Introduction to Functional Programming (1)

Introduction First Steps

Introduction to Functional Programming (1) – Language for Calculational Programming –

Zhenjiang Hu National Institute of Informatics Email: [email protected] URL: http://research.nii.ac.jp/˜ hu

Sokendai, 2013

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

The Software Crisis

How can we cope with the size and complexity of modern computer programs? How can we reduce the time and cost of program development? How can we increase our confidence that the finished programs work correctly?

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

Language-based Approach One approach to the software crisis is to design a good programming language that: Allow programs to be written clearly, concisely, and at a high-level of abstraction; Support reusable software components; Encourage the use of formal verification; Permit rapid prototyping; Provide powerful problem-solving tools; Suitable to be optimized, procedurally and algorithmically.

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

Language-based Approach One approach to the software crisis is to design a good programming language that: Allow programs to be written clearly, concisely, and at a high-level of abstraction; Support reusable software components; Encourage the use of formal verification; Permit rapid prototyping; Provide powerful problem-solving tools; Suitable to be optimized, procedurally and algorithmically. ⇑ Functional languages provide an elegant framework to address these goals. Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

What is a Functional Language?

Functional programming is style of programming in which the basic method of computation is the application of functions to arguments;

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

What is a Functional Language?

Functional programming is style of programming in which the basic method of computation is the application of functions to arguments; A functional language is one that supports and encourages the functional style.

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

An Example

Summing the integers from 1 to 10. In Java: Computation method is variable assignment total = 0; for (i = 1; i ≤ 10; i++) total = total + i;

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

An Example

Summing the integers from 1 to 10. In Java: Computation method is variable assignment total = 0; for (i = 1; i ≤ 10; i++) total = total + i;

In Haskell: Computation method is function application sum [1..10]

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

Historical Background 1930s Alonzo Church develops the lambda calculus, a simple but powerful theory of functions.

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

Historical Background 1930s Alonzo Church develops the lambda calculus, a simple but powerful theory of functions. 1950s John McCarthy develops Lisp, the first functional language, with some influences from the lambda calculus, but retaining variable assignments.

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

Historical Background 1930s Alonzo Church develops the lambda calculus, a simple but powerful theory of functions. 1950s John McCarthy develops Lisp, the first functional language, with some influences from the lambda calculus, but retaining variable assignments. 1960s Peter Landin develops ISWIM, the first pure functional language, based strongly on the lambda calculus, with no assignments.

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

Historical Background 1930s Alonzo Church develops the lambda calculus, a simple but powerful theory of functions. 1950s John McCarthy develops Lisp, the first functional language, with some influences from the lambda calculus, but retaining variable assignments. 1960s Peter Landin develops ISWIM, the first pure functional language, based strongly on the lambda calculus, with no assignments. 1970s John Backus develops FP, a functional language that emphasizes higher-order functions and reasoning about programs.

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

Historical Background 1930s Alonzo Church develops the lambda calculus, a simple but powerful theory of functions. 1950s John McCarthy develops Lisp, the first functional language, with some influences from the lambda calculus, but retaining variable assignments. 1960s Peter Landin develops ISWIM, the first pure functional language, based strongly on the lambda calculus, with no assignments. 1970s John Backus develops FP, a functional language that emphasizes higher-order functions and reasoning about programs. 1970s Robin Milner and others develop ML, the first modern functional language, which introduced type inference and polymorphic types.

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

Historical Background 1930s Alonzo Church develops the lambda calculus, a simple but powerful theory of functions. 1950s John McCarthy develops Lisp, the first functional language, with some influences from the lambda calculus, but retaining variable assignments. 1960s Peter Landin develops ISWIM, the first pure functional language, based strongly on the lambda calculus, with no assignments. 1970s John Backus develops FP, a functional language that emphasizes higher-order functions and reasoning about programs. 1970s Robin Milner and others develop ML, the first modern functional language, which introduced type inference and polymorphic types. 1970s-80s David Turner develops a number of lazy functional languages, culminating in the Miranda system.

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

Historical Background 1930s Alonzo Church develops the lambda calculus, a simple but powerful theory of functions. 1950s John McCarthy develops Lisp, the first functional language, with some influences from the lambda calculus, but retaining variable assignments. 1960s Peter Landin develops ISWIM, the first pure functional language, based strongly on the lambda calculus, with no assignments. 1970s John Backus develops FP, a functional language that emphasizes higher-order functions and reasoning about programs. 1970s Robin Milner and others develop ML, the first modern functional language, which introduced type inference and polymorphic types. 1970s-80s David Turner develops a number of lazy functional languages, culminating in the Miranda system. 1987 An international committee of researchers initiates the development of Haskell, a standard lazy pure functional language.

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

A Taste of Haskell

Can you guess what the following Haskell program does? f [] = [] f (x:xs) = f ys ++ [x] ++ y zs where ys = [a | a

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

The Prelude> means that the GHCi system is ready to evaluate an expression (like a calculator). Expression Evaluation Prelude> 2+3*4 14 Prelude> (2+3)*4 20 Prelude> sqrt (3^2 + 4^2) 5.0

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

The Standard Prelude The library file Prelude.hs provides a large number of standard functions. In addition to the familiar numeric functions such as + and ∗, the library also provides many useful functions on lists. Prelude> head [1,2,3,4,5] 1 Prelude> tail [1,2,3,4,5] [2,3,4,5] Prelude> take 3 [1,2,3,4,5] [1,2,3] Prelude> drop 3 [1,2,3,4,5] [4,5] Prelude> length [1,2,3,4,5] 5 Prelude> sum [1,2,3,4,5] 15 Prelude> [1,2,3,4,5] ++ [6,7,8] [1,2,3,4,5,6,7,8] Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

Function Application In mathematics, function application is denoted using parentheses, and multiplication is often denoted using juxtaposition or space. f(a,b) + c d In Haskell, function application is denoted using space, and multiplication is denoted using *. f a b + c*d And function application has higher priority than all other operators. f a + b = (f a) + b

Zhenjiang Hu

Introduction to Functional Programming (1)

Introduction First Steps

Haskell Scripts – Defining New Functions New functions are defined within a script, a text file comprising a sequence of definitions. test.hs double x = x + x quadruple x = double (double x) GHCi: Load New Functions Prelude> :load test.hs [1 of 1] Compiling Main Ok, modules loaded: Main. *Main> quadruple 10 40

Zhenjiang Hu

( test.hs, interpreted )

Introduction to Functional Programming (1)

Introduction First Steps

Exercise 1-1 Show how the following two functions can be defined using the functions introduced in this lecture, and test them with GHCi. last: selects the last element of a list. average: computes the average of all numbers in a list.

Zhenjiang Hu

Introduction to Functional Programming (1)