Notes and Tips

Credit

All credit for this assignment goes to Prof. Grossman and his team at UW.

Path To Victory

Code To Implement

file:	src/main/racket/uw5/uw5.rkt
functions:	racketlist->mupllist mupllist->racketlist mupl-value? expand-environment eval-exp ifaunit mlet* ifeq mupl-double mupl-sum-curry mupl-map-one mupl-map mupllist->racketlist eval-exp-c

Replace occurrences of "CHANGE" to complete the problems. 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 defined by the structs defined at the beginning of hw5.rkt. This is the definition 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 #f s2 e) is allowed for anonymous nonrecursive functions.
If e1, e2, and e3, and e4 are MUPL expressions, then (ifgreater e1 e2 e3 e4) is a MUPL expression. It is a conditional where the result is e3 if e1 is strictly greater than e2 else the result is e4. Only one of e3 and e4 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 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 (fst e1) is a MUPL expression (getting the first part of a pair).
If e1 is a MUPL expression, then (snd e1) is a MUPL expression (getting the second part of a pair).
(aunit) is a MUPL expression (holding no data, much like () in ML or null in Racket). Notice (aunit) is a MUPL expression, but aunit is not.
If e1 is a MUPL expression, then (isaunit e1) is a MUPL expression (testing for (aunit)).
(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 aunit, 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 aunit. 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 (aunit) (int 7)) or (fst (int 7)).

Warning

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

Problems

1. Warm-Up

1 a) racketlist->mupllist

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

1 b) mupllist->racketlist

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

2. Implementing the MUPL Language

mupl-value? (WashU Optional Utility)

(define (mupl-value? value)
       (error 'not-yet-implemented))

evaluates to #t if value is any of the MUPL value types.

Recall: A MUPL value is a MUPL integer constant, a MUPL closure, a MUPL aunit, or a MUPL pair of MUPL values.

Note: the or function will likely be useful here.

expand-environment (WashU Optional Utility)

(define (expand-environment name value env)
       (error 'not-yet-implemented))

Evaluates to an expanded version of the provided list env by consing a racket (name, value) pair onto env.

Raises an error if name is not a string? or value is not a mupl-value?.

Note: string-append and ~a are useful for generating better error messages.

For example:

(error (string-append "illegal name: " (~a name)))

eval-exp

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 modification 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.)
Functions are lexically scoped: A function evaluates to a closure holding the function and the current environment.
An ifgreater evaluates its first two subexpressions to values v₁ and v₂ respectively. If both values are integers, it evaluates its third subexpression if v₁ is a strictly greater integer than v₂ else it evaluates its fourth subexpression.
An mlet expression evaluates its first 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 first and second subexpressions to values. If the first 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 field is #f) 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 fst expression evaluates its subexpression. If the result for the subexpression is a pair, then the result for the fst expression is the e1 field in the pair.
A snd expression evaluates its subexpression. If the result for the subexpression is a pair, then the result for the snd expression is the e2 field in the pair.
An isaunit expression evaluates its subexpression. If the result is an aunit expression, then the result for the isaunit 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.

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).

3a) ifaunit

Write a Racket function ifaunit 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 aunit then it evaluates e2 and that is the overall result, else it evaluates e3 and that is the overall result. Sample solution: 1 line.

3b) mlet*

Write a Racket function mlet* that takes a Racket list of Racket pairs ’((s₁ . e₁) ... (s_i . e_i) ... (s_n . e_n)) and a final MUPL expression e_n+1. In each pair, assume s_i is a Racket string and e_i is a MUPL expression. mlet* returns a MUPL expression whose value is e_n+1 evaluated in an environment where each s_i is a variable bound to the result of evaluating the corresponding e_i for 1 ≤ i ≤ n. The bindings are done sequentially, so that each e_i is evaluated in an environment where s₁ through s_i−1 have been previously bound to the values e₁ through e_i−1.

3c) ifeq

Write a Racket function ifeq that takes four MUPL expressions e1, e2, e3, and e4 and returns a MUPL expression that acts like ifgreater except e3 is evaluated if and only if e1 and e2 are equal integers. 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.

mupl-double

WashU Exercise: mupl-double

mupl-sum-curry

WashU Exercise: mupl-sum-curry

mupl-map-one

WashU Exercise: mupl-map-one

4 a) mupl-map

Bind to the Racket variable mupl-map a MUPL function that acts like map (as we used extensively 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. Recall a MUPL list is aunit or a pair where the second component is a MUPL list.

4 b) mupl-mapAddN

Bind to the Racket variable mupl-mapAddN 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 that adds i to every element of the list. Use mupl-map (a use of mlet is given to you to make this easier).

5 Challenge Problem

eval-exp-c

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. Do this by writing a function compute-free-vars that takes an expression and returns a different expression that uses fun-challenge everywhere in place of fun. The new struct fun-challenge (provided to you; do not change it) has a field freevars to store exactly the set of free variables for the function. Store this set as a Racket set of Racket strings. (Sets are predefined 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 field — 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 definitions is the interesting one.

Test

Expand Environment

file:	mupl_expand_environment_test.rkt	Test
source folder:	src/test/racket/uw5	Test

note: ensure that you have removed all printing to receive credit for any assignment.

UW

Test your functions. The unit tests you have been provided are intentionally minimal.

file:	uw5test.rkt	Test
source folder:	src/test/racket/uw5	Test