comparative programming languages functional languages comparison: scheme, smalltalk, python, ruby

Comparative Programming Languages

Functional Languages Comparison: Scheme, Smalltalk, Python, Ruby

CS 363 Spring 2005 GMU 2

Fundamentals of Functional Programming Languages

• The objective of the design of a functional programming language (FPL) is to mimic mathematical functions to the greatest extent possible

• The basic process of computation is fundamentally different in a FPL than in an imperative language– In an imperative language, operations are done and the results are

stored in variables for later use– Management of variables is a constant concern and source of

complexity for imperative programming

• In an FPL, variables are not necessary, as is the case in mathematics


Fundamentals of Functional Programming Languages

• In an FPL, the evaluation of a function always produces the same result given the same parameters– This is called referential transparency


Lisp

• Lisp – based on lambda calculus (Church)– Uniform representation of programs and data

using single general data structure (list)– Interpreter based (written in Lisp)– Automatic memory management– Evolved over the years– Dialects: COMMON LISP, Scheme

5

Smalltalk• Smalltalk – a dynamically typed object oriented

programming and functional language designed at Xerox PARC by Alan Kay, Dan Ingalls, Ted Kaehler, Adele Goldberg, during the 1970s. – Released as Smalltalk-80

– Influenced the development of languages such as Objective-C, Java and Ruby

– Everything is an object

– Everything is available for modification. If you want to change the IDE, you can do it

– Types are dynamic -- you don't have to define types in the code

– Garbage collection is built in, invisible to the developer.

6

Squeak• Squeak is an open, highly-portable

Smalltalk-80 implementation whose virtual machine is written entirely in Smalltalk – The image below was created in Squeak, and illustrates

several of Squeak's abilities, including the ability to scale and rotate bitmap images at any colour depth, anti-aliased TrueType fonts and vector graphics

7

Ruby• Ruby – combines syntax inspired by Ada

and Perl with Smalltalk-like object-oriented features – Also shares some features with Python, Lisp

– Ruby is an interpreted language.

– Created by Yukihiro "Matz" Matsumoto, started working on Ruby in Feb. 1993 and released it to the public in 1995.

– Name chosen to reflect the language's Perl heritage.

– Designed Ruby to follow the principle of least surprise - the language should be free from traps and inconsistencies of other languages

8

Python• Python is an interpreted, interactive

programming language created by Guido van Rossum in 1990 – Originally as a scripting language for Amoeba OS

capable of making system calls.

– Amoeba distributed operating system is a microkernel-based research operating system written by Andrew S. Tanenbaum at Vrije Universiteit

– The aim of the project was to build a timesharing system that appeared to the user as a single machine even though it was running on multiple machines.

9

Python• Python

– Often compared to Tcl, Perl, Scheme, Java, and Ruby

– Developed as an open source project, managed by the non-profit Python Software Foundation.

– Python is a multi-paradigm language, like Perl, Oz or C++ and unlike Smalltalk or Haskell

– Rather than forcing coders to adopt one particular style of coding, it permits several

– Object orientation, structured programming, functional programming are all supported

– Python is dynamically type-checked and uses garbage collection for memory management

– origin of the name - after the television series Monty Python's Flying Circus

10

Python

• Python (from wikipedia)– Many similarities to Perl

– However, Python's designers reject Perl's exuberant syntax in favor of a more spare, less cluttered one

– As with Perl, Python's developers expressly promote a particular "culture" or ideology (http://python.org/dev/culture.html) based on what they want the language to be, favoring language forms they see as "beautiful", "explicit" and "simple".

– Although Python is sometimes classified as a "scripting language", it has been used to develop many large software projects such as the Zope application server

11

Python

• Python (from wikipedia)– Though the designer of Python is somewhat hostile to

functional programming and the Lisp tradition, there are significant parallels between the philosophy of Python and that of minimalist Lisp-family languages such as Scheme

– Many past Lisp programmers have found Python appealing for this reason

– Python is a dynamically typed language, like Lisp and unlike Java or C


Scheme (dr scheme, guile)

(define (gcd u v) (if ( = v 0) u (gcd v (remainder u v)) ))

(define (reverse l) (if (null? l) l (append (reverse (cdr l))(list (car l))) ))


Scheme (dr scheme, guile)

Using guile (gnu scheme):

(load "slides.scm")(gcd 56 108) --> 4(reverse '(2 3 556)) --> (556 3 2)

14

Common Lisp (clisp)(defun mygcd (u v)

(if (= v 0)

u

(mygcd v (rem u v))

)

)

(defun myreverse (l)

(if (null l) l

(append (myreverse (cdr l))(list (car l)))

)

)

;; (load "slides.lsp"), (mygcd 56 108) --> 4

;; (myreverse '(2 3 556)) --> (556 3 2)

15

Smalltalk (Squeak - inisqueak)

myGcd: numTwo

" 112 myGcd: 224 --> 112”

(numTwo = 0) ifTrue: [^self].

^numTwo myGcd: self \\ numTwo.

myReverse

"#(1 2 3 43 a b) myReverse -> ($b $a 43 3 2 1 )"

(self size = 0) ifTrue: [^self].

^self allButFirst myReverse,

self first asOrderedCollection.

16

Gnu-Smalltalk – gst

!SequenceableCollection methodsFor: 'algorithms'!

"Or use Array, but that limits your objects."

myCount

" #(1 2 3 $a $b $c myCount! --> 6

In gst: Filestream inFile: count.st "

(self size = 0) ifTrue: [^0].

^(1 + (self copyFrom: 2) myCount).

!

17

Gnu-Smalltalk – gst (cont.)

myReverse

"#(1 2 3 43 a b) myReverse -> » ($b $a 43 3 2 1 )"

| temp |

(self size = 0) ifTrue: [^self].

temp := OrderedCollection new: 1.

temp add: self first.

^(self copyFrom: 2) myReverse, temp.

!!

18

Gnu-Smalltalk – gst (cont.)

!Number methodsFor: 'algorithms'!

myGcd: numTwo

"120 myGcd: 200! --> 40"

(numTwo = 0) ifTrue: [^self].

^numTwo myGcd: self \\ numTwo.

!!

19

Ruby (ruby)def myGcd(numOne, numTwo)

if numTwo == 0

return numOne

end

return myGcd(numTwo, numOne % numTwo)

end

def myReverse(list)

if list.length == 1

return list

end

return myReverse(list[1..list.length-1]).concat(myReverse([list[0]]))

end

20

Ruby - “Class version”count.rb

class Integer

def myGcd(numTwo)

if numTwo == 0

return self

else

return numTwo.myGcd(self % numTwo)

end

end

end

- load “file.rb” into the Ruby interpreter (eval.rb)

- 120.myGcd(500) --> 20

21

Ruby - “Class version”class Integer

def greet

print "Hello world\n"

end

def plus(numTwo)

return self + numTwo

end

def times(numTwo)

return self * numTwo

end

end

- load “file.rb” into the Ruby interpreter (eval.rb)

- 120.greet --> “Hello..”, 3.plus(4).times(5) -> 35

22

Ruby (non-class vers.)def myCount (mylist)

if mylist.length == 0

return 0

else

return 1 + myCount(mylist[1..mylist.length-1])

end

end

print "Length of [1,2,3,4,5,6]= ",

myCount([1,2,3,4,5,6]), "\n"

To run: ruby count.rb

23

Ruby (class vers.)class Array

def myCount

if self.length == 0

return 0

else

return 1 + self[1..self.length].myCount

end

end

end

This version is “object oriented”...

[3,4,5,6,7,78].myCount --> 6

24

Python (python)def myGcd(numOne, numTwo):

if(numTwo == 0):

return numOne

return myGcd(numTwo, numOne % numTwo)

def myReverse(mylist):

if len(mylist) == 1:

return mylist

return myReverse(mylist[1:len(mylist)]) + myReverse([mylist[0]])

25

Python (python)def myCount (mylist):

if len(mylist) == 0:

return 0

else:

return 1 + myCount(mylist[1:len(mylist)])

print "Length of [1,2,3,4,5,6]= ", myCount([1,2,3,4,5,6])

To run: python count.py

Squeak Browser Window – Lists classes and methods in classes

Squeak Workspace WindowTo “run” each line, middle-button click, choose

“do it” or “print it”

Squeak Transcript WindowTo “run” each line, middle-button click, choose

“do it” or “print it”

Gnu Smalltalk Browser Window

Gnu Smalltalk, X11Worksheet and Transcript

Worksheet window Transcript window

To “run” a line, right click and choose “do it” and/or “print it”

Gnu Smalltalk - gst

Note the use of “!” at the end of each line.

Also, printNl is specific to gst.

Ruby – example run, see count.rb

Ruby – example run from eval.rb

Python – example run, see count.rb


Introduction to Scheme

• A mid-1970s dialect of LISP, designed to be a cleaner, more modern, and simpler version than the contemporary dialects of LISP

• Uses only static scoping• Functions are first-class entities

– They can be the values of expressions and elements of lists

– They can be assigned to variables and passed as parameters


Scheme


• Once defined in the interpreter: (gcd 25 10) 5


Scheme atoms

• Constants:– numbers, strings, #T = True, …

• Identifier names:

• Function/operator names– pre-defined & user defined


Scheme Expression vs. C

In Scheme:(+ 3 (* 4 5 ))

(and (= a b)(not (= a 0)))

(gcd 10 35)

In C:3 + 4 * 5

(a = = b) && (a != 0)

gcd(10,35)


Smalltalk Expressions vs. C

In Smalltalk:3 + 4 * 5

( = 35, “ + 4 mess. sent to 3, then * 5 mess.)

(a = = b) & (a ~= 0)

10 gcd: 35

gcd: 35 mess. sent to 10

In C:3 + 4 * 5

(a = = b) && (a != 0)

gcd(10,35)


Ruby/Python Expressions vs. C(very similar)

In Ruby/Python:3 + 4 * 5

(a = = b) && (a != 0)

gcd(10,35)

In C:3 + 4 * 5

(a = = b) && (a != 0)

gcd(10,35)


Ruby Expressions vs. CClass version

In Ruby:3.plus(4).times(5)

(= 35)

(a = = b) && (a != 0)

10.gcd(35)

In C:3 + 4 * 5

(a = = b) && (a != 0)

gcd(10,35)


Evaluation Rules for Scheme Expressions

1. Constant atoms (numbers, strings) evaluate to themselves

2. Identifiers are looked up in the current environment and replaced by the value found there (using dynamically maintained symbol table)

3. A list is evaluated by recursively evaluating each element in the list as an expression; the first expression must evaluate to a function. The function is applied to the evaluated values of the rest of the list.


Scheme Evaluation

To evaluate (* (+ 2 3)(+ 4 5))1. * is the function – must evaluate the two

expressions (+ 2 3) and (+ 4 5)2. To evaluate (+ 2 3)

1. + is the function – must evaluation the two expressions 2 and 3

2. 2 evaluates to the integer 23. 3 evaluates to the integer 34. + 2 3 = 5

3. To evaluate (+ 4 5) follow similar steps4. * 5 9 = 45

*

+ +

2 3 4 5


Scheme Conditionals

If statement:

(if ( = v 0)

u

(gcd v (remainder u v))

)

(if (= a 0) 0 (/ 1 a))

Cond statement:(cond (( = a 0) 0)

((= a 1) 1)

(else (/ 1 a))

)

Both if and cond functions usedelayed evaluation for the expressions in their bodies (i.e. (/ 1 a) is not evaluated unlessthe appropriate branch is chosen).


Smalltalk Conditionals

If statement:(v = 0) ifTrue: [^u].

^v gcd: u \\ v)

(a = 0) ifTrue: [^0].

^ 1/a

(or use ifFalse: for the

else portion above)

Cond statement:

None in Smalltalk(?)

http://c2.com/cgi/wiki?CaseStatementsConsideredHarmful

Case statements considered

harmful??


Ruby ConditionalsIf statement:if v == 0

return u

else

return

gcd(v, u % v)

end

if a == 0

return 0

else return 1/a

end

Use elsif for “else if”

Cond statement:case a

when 0

0

when 1

1

else

1/a

end


Python Conditionals

If statement:if v == 0:

return u

else:

return gcd(v, u % v)

if a == 0:

return 0

else:

return 1/a

Blocks are indented.

Use elif for “else if”

Cond statement:

Use:

if

elif

elif

...


Example of COND

(DEFINE (compare x y) (COND ((> x y) (DISPLAY “x is greater than y”)) ((< x y) (DISPLAY “y is greater than x”)) (ELSE (DISPLAY “x and y are equal”)) ) )


Example of CONDcompare: y (self > y) ifTrue: [

Transcript show: “x is greater than y”

printString.

Transcript show: cr.]

ifFalse: [

(self < y) ifTrue: [

Transcript show: “y is greater than x”

printString. Transcript show: cr.] ifFalse: [ Transcript show: “x and y are equal”

printString. Transcript show: cr.]].


Example of COND – Ruby class vers.

class Integer

def compare(y) if self > y

print “x is greater than y\n”

elsif self < y

print “y is greater than x\n”

else print “x and y are equal\n”

end

Syntax: 4 compare(5)


Example of COND – Ruby non-class vers.

def compare(x, y) if x > y

print “x is greater than y\n”

elsif x < y

print “y is greater than x\n”

else print “x and y are equal\n”

end

Syntax: compare(4,5)


Example of COND – Python

def compare(x, y): if x > y:

print “x is greater than y”

elif x < y:

print “y is greater than x”

else: print “x and y are equal\n”

Syntax: compare(4,5)

(Also – blocks are indented)


Predicate Functions

1. EQ? takes two symbolic parameters; it returns #T if both parameters are atoms and the two are the same

e.g., (EQ? 'A 'A) yields #T

(EQ? 'A '(A B)) yields ()– Note that if EQ? is called with list parameters, the result

is not reliable– EQ? does not work for numeric atoms (use = )


Predicate Functions

2. LIST? takes one parameter; it returns #T if the parameter is a list; otherwise()

3. NULL? takes one parameter; it returns #T if the parameter is the empty list; otherwise()

Note that NULL? returns #T if the parameter is()

4. Numeric Predicate Functions

=, <>, >, <, >=, <=, EVEN?, ODD?, ZERO?, NEGATIVE?


Predicate Functions - Python

1. == returns True if both parameters are the same

e.g., 'A' == 'A' yields True

'A' == 'A B' False

2. != returns True if both parameters are not the same.

e.g., 'A' != 'A' yields False

'A' != 'A B' True


Predicate Functions - Python3. type() returns the type of an object. type([1,2,3]) == list returns True

4. len([]) returns True if the parameter is the empty list; otherwise the length of the list

5. Numeric Predicate Functions

==, !=, >, <, >=, <=


let function

• Allows values to be given temporary names within an expression– (let ((a 2 ) (b 3)) ( + a b))– 5

• Semantics: Evaluate all expressions, then bind the values to the names; evaluate the body


List Comprehensions - Python

• provide a concise way to create lists without resorting to use of map(), filter() and/or lambda.– >>> freshfruit = [' banana', ' loganberry ',

'passion fruit ']– >>> [weapon.strip() for weapon in freshfruit]– ['banana', 'loganberry', 'passion fruit']


List Comprehensions - Python• >>> vec = [2, 4, 6]

– >>> [3*x for x in vec]– [6, 12, 18]– >>> [3*x for x in vec if x > 3]– [12, 18]– >>> [3*x for x in vec if x < 2]– []– >>> [[x,x**2] for x in vec]– [[2, 4], [4, 16], [6, 36]]


for statements - Python>>> # Measure some strings:

... a = ['cat', 'window', 'defenestrate']

>>> for x in a:

... print x, len(x)

cat 3

window 6

defenestrate 12


for statements - Python>>> for x in a[:]: # make a slice copy of the

entire list

... if len(x) > 6: a.insert(0, x)

...

>>> a

['defenestrate', 'cat', 'window', 'defenestrate']


range() function - Python>>> range(10)

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

>>> range(5, 10)

[5, 6, 7, 8, 9]

>>> range(0, 10, 3)

[0, 3, 6, 9]

>>> range(-10, -100, -30)

[-10, -40, -70]


range() function - Python>>> a = ['Mary', 'had', 'a', 'little', 'lamb']

>>> for i in range(len(a)):

... print i, a[i]

0 Mary

1 had

2 a

3 little

4 lamb


More looping - Python>>> knights = {'gallahad': 'the pure', 'robin':

'the brave'}

>>> for k, v in knights.iteritems():

... print k, v

...

gallahad the pure

robin the brave


More looping - Python

>>> for i, v in enumerate(['tic', 'tac', 'toe']):

... print i, v

...

0 tic

1 tac

2 toe


More looping - Python

>>> for i in reversed(xrange(1,10,2)):

... print i

...

9

7

5

3

1


More looping - Python>>> basket = ['apple', 'orange', 'apple', 'pear',

'orange', 'banana']

>>> for f in sorted(set(basket)):

... print f

apple

banana

orange

pear


Quote (‘) function• A list that is preceeded by QUOTE or a quote mark (‘) is

NOT evaluated.• QUOTE is required because the Scheme interpreter, named EVAL, always evaluates parameters to function applications before applying the function. QUOTE is used to avoid parameter evaluation when it is not appropriate– QUOTE can be abbreviated with the apostrophe prefix operator

• Can be used to provide function arguments– (myfunct ‘(a b) ‘(c d))


Output functions

• Output Utility Functions:

(DISPLAY expression)

(NEWLINE)


Output functions - Python

• printprint "Hello, World!"

print "(33 + 2) / 5 + 11.5 = ",(33 + 2) / 5 + 11.5

print "Halt!"

s = raw_input("Who Goes there? ")

print "You may pass,", s


define function

Form 1: Bind a symbol to a expression:

(define a 2)

(define emptylist ‘( ))

(define pi 3.141593)


assignment and def functions - Python


a = 2

emptylist = []

pi = 3.141593


“define” function - SmalltalkForm 1: Bind a symbol to a expression:

a := 2

mylist := OrderedCollection new: 0

mylist addAll: #(1 2 3 $a $b)

pi := 3.141593


“define” function - Ruby/Python


a = 2emptylist = []

mylist = [1,2,3,'a']

pi = 3.141593


define function

Form 2: To bind names to lambda expressions

(define (cube x) (* x (* x x )))


function name and parameters

function body – lambda expression


define function - Smalltalk

Form 2: To bind names to methods (the “first” parameter becomes the object of the message; it becomes “self” in the method definition)

cube ^(self * self * self)

gcd: v (v = 0) ifTrue: [^self]. ^(self gcd: (self \\ v))

syntax: 50 cube

syntax: 50 gcd: 2020


define function - RubyForm 2: To bind names to methods (the “first” parameter becomes the

object of the message; it becomes “self” in the method definition)

class Integer def cube return self * self * self end

def gcd(v) if v == 0 return self else return v.gcd(self % v) endend

syntax: 50.cube

syntax: 50.gcd(2020)


define function - Rubynon-class vers.

Form 2: To bind names to methods (the “first” parameter becomes the object of the message; it becomes “self” in the method definition)

def cube(x) return x * x * x end

def gcd(u, v) if v == 0 return u else return gcd(v, u % v) end

syntax: cube(50)

syntax: gcd(50, 2020)


define function - PythonForm 2: To bind names to methods (the “first” parameter becomes the

object of the message; it becomes “self” in the method definition)

def cube(x): return x * x * x

def gcd(u, v): if v == 0: return u else: return gcd(v, u % v) Note: blocks are indented

syntax: cube(50)

syntax: gcd(50, 2020)


Function Evaluation

• Evaluation process (for normal functions): 1. Parameters are evaluated, in no particular order

2. The values of the parameters are substituted into the function body

3. The function body is evaluated

4. The value of the last expression in the body is the value of the function

(Special forms use a different evaluation process)


Data Structures in Scheme: Box Notation for Lists

first element (car) rest of list (cdr)

1

List manipulation is typically written using ‘car’ and ‘cdr’


Data Structures in Scheme

1 2 3 (1,2,3)

c

da

b((a b) c (d))


Basic List Manipulation

• (car L) – returns the first element of L

• (cdr L) – returns L minus the first element

(car ‘(1 2 3)) = 1

(car ‘((a b)(c d))) = (a b)

(cdr ‘(1 2 3)) = (2 3)

(cdr ‘((a b)(c d))) = ((c d))


Basic List Manipulation - Python

• L[0] – returns the first element of L

• L[1:] – returns L minus the first element

x, y = [1,2,3], [['a','b'], ['c','d']]x[0] = 1

y[0] = ['a', 'b']

x[1:] = [2, 3]

y[1:] = [['c', 'd']]


Basic List Manipulation Smalltalk

• L first – returns the first element of L

• L allButFirst – returns L minus the first element (Squeak), in gst use L copyFrom:2

#(1 2 3) first -> 1

#(($a $b)($c $d))) first -> ($a $b)

#(1 2 3) copyFrom: 2 -> (2 3)

#(($a $b)($c $d))) copyFrom:2 ->(($c $d))


Basic List Manipulation Ruby

• L.first – returns the first element of L

• L.slice(1..m) – returns L minus the first element

[1, 2, 3].first -> 1

[['a', 'b'] ['c', 'd']].first ->[“a”,”b”]

#(1 2 3) copyFrom: 2 -> (2 3)

#(($a $b)($c $d))) copyFrom:2 ->(($c $d))


Basic List Manipulation

• (list e1 … en) – return the list created from the individual elements

• (cons e L) – returns the list created by adding expression e to the beginning of list L

(list 2 3 4) = (2 3 4)

(list ‘(a b) x ‘(c d) ) = ((a b)x(c d))

(cons 2 ‘(3 4)) = (2 3 4)

(cons ‘((a b)) ‘(c)) = (((a b)) c)



>>> a = ['spam', 'eggs', 100, 1234]>>> a['spam', 'eggs', 100, 1234]>>> a[0]

'spam'

>>> a[3]

1234

>>> a[-2]

100

>>> a[1:-1]

['eggs', 100]



>>> a[:2] + ['bacon', 2*2]

['spam', 'eggs', 'bacon', 4]

>>> 3*a[:3] + ['Boe!']

['spam', 'eggs', 100, 'spam', 'eggs', 100, 'spam', 'eggs', 100, 'Boe!']

List items can be changed:>>> a

['spam', 'eggs', 100, 1234]

>>> a[2] = a[2] + 23

>>> a

['spam', 'eggs', 123, 1234]



It is possible to nest lists (create lists containing other lists), for example:

>>> q = [2, 3]

>>> p = [1, q, 4]

>>> len(p)

3

>>> p[1]

[2, 3]

>>> p[1][0]

2



>>> p[1].append('xtra')

>>> p

[1, [2, 3, 'xtra'], 4]

>>> q

[2, 3, 'xtra']

Note that in the last example, p[1] and q really refer to the same object!


Example Functions

1. member - takes an atom and a simple list; returns #T if the atom is in the list; () otherwise

(DEFINE (member atm lis) (COND ((NULL? lis) '()) ((EQ? atm (CAR lis)) #T) ((ELSE (member atm (CDR lis))) ))


Example Functions2. equalsimp - takes two simple lists as parameters;

returns #T if the two simple lists are equal; () otherwise

(DEFINE (equalsimp lis1 lis2) (COND ((NULL? lis1) (NULL? lis2)) ((NULL? lis2) '()) ((EQ? (CAR lis1) (CAR lis2)) (equalsimp(CDR lis1)(CDR lis2))) (ELSE '())))


Example Functions3. equal - takes two general lists as parameters; returns #T if the two

lists are equal; ()otherwise(DEFINE (equal lis1 lis2) (COND ((NOT (LIST? lis1))(EQ? lis1 lis2)) ((NOT (LIST? lis2)) '()) ((NULL? lis1) (NULL? lis2)) ((NULL? lis2) '()) ((equal (CAR lis1) (CAR lis2)) (equal (CDR lis1) (CDR lis2))) (ELSE '())))


Example Functions

(define (count L)

(if (null? L) 0

(+ 1 (count (cdr L)))

)

)

(count ‘( a b c d)) =

(+ 1 (count ‘(b c d))) =

(+ 1 (+ 1(count ‘(c d))))

(+ 1 (+ 1 (+ 1 (count ‘(d)))))=

(+ 1 (+ 1 (+ 1 (+ 1 (count ‘())))))=

(+ 1 (+ 1 (+ 1 (+ 1 0))))= 4


Scheme Functions

Now define(define (count1 L) ??

)

so that (count1 ‘(a (b c d) e)) = 5


Scheme Functions

This function counts the individual elements:

(define (count1 L)

(cond ( (null? L) 0 )

( (list? (car L))

(+ (count1 (car L))(count1 (cdr L))))

(else (+ 1 (count (cdr L))))

)

)

so that (count1 ‘(a (b c d) e)) = 5


Example Functions

(define (append L M)

(if (null? L) M

(cons (car L)(append(cdr L) M))

)

)

(append ‘(a b) ‘(c d)) = (a b c d)


How does append do its job?


(if (null? L) M

(cons (car L)(append(cdr L) M))))

(append ‘(a b) ‘(c d)) =

(cons a (append ‘(b) ‘(c d))) =




(if (null? L) M




(cons a (cons b (append ‘() ‘(c d)))) =



(define (append L M) (if (null? L) M (cons (car L)(append(cdr L) M))))

(append ‘(a b) ‘(c d)) =(cons a (append ‘(b) ‘(c d))) =

(cons a (cons b (append ‘() ‘(c d)))) =(cons a (cons b ‘(c d))) =




(if (null? L) M





(cons a (cons b ‘(c d))) =

(cons a ‘(b c d)) =




(if (null? L) M





(cons a (cons b ‘(c d))) =

(cons a ‘(b c d)) =

(a b c d)


Reverse

Write a function that takes a list of elements and reverses it:

(reverse ‘(1 2 3 4)) = (4 3 2 1)


Reverse

(define (reverse L)

(if (null? L) ‘()

(append (reverse (cdr L))(list (car L)))

)

)


Selection Sort in Scheme

Let’s define a few useful functions first:(DEFINE (findsmallest lis small) (COND ((NULL? lis) small) ((< (CAR lis) small) (findsmallest (CDR lis) (CAR lis))) (ELSE (findsmallest (CDR lis) small)) ) )



(DEFINE (remove lis item) (COND ((NULL? lis) ‘() ) ((= (CAR lis) item) lis) (ELSE (CONS (CAR lis) (remove (CDR lis)

item))) ))

Cautious programming!

Assuming integers



(DEFINE (selectionsort lis)

(IF (NULL? lis) lis

(LET ((s (findsmallest (CDR lis) (CAR lis))))

(CONS s (selectionsort (remove lis s)) )

)

)


Higher order functions

• Def: A higher-order function, or functional form, is one that either takes functions as parameters, yields a function as its result, or both

• Mapcar

• Eval


Higher-Order Functions: mapcar

Apply to All - mapcar - Applies the given function to all elements of the

given list; result is a list of the results

(DEFINE (mapcar fun lis) (COND ((NULL? lis) '()) (ELSE (CONS (fun (CAR lis)) (mapcar fun (CDR lis)))) ))


Higher-Order Functions: mapcar

• Using mapcar:(mapcar (LAMBDA (num) (* num num num)) ‘(3 4 2 6))

returns (27 64 8 216)


Higher Order Functions: EVAL

• It is possible in Scheme to define a function that builds Scheme code and requests its interpretation

• This is possible because the interpreter is a user-available function, EVAL


Using EVAL for adding a List of Numbers

Suppose we have a list of numbers that must be added:(DEFINE (adder lis) (COND((NULL? lis) 0) (ELSE (+ (CAR lis) (adder(CDR lis ))))))

Using Eval((DEFINE (adder lis) (COND ((NULL? lis) 0) (ELSE (EVAL (CONS '+ lis)))))

(adder ‘(3 4 5 6 6))Returns 24


Other Features of Scheme• Scheme includes some imperative features:

1. SET! binds or rebinds a value to a name

2. SET-CAR! replaces the car of a list

3. SET-CDR! replaces the cdr part of a list


COMMON LISP

• A combination of many of the features of the popular dialects of LISP around in the early 1980s

• A large and complex language – the opposite of Scheme


COMMON LISP

• Includes:– records

– arrays

– complex numbers

– character strings

– powerful I/O capabilities

– packages with access control

– imperative features like those of Scheme

– iterative control statements


ML

• A static-scoped functional language with syntax that is closer to Pascal than to LISP

• Uses type declarations, but also does type inferencing to determine the types of undeclared variables

• It is strongly typed (whereas Scheme is essentially typeless) and has no type coercions

• Includes exception handling and a module facility for implementing abstract data types


ML

• Includes lists and list operations

• The val statement binds a name to a value (similar to DEFINE in Scheme)

• Function declaration form:

fun function_name (formal_parameters) =

function_body_expression;

e.g.,

fun cube (x : int) = x * x * x;


Haskell

• Similar to ML (syntax, static scoped, strongly typed, type inferencing)

• Different from ML (and most other functional languages) in that it is purely functional (e.g., no variables, no assignment statements, and no side effects of any kind)


Haskell

• Most Important Features– Uses lazy evaluation (evaluate no

subexpression until the value is needed)– Has list comprehensions, which allow it to deal

with infinite lists


Haskell Examples

1. Fibonacci numbers (illustrates function definitions with different parameter forms)

fib 0 = 1

fib 1 = 1

fib (n + 2) = fib (n + 1)

+ fib n


Haskell Examples

2. Factorial (illustrates guards)

fact n

| n == 0 = 1

| n > 0 = n * fact (n - 1)

The special word otherwise can appear as a guard


Haskell Examples3. List operations

– List notation: Put elements in brackets

e.g., directions = [“north”, “south”, “east”, “west”]

– Length: #

e.g., #directions is 4– Arithmetic series with the .. operator

e.g., [2, 4..10] is [2, 4, 6, 8, 10]


Haskell Examples

3. List operations (cont)– Catenation is with ++

e.g., [1, 3] ++ [5, 7] results in

[1, 3, 5, 7]– CONS, CAR, CDR via the colon operator (as in Prolog)

e.g., 1:[3, 5, 7] results in

[1, 3, 5, 7]


Haskell Examples

• Quicksort:

sort [] = []

sort (a:x) = sort [b | b ← x; b <= a]

++ [a] ++

sort [b | b ← x; b > a]


Applications of Functional Languages

• LISP is used for artificial intelligence– Knowledge representation– Machine learning– Natural language processing– Modeling of speech and vision

• Scheme is used to teach introductory programming at a significant number of universities


Comparing Functional and Imperative Languages

• Imperative Languages:– Efficient execution– Complex semantics– Complex syntax– Concurrency is programmer designed

• Functional Languages:– Simple semantics– Simple syntax– Inefficient execution– Programs can automatically be made concurrent

comparative programming languages functional languages comparison: scheme, smalltalk, python, ruby

Documents

interpreted language

scripting language

portable smalltalk

multiparadigm language

languages perl heritage

development of languages

imperative programmingin

imperative languagein