concepts from functional programming languages

TIVDM2 Functional Programming Language Concepts

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Concepts from Functional Programming Languages

Peter Gorm Larsen


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Agenda

Introduction to the Functional Programming Paradigm• The notion of higher order functions• Polymorphic examples of standard higher order

functions


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Introduction to FP

• The design of the imperative languages is based directly on the von Neumann architecture• Efficiency is the primary concern, rather than the

suitability of the language for software development• The design of the functional languages is based on

mathematical functions• A solid theoretical basis that is also closer to the

user, but relatively unconcerned with the architecture of the machines on which programs will run


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Principles of FP

• Treats computation as evaluation of mathematical functions (and avoids state)

• Data and programs are represented in the same way• Functions as first-class values

– Higher-order functions: functions that operate on, or create, other functions

– Functions as components of data structures• Lambda calculus provides a theoretical framework for

describing functions and their evaluation• It is a mathematical abstraction rather than an imperative

programming language


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History

• lambda calculus (Church, 1932)• simply typed lambda calculus (Church, 1940)• lambda calculus as prog. lang. (McCarthy(?), 1960,

Landin 1965)• polymorphic types (Girard, Reynolds, early 70s)• algebraic types ( Burstall & Landin, 1969)• type inference (Hindley, 1969, Milner, mid 70s)• lazy evaluation (Wadsworth, early 70s)• Equational definitions Miranda 80s• Type classes Haskell 1990s• Microsoft F# etc 2000s


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Varieties of FP languages

• Typed (ML, Haskell) vs untyped (Scheme, Erlang)• Pure vs Impure

• impure have state and imperative features

• pure have no side effects, “referential transparency”

• Strict vs Lazy evaluation


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Declarative style of programming

• Declarative Style of programming - emphasis is placed on describing what a program should do rather than prescribing how it should do it.

• Functional programming - good illustration of the declarative style of programming.

• A program is viewed as a function from input to output.• Logic programming – another paradigm• A program is viewed as a collection of logical rules and

facts (a knowledge-based system). Using logical reasoning, the computer system can derive new facts from existing ones.


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Functional style of programming

• A computing system is viewed as a function which takes input and delivers output.

• The function transforms the input into output .• Functions are the basic building blocks from which

programs are constructed.• The definition of each function specifies what the

function does.• It describes the relationship between the input and the

output of the function.


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Agenda

Introduction to the Functional Programming Paradigm The notion of higher order functions• Polymorphic examples of standard higher order

functions


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First-Class Functions

Data values are first-class if they can• be assigned to local variables• be components of data structures• be passed as arguments to functions• be returned from functions• be created at run-time


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Higher-order Functions

• Every function has an order:• A function that does not take any functions as parameters, and

does not return a function value, has order 1• A function that takes a function as a parameter or returns a function

value has order n+1, where n is the order of its highest-order parameter or returned value

• A small example:Twice: (int -> int) * int -> intTwice(f,x) == f( f (x))

• OrTwiceCur: (int -> int)-> int -> intTwiceCur(f)(x) == f( f (x))


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Functions in Programming Languages

• How functions are treated by programming languages?

Language passed as arguments

returned from functions

nested scope

Java No No No

C Yes Yes No

C++ Yes Yes No

Pascal Yes No Yes

Modula-3 Yes No Yes

Scheme Yes Yes Yes

ML Yes Yes Yes


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Nested Functions and Closures

• Return a function from function call

function f(x) {

var y = x;

return function (z){y += z; return y;}

}

var h = f(5);

h(3);• In order to handle this one needs to introduce closures• A closure is a function that captures the bindings of free variables in

its lexical context.


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Agenda

Introduction to the Functional Programming Paradigm The notion of higher order functions Polymorphic examples of standard higher order

functions


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Predefined Higher-Order Functions in Functional Languages

• We will use three important predefined higher-order functions:• map• filter• foldr• foldl

• Actually, foldr and foldl are very similar, as you might guess from the names


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The Map Function

• Map applies a function to every element of a list:

Map[@A,@B]: (@A -> @B) -> seq of @A -> seq of @B

Map(f)(list) ==

[f(list(i)) | i in set inds list]


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The Filter Function

• Filter selects every element that satisfies a predicate:

Filter[@A]: (@A -> bool) -> seq of @A -> seq of @A

Filter(pred)(list) ==

[list(i) | i in set inds list & pred(list(i))]


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The FoldR Function

• Folds all elements in a list from the right into one value (a simple pattern of recursion):

FoldR[@A,@B]: (@A * @B -> @B) -> @B -> seq of @A -> @BFoldR(f)(neutral)(list) == if list = [] then neutral else f(hd list,FoldR(f)(neutral)(tl list))

Example usage:Sum = FoldR(+)(0)Product = FoldR(*)(1)Or = FoldR(or)(false)And = FoldR(and)(true)


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Summary

• What have I presented today?• Introduction to the Functional Programming Paradigm

• The notion of higher order functions

• Polymorphic examples of standard higher order functions

• What do you need to do now?• Complete your distributed real time model for your project


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Quote of the day

Program designers have a tendency to think of the users as idiots who need to be controlled. They should rather think of their program as a servant, whose master, the user, should be able to control it. If

designers and programmers think about the apparent mental qualities that their programs will have, they'll create programs that are easier and pleasanter —

more humane — to deal with.

John McCarthy

concepts from functional programming languages

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