Int -- Defined in ‘GHC.Num’
instance Num Float -- Defined in ‘GHC.Float’
instance Num Double -- Defined in ‘GHC.Float’

We have already seen the Fractional class, which requires Num and introduces the notions of "division" (/) and reciprocal of a number:

λ> :i Fractional
class Num a => Fractional a where
  (/) :: a -> a -> a
  recip :: a -> a
  fromRational :: Rational -> a
  {-# MINIMAL fromRational, (recip | (/)) #-}
      -- Defined in ‘GHC.Real’
instance RealFloat a => Fractional (Complex a) -- Defined in ‘Data.Complex’
instance Fractional Float -- Defined in ‘GHC.Float’
instance Fractional Double -- Defined in ‘GHC.Float’

The Real class models .. the real numbers. It requires Num and Ord, therefore it models an ordered numerical field. As a counterexample, Complex numbers are not an ordered field (i.e. they do not possess a natural ordering relationship):

λ> :i Real
class (Num a, Ord a) => Real a where
  toRational :: a -> Rational
  {-# MINIMAL toRational #-}
      -- Defined in ‘GHC.Real’
instance Real Word -- Defined in ‘GHC.Real’
instance Real Integer -- Defined in ‘GHC.Real’
instance Real Int -- Defined in ‘GHC.Real’
instance Real Float -- Defined in ‘GHC.Float’
instance Real Double -- Defined in ‘GHC.Float’

RealFrac represents numbers that may be rounded

λ> :i RealFrac
class (Real a, Fractional a) => RealFrac a where
  properFraction :: Integral b => a -> (b, a)
  truncate :: Integral b => a -> b
  round :: Integral b => a -> b
  ceiling :: Integral b => a -> b
  floor :: Integral b => a -> b
  {-# MINIMAL properFraction #-}
      -- Defined in ‘GHC.Real’
instance RealFrac Float -- Defined in ‘GHC.Float’
instance RealFrac Double -- Defined in ‘GHC.Float’

Floating (which implies Fractional) represents constants and operations that may not have a finite decimal expansion.

λ> :i Floating
class Fractional a => Floating a where
  pi :: a
  exp :: a -> a
  log :: a -> a
  sqrt :: a -> a
  (**) :: a -> a -> a
  logBase :: a -> a -> a
  sin :: a -> a
  cos :: a -> a
  tan :: a -> a
  asin :: a -> a
  acos :: a -> a
  atan :: a -> a
  sinh :: a -> a
  cosh :: a -> a
  tanh :: a -> a
  asinh :: a -> a
  acosh :: a -> a
  atanh :: a -> a
  GHC.Float.log1p :: a -> a
  GHC.Float.expm1 :: a -> a
  GHC.Float.log1pexp :: a -> a
  GHC.Float.log1mexp :: a -> a
  {-# MINIMAL pi, exp, log, sin, cos, asin, acos, atan, sinh, cosh,
              asinh, acosh, atanh #-}
      -- Defined in ‘GHC.Float’
instance RealFloat a => Floating (Complex a) -- Defined in ‘Data.Complex’
instance Floating Float -- Defined in ‘GHC.Float’
instance Floating Double -- Defined in ‘GHC.Float’

Caution: while expressions such as sqrt . negate :: Floating a => a -> a are perfectly valid, they might return NaN ("not-a-number"), which may not be an intended behaviour. In such cases, we might want to work over the Complex field (shown later).

See also SafeNewtypeDeriving.

Note: The naming for the normal, one argument functors is a little misleading: the Functor typeclass implements "covariant" functors, while "contravariant" functors are implemented in the Contravariant typeclass in Data.Functor.Contravariant, and previously the (misleadingly named) Cofunctor typeclass in Data.Cofunctor.