Functional programming{week 12}

The College of Saint RoseCIS 433 – Programming LanguagesDavid Goldschmidt, Ph.D.

from Concepts of Programming Languages, 9th edition by Robert W. Sebesta, Addison-Wesley, 2010, ISBN 0-13-607347-6

Von Neumann architecture Imperative Languages

Data and programs are both stored in memory

Variables mimic memory Assignment statements Arithmetic operations Iterative repetition Control structures etc.

History

Functional language design The design of imperative languages is based

directly on the von Neumann architecture Efficiency is a primary concern Variables are abstractions of memory locations

The design of functional languages is based directly on mathematical functions A solid theoretical basis more natural to users Minimally concerned with machine architecture

Mathematical functions (i) A mathematical function is a

mapping ofmembers from one set (the domain) tomembers of another set (the range) Parameters represent any

member of the domain Once set, a parameter is

fixed to represent exactly one value during the evaluation of the mapping expression

# Pythondef cube( x ): return x * x * x

Mathematical functions (ii) Mathematical functions define values

whereas typical programming language functions produce values

cube(x) ≡ x * x * x, where x is a real number

function namefunction parameter(s)

“is defined as” mapping expression

Lambda expressions (i) A lambda expression specifies the

parameters and mapping expression of a function Essentially a nameless function

During evaluation, parameter x is bound to a particular member of the domain

(x)x * x * x

function parameter(s)

# Pythonlambda x:x*x*x

mapping expression

Lambda expressions (ii)

The lambda expression is the function itself Apply the expression to one or more

parameters((x)x * x * x)(4)

# Python(lambda x:x*x*x)(4)

((x,y)x * y)(8,7)

# Python(lambda x,y:x*y)(8,7)

Functional forms

A functional form is a higher-order function that either takes functions as parameters oryields functions as its results (or both) Example: the apply-to-all (α) functional

form

cube(x) ≡ x * x * x, where x is a real number

α( cube, (3, 5, 2) ) ===> (27, 125, 8)

# Pythonmap( cube, [3, 5, 2] )map( math.sqrt, [2, 3, 4, 5] )map( lambda x,y:x+y, [3, 4, 5], [6, 7, 8] )

Functional languages (i)

In imperative languages,operations are performedand results are stored invariables for later use Management of variables is a constant

concern and source of complexity (and bugs!)

Functions in imperative languagehave side effects

Functional languages (ii)

Functional programming languages mimicmathematical functions and mappings to the extent possible The basic process of computation

is fundamentally different than inimperative languages

No flow of control No variables

Who needs variables?

Write a program to calculate n-factorial The input argument n is your only

variablefactorial(n) ≡1 if n = 0

n x factorial(n – 1) if n > 0{

LISP (LISt Processing)

LISP is a functional language designedat MIT by John McCarthy in 1958 Research in artificial intelligence

required a language to:▪ Process data in dynamic lists▪ Support symbolic computation

(rather than numeric)

LISP data structures

LISP has two data structures: Atom: either a symbol or a numeric

literal List: a sequence of atoms and/or lists(A B C D)

(A (B C) D (E (F G)))NIL

Scheme

Scheme was developed at MIT in the 1970s to be a cleaner and simpler version of LISP Scheme uses an interpreter and built-in

IDE Literals evaluate to themselves

Scheme is available as Racketat http://racket-lang.org

What next?

Read and study Chapter 15

Download Racket Do Exercises at the

end of Chapter 15