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Programming Languagesand Paradigms

Functional Programming

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Functional Programming Programs are (mathematical) functions Program execution corresponds to the

application of one or more functions

Program units: functions and values Pure functional programming:

no assignment

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Function Mapping from a domain set to a

range set Function definition: signature and

mapping rule Signature: name, domain, range

(e.g., square: integer integer) Mapping rule: specifies range value

for each domain value(e.g., square(n) n x n)

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Function Application Function application

Element of the domain is specified Element replaces the parameter in the

definition Other necessary function applications are

carried out Yields an associated element in the range

Example: square(2) yields the value 4

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Variables inFunctional Programs Concept of a variable in functional

programs is different from a programming variable

In a function definition, a variable stands for any member of the domain set

During function application, a variable is bound to one specific value(and it never changes thereafter)

Sometimes better to refer to variables as names

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Values Traditionally, functional languages

would support values for primitive types (e.g., numbers and strings) and a single high-level data structure type

such as a list Values are bound to variables or

names In fact, functions themselves are values

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Components of a Functional Programming Language A set of data objects

Numbers, lists, etc. A set of built-in functions

Primarily for manipulating data objects

A set of functional forms High-order functions For building new functions

(e.g., defun in LISP)

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Lambda Calculus A model of computation using

functions Expressions of lambda calculus

Identifiers (names) or constants( e.g., y or 2 )

Function definition( e.g., x.x*x )

Function application( e.g. (x.x*x 3) )

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Expression Evaluation Outermost evaluation

Replace arguments before evaluating them

Innermost evaluation Evaluate arguments first before

substituting

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Decision in Functional Programming Can view “if” as a function with

three arguments Condition Then-result Else-result

Example: abs(x) = if(x<0, -x, x)|x| = -x if x < 0

x otherwise

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“Iteration” in Functional Programming Use recursion to carry out the

equivalent of an iterative process Recurrence relations are common in

mathematical function specification Example: fac(n) = if(n=0,1,n*fac(n-

1))

n! = 1 if n = 0n * (n-1)! otherwise

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Functional Programming Environments Environments are often

interpreters that are interactive Commands from user are

expressions that are repeatedly evaluated

Set of bindings is maintained and updated on each command

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Sample Languages LISP: list processing APL: assignment-oriented but

applicative ML: strongly-typed functional

programming Haskell: outermost evaluation

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Summary and Final Points Functional programming puts functions

at the forefront of computation Elegance of mathematical functions

make verifiability/provability easier (versus iteration, for example)

Implementations are generally inefficient (mathematics and computer architecture not exactly compatible)

Hybrid languages are becoming more popular