Functional Programming

1
Functional Programming

• Theoretical foundation
• Churchs ?-calculus
• expressions and evaluation rules
• Characteristics
• Single assignment variables (pure FP)
• Recursion
• Rule-based and pattern matching (ML, Haskell, F)
• High-order functions
• Lazy evaluation (Haskell)
• Meta-programming (Scheme)

2
F

• A hybrid language
• ML-like functional programming
• Iimperative programming
• OOP
• Scripting
• Runs on the .NET platform
• It is possible to use any .NET library from F
• It is possible to use F library from other .NET
  languages such as C
• Available for free
• Works with Visual Studio
• Standalone fsharp interpreter fsi

3
F vs. Prolog

• Common characteristics
• Repetition via recursion
• High-order
• Garbage collection
• Differences
• Strongly typed vs. dynamically typed
• Functional vs. relational
• Prolog supports unification and backtracking

4
Types

• int -- 123, -10
• float -- 122.123, 0.23e-10
• bool -- true, false
• char -- a
• string -- abc
• list -- 123, 123, 1_at_23
• array -- 123
• tuple -- ("abc",1,true)
• union -- type MyBool True False

5
Operators

• , -, , /,
• , ,not
• , ltgt, lt, gt, lt, gt

6
let

• let x 123
• let f x y xy
• let f (x,y) xy
• let rec f n if n 0 then 1 else n(f n-1)

7
Pattern Matching
let rec len lst match lst with -gt 0
_lst1 -gt 1len lst1
8
Tail Recursion
let rec len1 ac lst match lst with
-gt ac (_lstr) -gt len1 (ac1) lstr let
len lst len1 0 lst
9
Unions
type SExp O S of Sexp let rec sum x y
match x with O -gt y S x1 -gt S(sum
x1 y)
10
Unions (Cont.)
type TreeInt Void Leaf of int
Node of intTreeIntTreeInt   let rec count tree
match tree with Void -gt 0 Leaf(_)
-gt 1 Node(_,left,right) -gt 1 (count left)
(count right)  
11
High-order Functions
let succ fun x -gt x1 List.map succ
123 List.map (fun x -gt x1) 123
12
map and fold
let rec map f lst match lst with
-gt (car cdr) -gt (f car)(map f
cdr)   let rec fold f lst acc match lst
with -gt acc (car cdr) -gt f car
(fold f cdr acc)   let rec foldl f lst acc
match lst with -gt acc (car
cdr) -gt foldl f cdr (f car acc)