1. Programming Languages
Meeting 9
November 1/2, 2016

2. Functional Programming Languages
Work with pure FP languages
No assignment statement
No loops
No objects or methods
Still have sequence implemented as composition
Recall [s1;s2] = [s2]○ [s1]
Still have if – then – else
Loops are replaced by recursion

3. FP (2) Four components Objects Primitive functions Functional forms
Function definition mechanism, for secondary functions

4. Objects The only data type Not the objects from Java, but: Objects
Atoms
Lists of objects
The symbol called bottom, signifying “undefined”

5. Atoms Forms of atoms sequence of characters, a string, an identifier
sequence of digits, an integer [perhaps with sign]
syntax of a real number
T, meaning true
F, meaning false

6. Functions
Functions on the set of objects, the only operation on objects
Programs are constructed using composition of functions.
Two types of functions
Entire: Defined on all objects
Partial: Defined on some, but not all objects

7. Notation for Semantics
One line function specification with choices, developed by John Backus
Symbols
: apply the function to the argument
is defined as
−> if – then
; else

8. Primitives Our set of primitives: first last head tail atom? null?
list?

9. More Primitives appendr appendl length The arithmetic functions
The comparison functions

10. Functional Forms The four Cs constant composition denoted by overbar
depends on one object
composition
denoted by centered small circle
depends on two functions

11. Functional Forms (2) construction conditional denoted by [ ]
depends on n functions
[f]:x <−> <f:x> (n=1)
conditional
denoted using −> and ;
depends on a predicate and two functions

12. Functional Forms (3) apply to all insert (also known as reduce)
denoted by αf
depends on one function
works only on lists
insert (also known as reduce)
denoted by /f
depends on one function with a number of properties