Functional Programming in Haskell Part 2 : Abstract dataypes and

131 Pages·2002·0.21 MB·English

Functional Programming in Haskell
Part 2 : Abstract dataypes and “infinite” structures
Madhavan Mukund
Chennai Mathematical Institute
92 G N Chetty Rd, Chennai 600 017, India
[email protected]
~
http://www.cmi.ac.in/ madhavan
MadrasChristianCollege,10December2003–p.1
(cid:17)
(cid:4) Computation Rewriting using definitions
(cid:4) Functions are associated with input and output types
(cid:4) isDigit :: Char -> Bool
isDigit ’0’ = True
isDigit ’1’ = True
...
isDigit ’9’ = True
isDigit c = False
(cid:4) isDigit c
| (c >= ’0’ && c <= ’9’) = True
| otherwise = False
Haskell review
(cid:17)
(cid:4) Program Collection of function definitions
MadrasChristianCollege,10December2003–p.2
(cid:4) Functions are associated with input and output types
(cid:4) isDigit :: Char -> Bool
isDigit ’0’ = True
isDigit ’1’ = True
...
isDigit ’9’ = True
isDigit c = False
(cid:4) isDigit c
| (c >= ’0’ && c <= ’9’) = True
| otherwise = False
Haskell review
(cid:17)
(cid:4) Program Collection of function definitions
(cid:17)
(cid:4) Computation Rewriting using definitions
MadrasChristianCollege,10December2003–p.2
(cid:4) isDigit :: Char -> Bool
isDigit ’0’ = True
isDigit ’1’ = True
...
isDigit ’9’ = True
isDigit c = False
(cid:4) isDigit c
| (c >= ’0’ && c <= ’9’) = True
| otherwise = False
Haskell review
(cid:17)
(cid:4) Program Collection of function definitions
(cid:17)
(cid:4) Computation Rewriting using definitions
(cid:4) Functions are associated with input and output types
MadrasChristianCollege,10December2003–p.2
isDigit ’0’ = True
isDigit ’1’ = True
...
isDigit ’9’ = True
isDigit c = False
(cid:4) isDigit c
| (c >= ’0’ && c <= ’9’) = True
| otherwise = False
Haskell review
(cid:17)
(cid:4) Program Collection of function definitions
(cid:17)
(cid:4) Computation Rewriting using definitions
(cid:4) Functions are associated with input and output types
(cid:4) isDigit :: Char -> Bool
MadrasChristianCollege,10December2003–p.2
(cid:4) isDigit c
| (c >= ’0’ && c <= ’9’) = True
| otherwise = False
Haskell review
(cid:17)
(cid:4) Program Collection of function definitions
(cid:17)
(cid:4) Computation Rewriting using definitions
(cid:4) Functions are associated with input and output types
(cid:4) isDigit :: Char -> Bool
isDigit ’0’ = True
isDigit ’1’ = True
...
isDigit ’9’ = True
isDigit c = False
MadrasChristianCollege,10December2003–p.2
Haskell review
(cid:17)
(cid:4) Program Collection of function definitions
(cid:17)
(cid:4) Computation Rewriting using definitions
(cid:4) Functions are associated with input and output types
(cid:4) isDigit :: Char -> Bool
isDigit ’0’ = True
isDigit ’1’ = True
...
isDigit ’9’ = True
isDigit c = False
(cid:4) isDigit c
| (c >= ’0’ && c <= ’9’) = True
| otherwise = False
MadrasChristianCollege,10December2003–p.2
(cid:4) Define list functions by induction on structure
(cid:4) Example Adding up a list of integers
sum :: [Int] -> Int
sum [] = 0
sum (x:l) = x + (sum l)
(cid:4) (Conditional) polymorphism
Most general type of sum is
sum :: (Num a) => [a] -> a
where Num a is true for any type a that supports basic
arithmetic operations +, -, . . .
Haskell review . . .
(cid:4) Basic collective type is a list
MadrasChristianCollege,10December2003–p.3
(cid:4) Example Adding up a list of integers
sum :: [Int] -> Int
sum [] = 0
sum (x:l) = x + (sum l)
(cid:4) (Conditional) polymorphism
Most general type of sum is
sum :: (Num a) => [a] -> a
where Num a is true for any type a that supports basic
arithmetic operations +, -, . . .
Haskell review . . .
(cid:4) Basic collective type is a list
(cid:4) Define list functions by induction on structure
MadrasChristianCollege,10December2003–p.3
sum :: [Int] -> Int
sum [] = 0
sum (x:l) = x + (sum l)
(cid:4) (Conditional) polymorphism
Most general type of sum is
sum :: (Num a) => [a] -> a
where Num a is true for any type a that supports basic
arithmetic operations +, -, . . .
Haskell review . . .
(cid:4) Basic collective type is a list
(cid:4) Define list functions by induction on structure
(cid:4) Example Adding up a list of integers
MadrasChristianCollege,10December2003–p.3