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 = [ CurrentValue FunctionToComputeNext]

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)))