Intro duction to Functional Programming Lecture
Intro duction to
Functional Programming
John Harrison
University of Cambridge
Lecture
Basics of ML
Topics covered
Versions of ML
Running ML on Thor
Interacting with ML
Higher order functions and currying
Evaluation order
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
The ML family
ML is not a single language Apart from
Standard ML which we use here there are many
descendants of the original ML used as the
metalanguage of Edinburgh LCF e g
CAML Light an excellent lightweight
system develop ed at INRIA
Ob jective CAML a new version of CAML
Light including ob ject oriented features
Lazy ML a version from Gothenburg using
Standard ML an agreed standard version
Standard ML has two parts the Core language
and the Modules We will not cover the mo dule
system at all
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
Implementations of Standard ML
There are several implementations of something
similar to Standard ML
Standard ML of New Jersey free but very
resource hungry
Moscow ML free but do esn t have the
Mo dules
Poly ML go o d but a commercial pro duct
and do esn t run under Linux
Harlequin ML a newer commercial system
with integrated development environment
We ll use Moscow ML This is a go o d lightweight
implementation based on CAML Light written
by Sergei Romanenko Moscow and Peter Sestoft
Cop enhagen
The features we use are general and can easily b e
translated to other dialects
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
Starting up ML
Moscow ML is already installed on Thor In order
to start it up typ e
group clteach jr h m os ml a rch bin m osm l
This will invoke the appropriate version
dep ending on the machine architecture
The system should start up and present its
prompt
group clteach jr h m os ml a rch bin m osm l
Moscow ML version July
Enter quit to quit
If you want to install Moscow ML on your own
computer see the Web page
http www dina kv l d k se st oft m osm l htm l
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
Interacting with ML
We will run ML as an interpreter rather like a
sophisticated calculator You just typ e an
expression into it terminated by a semicolon and
it prints the result of evaluating it e g
val it int
ML not only prints the result but also infers the
int If ML cannot type of the expression namely
assign a typ e to an expression then it is rejected
true
Type clash
ML knows the typ e of the built in op erator and
that is how it makes its typ e inference
We ll treat the typ e system more systematically
next time for the moment it should b e
intuitively clear
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
Loading from les
We have just b een typing things into ML and
thinking ab out the results However one do esn t
write real programs in this way
Typically one writes the expressions and
declarations in a le To try them out as you go
these can b e inserted in the ML window using cut
and paste
You can cut and paste using X windows and
similar systems or an editor like Emacs with
multiple bu ers
For larger programs it s convenient simply to
load them from le into the ML session This can
use command in ML e g b e done using the
use myprog ml
Programs can also include comments written
b etween and These are ignored by ML
but are useful for p eople reading the co de
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
Using functions
Since ML is a functional language expressions are
allowed to have function typ e The ML syntax for
x to t x is fn x t x For a function taking
example we can de ne the successor function
fn x x
val it fn int int
Again the typ e of the expression this time int
is inferred and displayed However the int
function itself is not printed the system merely
writes fn
Functions are applied by juxtap osition with or
without bracketing
fn x x
val it int
fn x x
val it int
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
Curried functions
Every function in ML takes a single argument
One way to get the e ect of multiple arguments is
to use a pair for the argument we ll discuss
this next time
Another way often more p owerful is to use
Currying making the function take its arguments
one at a time e g
fn x fn y x y
val it fn int int int
This function takes the rst argument and gives a
new function For example
fn x fn y x y
val it fn int int
is just the successor function again e g
fn x fn y x y
val it int
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
Curried functions
Because curried functions are so common in
functional programming ML xes the rules of
asso ciation to avoid the need for many
parentheses
E E E ML asso ciates it as When one writes
E E E For example all the following are
equivalent
fn x fn y x y
val it int
fn x fn y x y
val it int
fn x fn y x y
val it int
fn x fn y x y
val it int
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
Bindings
It is not necessary to evaluate an expresion all in
one piece You can bind an expression to a name
using val
val successor fn x x
val successor fn int int
successor successo r suc ce sso r
val it int
Note that this isn t an assignment statement
merely an abbreviation But bindings can b e
rec recursive just add
val rec fact
fn n if n then
else n fact n
val fact fn int int
fact
val it int
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
Bindings
When binding functions one can also use fun
The following are equivalent
val successor fn x x
fun successor x x
and
val rec fact
fn n if n then
else n fact n
fun fact n
if n then
else n fact n
Note that bindings with fun are always recursive
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
Higher order functions
Curried functions are an example of a function
that gives another function as a result
We can also de ne functions that take other
functions as arguments This one takes a p ositive
n
n and a function f and returns f i e integer
f f n times
fun funpow n f x
if n then x
else funpow n f f x
val funpow fn int a a
a a
funpow fn x x
val it int
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
Lo cal declarations
Bindings can b e made lo cal using
let decs in expr end
For example
let fun fact n
if n then
else n fact n
in fact
end
This binding is now invisible b eyond the
end Similarly one can make a terminating
declaration lo cal to another declaration by
local decs in decs end
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
ML s evaluation strategy
Execution of an ML program just means
evaluating an expression You can think of this
evaluation as happ ening by a kind of syntactic
unfolding of the program
Constants like and evaluate to themselves
Evaluation stops immediately at something of
fn x and do es not lo ok the form
inside the
When evaluating a combination s t then
s and t are evaluated to s and t rst b oth
s is not of the form fn x u x then If
u t the things stop there Otherwise
result of replacing the dummy variable x by
t is evaluated the evaluated form of
It is imp ortant to grasp this evaluation strategy
in order to understand ML prop erly
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
Which evaluation strategy
But do es evaluation order actually matter One
might guess not For example
and
give the same answer Do es this generalize
In fact for pure functional programs if two
di erent evaluation orders terminate they give
the same answer This is roughly the
Church Rosser theorem
But there are still reasons to care ab out
evaluation order termination e ciency and
imp erative features
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
Lazy evaluation
ML s evaluation strategy is called eager or
cal l by value b ecause the argument to a function
is evaluated even if it never ends up b eing used
fn x An alternative would b e when evaluating
to evaluate u t without yet u x t
evaluating t This is cal l by name evaluation
t if it isn t The advantage is we avoid evaluating
actually used and this evaluation might b e very
costly or even fail to terminate
The disadvantage of a naive implementation is
t if it s used more that one would re evaluate
than once So one needs a clever sharing
implementation lazy evaluation
Lazy evaluation seems b etter in principle and
many functional languages even ML s relative
Lazy ML use it But it s harder to implement
e ciently and do esn t seem to t with imp erative
features Hence ML s choice
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
ML evaluation examples
fn x fn y y y x
fn x fn y y y x
fn y y y
fn f fn x f x fn y y y
fn x fn y y y x
fn x fn y y y x
fn y y y
John Harrison University of Cambridge January
Intro duction to Functional Programming Lecture
The conditional
Consider evaluating a factorial as de ned earlier
where the conditional is evaluated eagerly To
fact we unfold it to evaluate
if then else fact
We need to cut this down to But under the
standard eager rules we would rst evaluate all
fact three sub expressions including
This leads to an in nite lo op
So we can t regard the conditional as an ordinary
function of three arguments it has to have its
own lazy reduction strategy
The test expression is evaluated rst and
according to its value precisely one of the arms
never b oth
John Harrison University of Cambridge January