Download 4.6 Lisp - University of Hawaii

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
1
Functional 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
2
Functional 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
Parameters
(possibly functions)
Function
Return Value
(possibly a Function)
3
Viewing 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")
4
Function 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
5
Function 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)
6
Function 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)
7
Function 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
8
Apply-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
9
mapcar 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)
10
Lisp – 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/
11
12
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.
Lisp 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
13
Symbolics Lisp Machine Family
14
Optimizations 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
15
Scheme 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
16
More 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
17
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
18
ML (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
19
ML
• 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;
20
Haskell
• 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!
21
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
22
Haskell Example: Fibonacci
• Fibonacci numbers
– illustrates function definitions
fib 0 = 1
fib 1 = 1
fib (n + 2) = fib (n + 1)
+ fib n
23
Haskell Example: Factorial
• Factorial
– illustrates guards
fact n
| n == 0 = 1
| n > 0 = n * fact (n - 1)
• Special word otherwise can be a guard
24
Applications 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!
25
Functional 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
26