Assignment 3 Solution

    • Introduction


This assignment is about implementing the environmental model of execution. At the end of the assignment, you will learn how a language with several interesting features is implemented. Let us give this language the name myracket. The implementation is not e cient|e ciency will be the subject of the course CS 302. However, it will teach you the principles behind the implementation of myracket.



    • Description of myracket


First let us see how the language being implemented will be represented. Remember that you are about to write a program for which the data is a program in myracket. Therefore we have to choose a suitable representation for programs in myracket. This is done through a series of structs that you will nd in the le called defs.rkt.

(struct pgm (deflist) #:transparent)

(struct def (var/fun exp) #:transparent)

A program is a list of de nitions, of which one of the de nitions de nes a special symbol main. You should write you myracket programs in such a way that, at the end of execution, main will have the result of the program. Each def binds a variable or a function name to an expression. A deflist is simply a list of defs so that nothing needs to be de ned for it. However one needs to de ne exp. Going further:

;A variable is an expression

;A constant is an expression

;A string is an expression.

;A list is an expression

(struct uexp (op exp) #:transparent); op = car, cdr

(struct bexp (op exp1 exp2) #:transparent); op = cons, +, -, *, <, =, <= (struct iff (cond exp1 exp2) #:transparent) (struct app (fun explist) #:transparent)

(struct lam (varlist exp) #:transparent)

(struct sett (var exp) #:transparent)

(struct lett (deflist exp2) #:transparent)

(struct lets (deflist exp2) #:transparent)

(struct beginexp (explist) #:transparent)

(struct defexp (deflist exp) #:transparent)

(struct debugexp () #:transparent)

As you can see, expressions consist of symbols, constants, strings, lists, unary and binary expressions with built-in operators, ifs, applications, lambdas, lets, begin expressions and de ne expressions. In addition, there is a debug expression (debug), that we shall talk about later. Note that there are certain kinds of expressions that are in the intersection of myracket and drracket. These are strings, numbers, booleans, strings and operators. This is to make the assignment easy.

Consider the program:

(define (f g x) (g (* x x)))

(define x 4)

(define (h y) (+ x y))

(define main (f h 5))

Using the structs de ned above, this program would be represented as follows:

(define prog1

(pgm (list

(def ’f (lam (list ’g ’x) (app ’g (list (bexp * ’x ’x)))))

(def ’x 4)

(def ’h (lam (list ’y) (bexp + ’x ’y)))

(def ’main (app    ’f (list ’h 5))))))

The    le examples.rkt contains ten examples that cover all those discussed in the class.



    • Representation of stack, frames, and closures


From the discussion on the environment model of execution, we know that as the program is running, it needs to create closures and frames. We also need a stack to keep track of the current environment. We thus need the following de nitions:

(struct frame (number bindings parent)    #:transparent)

(struct closure (lambda frame) #:transparent)

Each frame represents a local environment. It consists of a frame number, a sequence of bindings of symbols to their values, and the frame number of its parent frame. The parent frame is the

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begining of a chain of framcreateframees representing the global environment. The bindings should be implemented through a mutable hash table (Note: Read mutable hash tables). A closure is a lambda along with with an environment that helps in nding the values of the global symbols in the lambda. In this case also the environment is represented by the frame number of the beginning of a chain of frames. Finally, a stack is a list of frames, the top of the stack holds the frame beginning the current environment.

If you see the le defs.rkt, you will notice that the structs’s for closure and frame don’t look like what has been shown above. Instead, they seem to contain a lot of things after the #:transparent. The extra code is to ensure that when you display frames (by a display or displayln), the output is easy to read and understand. For example, in my implementation, just before the execution of the body of h (i.e. just before the execution of (+ x y)), . . . the environment would look like this

@@@@@@@@@@@@@@@@@@@@@@@

#<Frame: Number: 2

Bindings:

y --> 25

Parent:    0>

@@@@@@@@@@@@@@@@@@@@@@@

#<Frame: Number: 0

Bindings:

x --> 4

f --> #<: #<lam: (g x) #<app: g (#<+: x x>)>> Environment:    0>

h --> #<: #<lam: (y) #<beginexp: (#<debugexp> #<+: x y>)>> Environment:    0>

Parent:    #<emptyframe: >>

@@@@@@@@@@@@@@@@@@@@@@@

The environment starts with the frame numbered 2. This is the frame of h with the parameter y which has a value of 25. The parent of this frame is frame 0. This has bindings for x, f and h but not main. To display the current environment, I have a special expression called (debugexp). If you insert (debugexp) at a certain point in the program, it will show you the complete environment at that point. This, I hope, will be useful for you in debugging your program.



    • A summary of the implementation rules


Here I shall summarize the rules of the implementation that we have discussed many times in the class.


    1. defs extend the current frame by the new things being de ned. Each de nition binds the symbol being de ned by its value.

    2. The value of a symbol is whatever it is bound to.

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    3. The value of a constant is its value in drracket.

    4. The value of a unary or a binary operator is the corresponding racket operator applied to the values of its arguments.

    5. The value of a lambda is a closure.

    6. To nd value of an application of a function to a list of arguments a new frame is created with the parameters of the function bound to the actual arguments. The new frame becomes the current environment after the parent of the frame is set to the environment packed in the closure of the function being applied.

    7. A lett also creates a new frame with the current frame as parent. A lets can be translated to individual letts.

    8. A sett is an assignment.

    9. You know what beginexp and defexp do.

    10. debugexp is being given to you in an implemented form.



    • What you have to do


As usual, there will be the following    les:


    1. Files called defs.rkt and examples.rkt mentioned before.

    2. A signature le call my-interpreter.rkt which will have un lled functions with brief de-scriptions of what they do. This is the le that you have to ll.

    3. A trial le called try.rkt, in which you can try out di erent functions in my model imple-mentation. Everything in the model implementation is made visible to you in try.rkt.

    4. What you have to submit is the  le my-interpreter.rkt, with each de nition completed.


















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