Introduction to Scheme

1. Introduction to Scheme

2. Lisp and Scheme • Lisp: List processor language • Full recursion • Conditional expression • Extensibility • Interactive • Scheme: one of most popular dialects of Lisp. ( Another popular one: common lisp)

3. Dr.Scheme • Download Dr. Scheme from http://download.plt-scheme.org/drscheme/ • Install Dr. Scheme in your computer • Set language: “advanced student”

4. Primitive Elements • Atoms • A string of characters beginning with a letter, digit or special character other than a single left or right parenthesis. • Lists • (atoms +/or lists) • Null • Define a atom and a list in Dr. Scheme

5. Evaluation • Read->evaluate->print • Imperative language • f(x) • g(x, y, z) • Lisp • (f x) • (g x y z) • In a list, first element is expected to be a function which uses remaining elements as arguments

6. Manipulating lists • car: get the first element of list • cdr: get the rest of list • caar: get the first item of the first list in a list • cadr: get the second item of a non-empty list • cadar: get the second item of the first list of a list • caddr: get the third item of a non-empty list • cons: construct a list by two lists or a list and an atom. The second argument must be a list.

7. How they come? • caar == car(car list) • cadr == car(cdr list) • cadar == car(cdr(car list)) • caddr == car(cdr(cdr list))

8. A problem to solve A farmer is taking a fox, goose and bag of corn to market and must cross a river. The river has a boat that can hold the farmer and one item, so he must make multiple crossings while leaving some items unattended. If the fox gets a chance, it will eat the goose; likewise the goose will eat the corn. What’s a pair farmer to do?

9. Valid States • Representation: (left-bank list, right-bank list) • Initial state: ((fox goose corn boat) ()) • Tasks - define functions: • (left-bank state) : (fox goose corn boat) • (right-bank state): null • Another states: • ((fox corn) (goose boat)) • ((goose boat) (fox corn)) • Final state: (()(fox goose corn boat))

10. Defining functions • (define function_name (lambda (args) expressions ) ) • Function call: (function_name args)

11. Exercise • Current state := ((state on left bank)(state on right bank)) • Define initial state initState to be ((fox goose corn boat)()) • Write a function leftBank that returns state on left bank based on current state • Write a function rightBank that returns state on right bank based on current state

12. In scheme: (cond (cond1 val1) (cond2 val2) … (condn valn) (else default-val) ) In imperative language: if(cond1) return val1; else if(cond2) return val2; …. else if(condn) return valn; else return default-val; Conditional expressions

13. Useful build-in functions • (eq? val1 val2) -- compare two values • Return true if the two values are the same • (> val1 val2) -- compare numbers for greater-than • (< val1 val2) -- compare numbers for less-than • (= val1 val2) -- compare numbers for equality • (null? val) – if the value is empty list

14. Exercise • Write a function called otherBank that returns RIGHT if bank==LEFT returns LEFT if bank==RIGHT and otherwise returns HUH

15. Recursive list processing • If we want to process elements of a list L with function f • First, process first element of L : f( car L) • Next , recursively process rest of L: (cdr L) • Exercise: • Write a function isThere to test if x is on list L