CSE 341, Assignment 5 Solved

Set-up: For this assignment, grab the starter code. To complete these problems, edit hw5.rkt to replace all occurrences of "CHANGE" with your solutions.

Do not use any mutation (set!, set-mcar!, etc.) anywhere in the assignment.

Overview: This homework has to do with mupl (a Made Up Programming Language). mupl programs are written directly in Racket by using the constructors de ned by the structs de ned at the beginning of hw5.rkt. This is the de nition of mupl’s syntax:

    • If s is a Racket string, then (var s) is a mupl expression (a variable use).

    • If n is a Racket integer, then (int n) is a mupl expression (a constant).

    • If e1 and e2 are mupl expressions, then (add e1  e2) is a mupl expression (an addition).

    • If s1 and s2 are Racket strings and e is a mupl expression, then (fun s1 s2 e) is a mupl expression (a function). In e, s1 is bound to the function itself (for recursion) and s2 is bound to the (one) argument. Also, (fun null s2 e) is allowed for anonymous nonrecursive functions.

    • If e1 and e2 are mupl expressions, then (isgreater e1  e2) is a mupl expression (a comparison).

    • If e1, e2, and e3 are mupl expressions, then (ifnz e1 e2 e3) is a mupl expression. It is a condition where the result is e2 if e1 is not zero else the result is e3. Only one of e2 and e3 is evaluated.

    • If e1 and e2 are mupl expressions, then (call e1  e2) is a mupl expression (a function call).

    • If s is a Racket string and e1 and e2 are mupl expressions, then (mlet s e1 e2) is a mupl expression (a let expression where the value resulting from evaluating e1 is bound to s in the evaluation of e2).

    • If e1 and e2 are mupl expressions, then (apair e1  e2) is a mupl expression (a pair-creator).

    • If e1 is a mupl expression, then (first e1) is a mupl expression (getting the  rst part of a pair).

    • If e1 is a mupl expression, then (second e1) is a mupl expression (getting the second part of a pair).

    • (munit) is a mupl expression (holding no data, much like () in ML or null in Racket).  Notice

(munit) is a mupl expression, but munit is not.

    • If e1 is a mupl expression, then (ismunit e1) is a mupl expression (testing for (munit)).

    • (closure env f) is a mupl value where f is mupl function (an expression made from fun) and env is an environment mapping variables to values. Closures do not appear in source programs; they result from evaluating functions.

A mupl value is a mupl integer constant, a mupl closure, a mupl munit, or a mupl pair of mupl values. Similar to Racket, we can build list values out of nested pair values that end with a mupl munit. Such a mupl value is called a mupl list.

You should assume mupl programs are syntactically correct (e.g., do not worry about wrong things like (int "hi") or (int (int 37)). But do not assume mupl programs are free of type errors like (add (munit) (int 7)) or (first (int 7)).

Warning: What makes this assignment challenging is that you have to understand mupl well and debugging an interpreter is an acquired skill.

Turn-in Instructions: Upload your modi ed hw5.rkt and hw5tests.rkt to Gradescope.


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Problems:

    1. Warm-Up:

            (a) Write a Racket function racketlist->mupllist that takes a Racket list (presumably of mupl values but that will not a ect your solution) and produces an analogous mupl list with the same elements in the same order.

            (b) Write a Racket function mupllist->racketlist that takes a mupl list (presumably of mupl values but that will not a ect your solution) and produces an analogous Racket list (of mupl values) with the same elements in the same order.

    2. Implementing the mupl Language: Write a mupl interpreter, i.e., a Racket function eval-exp that takes a mupl expression e and either returns the mupl value that e evaluates to under the empty environment or calls Racket’s error if evaluation encounters a run-time mupl type error or unbound mupl variable.

A mupl expression is evaluated under an environment (for evaluating variables, as usual). In your interpreter, use a Racket list of Racket pairs to represent this environment (which is initially empty) so that you can use without modi cation the provided envlookup function. Here is a description of the semantics of mupl expressions:

        ◦ All values (including closures) evaluate to themselves. For example, (eval-exp (int 17)) would return (int 17), not 17.

        ◦ A variable evaluates to the value associated with it in the environment.

        ◦ An addition evaluates its subexpressions and, assuming they both produce integers, produces the integer that is their sum. (Note this case is done for you to get you pointed in the right direction.)

        ◦ An isgreater evaluates its two subexpressions to values v1 and v2 respectively. If both values are integers, then if v1 > v2 the result of the isgreater expression is the mupl value (int 1), else the result is the mupl value (int 0).

        ◦ An ifnz evaluates its rst expression to a value v1. If it is an integer, then if it is not zero, then ifnz evaluates its second subexpression, else it evaluates its third subexpression.

        ◦ Functions are lexically scoped: A function evaluates to a closure holding the function and the current environment.

        ◦ An mlet expression evaluates its rst expression to a value v. Then it evaluates the second expression to a value, in an environment extended to map the name in the mlet expression to v.

        ◦ A call evaluates its rst and second subexpressions to values. If the rst is not a closure, it is an error. Else, it evaluates the closure’s function’s body in the closure’s environment extended to map the function’s name to the closure (unless the name eld is null) and the function’s argument-name (i.e., the parameter name) to the result of the second subexpression.

        ◦ A pair expression evaluates its two subexpressions and produces a (new) pair holding the results.

        ◦ A rst expression evaluates its subexpression. If the result for the subexpression is a pair, then the result for the rst expression is the e1 eld in the pair.

        ◦ A second expression evaluates its subexpression. If the result for the subexpression is a pair, then the result for the second expression is the e2 eld in the pair.

        ◦ An ismunit expression evaluates its subexpression. If the result is an munit expression, then the result for the ismunit expression is the mupl value (int 1), else the result is the mupl value (int 0).

Hint: The call case is the most complicated. In the sample solution, no case is more than 12 lines and several are 1 line.


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    3. Expanding the Language: mupl is a small language, but we can write Racket functions that act like mupl macros so that users of these functions feel like mupl is larger. The Racket functions produce mupl expressions that could then be put inside larger mupl expressions or passed to eval-exp. In implementing these Racket functions, do not use closure (which is used only internally in eval-exp). Also do not use eval-exp (we are creating a program, not running it).

        (a) Write a Racket function ifmunit that takes three mupl expressions e1, e2, and e3. It returns a mupl expression that when run evaluates e1 and if the result is mupl’s munit then it evaluates e2 and that is the result, else it evaluates e3 and that is the result. Sample solution: 1 line.

        (b) Write a Racket function mlet* that takes a Racket list of Racket pairs ’((s1 . e1) . . . (si . ei)
. . . (sn . en)) and a nal mupl expression en+1. In each pair, assume si is a Racket string and ei is a mupl expression. mlet* returns a mupl expression whose value is en+1 evaluated in an environment where each si is a variable bound to the result of evaluating the corresponding ei for 1 i n. The bindings are done sequentially, so that each ei is evaluated in an environment where s1 through si 1 have been previously bound to the values e1 through ei 1.

        (c) Write a Racket function ifeq that takes four mupl expressions e1, e2, e3, and e4 and returns a mupl expression that acts like ifnz except e3 is evaluated if and only if e1 and e2 are equal integers. (An error occurs if the result of e1 or e2 is not an integer.) Assume none of the arguments to ifeq use the mupl variables _x or _y. Use this assumption so that when an expression returned from ifeq is evaluated, e1 and e2 are evaluated exactly once each.


    4. Using the Language: We can write mupl expressions directly in Racket using the constructors for the structs and (for convenience) the functions we wrote in the previous problem.

        (a) Bind to the Racket variable mupl-filter a mupl function that acts like lter (as we used in ML). Your function should be curried: it should take a mupl function and return a mupl function that takes a mupl list and applies the function to every element of the list returning a new mupl list with all the elements for which the function returns a number other than zero (causing an error if the function returns a non-number). Recall a mupl list is munit or a pair where the second component is a mupl list.

        (b) Bind to the Racket variable mupl-all-gt a mupl function that takes an mupl integer i and returns a mupl function that takes a mupl list of mupl integers and returns a new mupl list of mupl integers containing the elements of the input list (in order) that are greater than i. Use mupl-filter (a use of mlet is given to you to make this easier).

    5. Challenge Problem: Write a second version of eval-exp (bound to eval-exp-c) that builds closures

with smaller environments: When building a closure, it uses an environment that is like the current environment but holds only variables that are free variables in the function part of the closure. (A free variable is a variable that appears in the function without being under some shadowing binding for the same variable.)

Avoid computing a function’s free variables more than once by writing a function compute-free-vars that takes an expression and returns a di erent expression that uses fun-challenge everywhere in place of fun. The new struct fun-challenge (provided to you; do not change it) has a eld freevars to store exactly the set of free variables for the function. Store this set as a Racket set of Racket strings. (Sets are prede ned in Racket’s standard library; consult the documentation for useful functions such as set, set-add, set-member?, set-remove, set-union, and any other functions you wish.)

You must have a top-level function compute-free-vars that works as just described | storing the free variables of each function in the freevars eld | so the grader can test it directly. Then write a new \main part" of the interpreter that expects the sort of mupl expression that compute-free-vars returns. The case for function de nitions is the interesting one.


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