          Lecture 3 - Page 20 : 42
 Functional Programming in SchemeName binding, Recursion, Iteration, and Continuations * Name binding constructs The let name binding expression The equivalent meaning of let Examples with let name binding The let* name binding construct An example with let* The letrec namebinding construct LAML time functions * Conditional expressions Conditional expressions Examples with if Example with cond: leap-year? Example with cond: american-time Example with cond: as-string * Recursion and iteration Recursion List processing Tree processing (1) Tree processing (2) Recursion versus iteration Example of recursion: number-interval Examples of recursion: string-merge Examples with recursion: string-of-char-list? Exercises * Example of recursion: Hilbert Curves Hilbert Curves Building Hilbert Curves of order 1 Building Hilbert Curves of order 2 Building Hilbert Curves of order 3 Building Hilbert Curves of order 4 A program making Hilbert Curves * Continuations Introduction and motivation The catch and throw idea A catch and throw example The intuition behind continuations Being more precise The capturing of continuations Capturing, storing, and applying continuations Use of continuations for escaping purposes Practical example: Length of an improper list Practical example: Searching a binary tree
 Recursion versus iteration
 Recursive functions are - modulo use of memory resources - sufficient for any iterative needTail recursive functions in Scheme are memory efficient for programming of any iterative process
 Tail recursion is a variant of recursion in which the recursive call takes place without contextual, surrounding calculations in the recursive function.

A tail call is the last 'thing' to be done before the function returns. Therefore there is no need to maintain any activation record of such a call - we can reuse the previous activation record. The image series below will illustrate this. A recursive formulation of the function fak and the accompanying recursive process A tail recursive formulation of the function fak and the accompanying iterative process without memory optimization A tail recursive formulation of the function fak and the accompanying, memory optimized iterative process