Understanding Conditional Expressions and Procedures in Meta Language

1. thirteen conditional expressions:letting programs make “decisions”

2. Recap:The Meta language • Names: constants and variables • When evaluated, return a specific data objects • Can make new names with: [define name value] • Procedure calls [procedureargs…] • Procedure is run with the args as inputs • Compound procedures [args… →exp] • Makes a new procedure with the specified arguments and return value • Expression for return value can refer to args • Define and with [define name exp] [with name = exp …exp] • Introduce new names or values for names

3. [if test consequent alternative] If test is true, Then evaluate and return consequent Otherwise, evaluate and return alternative Some useful tests [= a b] Checks if a and b are the same [> a b], [≤a b], etc. Compares numbers A new kind of expression: if ►[define abs [n → [if [> n 0] n [- n]]]] <Procedure abs> ►[abs 5] 5 ►[abs -5] 5 ►

4. Some other useful tests • [number? value], [string? value],[bitmap? value], [integer? value],[procedure? value] • Tests what kind of data value is • [odd? number], [even? number] • Tests whether a number is odd or even • Okay, maybe this isn’t so useful … • [and test1test2 … testn][or test1test2 … testn][not test] Combines tests into more complicated tests

5. Boolean objects • Everything in Meta is an expression, • And all expressions have values, • So then what kind of value is [= a b] ? • Answer: a “truth value” – true or false • These are named Booleans after George Boole, who invented Boolean Algebra, an early form of symbolic logic • Meta has two magic data objects that are used to represent the answers to questions • They’re named true and false.

6. Suppose we say: [define a 7] [define b 8] [define c 9.5] What are the values of [> a b] [> a b] [not [= b c]] [integer? c] [odd? a] [and [< 5 a] [< a 10]] Examples

7. Executing a Boolean expression Evaluating tests is really just normal procedure execution [and [< 5 a] [< a 10]] • First, execute [< 5 a] • Call < with 5 and 7 as inputs • < returns true • Then call [< a 10] • Call < with 7 and 10 as inputs • < returns true • Call and with true and true as arguments • (actually, this part is a little more complicated, but that won’t matter until next quarter) • And returns true

8. Predicates (question answerers) • Procedures, like = or odd?, that return Booleans are called predicates • They can be thought of as tests or question answerers • [= 1 2] asks the question “are 1 and 2 the same?” • [odd? 7] asks the question “is 7 an odd number?” • And their return values can be thought of as the answers • [= 1 2] returns false • [odd? 7] returns true • Predicates are an important type of procedure

9. Predicates are just normal procedures That happen to return Booleans So you can (and will) write your own (sorry, you’ll see a less lame example soon) [define big-and-odd?[n → [and [> n 10000] [odd? n]]]] [big-and-odd? 239803] [and [big-and-odd? b] [< b 1000000]] User-defined predicates