A Lightning Tour of Haskell

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A Lightning Tour of Haskell

• Lecture 1,
• Designing and Using Combinators
• John Hughes

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Using Haskell The Hugs Interpreter
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Using Haskell The Hugs Interpreter
A module is loaded.
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Using Haskell The Hugs Interpreter
A module is loaded.
Type an expression at the prompt.
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Using Haskell The Hugs Interpreter
A module is loaded.
Type an expression at the prompt.
The value is printed.
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Using Haskell The Hugs Interpreter
A function call with two arguments. No brackets!
Brackets are only for grouping e.g. f (g x)
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Using Haskell The Hugs Interpreter
A linked list
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3
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1 3 5
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Defining Functions
insert Ord a a - a - a insert x
insert x (yxs) xy
yinsert x xs
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Defining Functions
Type signature. Optional!
insert Ord a a - a - a insert x
insert x (yxs) xy
yinsert x xs
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Defining Functions
Type signature. Optional!
Ignore for now
insert Ord a a - a - a insert x
insert x (yxs) xy
yinsert x xs
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Defining Functions
Type signature. Optional!
Ignore for now
Type of first argument a
insert Ord a a - a - a insert x
insert x (yxs) xy
yinsert x xs
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Defining Functions
Type signature. Optional!
Ignore for now
Type of first argument a
insert Ord a a - a - a insert x
insert x (yxs) xy
yinsert x xs
Type of second argument list of as
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Defining Functions
Type signature. Optional!
Ignore for now
Type of first argument a
Type of result
insert Ord a a - a - a insert x
insert x (yxs) xy
yinsert x xs
Type of second argument list of as
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Defining Functions
Type signature. Optional!
Ignore for now
Type of first argument a
Type of result
insert Ord a a - a - a insert x
insert x (yxs) xy
yinsert x xs
Type of second argument list of as
What is a?
A type variable which can stand for any
type. This function is polymorphic.
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Defining Functions
insert Ord a a - a - a insert x
insert x (yxs) xy
yinsert x xs
Definition by pattern matching case analysis
on the form of the arguments.
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Defining Functions
insert Ord a a - a - a insert x
insert x (yxs) xy
yinsert x xs
Definition by pattern matching case analysis
on the form of the arguments.
Guards define conditions for an equation to
apply.
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Defining Functions
We build a new structure as the
result purely functional.
insert Ord a a - a - a insert x
insert x (yxs) xy
yinsert x xs
Definition by pattern matching case analysis
on the form of the arguments.
Guards define conditions for an equation to
apply.
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Defining Data Types
data Tree a Node a (Tree a) (Tree a) Leaf
deriving Show
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Defining Data Types
Type name
data Tree a Node a (Tree a) (Tree a) Leaf
deriving Show
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Defining Data Types
Type name
Type parameter
data Tree a Node a (Tree a) (Tree a) Leaf
deriving Show

• Types may take parameters.
• Enables us to define polymorphic functions which
  work on a tree with any type of labels.

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Defining Data Types
Type name
Type parameter
data Tree a Node a (Tree a) (Tree a) Leaf
deriving Show
Constants start with upper case, variables with
lower

• Types may take parameters.
• Enables us to define polymorphic functions which
  work on a tree with any type of labels.

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Defining Data Types
Node and Leaf are alternative forms of Tree.
data Tree a Node a (Tree a) (Tree a) Leaf
deriving Show
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Defining Data Types
Node and Leaf are alternative forms of Tree.
data Tree a Node a (Tree a) (Tree a) Leaf
deriving Show
Types of the components.
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Defining Data Types
Node and Leaf are alternative forms of Tree.
data Tree a Node a (Tree a) (Tree a) Leaf
deriving Show
Types of the components.
Ignore for now.
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Defining Data Types
data Tree a Node a (Tree a) (Tree a) Leaf
deriving Show
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Defining Data Types
data Tree a Node a (Tree a) (Tree a) Leaf
deriving Show
Type Tree Integer
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Tree Insertion
insertTree Ord a a - Tree a - Tree
a insertTree x Leaf Node x Leaf Leaf insertTree
x (Node y l r) x l) r x y Node y l (insertTree x r)
xy Node y l r
Pattern matching works as for lists.
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Overloading

• Polymorphic functions use the same definition at
  each type.
• Overloaded functions may have a different
  definition at each type.

Class name.
Read a is a type in class Eq, if it has the
following methods.
class Eq a where () a - a - Bool
(/) a - a - Bool x/y not (xy)
Class methods and types.
Default definition.
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The Class Hierarchy
Read Type a in class Eq is also in class Ord,
if it provides the following methods
class Eq a Ord a where ( a -
Bool
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Instance Declarations
instance Eq Integer where xy primitive
instance Eq a Eq a where
True xxs yys x y xs ys
Provided a is in class Eq, then a is in class
Eq, with the method definition given.
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Types of Overloaded Functions
a may be any type in class Ord.
insert Ord a a - a - a insert x
insert x (yxs) xy
yinsert x xs
Because insert uses a method from class Ord.
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Show and Read
class Show a where show a - String
class Read a where read String - a
These are simplifications there are more methods
in reality.
read . show id (usually)
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Derived Instances
data Tree a Node a (Tree a) (Tree a) Leaf
deriving Show
Constructs a default instance of class Show.
Works for many standard classes.
Main show (Node 1 Leaf (Node 2 Leaf Leaf)) "Node
1 Leaf (Node 2 Leaf Leaf)"
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Multi-Parameter Classes
Define relations between classes.
class Collection c a where empty c add
a - c - c member a - c - Bool
c is a collection with elements of type a.
instance Eq a Collection a a where
empty add () member elem
instance Ord a Collection (Tree a) a where
empty Leaf add insertTree member
elemTree
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Functional Dependencies
A functional dependency
class Collection c a c - a where empty
c add a - c - c member a - c -
Bool

• Declares that c determines a there can be only
  one instance for each type c.
• Helps the type-checker resolve ambiguities
  (tremendously).

add x (add y empty) -- x and y must be the same
type.
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Side Effects in Haskell

• Suppose
• tick String - Integer
• reads an integer n from a file with given name,
• writes n1 back to the file
• returns n

Then tick tick might be False!
Cannot replace equals by equals. Not purely
functional!
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Haskells Solution
Performs I/O and delivers a String.
Side effects are recorded in the type!
readFile String - IO String writeFile
String - String - IO ()
So the type of tick is tick String - IO
Int and tick tick is ill-typed.
IO is a monad -- more later!
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The do notation
I/O actions may be combined in sequence.
tick String - IO Integer tick f
do contents contents writeFile f (show (n1)) return n
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The do notation
I/O actions may be combined in sequence.
Type IO String
tick String - IO Integer tick f
do contents contents writeFile f (show (n1)) return n
Type String
Scope of contents
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The do notation
I/O actions may be combined in sequence.
tick String - IO Integer tick f
do contents contents writeFile f (show (n1)) return n
Local declaration
Scope
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The do notation
I/O actions may be combined in sequence.
tick String - IO Integer tick f
do contents contents writeFile f (show (n1)) return n
Type IO ()
No need to bind a name to the result.
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The do notation
I/O actions may be combined in sequence.
tick String - IO Integer tick f
do contents contents writeFile f (show (n1)) return n
Type IO Integer Defines result of tick.
return a - IO a
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IO a Action Yeilding an a
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IO a Action Yeilding an a
Action at the prompt is performed.
The action returned by tick has a side-effect.
Yields a different Integer each time it is
performed.
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IO a Action Yeilding an a
twice1 IO a - (IO a, IO a) twice1 c (c,c)
Result is not an action! Therefore not performed.
Next call reveals no side-effects occurred.
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IO a Action Yeilding an a
twice2 IO a - IO (a,a) twice2 a do x a return (x,x) twice3 IO a - IO
(a,a) twice3 a do x The same action can be performed many times.
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References
Variables in Haskell cannot be updated --
references can.
newIORef a - IO (IORef a) readIORef IORef
a - IO a writeIORef IORef a - a - IO ()
Reference operations have side-effects -- hence
IO type.
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Example Destructive List Insertion
Updateable tail.
data RList a Nil Cons a (IORef (RList
a)) insertRList Ord a a - IORef (RList a)
- IO () insertRList x xs do cell readIORef xs case cell of Nil - do
new (Cons x new) Cons y xs' x do
new (Cons x new) xy - insertRList x xs'
Must read the list cell.
Create new cell and update old.
case is inline pattern matching.
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Encapsulated Side Effects

• IORefs can only be updated at the top level.
• Can we use references internally to define a pure
  function?
• Example
• removeDuplicates Hashable a a - a

Array operations resemble reference ones.
Use a hash table internally to make comparison
fast.
No IO type no externally visible side-effects!
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Encapsulation The ST Monad
newSTRef a - ST s (STRef s a) readSTRef
STRef s a - ST s a writeSTRef STRef s a - a
- ST s ()
Similar family of operations.
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Encapsulation The ST Monad
newSTRef a - ST s (STRef s a) readSTRef
STRef s a - ST s a writeSTRef STRef s a - a
- ST s ()
s ties together the type of a reference and
the action which uses it.
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Encapsulation The ST Monad
newSTRef a - ST s (STRef s a) readSTRef
STRef s a - ST s a writeSTRef STRef s a - a
- ST s ()
The encapsulation function runST (forall s .
ST s a) - a
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Encapsulation The ST Monad
newSTRef a - ST s (STRef s a) readSTRef
STRef s a - ST s a writeSTRef STRef s a - a
- ST s ()
The encapsulation function runST (forall s .
ST s a) - a
Result type free from ST pure.
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Encapsulation The ST Monad
newSTRef a - ST s (STRef s a) readSTRef
STRef s a - ST s a writeSTRef STRef s a - a
- ST s ()
The encapsulation function runST (forall s .
ST s a) - a
Each use binds a fresh variable s labels
references created, guarantees used only here.
Result type free from ST pure.
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Encapsulation The ST Monad
newSTRef a - ST s (STRef s a) readSTRef
STRef s a - ST s a writeSTRef STRef s a - a
- ST s ()
The encapsulation function runST (forall s .
ST s a) - a
The argument of runST must be polymorphic in s.
This is a rank 2 type. Cannot be inferred
-- must be declared.
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Overloading Side-Effects
Why should we choose between IO and ST when we
want side-effects?
class Monad m RefMonad m r m - r where
newRef a - m (r a) readRef r a - m a
writeRef r a - a - m ()
instance RefMonad IO IORef
instance RefMonad (ST s) (STRef s)
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Overloading Side-Effects
Why should we choose between IO and ST when we
want side-effects?
class Monad m RefMonad m r m - r where
newRef a - m (r a) readRef r a - m a
writeRef r a - a - m ()
Partial type application. Plug in ST s and STRef
s for m and r in the types
instance RefMonad IO IORef
instance RefMonad (ST s) (STRef s)
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Overloading Side-Effects
Why should we choose between IO and ST when we
want side-effects?
class Monad m RefMonad m r m - r where
newRef a - ST s (STRef s a) readRef
STRef s a - ST s a writeRef STRef s a -
a - ST s ()
instance RefMonad IO IORef
instance RefMonad (ST s) (STRef s)
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Overloading Side-Effects
Why should we choose between IO and ST when we
want side-effects?
class Monad m RefMonad m r m - r where
newRef a - m (r a) readRef r a - m a
writeRef r a - a - m ()
Example
data RList r a Nil Cons a (r (RList r
a)) insertRList (Ord a, RefMonad m r) a
- r (RList r a) - m ()
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Higher-Order Functions

• Functions are values in Haskell.
• Program skeletons take functions as parameters.

takeWhile (a - Bool) - a - a takeWhile
p takeWhile p (xxs) p x
xtakeWhile p xs otherwise
Takes a prefix of a list, satisfying a predicate.
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Denoting Functions
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Denoting Functions
below a b b 63
Denoting Functions
below a b b takeWhile (a - Bool) - a - a takeWhile
p takeWhile p (xxs) p x
xtakeWhile p xs otherwise
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Denoting Functions
below a b b takeWhile (a - Bool) - a - a takeWhile
p takeWhile p (xxs) below 10 x
xtakeWhile p xs otherwise
A partial function application.
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More Ways to Denote Functions
below a b b

takeWhile (below 10) 1,5,9,15,20

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More Ways to Denote Functions
below a b b

takeWhile (below 10) 1,5,9,15,20

takeWhile (\b - b
Lambda expression. Function definition in place.
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More Ways to Denote Functions
below a b b

takeWhile (below 10) 1,5,9,15,20

takeWhile (\b - b
Lambda expression. Function definition in place.
f b b
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More Ways to Denote Functions
below a b b

takeWhile (below 10) 1,5,9,15,20

takeWhile (\b - b

takeWhile (
Lambda expression. Function definition in place.
f b b
Partial operator application -- argument replaces
missing operand.
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Lazy Evaluation

• Expressions are evaluated only when their value
  is really needed!
• Function arguments, data structure components,
  are held unevaluated until their value is used.

from n n from (n1)
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Lazy Recursive Definitions
nats 0 map (1) nats
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A Confession
This program doesnt work!
tick String - IO Integer tick f
do contents contents writeFile f (show (n1)) return n
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A Confession
This program doesnt work!
The file is only opened here, it is read
when contents is needed.
tick String - IO Integer tick f
do contents contents writeFile f (show (n1)) return n
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A Confession
This program doesnt work!
The file is only opened here, it is read
when contents is needed.
tick String - IO Integer tick f
do contents contents writeFile f (show (n1)) return n
Not needed yet! n isnt needed
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A Confession
This program doesnt work!
The file is only opened here, it is read
when contents is needed.
tick String - IO Integer tick f
do contents contents writeFile f (show (n1)) return n
Not needed yet! n isnt needed
Not needed until after the file is opened for
writing!
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A Confession
This program doesnt work!
The file is only opened here, it is read
when contents is needed.
tick String - IO Integer tick f
do contents contents writeFile f (show (n1)) return n
Not needed yet! n isnt needed
Not needed until after the file is opened for
writing!
So readFile sees an empty file!
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A Confession
This program doesnt work!
tick String - IO Integer tick f
do contents contents n seq writeFile f (show
(n1)) return n
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A Confession
This program doesnt work!
tick String - IO Integer tick f
do contents contents n seq writeFile f (show
(n1)) return n
seq evaluates its first argument, then returns
its second.
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A Confession
This program doesnt work!
tick String - IO Integer tick f
do contents contents n seq writeFile f (show
(n1)) return n
seq evaluates its first argument, then returns
its second.
Backquotes turn a function name into
an operator.
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Time for a Demo
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Course Home Page
www.cs.chalmers.se/rjmh/Combinators Begin with
some finger exercises in Haskell.