CS535 Programming Languages

Chapter - 10 Functional Programming With Lists

Outline

• Functional Language: LISP

• Scheme, a Dialect of LISP

• The structure of lists

• List manipulation • Storage allocation for lists

Functional Language: LISP

• Includes all the basic concepts of functional programming

• First designed in 1958 by John McCarthy

• Functions include recursion, first-class functions and garbage collection

• Lisp implementation led the way in integrated programming environments

Scheme, A Dialect Of LISP

A scheme is a small language that provides

constructs at the core of Lisp

Constructs include:

1. Conditionals

2. The “ let ” construct

3. Quoting (data in the form of expressions)

Expression Scheme uses a form of prefix notation for

expressions The general form of an expression in

Scheme is

( E1 E2 E3 …… Eη) The expression 4 + 5 * 7 is written as

( + 4 (* 5 7) ) The above uniformity in Lisp syntax makes

it easy to manipulate programs as data

Function Definition The recursive and non recursive function

definition associates a function value

with a name

The general syntax of function definition:( define (<function name> <arguments>) <expression>)

An example: ( define ( Square X ) ( * X X ) )

; (Square 5) = 25

Conditionals Conditional expressions come in two forms

1. (if P E1 E2)

2. ( cond ( P1 E1) ….

( Pn E n )

( else E n + 1 ) )

Conditionals are generally required for

recursive functions

let Construct The general syntax of the let construct is

( let ( (X1 E1 ) (X 2 E 2) … (X k E k) ) F )

For instance (3*3) + (4*4) is written as

( let ( (three-sq(square 3))

(four-sq(square 4) )

(+ three -sq four-sq) )

25

Quoting Used to choose a spelling as a symbol or a

variable name Two methods of quoting are:

1. ( quote <item> )

2. `<item>

( define f * ) // Unquoted

( f 2 3 ) 6

( define f `* ) //Quoted represents symbol which is a bad procedure

( f 2 3 )

The Structure of ListsList 1 : (this is (a list) of elements)

this

is

a

list ( ) nil

of

elements

( )

Fig1: Tree representation of the structure of List 1 - () are important

Operations on Lists

List X: ()

List Y: ( this is (a list) of elements)

Basic Operation Result

1. (null? X) # t (rue)

2. ( car Y ) this (first element)

3. ( cdr X ) (is (a list) of elements) (rest of the list after the first is removed)

4. (car (cdr X) ) is

5. (cdr (cdr X) ) ( (a list) of elements )

6. (cons a X ) ( a )

List Manipulation

1. Length function:

The equation for non empty list X :

(length x) = (+ 1 (length (cdr x) ) )

Corresponding length function definition:

( define (length X)

( cond ( (null? X) 0)

(else (+ 1 ( length (cdr x) ) )

)

)

2. Append function:

The equation for appending two lists is:(append X Z) = (cons (car X) (append (cdr X) Z))

Corresponding append function definition:

(define (append X Z) ( cond ( ( null? X) Z) (else (cons (car X) (append (cdr X) Z) ) ) ))

3. Mapping a function

A function f applied to a single list element can be extended using map and applied to all elements of the same list

Eg: Considering the square function ,

( define (square n) (* n n ) )

( map square `( 1 2 3 4 5 ) )Result : (1 4 9 16 25)

Storage allocation for lists

• Implementation of lists in Scheme and ML is usually done by using cells. •Each cell holds pointers to the head and tail or car and cdr, respectively

• The cons operation allocates a single cell

• Each execution of cons returns a pointer to a newly allocated cell

Consider the list formed from the expressions:

1. ( cons `it (cons `seems (cons `that `() ) ) )

it seems that

( )

Fig2: List X created by executing the above expression

List formed : (it seems that)

X

2. ( cons (car X) (cdr X) )

List Y formed: (it seems that)

it seems that

( )

Fig 3: List Y created by executing the above expression

Y

X

Allocation and Deallocation Cells no longer in use have to be deallocated

to avoid the problems of memory shortage A standard technique is to link the cells on a

list called a free list A free list acts as a stack of cells on which the

standard PUSH and POP operations are performed

A language implementation performs the garbage collection when it returns cells to the

free list

Approaches to Deallocation of cells

1. Lazy approach:

• Deallocation starts only after all the memory is exhausted, after which all the dead cells are collected.

• This method is time consuming

• Possibility of interrupting the ongoing processing

2. Eager approach:

• Deallocating is done by checking a cell for any future requirement in an operation

• The cell is then placed on the free list to be freshly allocated on a POP operation

• Standard technique is to reserve some space in each cell for a reference count of the number of pointers to the cell.

Implementation of garbage collection

The Mark Sweep Approach:

1. Mark phase involves marking all the cells which

can be reached by following pointers.

2. Sweep phase involves sweeping through the memory, looking for any unmarked cells.

3. The sweeping phase starts at one end of the

memory and looks at every cell

4. Once identified, all the unmarked cells are sent

to the free list for fresh allocation.

Equal? And Eq?

Equal? - value equality eq? - pointer equality