Functional Languages

Key Concepts

• based on mathematical functions (a mapping of members of one set (domain) to another set (range set)
  • evaluation order of their mapping expression is controlled by recursion and conditional expressions rather than by sequencing and iterative repetition
  • no side effects, so functions always define the same value given the same set of arguments (referential transparency)
• Functions are first-class entities — can be used as parameters or return values
• No state, no variables, no assignment statements
• Functions and data take the same form (that of lists)
• Can easily express even basic operations as functions

Introduction to Scheme

(Most of the Scheme we will look at would require only minor modifications to be rewritten as LISP functions.)

• Scheme interpreter -- a read-evaluate-write infinite loop
  reads an expression type by user (in form of a list)
  interprets the expression (by the function EVAL)
  displays results
• Primitive functions -- deal only with numeric atoms

  (* 3 7)	21	3*7
  (+ 5 7 2)	14	5+7+2
  (- 5 6)	-1	5-6
  (- 15 7 2)	6	15 - 7 - 2
  (-24 (* 4 3))	12	24 - (4 * 3)
  (sqrt 49)	7	square root of 49
  (sqrt -2)	1.41421... i	v- 2i