Project 4: A Scheme Interpreter

Money Tree

Eval calls apply,
which just calls eval again!
When does it all end?

Table of Contents

Introduction

In this project, you will develop an interpreter for a subset of the Scheme language. As you proceed, think about the issues that arise in the design of a programming language; many quirks of languages are byproducts of implementation decisions in interpreters and compilers. The subset of the language used in this project is described in the functional programming section of Composing Programs.

You will also implement some small programs in Scheme. Scheme is a simple but powerful functional language. You should find that much of what you have learned about Python transfers cleanly to Scheme as well as to other programming languages. To learn more about Scheme, you can read Structure and Interpretation of Computer Programs online for free. Examples from Chapters 1 and 2 are included as test cases for this project. Language features from Chapters 3, 4, and 5 are not part of this project, but of course you are welcome to extend your interpreter to implement more of the language. Since we only include a subset of the language, your interpreter will not exactly match the behavior of other interpreters such as STk.

The project concludes with an open-ended graphics contest that challenges you to produce recursive images in only a few lines of Scheme. As an example, the picture above abstractly depicts all the ways of making change for $0.50 using U.S. currency. All flowers appear at the end of a branch with length 50. Small angles in a branch indicate an additional coin, while large angles indicate a new currency denomination. In the contest, you too will have the chance to unleash your inner recursive artist.

This project includes several files, but all of your changes will be made to the first four: scheme.py, scheme_reader.py, questions.scm, and tests.scm. You can download all of the project code as a zip archive, which contains the following files:

scheme.py The Scheme evaluator
scheme_reader.py The Scheme syntactic analyzer
questions.scm A collection of functions written in Scheme
tests.scm A collection of test cases written in Scheme
scheme_tokens.py A tokenizer for Scheme
scheme_primitives.py Primitive Scheme procedures
scheme_test.py A testing framework for Scheme
buffer.py A buffer implementation
ucb.py Utility functions for 61A
ok Autograder software
tests A directory of tests used by ok

Logistics

You'll work in a team of two people, Partner A and Partner B. In each part, you will do some of the work separately and some together with your partner. For example, if a problem is marked 5A, then it is a solo problem for Partner A. Both partners should read, think about, and understand the solution to all questions. Feel free to help each other on the solo questions. If you choose to work on the whole project alone, you must complete all questions yourself.

In Parts I and II, you will develop the interpreter in these stages:

In Part III, you will implement Scheme procedures.

There are 27 possible correctness points and 3 composition points. The composition score in this project will evaluate the clarity of your code and your ability to write tests that verify the behavior of your interpreter.

Submit the project by running python3 ok --submit. Only partner A should submit with this command.

In addition to submitting the project via this command, create a group on the ok website. A video walkthrough of this process is available here.

We also ask that you submit your final version through the homework submission system by copying scheme.py, scheme_reader.py, tests.scm, and questions.scm to your class account and running submit proj4. This secondary submission will be used to resolve any issues with the ok system.

Details of Scheme

Read-Eval-Print. The interpreter reads Scheme expressions, evaluates them, and displays the results.

scm> 2
2
scm> (((lambda (f) (lambda (x) (f f x)))
       (lambda (f k) (if (zero? k) 1 (* k (f f (- k 1)))))) 5)
120

The starter code for your Scheme interpreter in scheme.py can successfully evaluate the first expression above, since it consists of a single number. The second (a computation of 5 factorial) will not work just yet.

Load. Our load procedure differs from standard Scheme in that we use a symbol for the file name. For example, to load tests.scm, evaluate the following call expression.

scm> (load 'tests)

Symbols. Unlike some implementations of Scheme, in this project numbers and boolean values cannot be used as symbols. Also, symbols are always lowercased. This is illustrated in the following example, which won't work until a little bit later:

scm> (define 2 3)
Traceback (most recent call last):
  0 (#define 2 3)
Error: bad argument to define
scm> 'Hello
hello

Turtle Graphics. In addition to standard Scheme procedures, we include procedure calls to the Python turtle package. This will come in handy in Part IV, for the contest.

You can read the turtle module documentation online.

Note: The turtle Python module may not be installed by default on your personal computer. However, the turtle module is installed on the instructional machines. So, if you wish to create turtle graphics for this project (i.e. for the contest), then you'll either need to setup turtle on your personal computer or use university computers.

Development

Testing. The tests.scm file contains a long list of example Scheme expressions and their expected values.

(+ 1 2)
; expect 3
(/ 1 0)
; expect Error

You can compare the output of your interpreter to the expected output by running:

python3 scheme_test.py

For the example above, scheme_test.py will evaluate (+ 1 2) using your code in scheme.py, then output a test failure if 3 is not returned as the value. The second example tests for an error (but not the specific error message.

Only a small subset of tests are designated to run by default because tests.scm contains an (exit) call near the beginning, which halts testing. As you complete more of the project, you should move or remove this call.

Note: your interpreter doesn't know how to exit until Problems 3 and 4 are completed; all tests will run until then.

Important: As you proceed in the project, add new tests to the top of tests.scm to verify the behavior of your implementation. Your composition score for this project will depend on whether or not you have tested your implementation in ways that are different from the ok tests.

As always, you can run the doctests for the project:

python3 -m doctest scheme.py scheme_reader.py

We've included an autograder which includes tests for each question. You will have to unlock some of the tests first before you can use them to test your implementations. To unlock tests for question 1, run the following command from your terminal:

python3 ok -u -q 01

Once you have unlocked the tests, you can run the tests for question 1 as follows:

python3 ok -q 01

You can also invoke the autograder for all problems at once using:

python3 ok

The tests directory is used to store autograder tests, so make sure not to modify it. You may lose all your unlocking progress if you do. If you need to get a fresh copy, you can download the zip archive and copy it over, but you will need to start unlocking from scratch.

If you have any problems logging in or communicating with the server, use the --local flag to inhibit any server communication.

Note that the tests we provide you through the autograder are not comprehensive. To ensure that your interpreter is correct and bug-free, you will have to add your own tests to tests.scm, and ensure that they cover as many cases as possible.

Debugging. If you're stuck, try using the trace decorator from the ucb module to follow the path of execution in your interpreter.

You can also use ok to help with debugging, by adding the -i flag to start an interactive session:

python3 ok -q 1 -i

If you get stuck, try this guide to debugging.

Exceptions. As you develop your Scheme interpreter, you may find that Python raises various uncaught exceptions when evaluating Scheme expressions. As a result, your Scheme interpreter will halt. Some of these may be the results of bugs in your program, and some may be useful indications of errors in user programs. The former should be fixed (of course!) and the latter should be handled, usually by raising a SchemeError. All SchemeError exceptions are handled and printed as error messages by the read_eval_print_loop function in scheme.py. Ideally, there should never be unhandled Python exceptions for any input to your interpreter.

Running Your Scheme Interpreter

To run your Scheme interpreter in an interactive session, type:

python3 scheme.py

You can use your Scheme interpreter to evaluate the expressions in an input file by passing the file name as a command-line argument to scheme.py:

python3 scheme.py tests.scm

Currently, your Scheme interpreter can handle a few simple expressions, such as:

scm> 1
1
scm> 42
42
scm> #t
True

To exit the Scheme interpreter, press either Ctrl-c or Ctrl-d or evaluate the exit procedure (after completing questions 3 and 4):

scm> (exit)

Part I: The Reader

The function scheme_read in scheme_reader.py parses a Buffer (see buffer.py) instance that returns valid Scheme tokens when its current and pop methods are invoked. It returns the next full Scheme expression in the src buffer, using this representation:

Scheme Data Type Our Internal Representation
Numbers Python's built-in int and float data types.
Symbols Python's built-in string data type.
Booleans (#t, #f) Python's built-in True, False values.
Pairs The Pair class, defined in scheme_reader.py.
nil The nil object, defined in scheme_reader.py.

Problem 1 (1 pt)

Complete the scheme_read function in scheme_reader.py by adding support for quotation. This function selects behavior based on the type of the next token:

Test your understanding and implementation before moving on:

python3 ok -q 1 -u
python3 ok -q 1 -i

Problem 2 (2 pt)

Complete the read_tail function in scheme_reader.py by adding support for dotted lists. A dotted list in Scheme is not necessarily a well-formed list, but instead has an arbitrary second attribute that may be any Scheme value.

The read_tail function expects to read the rest of a list or dotted list, assuming the open parenthesis of that list has already been popped by scheme_read.

Consider the case of calling scheme_read on input "(1 2 . 3)". The read_tail function will be called on the suffix "1 2 . 3)", which is

Thus, read_tail would return Pair(1, Pair(2, 3)).

Hint: In order to verify that only one element follows a dot, after encountering a '.', read one additional expression and then check to see that a closing parenthesis follows.

Test your understanding and implementation before moving on:

python3 ok -q 2 -u
python3 ok -q 2 -i

You should also run the doctests for scheme_reader.py and test your parser interactively by running python3 scheme_reader.py. Every time you type in a value into the prompt, both the str and repr values of the parsed expression are printed.

read> 42
str : 42
repr: 42
read> '(1 2 3)
str : (quote (1 2 3))
repr: Pair('quote', Pair(Pair(1, Pair(2, Pair(3, nil))), nil))
read> nil
str : ()
repr: nil
read> '()
str : (quote ())
repr: Pair('quote', Pair(nil, nil))
read> (1 (2 3) (4 (5)))
str : (1 (2 3) (4 (5)))
repr: Pair(1, Pair(Pair(2, Pair(3, nil)), Pair(Pair(4, Pair(Pair(5, nil), nil)), nil)))
read> (1 (9 8) . 7)
str : (1 (9 8) . 7)
repr: Pair(1, Pair(Pair(9, Pair(8, nil)), 7))
read> (hi there . (cs . (student)))
str : (hi there cs student)
repr: Pair('hi', Pair('there', Pair('cs', Pair('student', nil))))

Part II: The Evaluator

All further changes to the interpreter will be made in scheme.py. For each question, add a few tests to the top of tests.scm to verify the behavior of your implementation.

In the implementation given to you, the scheme_eval function is complete, but most of the functions or methods it uses are not implemented. In fact, the evaluator can only evaluate self-evaluating expressions: numbers, booleans, and nil.

Some Core Functionality

Problem 3 (2 pt)

Implement apply_primitive, which is called by scheme_apply. Primitive procedures are applied by calling a corresponding Python function that implements the procedure.

Scheme primitive procedures are represented as instances of the PrimitiveProcedure class, defined in scheme_primitives.py. A PrimitiveProcedure has two instance attributes:

To see a list of all Scheme primitive procedures used in the project, look in the scheme_primitives.py file. Any function decorated with @primitive will be added to the globally-defined _PRIMITIVES list.

The apply_primitive function takes a PrimitiveProcedure instance, a Scheme list of argument values, and the current environment. Your implementation should:

Test your understanding and implementation before moving on:

python3 ok -q 3 -u
python3 ok -q 3 -i

The doctest for apply_primitive should now pass. However, your Scheme interpreter will still not be able to apply primitive procedures, because your Scheme interpreter still doesn't know how to look up the values for built-in symbols (such as +, *, and car). Let's fix that.

Problem 4 (2 pt)

Implement the lookup method of the Frame class. It takes a symbol (Python string) and returns the value bound to that name in the first Frame of the environment in which that name is found. A Frame represents an environment via two instance attributes:

Your lookup implementation should:

After you complete this problem, you should be able to evaluate primitive procedure calls, giving you the functionality of the Calculator language and more.

scm> +
#[primitive]
scm> (+ 1 2)
3
scm> (* 3 4 (- 5 2) 1)
36
scm> (odd? 31)
True

Test your understanding and implementation before moving on:

python3 ok -q 4 -u
python3 ok -q 4 -i

Problem 5A (1 pt)

There are two missing parts in the do_define_form function, which handles the (define ...) special forms. Implement just the first part, which binds names to values but does not create new procedures. do_define_form should return the name after performing the binding.

scm> (define tau (* 2 3.1415926))
tau

Test your understanding and implementation before moving on:

python3 ok -q 5 -u
python3 ok -q 5 -i

You should now be able to give names to values and evaluate symbols to those values.

scm> (define x 15)
x
scm> (define y (* 2 x))
y
scm> y
30
scm> (+ y (* y 2) 1)
91
scm> (define x 20)
x
scm> x
20

Problem 6B (1 pt)

Implement the do_quote_form function, which evaluates the quote special form.

Test your understanding and implementation before moving on:

python3 ok -q 6 -u
python3 ok -q 6 -i

You should now be able to evaluate quoted expressions.

scm> 'hello
hello
scm> '(1 . 2)
(1 . 2)
scm> '(1 (2 three . (4 . 5)))
(1 (2 three 4 . 5))
scm> (car '(a b))
a
scm> (eval (cons 'car '('(1 2))))
1

At this point in the project, your Scheme interpreter should be be able to support the following features:

User-Defined Procedures

User-defined procedures are represented as instances of the LambdaProcedure class, defined in scheme.py. A LambdaProcedure instance has three instance attributes:

Problem 7 (2 pt)

First, implement the begin special form, which includes a list of one or more sub-expressions that are each evaluated in order. The value of the begin expression is the value of the final sub-expression.

scm> (begin (+ 2 3) (+ 5 6))
11
scm> (define x (begin (display 3) (newline) (+ 2 3)))
3
x
scm> (+ x 3)
8
scm> (begin (print 3) '(+ 2 3))
3
(+ 2 3)

Hint: When scheme_eval evaluates one of the LOGICAL_FORMS in scheme.py, it calls scheme_eval on the returned value. Take care that your Scheme interpreter doesn't inadvertently call scheme_eval on the same value twice, or else you might have the following incorrect behavior:

scm> (begin 30 'hello)
Error: unknown identifier: hello

Test your understanding and implementation before moving on:

python3 ok -q 7 -u
python3 ok -q 7 -i

Problem 8 (2 pt)

Implement the do_lambda_form method, which creates LambdaProcedure instances by evaluating lambda expressions. While you cannot call a user-defined procedure yet, you can verify that you have read the procedure correctly by evaluating a lambda expression:

scm> (lambda (x y) (+ x y))
(lambda (x y) (+ x y))

In Scheme, it is legal to have function bodies with more than one expression. In order to implement this feature, your do_lambda_form should detect when the body of a lambda expression contains multiple expressions. If so, then do_lambda_form should place those expressions inside of a (begin ...) form, and use that begin expression as the body:

scm> (lambda (y) (print y) (* y 2))
(lambda (y) (begin (print y) (* y 2)))

Test your understanding and implementation before moving on:

python3 ok -q 8 -u
python3 ok -q 8 -i

Problem 9A (1 pt)

Currently, your Scheme interpreter is able to define user-defined procedures in the following manner:

scm> (define f (lambda (x) (* x 2)))
f

However, we'd like to be able to use the shorthand form of defining procedures:

scm> (define (f x) (* x 2))
f

Modify the do_define_form function so that it correctly handles the shorthand procedure definition form above. Make sure that it can handle multi-expression bodies.

Test your understanding and implementation before moving on:

python3 ok -q 9 -u
python3 ok -q 9 -i

You should now find that defined procedures evaluate to lambda procedures.

scm> (define (square x) (* x x))
square
scm> square
(lambda (x) (* x x))

Problem 10 (2 pt)

Implement the make_call_frame method of the Frame class, which:

Test your understanding and implementation before moving on:

python3 ok -q 10 -u
python3 ok -q 10 -i

Problem 11B (1 pt)

Implement the check_formals function to raise an error whenever the Scheme list of formal parameters passed to it is invalid. Raise a SchemeError if the list of formals is not a well-formed list of symbols or if any symbol is repeated.

Hint: The scheme_symbolp function in scheme_primitives.py returns whether a value is a Scheme symbol.

Test your understanding and implementation before moving on:

python3 ok -q 11 -u
python3 ok -q 11 -i

Problem 12 (2 pt)

Implement scheme_apply to correctly apply user-defined LambdaProcedure instances. (The case for MuProcedure is handled later in the project). It should:

Test your understanding and implementation before moving on:

python3 ok -q 12 -u
python3 ok -q 12 -i

After you complete scheme_apply, user-defined functions (and lambda functions) should work in your Scheme interpreter. Now is an excellent time to revisit the tests in tests.scm and ensure that you pass the ones that involve definition (Sections 1.1.2 and 1.1.4). You should also add additional tests of your own at the top of tests.scm to verify that your interpreter is behaving as you expect.

Special Forms

Logical special forms include if, and, or, and cond. These expressions are special because not all of their sub-expressions may be evaluated.

In Scheme, only #f is a false value. All other values are true values. You can test whether a value is a true value or a false value using the provided Python functions scheme_true and scheme_false, defined in scheme_primitives.py. Note that, in our interpreter, like in STk, false and False can be used in place of #f. Similarly, true and True can be used in place of #t.

Problem 13A (1 pt)

Implement do_if_form so that if expressions are evaluated correctly. This function should return either the second (consequent) or third (alternative) expression of the if expression, depending on the value of the first (predicate) expression.

scm> (if (= 4 2) #t #f)
False
scm> (if (= 4 4) (* 1 2) (+ 3 4))
2

It is legal to pass in just two expressions to the if special form. In this case, you should return the second expression if the first expression evaluates to a true value. Otherwise, return the special okay value, which represents an undefined value.

scm> (if (= 4 2) #t)
okay

Test your understanding and implementation before moving on:

python3 ok -q 13 -u
python3 ok -q 13 -i

Problem 14B (2 pt)

Implement do_and_form and do_or_form so that and and or expressions are evaluated correctly.

The logical forms and and or are short-circuiting. For and, your interpreter should evaluate each sub-expression from left to right, and if any of these evaluates to a false value, then False is returned. If all but the last sub-expressions evaluate to true values, return the last sub-expression from do_and_form.

For or, evaluate each sub-expression from left to right. If any evaluates to a true value, then quote that value and return it. The return value must be quoted because it will be evaluated as an expression in scheme_eval. If all but the last sub-expression evaluate to a false value, return the last sub-expression from do_or_form without quoting it.

scm> (and)
True
scm> (or)
False
scm> (and 4 5 6)  ; all operands are true values
6
scm> (or 5 2 1)  ; 5 is a true value
5
scm> (and #t #f 42 (/ 1 0))  ; short-circuiting behavior of and
False
scm> (or 4 #t (/ 1 0))  ; short-circuiting behavior of or
4

Test your understanding and implementation before moving on:

python3 ok -q 14 -u
python3 ok -q 14 -i

Problem 15A (1 pt)

Implement do_cond_form so that it returns the first result sub-expression corresponding to a true predicate, or the sub-expression corresponding to else. Your implementation should match the following examples and the additional tests in tests.scm.

scm> (cond ((= 4 3) 'nope)
           ((= 4 4) 'hi)
           (else 'wait))
hi
scm> (cond ((= 4 3) 'wat)
           ((= 4 4))
           (else 'hm))
True
scm> (cond ((= 4 4) 'here 42)
           (else 'wat 0))
42

For the last example, where the body of a cond case has multiple expressions, you might find it helpful to replace cond-bodies with multiple expression bodies into a single begin expression, i.e., the following two expressions are equivalent.

(cond ((= 4 4) 'here 42))
(cond ((= 4 4) (begin 'here 42)))

If the body of a cond case is empty, then do_cond_form should quote the value of the predicate and return it, if the predicate evaluates to a true value.

scm> (cond (12))
12
scm> (cond ((= 4 3))
           ('hi))
hi

The value of a cond is undefined if there are no true predicates and no else. In such a case, do_cond_form should return okay.

Test your understanding and implementation before moving on:

python3 ok -q 15 -u
python3 ok -q 15 -i

Problem 16 (2 pt)

The let special form introduces local variables, giving them their initial values. For example:

scm> (define x 'hi)
x
scm> (define y 'bye)
y
scm> (let ((x 42) (y (* 5 10)))
       (list x y))
(42 50)
scm> (list x y)
(hi bye)

Implement the do_let_form method to have this effect and test it, by adding test cases to the top of tests.scm. Make sure your let correctly handles multi-expression bodies:

scm> (let ((x 42)) x 1 2)
2

A let form creates a new Frame (containing the let bindings) which extends the current environment and evaluates the body of the let in this new environment.

Test your understanding and implementation before moving on:

python3 ok -q 16 -u
python3 ok -q 16 -i

Problem 17 (2 pt)

Implement do_mu_form to evaluate the mu special form, a non-standard Scheme expression type. A mu expression is similar to a lambda expression, but evaluates to a MuProcedure instance that is dynamically scoped. The MuProcedure class has been provided for you.

Additionally, complete scheme_apply to call MuProcedure procedures using dynamic scoping. Calling a LambdaProcedure uses lexical scoping: the parent of the new call frame is the environment in which the procedure was defined. Calling a MuProcedure created by a mu expression uses dynamic scoping: the parent of the new call frame is the environment in which the call expression was evaluated. As a result, a MuProcedure does not need to store an environment as an instance attribute. It can refer to names in the environment from which it was called.

scm> (define f (mu (x) (+ x y)))
f
scm> (define g (lambda (x y) (f (+ x x))))
g
scm> (g 3 7)
13

To test yourself, figure out what the expression (g 3 7) would evaluate to if the function f were instead a lambda function.

Test your understanding and implementation before moving on:

python3 ok -q 17 -u
python3 ok -q 17 -i

Your Scheme interpreter implementation is now complete. You should have been adding tests to the top of tests.scm as you did each problem. These tests will be evaluated as part of your composition score for the project.

Part III: Write Some Scheme

Not only is your Scheme interpreter itself a tree-recursive program, but it is flexible enough to evaluate other recursive programs. Implement the following procedures in Scheme in the questions.scm file.

Problem 18 (1 pt)

Implement the zip procedure, which takes in a list of pairs and converts it into a pair of lists, where the first list contains all of the first elements of the original pairs, and the second list contains all of the second elements.

The "pairs" in the input are well-formed two-element lists, not Scheme pairs.

scm> (zip '((1 2)))
((1) (2))
scm> (zip '((1 2) (3 4) (5 6)))
((1 3 5) (2 4 6))

Test your understanding and implementation before moving on:

python3 ok -q 18 -u
python3 ok -q 18 -i

Problem 19 (1 pt)

Implement the list-partitions procedure, which lists all of the ways to partition a positive integer total into at most max-pieces pieces, where all of the pieces are less than or equal to a positive integer max-value.

Hint: Define a helper procedure to construct partitions.

The number 5 has 4 partitions using pieces up to a max-value of 3 and a max-pieces of 4:

3, 2          (two pieces)
3, 1, 1       (three pieces)
2, 2, 1       (three pieces)
2, 1, 1, 1    (four pieces)

Test your understanding and implementation before moving on:

python3 ok -q 19 -u
python3 ok -q 19 -i

Problem 20 (2 pt)

In Scheme, source code is data. Every non-primitive expression is a list, and we can write procedures that manipulate other programs just as we write procedures that manipulate lists.

Re-writing programs can be useful: we can write an interpreter that only handles a small core of the language, and then write a procedure analyze that converts other special forms into the core language before a program is passed to the interpreter.

For example, the let special form is equivalent to a call expression that begins with a lambda expression. Both create a new frame extending the current environment and evaluate a body within that new environment.

(let ((x 42) (y 16)) (+ x y))
;; Is equivalent to:
((lambda (x y) (+ x y)) 42 16)

We can use this rule to rewrite all let special forms into lambda expressions. We prevent evaluation of a program by quoting it, and then pass it to analyze:

scm> (analyze '(let ((a 1) (b 2)) (+ a b)))
((lambda (a b) (+ a b)) 1 2)
scm> (analyze '(let ((a 1)) (let ((b a)) b)))
((lambda (a) ((lambda (b) b) a)) 1)

In order to handle all programs, analyze must be aware of Scheme syntax. Since Scheme expressions are recursively nested, analyze must also be recursive. In fact, the structure of analyze looks like that of scheme_eval:

(define (analyze expr)
  (cond ((atom?   expr) <Analyze atom>)
        ((quoted? expr) <Analyze quoted>)
        ((lambda? expr) <Analyze lambda>)
        ((define? expr) <Analyze define>)
        ((let?    expr) <Analyze let>)
        (else           <Analyze other>)))

Implement the analyze procedure, which takes in an expression and converts all of the let special forms in the expression into their equivalent lambda expressions.

Hint: You may want to use the provided apply-to-all procedure and the 'zip' procedure from Q18.

Test your understanding and implementation before moving on:

python3 ok -q 20 -u
python3 ok -q 20 -i

Note: We used let while defining analyze. What if we want to run analyze on an interpreter that does not recognize let? We can pass analyze to itself to compile itself into an equivalent program that does not use let:

;; The analyze procedure
(define (analyze expr)
  ...)

;; A list representing the analyze procedure
(define analyze-code
  '(define (analyze expr)
     ...))

;; An analyze procedure that does not use 'let'
(define analyze-without-let
  (analyze analyze-code))

Problem 21 (0 pt; optional)

Implement the hax procedure that draws the following recursive illustration when passed two arguments, a side length d and recursive depth k. The example below is drawn from (hax 200 4).

hax

To see how this illustration is constructed, consider this annotated version that gives the relative lengths of lines of the component shapes in the figure.

hax_annotated

Part IV: Extra

Extra Credit Problem 22 (2 pt)

Complete the function scheme_optimized_eval in scheme.py. This alternative to scheme_eval is properly tail recursive. That is, the interpreter will allow an unbounded number of active tail calls in constant space.

Instead of recursively calling scheme_eval for tail calls, logical special forms, and let, replace the current expr and env with different expressions and environments. For call expressions, this change only applies to calling user-defined procedures.

Once you finish, uncomment the following line in scheme.py:

scheme_eval = scheme_optimized_eval

Test your understanding and implementation before moving on:

python3 ok -q 22 -u
python3 ok -q 22 -i

Congratulations! You have finished the final project for 61A! Assuming your tests are good and you've passed them all, consider yourself a proper computer scientist!

Now, get some sleep. You've earned it!

Recursive Art Contest

We've added a number of primitive drawing procedures that are collectively called "turtle graphics". The turtle represents the state of the drawing module, which has a position, an orientation, a pen state (up or down), and a pen color. The tscheme__x_ functions in scheme_primitives.py are the implementations of these procedures, and show their parameters with a brief description of each.

The Python documentation of the turtle module contains more detail.

Contest: Create a visualization of an iterative or recursive process of your choosing, using turtle graphics. Your implementation must be written entirely in Scheme using the interpreter you have built. However, you may add primitive procedures to interface with Python's turtle or math modules. Other than that all computation must be done in Scheme. If you do add new primitives, then make sure to submit scheme_primitives.py in addition to contest.scm.

Prizes, as well as 3 extra credit points, will be awarded for the winning entry in each of the following categories.

Entries (code and results) will be posted online, and winners will be selected by popular vote as part of a future homework. The voting instructions will read:

Please vote for your favorite entry in this semester's 61A Recursion Exposition contest. The winner should exemplify the principles of elegance, beauty, and abstraction that are prized in the Berkeley computer science curriculum. As an academic community, we should strive to recognize and reward merit and achievement (translation: please don't just vote for your friends).

To improve your chance of success, you are welcome to include a title and descriptive haiku in the comments of your entry, which will be included in the voting.

Entries that do not construct an image iteratively or recursively may be disqualified. This includes just drawing a preexisting image, even if the drawing function is iterative or recursive.

Submission instructions are posted.

Extra Challenge

We have implemented a significant subset of Scheme in this project, but our interpreter can be extended with more features by following the extension instructions.