38 KiB
- Haskell Study Plan
- About This Guide
- Table of Contents
- Beginning
- More Basics Drill Down
- Useful Packages
- Tools
- Exercises
- Lambda Calculus
- Kinds
- What is IO?
- Type classes
- Monoids, Functors, Applicative, Monads and More
- Error Handling
- Debugging
- Laziness
- Performance
- Monad Transformers
- GHC Language Extensions
- Functional Patterns
- More
Haskell Study Plan
About This Guide
This guide is an opinionated list of resources for learning Haskell.
It is aimed at more experienced programmers that would like a denser Haskell tutorial.
If you prefer a gentler introduction, try one of these resources:
Table of Contents TOC_3
Beginning
- Get Started
- Reading Simple Haskell
- Writing Simple Haskell
- Indentation
- Haskell intro (cis194)
- Haskell Basics (cs240h)
-
- Read until "Everything is a Monoid" (right after "Chaining proofs")
The basics are important, each resource here brings it's own view on it which will help solidify this material. If there are exercises to do, do them!
Key ideas:
-
In Haskell we use a different computation model
- Instead of "telling the machine what to do in order to change the state of the machine" we "transform data until we have the result we want"
- Referential Transparency enables equational reasoning
- Types help prevent errors and help model programs
More Basics Drill Down
Useful Packages
Here are a few useful packages you might want to use when building software with Haskell:
- base - Haskell standard library. Contains large collection of useful libraries ranging from data structures to parsing combinators and debugging utilities.
- containers - Contains efficient general-purpose implementations of various immutable container types including sets, maps, sequences, trees, and graphs.
- vector - Efficient arrays.
- text - An efficient unicode text type. It is much more efficient than the built in
String
type. - bytestring - An efficient vector of byte type.
- async - API for running IO operations asynchronously.
- network - Low-level networking interface.
- random - random number library.
Tools
- How to Play with Stack
- Using GHCi Effectively
- Hoogle
- GHCid
-
Editor Integration
Exercises
Sort a List
Sort a list of ints by inserting all its elements into a binary tree.
- Define a data type of a binary tree
- Define the types of operations relevant to the task (sort, insert, insertList, flatten, display)
- Implement these functions
Think of scenarios and unit test your functions
Dict
Compress and decompress a file using dict compression.
Dict compression takes text, splits it by words, and creates two things:
- A mapping from each word in the text to a number
- the original text where each word is replaced by it's map's number
Your task is to create an application that can either compress or decompress a text file.
There are two commands: compress and decompress, they both get a text file.
- To compress:
> dict compress file.txt
- To decompress:
> dict decompress file.txt
For the compress command, the output should be the compressed items ((1) and (2)). For the decompress command, the output should be the original text.
Note: You can use the functions read
and show
to convert from/to some types and String
.
PPM
Create a program that will output a PPM file.
- The size of each "pixel" should be controlled by a parameter
- Your input should be a list of list of colors
- If a row is not long enough fill the rest of it with the color white
- Bonus: Choose a pallete of 8 or 16 basic colors and read a file containing numbers from 0 to 7 (or 15) separated by spaces and newlines, and output it's image
RPN Calculator
Create a program that calculates an arithmetic expression written in reverse polish notation.
Implement the following operations:
literal integers, +, -, *, /, negate
Example execution:
$ rpn-calc 5 7 2 negate + *
0
Lambda Calculus
Overview
The lambda calculus is a minimalistic language that is in the core of functional programming.
It presents a minimalistic framework to learn about many common features in functional languages.
Exercises
-
Reduce the following expressions to normal form using pen and paper
λx. x
(λx. x) y
(λx. x x) (λy. y)
(λw. λx. λz. x w z) a (λb. λc. c b) (λd. d)
-
Use eta conversion on the following expression
λx. f x
λf. λy. (λx. f x) y
- Write the expression
2 + 3
in the lambda calculus and evaluate it using pen and paper - Write the expression
factorial 5
in the lambda calculus and evaluate it using pen and paper
Use this Lambda Machine to check your answers
Kinds
Overview
Every expression has a concrete type.
Kinds are the types of types.
Definition of kinds in GHC:
data Kind
= Type -- can also be written as: *
| KArr Kind Kind -- KArr in Haskell this is written as: ->
Think of Type
being the kind of concrete types, and KArr
is a function from Kind
to Kind
.
If a type is parametarized (when defining the ADT you pass it parameters) then in order for it to be concrete you have to supply it with all the types it expects to get.
Example:
data Bool
= True
| False
data Maybe a
= Just a
| Nothing
Bool
is not parametarized so it is a concrete type (which means it's kind is Type
)
and has the Values True
and False
.
Maybe
is not a concrete type, it need to be supplied with a type for a
. (It has the kind Type -> Type
).
Maybe Bool
is a concrete type because all of the paramters for Maybe
have been supplied.
More examples:
Value | Type | Kind | Comments |
---|---|---|---|
True | Bool | Type (also written * ) |
a value |
'c' | Char | Type | |
"Hello" | String | Type | |
not True | Bool | Type | function application |
Just True | Maybe Bool | Type | |
["Hello"] | [String] | Type | |
Nothing | Maybe a | Type | polymorphic |
id | a -> a | Type | a function |
map | (a -> b) -> [a] -> [b] | Type | |
map not | [Bool] -> [Bool] | Type | partially applied function |
getLine | IO String | Type | |
putStrLn | String -> IO () | Type | |
Void | Type | a concrete types with no values | |
Maybe | Type -> Type | isn't fully supplied with parameters | |
IO | Type -> Type | ||
Either | Type -> Type -> Type | ||
Either a | Type -> Type | partially supplied with parameters | |
Free | (Type -> Type) -> Type -> Type | the first argument is of higher kind |
You can use ghci to query the kind of a type using :kind
Why do we care about Kinds? It let us generalize things and create abstractions.
Let's take a look at a data type that uses higher kinds:
data Rec f a
= Rec a (f (Rec f a))
- This data type has two type parameters,
f
anda
.
From their use in the right side of the =
we can see that a
has the kind Type
because
it is placed as a field without type arguments. We can also see that f
has kind Type -> Type
because it is placed as a field with one type argument (which in this case, is the same data type we defined).
This makes Rec
kind to be (Type -> Type) -> Type -> Type
.
Why is this data type interesting? Let's try to plug some types and see.
We need some a
which as kind Type
so let's just choose Int
for now, and let's use Maybe
for f
.
Let's look at some values of our new type Rec Maybe Int
.
x1 = Rec 1 Nothing
x2 = Rec 1 (Just (Rec 2 Nothing))
x3 = Rec 1 (Just (Rec 2 (Just (Rec 3 Nothing))))
See a pattern here? it seems like this is an encoding of a non-empty list:
- You always have at least one value
Nothing
is similar toNil
Just
is similar toCons
Let's take a look at another example with this type:
data Identity a
= Identity a
Identity
basically just holds a value of type a
. Nothing interesting here.
Let's try to plug it in Rec
(and get Rec Identity Int
) and see what kind of value we can have:
y1 = Rec 1 (Identity (Rec 2 (Identity (Rec 3 (Identity ...)))))
y2 = Rec 0 y2
As you can see we basically need to keep providing new values with no way of bailing out. So we got an infinite list of values (or a stream).
We can write all kinds of generic algorithms on this data type and reuse them
for different scenarios and needs simply by pluging in a different f
!
We'll see more of those after we talk about type classes.
And by the way, the real name of Rec
is Cofree.
Exercise
Try to plug into our Rec
a different type of kind Type -> Type
that you know and see what happens!
What is IO?
Overview
It is a parametarized type constructor (it has the kind Type -> Type
).
IO a
represents a description of a program (or subroutine) that when executed
will produce some value of type a
and may do some I/O effects while at it.
Evaluating an IO a
is pure - the evaluation will always reduce to the same description of a program.
In an executable, you need to define main :: IO ()
- a description of a program to run. The Haskell runtime will execute this.
You can combine subroutine descriptions to create bigger subroutine descriptions:
- ~pure
-
a -> IO a~
Produces a value without doing any I/O.
- Example:
pure True
Which has the type
IO Bool
, will not do any I/O and when executed will produce a value of typeBool
, specificallyTrue
. - Example:
- ~fmap
-
(a -> b) -> IO a -> IO b~
Similar to
map
on lists, it will apply a function on the parameter ofIO
.- Example:
fmap not (pure True)
Which has the type
IO Bool
will not do any I/O and when executed will produce a value of typeBool
by first applying the functionnot
on the result ofpure True
, and so will produce the valueFalse
. - Example:
- ~(>>)
-
IO a -> IO b -> IO b~
Run this first thing, discard the result, and then run the second thing.
-
Example:
putStrLn "Hello" >> putStrLn "World"
Which has the type
IO ()
, when executed, will print the stringHello
and then will print the stringWorld
and will produce a value of type()
, specifically()
(in this case the value has the same name as the type). -
- ~(>>=)
-
IO a -> (a -> IO b) -> IO b~
Run this first thing, take its result, pass it to the function which is the second argument, and then execute that.
- Example:
getLine >>= putStrLn
Which has the type
IO ()
will read aString
from the user, apply that String toputStrLn
and then execute it, thus printing the same string it got from the user. Then it will produce a value of type()
, specifically()
.Note: You can implement
(>>)
using(>>=)
like this:(>>) prog1 prog2 = prog1 >>= \_ -> prog2
- Example:
- ~join
-
IO (IO a) -> IO a~
Takes a description of a program that produces a description of a program that produces a value of type
a
and converts it to a descrption of a program that will produce a value of typea
by executing the first, and then executing the result.- Example:
join (fmap putStrLn getLine)
Which is the same as
getLine >>= putStrLn
. As you can see we can implement>>=
usingfmap
andjoin
(>>=) prog func = join (fmap func prog)
- Example:
There are many more functions and combinators that return IO a
. You can view some of them in the module System.IO.
Do notation
do notation is syntactic sugar around >>
and >>=
.
Example:
main = do
putStrLn "Tell me your name."
let greet name = "Hello, " ++ name ++ "!"
name <- getLine
putStrLn (greet name)
Will be desugared to:
main =
putStrLn "Tell me your name." >>
let
greet name = "Hello, " ++ name ++ "!"
in
getLine >>= \name ->
putStrLn ("Hello, " ++ name ++ "!")
- A regular line that does not create a binding will be sequenced to the next using
>>
- A new definition can be created using
let
, it will be translated tolet <definition> in <rest of the lines in the do>
- A line that creates a binding with
<-
will use>>=
to pass the result and the lambda (\name ->
) is used to bind the variable to the result - The last line will remain the same - no desugar needed
This is basically CPS (continuation passing style).
code | operator | type of the left side | type of the right side | comments |
---|---|---|---|---|
let gretting = "hello" | = |
String | String | = means both side are interchangeable (they both mean exactly the same thing) |
name <- getLine | <- |
String | IO String | <- is syntactic sugar for >>= where we bind the result of the computation to the name |
IO's API fits a pattern that can be seen in more types in Haskell, which is why the type signatures of the functions presented here are more general. We'll discuss that later.
Exercises
-
Implement a number guessing game
-
Generate a random number between 1 and 100, the user should try to guess what it is.
- If the user guess is too high, say it's too high.
- If the user guess is too low, say it's too low.
- Hint: you can use randomRIO to generate a random number
-
Bonus: Remember the amount of times the user guess and print that at the end of the game.
- Hint: In pure functional programming we use recursion to emulate state
- Bonus: Remember the user's guesses and tell them if they already tried that guess.
-
-
Implement a REPL interface to your RPN Calculator
- Create an interactive interface that lets the user repeatedly write calculations and return the evaluations for them
Type classes
Overview
We use type classes to describe groups of types that all behave in a similar way and refer to the generically.
A good type class will have operations on the type and laws attached to it - similar to abstract algebra.
Laws cannot be enforced by the compiler - a good convention in Haskell is not to define lawless type classes and not implement unlawful instances.
We define a type class like this:
class Eq (a :: *) where
(==) :: a -> a -> Bool
We define a class of types that can implement the operation (==)
.
We implement an instance of a type class for a given type like this:
-- In this case we place `Bool` in place of `a` everywhere
instance Eq Bool where
(==) b1 b2 = case (b1, b2) of
(True, True) -> True
(False, False) -> True
_ -> False
Now we can implement polymorphic functions that will work on a subset of all types - all types that fill the constraint - have instances of a type class.
(/=) :: Eq a => a -> a -> Bool
(/=) x y = not (x == y)
class instances should be defined in the same place as the type class definition or at the same place as the type definitions. Failing to do that may cause Orphan Instances.
Abstraction | definition | different substitutions | comments |
---|---|---|---|
No polymorphism | func1 :: Int -> Int -> Int | none | we know exactly which types are used and can do all kinds of operations on them |
Parametric polymorphism | func2 :: a -> a -> a | a can be any type |
We don't know which types a and b are and can't do any type related operations on them |
Type classes (ad-hoc) | func3 :: Ord a => a -> a -> a | a can be any type that can be ordered (Bool, Int, String) |
anything to the left of => is a constraint on the type |
More Material
Exercise
-
Read about a few common type classes:
- Show
- Read
- Eq
- Ord
- Num
- Integral
- Floating
- Go back to Sort a List exercise and change it to work on more types than just
Int
Note: We can create instances for higher kinded types (for example: Type -> Type
). We will see some of those next.
Monoids, Functors, Applicative, Monads and More
Overview
Key idea:
These are abstract algebraic structures
The define operations and laws on them such as identity and associativity.
Many patterns fit these structures, making them useful as abstractions!
Type classes you should care about (at the moment):
- Semigroup
- Monoid
- Functor
- Applicative
- Monad
- Foldable
- Traversable
Read about them in the typeclassopedia in this order.
After that: read The monads section in wiwik to meet some useful monad instances.
-
- Read from "Everything is a Monoid" (right after "Chaining proofs") or from the beginning if you want to review it again
Instances
Make sure to meet:
- Maybe
- Either
- List
->
(Functions)- IO
- Reader
- State
- Writer
And understand why and how they work!
Exercises
- Implement some instances to a few types you like.
- Implement
Functor
,Foldable
andTraversable
instances for theTree
data type you defined at Sort a list and revised in Type Classes -
Implement a
Foldable
instance for theRec
data type we defined in the section on Kinds.- Test your solution by using
Sum
,Product
,Any
orAll
fromData.Monoid
.
- Test your solution by using
-
Implement a
Functor
instance for theRec
data type we defined in the section on Kinds.- Test your solution by mapping and then folding
Error Handling
Using Either for errors
There are quite a few ways to indicate and handle errors in Haskell. We are going to look at one solution: using the type Either. Either is defined like this:
data Either a b
= Left a
| Right b
Simply put, a value of type Either a b
can contain either a value of type a
, or a value of type b
.
Well can tell them apart from the contructor used.
Left True :: Either Bool b
Right 'a' :: Either a Char
Using this type, we can represent computations that may fail by using Either
with one type to represent error values
and the other type to represent the values we want if the computation succeeds.
For example, let's say that we want to parse a String
as a decimal digit to an Int
. We have two possible failures:
- The string contains more than one character
- The string is empty
- The character is not one of 0,1,2,3,4,5,6,7,8,9
We can represent this as a type
data ParseDigitError
= EmptyString
| StringIsTooLong
| NotADigit Char
deriving Show
And our function can have the type
parseDigit :: String -> Either ParseDigitError Int
Now when we check our string we can return Left
on error and Right
on successful parsing.
parseDigit :: String -> Either ParseDigitError Int
parseDigit str = case str of
-- empty string
[] -> Left StringIsTooLong
-- more than one character
_ : _ : _ -> Left StringIsTooLong
[c] ->
if elem c "0123456789"
then Right (read [c])
else Left (NotADigit c)
Either a
is also an instance of Functor
, Applicative
, and Monad
, so we have some combinators to work with
if we want to combine these kind of computations.
For example, we can use our function to parse an integer by trying to
parse each character (using traverse
) and then use a function to sum them all together
by applying it to the Int
value using fmap
.
parseInteger :: String -> Either ParseDigitError Int
parseInteger str =
let
-- We use (:[]) first because each element of a `String` is a `Char` and our functions works on `String`.
-- This also means that in this case only NotADigit error can be return, which is still fine.
digits = traverse (parseDigit . (:[])) str
in
fmap
(foldr (+) 0 . zipWith (\e n -> 10 ^ e * n) [0..] . reverse)
digits
Try it!
Note that since Either
has kind Type -> Type -> Type
and Functor
, Applicative
and Monad
expect something of kind Type -> Type
, we can only create instances for Either a
and not Either
.
This means that when we use, for example, <*>
which has the type
(<*>) :: Applicative f => f (a -> b) -> f a -> f b
we replace f
with Either a
and not Either
:
-- We'll use `e` for the left type of the either instead of `a` here because `a` is already taken
(<*>) :: Either e (a -> b) -> Either e a -> Either e b
This means that e
must be the same. If you want, for example, to use two different error types,
two approaches you can use are:
- Replace them with one big ADT that contain both errors
- Make one ADT that combines both types just like
Either
does witha
andb
and use the functionfirst
from Data.Bifunctor to convert from one error type to the other. (first
is likefmap
but for the first type variable inEither
)
Exceptions
Exercises
- Revise your RPN Calculator to use
Either
to terminate early due to errors.
Debugging
Laziness
Performance
Resources
Data Structures
The choice of a data structure is determined by the properties and the algorithms used.
Single-linked lists are a fairly ubiquious data structure in Haskell.
Due to the simplicity and their syntactic sugar, they are used all over the place - often when they are not a good choice.
Lists are good for:
- You only need to add or take the beginning of the list (consing), which is O(1)
- You use map, filter, zip and folds, which are O(N) anyway and are subject to operation fusion (aka.
map f . map g = map (f . g)
- Your list is really small and is not expected to grow
- Your list is infinite
Lists are not good if:
- You use
lookup
- useMap
- You want the elements to be unique - use
Set
- You expect the list to have at least one argument, use
NonEmpty
- You use append or concat, use
DList
orSeq
- You use sort with non-unique values, use
Seq
Monad Transformers
Overview
Functors and applicative interfaces can be composed easily, but monads cannot.
Monad transformers are a way to compose the capabilities of multiple type's monadic interface to one type.
Exercises
-
To your RPN Calculator REPL:
- Use
Either
to terminate an evaluation of an expression early when encountering errors - Add the
Reader
interface to thread through the evaluation the build-in operations - Add the ability for the user to define new words (with the syntax:
: <word> <expressions>
)
- Use
GHC Language Extensions
Haskell is a standartized programming language. The last standard is Haskell 2010.
GHC, the most popular Haskell compiler, contains more features than what's available in Haskell 2010.
To use those features, we must tell the compiler that we want to use them.
We do this by invoking a compiler flag or adding a LANGUAGE
pragma at the top of the source file.
Functional Patterns
Effectful outer layer, Uneffectful core
Code that does no effects is easier to test, debug and reason about.
Keeping most of our program's logic uneffectful makes it more flexible.
But programs still need to interact with the outside world.
For that, we can create an outer layer that is responsible for interacting with the user and dispatching the right logic functions.
Notice this pattern in these Basic Haskell Exmaples.
Compose Smaller Things to Bigger Things
Type Classes Patterns
Type Classes such as Monoid
, Functor
, Applicative
and Monad
can be thought of as patterns.
They are all around us and are at the core API of many libraries.
You can find them when doing web development, streaming, IO, concurrency, parsing, error handling, testing, build systems and more.
Examples:
More
More
Some Advanced Topics
These may not be as useful for your everyday programming tasks, but it's nice to know they exist when you need them
References and Tools
Simple Example Programs
A Few Cool Open-Source Applications
Here are a few cool open source applications written in Haskell that might accept contributions if you're interested.
- Aura - A package manager for Arch Linux and its AUR.
- CodeWorld - CodeWorld is an educational environment using Haskell.
- hledger - Friendly, robust, plain text accounting.
- Komposition - The video editor built for screencasters
- Matterhorn - A terminal client for the Mattermost chat system.
- Movie-Monad - A free and simple to use video player made with Haskell.
- patat - Terminal-based presentations using Pandoc.
- postgrest - REST API for any Postgres database.
- PureScript - A strongly-typed language that compiles to Javascript.
- Project:m36 - A relational algebra engine as inspired by the writings of Chris Date.
- termonad - A terminal emulator configurable in Haskell.
- Tidal - Language for live coding of pattern.