[PDF] - In tro duction to F unctional Programming: Lecture 1 1 In PDF Document

SLIDE 1 In tro duction to F unctional Programming: Lecture 1 1 In tro duction to F unctional Programming John Harrison Univ ersit y

f

Cam bridge Lecture 1 In tro duction and Ov erview T

pics

co v ered:

Imp

erativ e programming

F

unctional programming

The

merits

f

functional programming

Historical

remarks

Ov

erview

f

the course John Harrison Univ ersit y

f

Cam bridge, 15 Jan uary 1998

SLIDE 2 In tro duction to F unctional Programming: Lecture 1 2 Imp erativ e programming Imp erativ e (or pro cedural) programs rely

n

mo difying a state b y using a sequence

f

c

mmands.

The state is mainly mo died b y the assignment command, written v = E

r

v := E. W e can execute

ne

command b efore another b y writing them in sequence, p erhaps separated b y a semicolon: C 1 ; C 2 . Commands can b e executed conditionally using if, and rep eatedly using while. Programs are a series

f

instructions

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ho w to mo dify the state. Imp erativ e languages, e.g. F OR TRAN, Algol, C, Mo dula-3 supp

rt

this st yle

f

programming. John Harrison Univ ersit y

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Cam bridge, 15 Jan uary 1998

SLIDE 3 In tro duction to F unctional Programming: Lecture 1 3 An abstract view W e ignore input-output

p

erations, and assume that a program runs for a limited time, pro ducing a result. W e can consider the execution in an abstract w a y as:

!
1

!

2

!

!
n

The program is started with the computer in an initial state

,

including the inputs to the program. The program nishes with the computer in a nal state

n

, con taining the

utput(s)
f

the program. The state passes through a nite sequence

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c hanges to get from

to
n

; in general, eac h command ma y mo dify the state. John Harrison Univ ersit y

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Cam bridge, 15 Jan uary 1998

SLIDE 4 In tro duction to F unctional Programming: Lecture 1 4 F unctional programming A functional program is simply an expr ession, and executing the program means evaluating the expression. W e can relate this to the imp erativ e view b y writing

n

= E [ ].

There

is no state, i.e. there are no v ariables.

Therefore

there is no assignmen t, since there's nothing to assign to.

And

there is no sequencing and no rep etition, since

ne

expression do es not aect another. But

n

the p

sitiv

e side:

W

e can ha v e recursiv e functions, giving something comparable to rep etition.

F

unctions can b e used m uc h more exibly , e.g. w e can ha v e higher

rder

functions. F unctional languages supp

rt

this st yle

f

programming. John Harrison Univ ersit y

f

Cam bridge, 15 Jan uary 1998

SLIDE 5 In tro duction to F unctional Programming: Lecture 1 5 Example: the factorial The factorial function can b e written imp erativ ely in C as follo ws: int fact(int n) { int x = 1; while (n > 0) { x = x * n; n = n

1;

} return x; } whereas it w

uld

b e expressed in ML as a recursiv e function: fun fact n = if n = then 1 else n * fact(n

1);

John Harrison Univ ersit y

f

Cam bridge, 15 Jan uary 1998

SLIDE 6 In tro duction to F unctional Programming: Lecture 1 6 Wh y? A t rst sigh t a language without v ariables, assignmen t and sequencing lo

ks

v ery impractical. W e will sho w in this course ho w a lot

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in teresting programming can b e done in the functional st yle. Imp erativ e programming languages ha v e arisen as an abstraction

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the hardw are, from mac hine co de, through assem blers and macro assem blers, to F OR TRAN and b ey

nd.

P erhaps this is the wrong approac h and w e should approac h the task from the h uman side. Ma yb e functional languages are b etter suited to p eople. But what concrete reasons are there for preferring functional languages? John Harrison Univ ersit y

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Cam bridge, 15 Jan uary 1998

SLIDE 7 In tro duction to F unctional Programming: Lecture 1 7 Merits

f

functional programming By a v

iding

v ariables and assignmen ts, w e gain the follo wing adv an tages:

Clearer

seman tics. Programs corresp

nd

more directly to abstract mathematical

b

jects.

More

freedom in implemen tation, e.g. parallelizabilit y . By the more exible use

f

functions, w e gain:

Conciseness

and elegance.

Better

parametrization and mo dularit y

f

programs.

Con

v enien t w a ys

f

represen ting innite data. John Harrison Univ ersit y

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Cam bridge, 15 Jan uary 1998

SLIDE 8 In tro duction to F unctional Programming: Lecture 1 8 Denotational seman tics W e can iden tify

ur

ML factorial function with an abstract mathematical (partial) function Z ! Z : [ [fact ] ](n) = 8 < : n! if n

?
therwise

where ? denotes undenedness, since for negativ e argumen ts, the program fails to terminate. Once w e ha v e a state, this simple in terpretation no longer w

rks.

Here is a C `function' that do esn't corresp

nd

to an y mathematical function: int rand(void) { static int n = 0; return n = 2147001325 * n + 715136305; } This giv es dieren t results

n

successiv e calls! John Harrison Univ ersit y

f

Cam bridge, 15 Jan uary 1998

SLIDE 9 In tro duction to F unctional Programming: Lecture 1 9 Seman tics

f

imp erativ e programs In

rder

to giv e a corresp

nding

seman tics to imp erativ e programs, w e need to mak e the state explicit. F

r

example w e can mo del commands as:

P

artial functions

!
(Strac

hey)

Relations
n
(Hoare)
Predicate

transformers, i.e. total functions ( ! bool ) ! ( ! bool ) (Dijkstra) If w e allo w the goto statemen t, ev en these are not enough, and w e need a seman tics based

n

c

ntinuations

(W adsw

rth,

Morris). All these metho ds are quite complicated. With functional programs, w e ha v e a real c hance

f

pro ving their correctness,

r

the correctness

f

certain transformations

r
ptimizations.

John Harrison Univ ersit y

f

Cam bridge, 15 Jan uary 1998

SLIDE 10 In tro duction to F unctional Programming: Lecture 1 10 Problems with functional programs F unctional programming is not without its deciencies. Some things are harder to t in to a purely functional mo del, e.g.

Input-output
In

teractiv e

r

con tin uously running programs (e.g. editors, pro cess con trollers). Ho w ev er, in man y w a ys, innite data structures can b e used to accommo date these things. F unctional languages also corresp

nd

less closely to curren t hardw are, so they can b e less ecien t, and it can b e hard to reason ab

ut

their time and space usage. ML is not a pure functional language, so y

u

can use v ariables and assignmen ts if required. Ho w ev er most

f
ur

w

rk

is in the pure functional subset. John Harrison Univ ersit y

f

Cam bridge, 15 Jan uary 1998

SLIDE 11 In tro duction to F unctional Programming: Lecture 1 11 Historical remarks Some

f

the ideas b ehind functional programming go bac k a long w a y , e.g. to `lam b da calculus', a logical formalism due to Alonzo Ch urc h, in v en ted in the 1930s b efore electronic computers. The earliest real functional programming language w as LISP , in v en ted b y McCarth y in the 50s. Ho w ev er this had a n um b er

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defects, whic h w e will discuss later. The mo dern trend really b egins with ISWIM, in v en ted b y P eter Landin in the 1960s. The ML family started with Robin Milner's theorem pro v er `Edin burgh LCF' in the late 70s. The language w e shall study is essen tially (core) Standard ML, but there are

ther

imp

rtan

t dialects, notably CAML and Ob jectiv e CAML. John Harrison Univ ersit y

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Cam bridge, 15 Jan uary 1998

SLIDE 12 In tro duction to F unctional Programming: Lecture 1 12 Ov erview

f

the course (1)

Practicalities
f

in teracting with ML.

Key

functional concepts, e.g. ev aluation strategy , higher

rder

functions.

P
lymorphic

t yp es.

Recursiv

e functions and recursiv e structures.

Hin

ts for eectiv e programming.

Exceptions,

references and

ther

imp erativ e features.

Pro

ving programs correct. John Harrison Univ ersit y

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Cam bridge, 15 Jan uary 1998

SLIDE 13 In tro duction to F unctional Programming: Lecture 1 13 Ov erview

f

the course (2) W e w an t to sho w the p

w

er

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ML, so w e'll nish with more substan tial examples that illustrate some

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the p

ssibilities:
Sym

b

lic

dieren tiation

Recursiv

e descen t parsing

A

Prolog in terpreter

A

theorem pro v er The co de for these examples will b e made a v ailable

n

Thor. John Harrison Univ ersit y

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Cam bridge, 15 Jan uary 1998