Money Tree

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


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. Since we only include a subset of the language, your interpreter will not exactly match the behavior of other interpreters.

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.

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:,, questions.scm, and tests.scm. You can download all of the project code as a zip archive, which contains the following files:

  • the Scheme evaluator
  • the Scheme syntactic analyzer
  • questions.scm: a collection of functions written in Scheme
  • tests.scm: a collection of test cases written in Scheme
  • a tokenizer for Scheme
  • definitions for primitive Scheme procedures
  • a Buffer implementation, used in
  • utility functions for 61A
  • ok: the autograder
  • tests: a directory of tests used by ok

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

  • Reading Scheme expressions
  • Symbol evaluation
  • Calling built-in procedures
  • Definitions
  • Lambda expressions and procedure definition
  • Calling user-defined procedures
  • Evaluation of special forms

In Part III, you will implement Scheme procedures.

Important submission note: For full credit, submit with Part I complete by Thursday 4/13, submit again with Part II complete by Tuesday 4/18, and submit the entire project by Thursday 4/20. You will get an extra credit point for submitting the entire project by Wednesday 4/19.

We've written a language specification and primitive procedure reference for the 61A subset of Scheme that you'll be building in this project. Reading the entirety of either of these documents should not be necessary, although a TA may direct you to certain sections if you are having trouble.


This is a 2 week project. You may work with one other partner. You should not share your code with students who are not your partner or copy from anyone else's solutions.

Remember that you can earn an additional bonus point by submitting the project at least 24 hours before the deadline.

In the end, you will submit one project for both partners. The project is worth 31 points. 29 points are assigned for correctness, and 2 points for the overall composition of your program.

You will turn in the following files:

  • questions.scm
  • tests.scm

You do not need to modify or turn in any other files to complete the project. To submit the project, run the following command:

python3 ok --submit

You will be able to view your submissions on the OK dashboard.

For the functions that we ask you to complete, there may be some initial code that we provide. If you would rather not use that code, feel free to delete it and start from scratch. You may also add new function definitions as you see fit.

However, please do not modify any other functions. Doing so may result in your code failing our autograder tests. Also, please do not change any function signatures (names, argument order, or number of arguments).


Throughout this project, you should be testing the correctness of your code. It is good practice to test often, so that it is easy to isolate any problems. However, you should not be testing too often, to allow yourself and your partner the time to think through problems.

We have provided an autograder called ok to help you with testing your code and tracking your progress. The first time you run the autograder, you will be asked to log in with your OK account using your web browser. Please do so. Each time you run ok, it will back up your work and progress on our servers.

The primary purpose of ok is to test your implementations, but there are two things you should be aware of.

First, some of the test cases are locked. To unlock tests, run the following command from your terminal:

python3 ok -u

This command will start an interactive prompt that looks like:

Assignment: A Scheme Interpreter
OK, version ...

Unlocking tests

At each "? ", type what you would expect the output to be.
Type exit() to quit

Question 0 > Suite 1 > Case 1
(cases remaining: 1)

>>> Code here

At the ?, you can type what you expect the output to be. If you are correct, then this test case will be available the next time you run the autograder.

The idea is to understand conceptually what your program should do first, before you start writing any code.

Once you have unlocked some tests and written some code, you can check the correctness of your program using the tests that you have unlocked:

python3 ok

Most of the time, you will want to focus on a particular question. Use the -q option as directed in the problems below.

Second, there may be some test cases that are hidden. These test cases are not run by the command:

python3 ok

We keep test cases hidden to ensure that you write your code with the intention of solving the question at hand, not purely to pass the given tests. The hidden tests will be run when you submit your project. You will receive an email with part of the autograder results after submitting. However, the autograder has a 15 minute cooldown period. If you submit before 15 minutes have passed, the autograder will not run.

We recommend that you submit after you finish each problem. Only your last submission will be graded. It is also useful for us to have more backups of your code in case you run into a submission issue.

The tests folder is used to store autograder tests, so do not 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 do not want us to record a backup of your work or information about your progress, use the --local option when invoking ok. With this option, no information will be sent to our course servers.

Details of Scheme

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

scm> 2
scm> (+ 2 3)
scm> (((lambda (f) (lambda (x) (f f x)))
       (lambda (f k) (if (zero? k) 1 (* k (f f (- k 1)))))) 5)

The starter code for your Scheme interpreter in can successfully evaluate the first expression above, since it consists of a single number. The second (a primitive call) and the third (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. Various dialects of Scheme are more or less permissive about identifiers (which serve as symbols and variable names).

Our rule is that:

An identifier is a sequence of letters (a-z and A-Z), digits, and characters in !$%&*/:<=>?@^_~-+. that do not form a valid integer or floating-point numeral.

Our version of Scheme is case-insensitive: two identifiers are considered identical if they match except possibly in the capitalization of letters. They are internally represented and printed in lower case:

scm> 'Hello

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

Testing Your Scheme Interpreter

Testing. The tests.scm file contains a long list of sample Scheme expressions and their expected values. Many of these examples are from Chapters 1 and 2 of Structure and Interpretation of Computer Programs, the textbook that Composing Programs is adapted from.

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

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

python3 ok -q tests.scm

For the example above, your Scheme interpreter will evaluate (+ 1 2) using your code in, 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. However, your interpreter doesn't know how to exit until Problems 3 and 4 are completed; all tests will run until then.

Writing Tests. As you proceed in the project, add new tests to the top of tests.scm to verify the behavior of your implementation. Half of your composition score for this project depends on whether you have tested your implementation in ways that are different from the ok tests and other Scheme assignments you may have seen in class.

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 Ideally, there should never be unhandled Python exceptions for any input to your interpreter.

Running Your Scheme Interpreter

To start an interactive Scheme interpreter session, type:


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

python3 tests.scm

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

scm> 1
scm> 42
scm> true

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

scm> (exit)


Here is a brief overview of each of the Read-Eval-Print Loop components in our interpreter.

  • Read: This step parses user input (a string of Scheme code) into our interpreter's internal Python representation of Scheme expressions (e.g. Pairs).

    • Lexical analysis has already been implemented for you in the tokenize_lines function in This function returns a Buffer (from of tokens. You do not need to read or understand the code for this step.
    • Syntactic analysis happens in, in the scheme_read and read_tail functions. Together, these mutually recursive functions parse Scheme tokens into our interpreter's internal Python representation of Scheme expressions. You will complete both functions.
  • Eval: This step evaluates Scheme expressions (represented in Python) to obtain values. Code for this step is in the main file.

    • Eval happens in the scheme_eval function. If the expression being evaluated is a special form, the corresponding do_XXX_form function is called. You will fill in part of scheme_eval, as well as several of the do_XXX_form functions.
    • Apply happens in the scheme_apply function. scheme_apply calls the apply method of a Procedure, which is implemented in its subclasses PrimitiveProcedure and UserDefinedProcedure. For user-defined procedures, the apply method evaluates the procedure body, resulting in a mutually recursive eval-apply loop.
  • Print: This step prints the __str__ representation of the obtained value.
  • Loop: The step is handled by the read_eval_print_loop function in You do not need to understand the entire implementation.

Part I: The Reader

Important submission note: For full credit, submit with Part I complete by Thursday 4/13, submit again with Part II complete by Tuesday 4/18, and submit the entire project by Thursday 4/20. You will get an extra credit point for submitting the entire project by Wednesday 4/19.

The first part of this project deals with reading and parsing user input. All changes in this part should be made in

scheme_read and read_tail in are mutually recursive functions. Together they parse Scheme code into Python values with the following representation:

Input Example Scheme Data Type Our Internal Representation
scm> 1 Numbers Python's built-in int and float values
scm> x Symbols Python's built-in string values
scm> true Booleans (#t, #f) Python's built-in True, False values
scm> (+ 2 3) Pairs Instances of the Pair class, defined in
scm> nil nil The nil object, defined in

Both scheme_read and read_tail take in a single parameter, src, which is an instance of Buffer (see A Buffer is a mutable object, which keeps a record of all tokens that haven't been processed yet. There are two methods you'll use to interact with src:

  • src.remove_front(): mutates src by removing the first token in src and returns it. For example, if src currently contains the tokens [4, '.', 3, ')'], then src.remove_front() will return 4, and src will be left with ['.', 3, ')'].
  • src.current(): returns the first token in src without removing it. For example, if src currently contains the tokens [4, '.', 3, ')'], then src.current() will return 4 but src will remain the same.

Problem 1 (2 pt)

Implement the scheme_read and read_tail functions in

The behavior of scheme_read depends on the type of the first token currently in src:

  • If the token is the string "nil", return the nil object.
  • If the token is (, recursively call read_tail and return its result.
  • If the next token is not a delimiter, then it must be self-evaluating. Return it. (provided)
  • If none of the above cases apply, raise an error. (provided)

The behavior of read_tail also depends on the type of the first token currently in src:

  • If there are no more tokens, raise an error. (provided)
  • If the token is ), return the nil object.
  • If the token is ., it is a dotted list. Implement this in Problem 2.
  • If none of the above cases apply, the src is at the beginning of an expression. Then:

    1. Read the next expression (Hint: Which function do we use to read an expression?)
    2. Recursively read the rest of the original expression until the matching closing parenthesis.
    3. Return the results as a Pair instance.

Some implementation tips:

  • scheme_read should be called when a complete Scheme expression needs to be extracted from src. It will remove enough tokens to form one expression and return that expression in the correct internal representation.
  • read_tail expects to read the rest of a list or dotted list, assuming the open parenthesis of that list has already been removed by scheme_read. It will read expressions (and thus remove tokens) until the matching closing parenthesis ) is seen. This list of expressions is returned in the correct internal representation (i.e. instances of the Pair class).

Test your understanding and implementation before moving on:

python3 ok -q 01 -u
python3 ok -q 01

Problem 2 (1 pt)

Complete the read_tail function by adding support for dotted lists.

  • An ordinary list denotes a linked sequence of Pairs in which the second attribute of the final pair is nil.
  • A dotted list denotes a sequence of Pairs in which the second attribute of the final pair may be any Scheme value.

For example:

(1 2 . 3) should be converted to Pair(1, Pair(2, 3))

A dotted list must have exactly one item after the dot; anything else is a syntax error.

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

  • The pair consisting of the Scheme value 1 and the value of the tail "2 . 3)", which is
  • The pair consisting of the Scheme value 2 and the Scheme value 3.

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 02 -u
python3 ok -q 02

You should also test your parser by:

  • Running the doctests for (python3 -m doctest
  • Testing interactively by running python3 Every time you type in a value into the prompt, both the str and repr values of the parsed expression are printed. You can try the following inputs:

    read> 42
    str : 42
    repr: 42
    read> nil
    str : ()
    repr: 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

Important submission note: For full credit, submit with Part I complete by Thursday 4/13, submit again with Part II complete by Tuesday 4/18, and submit the entire project by Thursday 4/20. You will get an extra credit point for submitting the entire project by Wednesday 4/19.

All changes in this part should be made in

In the starter implementation given to you, the evaluator can only evaluate self-evaluating expressions: numbers, booleans, and nil.

Read the first two sections of, called Eval/Apply and Environments.

  • The scheme_apply function is complete, but part of scheme_eval and most of the functions or methods they use are not yet implemented.
  • The .apply methods in subclasses of Procedure and the make_call_frame function assist in applying built-in and user-defined procedures.
  • The Frame class implements an environment frame.
  • The LambdaProcedure class (in the Procedures section) represents user-defined procedures.

These are all of the essential components of the interpreter; the rest of defines special forms and input/output behavior.

Test your understanding of how these components fit together by unlocking the tests for eval_apply.

python3 ok -q eval_apply -u

Some Core Functionality

Problem 3 (1 pt)

Implement both define and lookup methods of the Frame class. Each Frame object has the following instance attributes:

  • bindings is a dictionary that maps Scheme symbol keys (represented as Python strings) to Scheme values.
  • parent is the parent Frame instance. The parent of the Global Frame is None.

define takes a symbol (represented by a Python string) and value and binds the value to that symbol in the frame.

lookup takes a symbol and returns the value bound to that name in the first Frame of the environment in which that name is found. Your implementation should:

  • Return the value of the symbol in self.bindings if it exists.
  • Otherwise, lookup that symbol in the parent if the parent exists.
  • Otherwise, raise a SchemeError. (provided)

Test your understanding and implementation before moving on:

python3 ok -q 03 -u
python3 ok -q 03

After you complete this problem, you can open your Scheme interpreter (with python3 You should be able to look up built-in procedure names:

scm> +
scm> odd?
scm> display

However, your Scheme interpreter will still not be able to apply these procedures. Let's fix that.

Problem 4 (2 pt)

Complete the apply method in the class PrimitiveProcedure, which is called by scheme_apply. Primitive procedures are applied by calling a corresponding Python function that implements the procedure. Instances of the PrimitiveProcedure class, defined in, represent the values of Scheme primitive procedures. A PrimitiveProcedure has two instance attributes:

  • fn is the Python function that implements the primitive Scheme procedure.
  • use_env is a Boolean flag that indicates whether or not this primitive procedure will expect the current environment to be passed in as the last argument. The environment is required, for instance, to implement the primitive eval procedure.

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

The apply method of PrimitiveProcedure takes a Scheme list of argument values, and the current environment. Your implementation should:

  • Convert the Scheme list to a Python list of arguments. (provided)
  • If self.use_env is True, then add the current environment env as the last argument to this Python list.
  • Call self.fn on all of those arguments (Hint: Use *args notation).
  • If calling the function results in a TypeError exception being raised, then the wrong number of parameters were passed. Intercept the exception and raise an appropriate SchemeError in its place.

Test your understanding and implementation before moving on:

python3 ok -q 04 -u
python3 ok -q 04

Problem 5 (2 pt)

scheme_eval evaluates a Scheme expression in a given environment. Most of scheme_eval has already been implemented for you. It currently looks up names in the current environment, returns self-evaluating expressions (like numbers) and evaluates special forms.

Implement the missing part of scheme_eval, which evaluates a call expression. To evaluate a call expression, we do the following:

  1. Evaluate the operator (which should evaluate to a Scheme procedure)
  2. Evaluate the operands
  3. Apply the procedure on the evaluated operands.

The check_procedure function, which raises an error if the provided argument is not a Scheme procedure, may be useful to check that your operator is indeed a procedure. Once you have checked that it is, the rest of the operation (steps 2 and 3 above) should be carried out in the eval_call method of the Procedure class, which you must also complete.

The map method of Pair can apply a function to every item in a Scheme list. The scheme_apply function applies a Scheme procedure to some arguments.

Test your understanding and implementation before moving on:

python3 ok -q 05 -u
python3 ok -q 05

Your interpreter should now be able to evaluate primitive procedure calls, giving you the functionality of the Calculator language and more.

scm> (+ 1 2)
scm> (* 3 4 (- 5 2) 1)
scm> (odd? 31)

Now would be a good time to start adding tests to tests.scm. For each new problem you complete from now on, add a few tests to the top of tests.scm to verify the behavior of your implementation.

Problem 6 (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))

Test your understanding and implementation before moving on:

python3 ok -q 06 -u
python3 ok -q 06

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

scm> (define x 15)
scm> (define y (* 2 x))
scm> y
scm> (+ y (* y 2) 1)
scm> (define x 20)
scm> x
scm> (eval (define tau 6.28))

Problem 7 (1 pt)

First, implement the do_quote_form function, which evaluates the quote special form. The quote special form returns its operand expression without evaluating it.

You should now be able to evaluate quoted expressions.

scm> (quote hello)
scm> (quote (1 . 2))
(1 . 2)
scm> (quote (1 (2 three . (4 . 5))))
(1 (2 three 4 . 5))
scm> (car (quote (a b)))

Next, complete your implementation of scheme_read in by handling one last case:

  • If the token is a single quote ('), such as the first character of 'bagel, then return a Pair that wraps the Scheme expression after the quote (which you can get by recursively calling scheme_read) in quote (e.g. Pair('quote', Pair('bagel', nil)).

After completing your scheme_read implementation, the following quoted expressions should now work as well.

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

Test your understanding and implementation before moving on:

python3 ok -q 07 -u
python3 ok -q 07

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

  • Evaluate atoms, which include numbers, Booleans, nil, and symbols,
  • Evaluate the quote special form,
  • Define symbols, and
  • Call primitive procedures, for example evaluating (+ (- 4 2) 5).

User-Defined Procedures

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

  • formals is a Scheme list of the formal parameters (symbols) that name the arguments of the procedure.
  • body is a Scheme list of expressions; the body of the procedure.
  • env is the environment in which the procedure was defined.

Problem 8 (1 pt)

Implement the eval_all function (which is called from do_begin_form), to complete the implementation of the begin special form. A begin expression is evaluated by evaluating all sub-expressions in order. The value of the begin expression is the value of the final sub-expression.

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

If eval_all is passed an empty list of expressions (nil), then it should return the Python value None, which represents an undefined Scheme value.

Test your understanding and implementation before moving on:

python3 ok -q 08 -u
python3 ok -q 08

Problem 9 (1 pt)

Implement the do_lambda_form function, which creates LambdaProcedure instances. While you cannot call a user-defined procedure yet, you can verify that you have created the procedure correctly by typing a lambda expression into the interpreter prompt:

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

In Scheme, it is legal to place more than one expression in the body of a procedure (there must be at least one expression). The body attribute of a LambdaProcedure instance is a Scheme list of body expressions.

Test your understanding and implementation before moving on:

python3 ok -q 09 -u
python3 ok -q 09

Problem 10 (2 pt)

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

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

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

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

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 10 -u
python3 ok -q 10

You should now find that defined procedures evaluate to LambdaProcedure instances.

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

Problem 11 (2 pt)

Implement the make_child_frame method of the Frame class, which:

  • Creates a new Frame instance, the parent of which is self. (provided)
  • If the number of argument values does not match with the number of formal parameters, raises a SchemeError.
  • Binds formal parameters to their corresponding argument values in the newly created frame.

Test your understanding and implementation before moving on:

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

Problem 12 (1 pt)

Implement the make_call_frame method in LambdaProcedure, which is needed by the apply method defined in UserDefinedProcedure. It should create a new Frame instance using the make_child_frame method of the appropriate parent frame, binding formal parameters to argument values.

Since lambdas are lexically scoped, your new frame should be a child of the frame in which the lambda is defined. The env provided as an argument to make_call_frame is instead the frame in which the procedure is called, which will be useful when you implement a dynamically scoped procedure in problem 16.

Test your understanding and implementation before moving on:

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

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

  • Create procedures using lambda expressions,
  • Define named procedures using define expressions, and
  • Call user-defined procedures.

Now is an excellent time to revisit the tests in tests.scm and ensure that you pass the tests 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.

To run your tests, run the command:

  python3 ok -q tests.scm

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 False is a false value. All other values (including 0 and nil) are true values. You can test whether a value is a true or false value using the provided Python functions scheme_truep and scheme_falsep, defined in

Note: Scheme traditionally uses #f to indicate the false Boolean value. In our interpreter, that is equivalent to false or False. Similarly, true, True, and #t are all equivalent.

To get you started, we've provided an implementation of the if special form in the do_if_form function. Make sure you understand that implementation before starting the following questions.

Problem 13 (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. Otherwise, it should return the value of the last sub-expression. If there are no sub-expressions in an and expression, it evaluates to True.

scm> (and)
scm> (and 4 5 6)  ; all operands are true values
scm> (and 4 5 (+ 3 3))
scm> (and True False 42 (/ 1 0))  ; short-circuiting behavior of and

For or, evaluate each sub-expression from left to right. If any sub-expression evaluates to a true value, return that value. Otherwise, return False. If there are no sub-expressions in an or expression, it evaluates to False.

scm> (or)
scm> (or 5 2 1)  ; 5 is a true value
scm> (or False (- 1 1) 1)  ; 0 is a true value in Scheme
scm> (or 4 True (/ 1 0))  ; short-circuiting behavior of or

Test your understanding and implementation before moving on:

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

Problem 14 (2 pt)

Fill in the missing parts of do_cond_form so that it returns the value of the first result sub-expression corresponding to a true predicate, or the result sub-expression corresponding to else. Some special cases:

  • When the true predicate does not have a corresponding result sub-expression, return the predicate value.
  • When a result sub-expression of a cond case has multiple expressions, evaluate them all and return the value of the last expression. (Hint: Use eval_all.)

Your implementation should match the following examples and the additional tests in tests.scm.

scm> (cond ((= 4 3) 'nope)
           ((= 4 4) 'hi)
           (else 'wait))
scm> (cond ((= 4 3) 'wat)
           ((= 4 4))
           (else 'hm))
scm> (cond ((= 4 4) 'here (+ 40 2))
           (else 'wat 0))

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 None.

scm> (cond (False 1) (False 2))

Test your understanding and implementation before moving on:

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

Problem 15 (2 pt)

The let special form binds symbols to values locally, giving them their initial values. For example:

scm> (define x 5)
scm> (define y 'bye)
scm> (let ((x 42)
           (y (* x 10)))  ; x refers to the global value of x, not 42
       (list x y))
(42 50)
scm> (list x y)
(5 bye)

Implement make_let_frame, which returns a child frame of env that binds the symbol in each element of bindings to the value of its corresponding expression. The bindings scheme list contains pairs that each contain a symbol and a corresponding expression.

You may find the following functions and methods useful:

  • check_form: this function can be used to check the structure of each binding.
  • check_formals: this function checks that formal parameters are a Scheme list of symbols for which each symbol is distinct.
  • make_child_frame: this method (which you implemented in Problem 11) takes a Pair of formal parameters (symbols) and a Pair of values, and returns a new frame with all the symbols bound to the corresponding values.

Test your understanding and implementation before moving on:

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

Problem 16 (1 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. Most of the MuProcedure class has been provided for you.

Complete the MuProcedure class so that when a call on such a procedure is executed, it is dynamically scoped. 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)))
scm> (define g (lambda (x y) (f (+ x x))))
scm> (g 3 7)

Looking at LambdaProcedure should give you a clue about what needs to be done to MuProcedure to complete it. Test your understanding and implementation before moving on:

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

Congratulations! Your Scheme interpreter implementation is now complete!

The autograder tests for the interpreter are not comprehensive, so you may have uncaught bugs in your implementation. You should have been adding tests to the top of tests.scm as you did each problem, which will help you discover bugs on your own. The tests that you have written tests will be evaluated as part of your composition score for the project.

To run your tests, run the command:

  python3 ok -q tests.scm

Make sure to remove all of the (exit) commands, so that all the tests are run! We've provided 115 tests (not counting the extra credit tests), so if you don't see at least that many tests passed, you haven't removed all the (exit) commands. (Of course, you should have many more than that, since you've been writing your own as well.)

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.

All changes in this part should be made in questions.scm.

The autograder tests for the interpreter are not comprehensive, so you may have uncaught bugs in your implementation. Therefore, you may find it useful to test your code for these questions in the staff interpreter or the web interpreter and then try it in your own interpreter once you are confident your Scheme code is working.

Problem 17 (1 pt)

Implement the enumerate procedure, which takes in a list of values and returns a list of two-element lists, where the first element is the index of the value, and the second element is the value itself.

scm> (enumerate '(3 4 5 6))
((0 3) (1 4) (2 5) (3 6))
scm> (enumerate '())

Test your implementation before moving on:

python3 ok -q 17

Problem 18 (2 pt)

Implement the list-change procedure, which lists all of the ways to make change for a positive integer total amount of money, using a list of currency denominations, which is sorted in descending order. The resulting list of ways of making change should also be returned in descending order.

To make change for 10 with the denominations (25, 10, 5, 1), we get the possibliites:

5, 5
5, 1, 1, 1, 1, 1
1, 1, 1, 1, 1, 1, 1, 1, 1, 1

To make change for 5 with the denominations (4, 3, 2, 1), we get the possibilities:

4, 1
3, 2
3, 1, 1
2, 2, 1
2, 1, 1, 1
1, 1, 1, 1, 1

You may find that implementing a helper function, cons-all, will be useful for this problem. To implement cons-all, first implement the map procedure, which applies a one-argument procedure to each element in a list. Then, implement cons-all using map. cons-all takes in an element first and a list of lists rests, and adds first to the beginning of each list in rests:

scm> (cons-all 1 '((2 3) (2 4) (3 5)))
((1 2 3) (1 2 4) (1 3 5))

You may also find the built-in append procedure useful.

Test your implementation before moving on:

python3 ok -q 18

Problem 19 (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.

Rewriting programs can be useful: we can write an interpreter that only handles a small core of the language, and then write a procedure 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 a procedure called let-to-lambda:

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

In order to handle all programs, let-to-lambda must be aware of Scheme syntax. Since Scheme expressions are recursively nested, let-to-lambda must also be recursive. In fact, the structure of let-to-lambda is somewhat similar to that of scheme_eval--but in Scheme!

(define (let-to-lambda expr)
  (cond ((atom?   expr) <rewrite atoms>)
        ((quoted? expr) <rewrite quoted expressions>)
        ((lambda? expr) <rewrite lambda expressions>)
        ((define? expr) <rewrite define expressions>)
        ((let?    expr) <rewrite let expressions>)
        (else           <rewrite other expressions>)))

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

Hint: You may want to implement map and zip at the top of questions.scm.

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

Test your understanding and implementation before moving on:

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

Note: We used let while defining let-to-lambda. What if we want to run let-to-lambda on an interpreter that does not recognize let? We can pass let-to-lambda to itself to rewrite itself into an equivalent program without let:

;; The let-to-lambda procedure
(define (let-to-lambda expr)

;; A list representing the let-to-lambda procedure
(define let-to-lambda-code
  '(define (let-to-lambda expr)

;; An let-to-lambda procedure that does not use 'let'!
(define let-to-lambda-without-let
  (let-to-lambda let-to-lambda-code))

Part IV: Extra Credit

Problem 20 (+2 pt)

Complete the function scheme_optimized_eval in 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.

The Thunk class represents a thunk, an expression that needs to be evaluated in an environment. When scheme_optimized_eval receives an expression in a tail context, then it returns an Thunk instance. Otherwise, it repeatedly evaluates expressions within the body of a while statement, updating result in each iteration.

A successful implementation will require changes to several other functions, including some functions that we provided for you. All tail calls should call scheme_eval with True as a third argument, indicating a tail call. Think about what Scheme expressions are in a tail context!

Once you finish, uncomment the following line in to use your implementation:

scheme_eval = scheme_optimized_eval

Test your understanding and implementation before moving on:

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


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

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

Extra Challenge

We've implemented a significant subset of Scheme in this project, but your interpreter can be extended with even more features! If you enjoyed this project, we have some suggestions in the extension instructions.