Functional Design and Programming Lecture 6: Functions as data

Literature (Pensum)  Paulson, chap. 5: Functions as values ( ) Standard combinators List combinators ( ) Other combinators (5.11) Infinite lists ( ) Search strategies and infinite lists ( )

Exercises  Paulson, chap. 5:

Overview  Functions as values  Standard combinators List combinators Other combinators  Infinite lists  Search strategies and infinite lists

Functions as values  Lambda-notation (anonymous functions)  Currying and uncurring  Functions in data structures  Functions as arguments and results

Lambda-notation

Currying and uncurrying

Functions in data structures  Example: Mapping keywords to comparison functions (for sorting)

Functions as arguments and results  Examples: Lookup function for comparison functions parameterized sort function Summation

Standard combinators  List combinators: map, filter takewhile, dropwhile exists, all foldl, foldr  Other combinators: compose ( o ) repeat treefold

Infinite lists (sequences)  Datatypes for delayed evaluation  Elementary sequence processing  Elementary applications of sequences: Random numbers Prime numbers Numerical computing

Search strategies  Infinite trees  Search strategies for infinite trees: depth-first breadth-first depth-first iterative best-first  Toy applications: palindromes 8-queens