Streams Review

1. Streams Review A Review of Streams Mark Boady

2. What Are Steams? • Delayed lists • We pretend that the stream is a list • In reality we only know the next value, but we know how to compute the rest • When the user asks for a value, compute exactly what is needed • L = [ CurrentValueFunctionToComputeNext]

3. Theory Example • We want a stream with every prime number • Finding every prime number is obviously impossible • Assume we have the function • NextPrime(n) returns the first prime found after n • The stream object starts with • Prime-stream ={ 2, NextPrime} • When the user asks for the cdr of the stream, we use NextPrime to find it.

4. Theory Example • prime-stream ={ 2, NextPrime} • Car prime-stream would return 2 • Cdr of prime-stream is {NextPrime(2), NextPrime} • Which is {3, NextPrime} • Applying cdr again repeats the process • Cdr of cdr of primestream is {NextPrime(3), NextPrime}

5. The point • We can use list operations on a huge or infinite list without needing to actually store the list in memory • In scheme, the following special commands are used • stream-cons creates a stream • stream-car gets the current first element • stream-cdr get the tail of the stream • Homework Assignment • ( stream-seq f rlist )

6. Scheme Example (define (integers-starting-from n) (cons-stream n (integers-starting-from (+ n 1)))) (define integers (integers-starting-from 1)) (stream-car integers) (stream-car (stream-cdr integers)) (stream-car (stream-cdr (stream-cdr integers)))