Project代做 | Racket代做 – 这是一个racket基础训练题目
racket project and Macros
The purpose of this assignment is to give you experience with writing a larger program in Racket, and also with using Racket macros. You can (and should) use side effects, with care, in Question 3. Dont use side effects for the answers to any of the other questions.
Points: 15 points Question 1, 4 points each Questions 2, 3 and 4.
You can use up to 3 late days for this assignment.
Turnin: Turn in two files: polynomials.rkt, with the functions and unit tests for Questions 1 and 2; and macros.rkt, with the functions, macros, and unit tests for Questions 3 and 4. You dont need to turn in sample output the unit tests are enough for those. As before, your program should be tastefully commented (i.e. put in a comment before each function definition saying what it does). Style counts!
- Write and test a Racket functionpoly-multiplythat multiplies two polynomials in a symbolic variable and returns the result. The polynomials should be represented as lists of terms, where each term is in turn a list consisting of a coefficient and an exponent of the symbolic variable. The polynomials should be normalized: they should be sorted with the largest exponent first, there shouldnt be two terms with the same exponent, and that shouldnt be any terms with a coefficient of 0. You can assume that the exponents will be non-negative integers. The zero polynomial is represented as the empty list. The result returned bypoly-multiplyshould be normalized as well. For example:
(poly-multiply '((1 3) (1 2) (1 1) (1 0)) '((1 1) (-1 0)))
should evaluate to'((1 4) (-1 0)).
In standard algebraic notation, this represents
x^4 1 = (x^3 +x^2 +x+ 1)(x1)
Here are some other polynomial pairs that you can turn into unit tests for your function:
( 3 x^4 +x+ 5) 0
0 x^2
(x^3 +x1) 5
( 10 x^2 + 100x+ 5)(x^999 x^7 +x+ 3)
3 x
x 3
- Define a functionpoly->codethat converts a polynomial in normalized form as in Question 1 into evaluable Racket code. It should take two parameters: the list representing the polynomial, and the symbolic variable. Here are some examples:
(poly->code '((1 3) (5 2) (7 1) (10 0)) 'x) =>
'(+ (expt x 3) (* 5 (expt x 2)) (* 7 x) 10)
(poly->code '((1 1) (-10 0) 'x) => '(+ x -10)
1
(poly->code '((1 1)) 'x) => 'x
(poly->code '((10 0)) 'x) => 10
(poly->code '((1 0)) 'x) => 1
(poly->code '() 'x) => 0
So in general, the result will be a sum of terms, but if there is just one term, just return that term. In
general a term is the coefficient times the variable raised to the exponent; but omit the coefficient if it
is 1 and the exponent isnt 0, omit the exponent if it is 1, and omit both the variable and the exponent
if the exponent is 0. Finally, return 0 for the zero polynomial.
Add appropriate unit tests for yourpoly->codefunction.
Since the result returned frompoly->codeis legal Racket code, we should be able to evaluate it.
Suppose we define two polynomialsp1andp2and a numberxin the interaction pane:
(define p1 '((1 3) (1 2) (1 1) (1 0)))
(define p2 '((1 1) (-1 0)))
(define x 4)
Then both of these expressions should evaluate to the same number, namely 255:
(eval (poly->code (poly-multiply p1 p2) 'x))
(* (eval (poly->code p1 'x)) (eval (poly->code p2 'x)))
(If you use these examples in the definition pane, for example in unit tests, youll need to use an
additional namespace argument toeval.)
- Racket macros: the lecture notes and code fordelayandforceinclude functionsmy-delayand my-force. Rewritemy-delayas a macro, so that the user doesnt have to manually wrap the delayed expression in a lambda. So the syntax formy-delayshould be just like Racketsdelay. Note in particular that you can have multiple expressions in the body. For example, this should work: (my-delay (write "hi there ") (+ 3 4)) Rewrite themy-forcefunction from the lecture notes if necessary so that it works correctly with your my-delaymacro. (Or perhaps it will be OK as is.) Leavemy-forceas a function in any case, rather than making it a macro. You should demonstrate that the expressions arent evaluated when you construct the delay, that they are evaluated the first time you usemy-forceand that it returns the correct value, and that additional uses ofmy-forcecontinue to return the correct value without re-evaluating the expressions. When you are debugging, you could do this just by including some print statements. However, for the assigment, you need to include unit tests that check this, and print statements wont accomplish this the tests need to be automated rather involving a human looking at output. (Well, maybe there is some way to capture the output and automate checking it, but this would be more complicated than necessary.) Here is a hint for one easy way to do it. Use a counter that gets incremented every time the given expression is evaluated. Check that the counter is not incremented by doing the delay, that itis incremented the first time the expression is forced, and that additional evaluations dont increment it.
- Another Racket macro: define a macromy-andthat does exactly the same thing as the built-in Racket and. (Hint: see the handouts for macros, in particular themy-orexample. Remember thatandworks on an indefinite number of expressions, including 0 expressions.) Include suitable unit tests.