1

Lisp and Functional Languages

• Functional forms• Referential transparency• Function construction• Function composition• Mapping functions• Designing functional languages• Other functional language: Scheme, ML, APL,Haskell• Applications of Functional Languages• Functional and Imperative Language – a comparison• Reference: Sebesta Chapter 15

2Functional Programming Language Design

• The objective of the design of a FPL is to create and use pure functions to the greatest extent possible

• Process of computation is fundamentally different– In an imperative language, operations are executed 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 a purely FPL variables are not necessary– as is the case in mathematics

• Results of each function application are passed as input to other functions– or are the final result of all computations

3Functional Forms

• Definition: – A higher-order function, or functional form, either

1. takes function(s) as parameters

2. or yields a function as its result,

3. or both – takes and returns functions

FunctionParameters

(possibly functions)Return Value

(possibly a Function)

4Viewing Information and Using Functions

> (function write-sentence) ; returns defn

#<Interpreted Function WRITE-SENTENCE>

> (setq L1 (list "dogs" "cats" "rats" "gerbils"))

("dogs" "cats" "rats" "gerbils")

> L1

("dogs" " cats" "rats" "gerbils" )

> (setq L2 ; pass function as parameter

(sort L1 (function string<)))

("cats" "dogs" "gerbils" "rats")

> L2

("cats" "dogs" "gerbils" "rats")

5Function Construction

• A functional form that– takes a list of functions as parameters, and – yields a list of the results of

applying each parameter function to a parameter

Form: [f, g]

means [f, g] (x) ≡ (f (x), g (x))

For f (x) ≡ x * x * x and g (x) ≡ x + 3,

[f, g] (4) yields (f (4), g (4)) = (64, 7)

• Application of multiple functions (passed as parameters) to the same piece of data

6Function Construction Examples> (defun cube (x) (* x x x))

CUBE

> (defun add3 (y) (+ y 3))

ADD3

> (defun myfun (fn1 fn2 data)

(list (funcall fn1 data)

(funcall fn2 data)))

MYFUN

> (myfun (function cube) (function add3) 4)

(64 7)

> (myfun #'cube #'add3 4) ; #'… same as (function …)

(64 7)

7Function Composition

• A functional form that– takes two functions as parameters and– yields a function containing the first actual parameter function

applied to the result of application of the second form

Form: f ° g

means f ° g (x) ≡ f ( g (x))

For f (x) ≡ x * x * x and g (x) ≡ x + 3,

f ° g (x) yields (x + 3) * (x + 3) * (x + 3)

• Continuous application of multiple functions (passed as parameters). Each function is applied to the result of applying the preceding function(s)

8Function Composition Examples> (defun cube (x) (* x x x))

CUBE

> (defun add3 (y) (+ y 3))

ADD3

> (defun myfun (fn1 fn2 data)

(funcall fn1

(funcall fn2 data)))

MYFUN

> (myfun (function cube) (function add3) 4)

343

> (myfun #'cube #'add3 4) ; #'… same as (function …)

343

9Apply-to-all (Mapping) Functions

• A functional form that– takes a single function as a parameter– yields a list of values obtained by applying the given function to

each element of a list of parameters

Form: α

means α (f, (x1, … , xn)) ≡ (f (x1), … , f (xn))

For h (x) ≡ x * x * x

α (h, (3, 2, 4)) yields (27, 8, 64)

• Application of one function to multiple pieces of data

10mapcar Examples> (defun mydouble (num)

"returns 2 times its argument" (* 2 num))

MYDOUBLE

> (mapcar (function mydouble) (list 1 2 3))

(2 4 6)

> (mapcar #'+ (list 1 2 3)

(list 10 20 30))

(11 22 33)

11Lisp – The First Functional Language

• John McCarthy• Stanford since 1953

– MIT & Dartmouth 1954-1962

• Invented Lisp – 1958• Pioneered logical and commonsense

reasoning• Lisp’s 20th birthday article (from 1980)

– www2.hawaii.edu/~janst/313/lisp/20th.pdf

• Web:– http://www.formal.stanford.edu/jmc/

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John McCarthy, professor emeritus of computer science, Stanford Univ., helped to invent the field of artificial intelligence. McCarthy received the Benjamin Franklin Medal in Computer and Cognitive Science on April 24, 2003.

13Lisp Hardware

• Problem– Limited processing power in 70s and 80s – Slow execution of Lisp programs

• Solution– Specialized hardware to improve efficiency of execution and

garbage collection– Different from von Neumann machine

• Symbolics Lisp Machine – mid 1980s– http://www.sts.tu-harburg.de/~r.f.moeller/symbolics-info/symbolics.html

• Software - OS was written in Lisp!• Other lisp machines by

– LMI (Lisp Machine Inc.)– Texas Instruments Explorer

14Symbolics Lisp Machine Family

15Optimizations in Lisp Machines

• Hardware Type Checking– Special type bits let a value’s type be checked

efficiently at run-time

• Hardware Garbage Collection– Special "gc" bits make garbage collection efficient

• Fast Function Calls• Efficient Representation of Lists• System Software • Integrated Programming Environments

16Scheme and Common Lisp

• Scheme is a dialect of LISP (mid-1970s) – Designed to be a cleaner and simpler version of LISP– Uses only static scoping– Functions are first-class entities

• Can be the values of expressions and elements of lists• Can be assigned to variables and passed as parameters

• Scheme has syntax very similar to Lisp• We learn Common Lisp

– most used and practical

• Sebesta text has Scheme examples

17More Functional Languages

• APL – A Programming Language– Kenneth Iverson at IBM– About 1960 (book released in 1962)– Not related to ALGOL or other early languages– Dynamic typing and dynamic storage allocation– Large collection of operators– First to include matrix operations– Powerful capabilities– Poor readability– Still in limited use

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APL Program Example

• This line of code calculates the prime numbers from 2 to the starting value of R, in this example 20.

• the "iota function" of R fills a vector (and that will be R again) with numbers from 1 to the value of the variable (20 in this example), the first element is dropped (that is the 1); so to the right of the "/" there will be 2 3 4 5 ... 18 19 20

• the "small.circle-dot-multiply" defines an outer product so all elements of R are multiplied by all elements of R giving a matrix; check whether elements of R are in the matrix and make a vector containing "1"-s at the place where that is true and "0"-s where that is not true

• inverse that vector and use it to grab the elements from R using the "over" function

• http://www.thocp.net/software/languages/apl.htm

19ML (Meta Language)

• Robert Milner, University of Edinburgh,1980s• Designed for program verification• A statically scoped functional language • Pascal-like syntax• Strongly typed, no type coercions• Uses type declarations as well as type inferencing to

determine the type of a variable• “Variables” are only bound once, they cannot change

value after binding

20ML

• List functions: hd (head or car), tl (tail or cdr)• The val statement binds a name to a value

– similar to setq in Lisp

• Function declaration form:

fun <function-name> (<formal-parameters>) =

<function-body-expression>;

e.g.,

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

21Haskell

• Group formed at 1987 FPL meeting• Named after logician Haskell B. Curry• Version 1 – 1990

– report centered at the University of Glasgow, Scotland– Also Yale, MIT, U of Wellington AU, Cambridge, Chalmers SE, …

• Syntax similar to ML• Static scoping• Strongly typed, type inferencing• Purely functional

– E.g., no variables, no assignment statements• and no side effects of any kind!

– unlike most other functional languages!

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Haskell Features• Most Important Features

– Lazy evaluation• evaluate no sub-expression until its value is needed

– "List comprehensions"• allow it to deal with infinite lists

23Haskell Example: Fibonacci

• Fibonacci numbers – illustrates function definitions

fib 0 = 1

fib 1 = 1

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

+ fib n

24Haskell Example: Factorial

• Factorial – illustrates guards

fact n

| n == 0 = 1

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

• Special word otherwise can be a guard

25Applications of Functional Languages

• APL is used primarily for throw-away programs (why?)• LISP is used for artificial intelligence research and

applications– Knowledge representation

– Machine learning

– Natural language processing

– Modeling of speech and vision

• AI techniques in Common Lisp power Orbitz• Google sponsors summer of code, several Lisp projects• Scheme is

– Used to teach introductory programming (MIT, Stanford)

– Used in the Final Fantasy film to automate the generation of frames (Square USA)

– Used in courses at UH on game programming!

26Functional vs. Imperative Languages

• Imperative Languages:– Complex syntax

– Complex semantics

– Closer to von Neumann hardware – machine language

– Moderate - efficient execution speed

– Concurrency is programmer designed

• Functional Languages:– Simple syntax

– Simple semantics

– Slower execution unless compiled

– More abstract/higher level – shorter programs, more flexibility

– Faster development – shorter design & test cycle

– Programs can automatically be made concurrent

– More flexible - easily extend the language, creating new ones