#### 3.15Laziness and Infinite Data

Develop the following functions and data structures in the Lazy Racket language.

##### 3.15.1A note on testing

There is no testing facility built in to the Lazy Racket language. So, you should add one for your file:
 (define print-only-errors #t) (define (test l r) (if (equal? l r) (if print-only-errors () (printf "Test Passed~n")) (printf "Test Failed.~nActual:   ~S ~nExpected: ~S~n" l r)))
For example,
 (test (take-while odd? (list 1 3 4)) (list 1 3))

##### 3.15.2Utility Functions

 procedure(take-while p l) → (listof any/c) p : (any/c . -> . boolean?) l : (listof any/c)
Returns the prefix of l such that for all elements p returns true. This is not filter.

For example, (take-while (lambda (n) (< n 5)) (list 1 2 3 4 5 1 2)) returns (list 1 2 3 4).

 procedure f : (exact-nonnegative-integer? . -> . any/c)
Lazily constructs the infinite list such that (list-ref (build-infinite-list f) i) returns (f i).

##### 3.15.3Primes

 procedure(prime? n) → boolean? n : exact-positive-integer?
Returns true if n is prime.

 value
The list of all primes.

You may find filter, prime?, and build-infinite-list useful.

 procedure(prime?/fast n) → boolean n : exact-positive-integer?
Returns true if n is prime, but tests only prime factors from primes/fast.

 value
The list of all primes constructed with prime?/fast.

##### 3.15.4Longest Common Subsequence

 procedure(build-table rows cols f) → (vectorof (vectorof any/c)) rows : exact-positive-integer? cols : exact-positive-integer? f : (exact-nonnegative-integer? exact-nonnegative-integer? . -> . any/c)
Lazily constructs a vector such that (vector-ref (vector-ref (build-table rows cols f) i) j) equals (f i j), when (< i rows) (< j cols).

You will find the following function helpful:

 (define (build-vector num f) (apply vector (build-list num f)))

 procedure s1 : string? s2 : string?
Computes the length of the longest common subsequence of two strings s1 and s2.

You must use build-table to construct a table of the answer for sub-problem made from prefixes of s1 and s2 then synthesize the result from these intermediate points. You will not get credit if you do a computation twice.

You may find string-ref, char=?, apply, and max useful.

Warning: Many people errorneously implement the longest common substring. The longest common substring of Artist and Artsy is Art. The longest common subsequence of Artist and Artsy is Arts. You are implementing longest common subsequence.