Download Introduction to Functional Programming, used in the

Introduction to Functional
Programming
Notes for CSCE 190
Based on Sebesta, Hutton, Ullman
Marco Valtorta
UNIVERSITY OF SOUTH CAROLINA
Department of Computer Science and Engineering
Language Families
• Imperative (or Procedural, or Assignment-Based)
• Functional (or Applicative)
• Logic (or Declarative)
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Imperative Languages
• Mostly influenced by the von Neumann computer
architecture
• Variables model memory cells, can be assigned to,
and act differently from mathematical variables
• Destructive assignment, which mimics the movement
of data from memory to CPU and back
• Iteration as a means of repetition is faster than the
more natural recursion, because instructions to be
repeated are stored in adjacent memory cells
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Functional Languages
• Model of computation is the lambda calculus (of
function application)
• No variables or write-once variables
• No destructive assignment
• Program computes by applying a functional form
to an argument
• Program are built by composing simple functions
into progressively more complicated ones
• Recursion is the preferred means of repetition
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Logic Languages
•
•
•
•
•
Model of computation is the Post production system
Write-once variables
Rule-based programming
Related to Horn logic, a subset of first-order logic
AND and OR non-determinism can be exploited in
parallel execution
• Almost unbelievably simple semantics
• Prolog is a compromise language: not a pure logic
language
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What is a Functional Language?
Opinions differ, and it is difficult to give a precise
definition, but generally speaking:
• 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.
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Example
Summing the integers 1 to 10 in Java:
total = 0;
for (i = 1; i  10; ++i)
total = total+i;
The computation method is variable assignment.
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7
Example
Summing the integers 1 to 10 in Haskell:
sum [1..10]
The computation method is function application.
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8
Simple Function Definition
fact 0 = 1
fact n = n * fact (n -1)
fact1 = prod [1..n]
fib 0 = 1
fib 1 = 1
fib (n + 2) = fib (n + 1) + fib n
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Guards and otherwise
fact n
| n == 0 = 1
| n > 0 = n * fact (n – 1)
• fact will not loop forever for a negative argument!
sub n
| n < 10 = 0
| n > 100 = 2
| otherwise = 1
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Local scope: where
quadratic_root a b c =
[minus_b_over_2a – root_part_over_2a,
minus_b_over_2a + root_part_over_2a]
where
minus_b_over_2a = -b / (2.0 * a)
root_part_over_2a =
sqrt(b ^ 2 – 4.0 * a * c) / (2.0 * a)
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List comprehensions, generators,
and tests
• List comprehensions are used to define lists that
represent sets, using a notation similar to
traditional set notation: [body | qualifiers], e.g.,
[n * n * n | n <- [1..50]] defines a list of cubes of
the numbers from 1 to 50
• Qualifiers can be generators (as above) or tests
• The following function returns the list of factors of n
factors n = [i | i <- [1 .. n div 2], n mod i == 0]
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A Taste of Haskell
f []
= []
f (x:xs) = f ys ++ [x] ++ f zs
where
ys = [a | a  xs, a  x]
zs = [b | b  xs, b > x]
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Quicksort
The quicksort algorithm for sorting a list of integers
can be specified by the following two rules:
• The empty list is already sorted;
• Non-empty lists can be sorted by sorting the tail
values  the head, sorting the tail values  the head,
and then appending the resulting lists on either side
of the head value.
UNIVERSITY OF SOUTH CAROLINA
Department of Computer Science and Engineering
Using recursion, this specification can be translated
directly into an implementation:
qsort
:: [Int]  [Int]
qsort []
= []
qsort (x:xs) =
qsort smaller ++ [x] ++ qsort larger
where
smaller = [a | a  xs, a  x]
larger = [b | b  xs, b  x]
Note:
• This is probably the simplest implementation of
quicksort in any programming language!
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For example (abbreviating qsort as q):
q [3,2,4,1,5]
q [2,1] ++ [3] ++ q [4,5]
q [1] ++ [2] ++ q []
[1]
[]
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q [] ++ [4] ++ q [5]
[]
[5]
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Lazy evaluation
• Lazy evaluation allows infinite data structures, e.g.:
positives = [0 ..]
squares = [n * n | n <- [0..]]
• member squares 16
• member [] b = False
member (a:x) b = (a == b) || member x b
• member2 (m:x) n
| m < n = member2 x n
| m == n true
otherwise = False
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