Project 4: Scheme Interpreter

Money Tree

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

Introduction

Important submission note: For full credit:

  • submit with Parts I and II complete by Friday, 12/13 (worth 1 pt), and
  • submit the entire project by Sunday, 12/22.

The Scheme project involves writing an interpreter for the Scheme language which is no small task! Start working on the project now! There are many parts and students often get stuck throughout the project so it's best to solve these problems early while there's still plenty of time. Remember that you can ask questions about the project in lab and office hours too!

We've also written a language specification and built-in procedure reference for the CS 61A subset of Scheme that you'll be building in this project. Reading the entirety of either of these documents should not be necessary, but we'll point out useful sections from the documentation in each part of the project.

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.

Later, there will also be an open-ended graphics contest (released separately) 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.

Download starter files

You can download all of the project code as a zip archive. This project includes several files, but all of your changes will be made to only four: scheme.py, scheme_reader.py, questions.scm, and tests.scm. Here are all the files included in the archive:

  • scheme.py: implements the REPL and a evaluator for Scheme expressions
  • scheme_reader.py: implements the reader for Scheme input
  • scheme_tokens.py: implements the tokenizer for Scheme input
  • scheme_builtins.py: implements built-in Scheme procedures in Python
  • buffer.py: implements the Buffer class, used in scheme_reader.py
  • ucb.py: utility functions for use in 61A projects
  • questions.scm: contains skeleton code for Phase III
  • tests.scm: a collection of test cases written in Scheme

Logistics

This is a 20-day 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. In the end, you will submit one project for both partners. We strongly encourage you to work on all parts of the project together rather than splitting up the work. Switch off who writes the code, but whoever is not coding should contribute by looking at the code and providing comments on a direction to go and catching bugs.

The project is worth 25 points. 24 points are assigned for correctness, including 1 point for passing tests.scm, and 1 point for submitting Parts I and II by the first checkpoint.

You will turn in the following files:

  • scheme_reader.py
  • scheme.py
  • questions.scm
  • tests.scm

You do not need to modify or turn in any other files to complete the project.

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 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 time to think through problems.

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.

Interpreter details

Scheme features

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

scm> 2
2
scm> (+ 2 3)
5
scm> ((lambda (x) (* x x)) 5)
25

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 call to a built-in procedure) and the third (a computation of 5 factorial) will not work just yet.

Load. You can load a file by passing in 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
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.

Implementation overview

Here is a brief overview of each of the Read-Eval-Print Loop components in our interpreter. Refer to this section as you work through the project as a reminder of how all the small pieces fit together!

  • 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 scheme_tokens.py. This function returns a Buffer (from buffer.py) of tokens. You do not need to read or understand the code for this step.
    • Syntactic analysis happens in scheme_reader.py, 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 scheme.py file.

    • Eval happens in the scheme_eval function. If the expression is a call expression, it gets evaluated according to the rules for evaluating call expressions (you will implement this). If the expression being evaluated is a special form, the corresponding do_?_form function is called. You will complete several of the do_?_form functions.
    • Apply happens in the scheme_apply function. If the function is a built-in procedure, scheme_apply calls the apply method of that BuiltInProcedure instance. If the procedure is a user-defined procedure, scheme_apply creates a new call frame and calls eval_all on the body of the procedure, resulting in a mutually recursive eval-apply loop.
  • Print: This step prints the __str__ representation of the obtained value.
  • Loop: The logic for the loop is handled by the read_eval_print_loop function in scheme.py. You do not need to understand the entire implementation.

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, but some might just be errors in user programs. The former should be fixed by debugging your interpreter 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 the interpreter

To start an interactive Scheme interpreter 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> true
#t

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

scm> (exit)

Part 0: Testing Your Interpreter

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 from which Composing Programs is adapted.

Part I: The Reader

Important submission note: For full credit:

  • submit with Parts I and II complete by Friday, 12/13 (worth 1pt).

All changes in this part should be made in scheme_reader.py.

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

The first part of this project deals with reading and parsing user input. Our reader will parse Scheme code into Python values with the following representations:

Input Example Scheme Expression 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> #t Booleans (#t, #f) Python's built-in True, False values
scm> (+ 2 3) Combinations Instances of the Pair class, defined in scheme_reader.py
scm> nil nil The nil object, defined in scheme_reader.py

When we refer to combinations in this project, we are referring to both call expressions and special forms.

If you haven't already, make sure to read the Implementation overview section above to understand how the reader is broken up into parts.

In our implementation, we store tokens ready to be parsed in Buffer instances. For example, a buffer containing the input (+ (2 3)) would have the tokens '(', '+', '(', 2, 3, ')', and ')'. See the doctests in buffer.py for more examples. You do not have to understand the code in this file.

You will write the parsing functionality, which consists of two mutually recursive functions scheme_read and read_tail. These functions each take in a single parameter, src, which is an instance of Buffer.

There are two methods defined in buffer.py that you'll use to interact with src:

  • src.pop_first(): mutates src by removing the first token in src and returns it. For the sake of simplicity, if we imagine src as a Python list such as [4, 3, ')'], src.pop_first() 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)

First, implement scheme_read and read_tail so that they can parse combinations and atomic expressions. The expected behavior is as follows:

  • scheme_read removes enough tokens from src to form a single expression and returns that expression in the correct internal representation (see above table).
  • read_tail expects to read the rest of a list or pair, assuming the open parenthesis of that list or pair 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 as a linked list of Pair instances.

In short, scheme_read returns the next single complete expression in the buffer and read_tail returns the rest of a list or pair in the buffer. Both functions mutate the buffer, removing the tokens that have already been processed.

The behavior of both functions depends on the first token currently in src. They should be implemented as follows:

scheme_read:

  • If the current token is the string "nil", return the nil object.
  • If the current token is (, the expression is a pair or list. Call read_tail on the rest of src and return its result.
  • If the current token is ', `, or , the rest of the buffer should be processed as a quote, quasiquote, or unquote expression, respectively. You don't have to worry about this until Problem 6.
  • If the next token is not a delimiter, then it must be a primitive expression. Return it. (provided)
  • If none of the above cases apply, raise an error. (provided)

read_tail:

  • If there are no more tokens, then the list is missing a close parenthesis and we should raise an error. (provided)
  • If the token is ), then we've reached the end of the list or pair. Remove this token from the buffer and return the nil object.

  • If none of the above cases apply, the next token is the operator in a combination, e.g. src contains + 2 3). To parse this:

    1. Read the next complete expression in the buffer. (Hint: Which function can we use to read a complete expression and remove it from the buffer?)
    2. Read the rest of the combination until the matching closing parenthesis. (Hint: Which function can we use to read the rest of a list and remove it from the buffer?)
    3. Return the results as a Pair instance, where the first element is the next complete expression and the second element is the rest of the combination.

Now that your parser is complete, you should test the read-eval-print loop by running python3 scheme_reader.py --repl. 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)))

To exit the interpreter, you can type exit.

Part II: The Evaluator

Important submission note: For full credit:

  • submit with Part II complete by Friday, 12/13 (worth 1 pt), and
  • submit the entire project by Sunday, 12/22. All changes in this part should be made in scheme.py.

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 scheme.py, called Eval/Apply and Environments.

  • scheme_eval evaluates a Scheme expression in the given environment. This function is nearly complete but is missing the logic for call expressions.
  • When evaluating a special form, scheme_eval redirects evaluation to an appropriate do_?_form function found in the Special Forms section in scheme.py.
  • scheme_apply applies a procedure to some arguments. This function is complete.
  • 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 scheme.py defines special forms and input/output behavior.

Some Core Functionality

Problem 2 (1 pt)

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

  • bindings is a dictionary representing the bindings in the frame. It maps Scheme symbols (represented as Python strings) to Scheme values.
  • parent is the parent Frame instance. The parent of the Global Frame is None.

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

2) lookup takes a symbol and returns the value bound to that name in the first Frame that the name is found in the current environment. Recall that an environment is defined as a frame, its parent frame, and all its ancestor frames, including the Global Frame. Therefore,

  • If the name is found in the current frame, return its value.
  • If the name is not found in the current frame and the frame has a parent frame, continue lookup in the parent frame.
  • If the name is not found in the current frame and there is no parent frame, raise a SchemeError (provided).

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

scm> +
#[+]
scm> odd?
#[odd?]
scm> display
#[display]

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

Remember, at this point you can only exit the interpreter by pressing Ctrl-d.

Problem 3 (1 pt)

To be able to call built-in procedures, such as +, you need to complete the apply method in the class BuiltinProcedure. Built-in procedures are applied by calling a corresponding Python function that implements the procedure. For example, the + procedure in Scheme is implemented as the add function in Python.

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

A BuiltinProcedure has two instance attributes:

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

The apply method of BuiltinProcedure takes a list of argument values and the current environment. Note that args is a Scheme list represented as a Pair object. Your implementation should do the following:

  • 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 using *args notation (f(1, 2, 3) is equivalent to f(*[1, 2, 3]))
  • If calling the function results in a TypeError exception being raised, then the wrong number of arguments were passed. Use a try/except block to intercept the exception and raise an appropriate SchemeError in its place.

Problem 4 (1 pt)

scheme_eval evaluates a Scheme expression, represented as a sequence of Pair objects, 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 an instance of Procedure)
  2. Evaluate all of the operands
  3. Apply the procedure on the evaluated operands

You'll have to recursively call scheme_eval in the first two steps. Here are some other functions/methods you should use:

  • The check_procedure function raises an error if the provided argument is not a Scheme procedure. You can use this to check that your operator indeed evaluates to a procedure.
  • The map method of Pair returns a new Scheme list constructed by apply ing a one-argument function to every item in a Scheme list.
  • The scheme_apply function applies a Scheme procedure to some arguments.

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

scm> (+ 1 2)
3
scm> (* 3 4 (- 5 2) 1)
36
scm> (odd? 31)
#t

Problem 5 (1 pt)

Next, we'll implement defining names. Recall that the define special form in Scheme can be used to either assign a name to the value of a given expression or to create a procedure and bind it to a name:

scm> (define a (+ 2 3))  ; Binds the name a to the value of (+ 2 3)
a
scm> (define (foo x) x)  ; Creates a procedure and binds it to the name foo
foo

The type of the first operand tells us what is being defined:

  • If it is a symbol, e.g. a, then the expression is defining a name
  • If it is a list, e.g. (foo x), then the expression is defining a procedure.

Read the Scheme Specifications to understand the behavior of the define special form! This problem only provides the behavior for binding expressions, not procedures, to names.

There are two missing parts in the do_define_form function, which handles the (define ...) special forms. For this problem, implement just the first part, which evaluates the second operand to obtain a value and binds the first operand, a symbol, to that value. do_define_form should return the name after performing the binding.

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

You should now be able to give names to values and evaluate the resulting symbols. Note that eval takes an expression represented as a list and evaluates it.

scm> (eval (define tau 6.28))
6.28
scm> (eval 'tau)
6.28
scm> tau
6.28
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

Consider the following test:

(define x 0)
; expect x
((define x (+ x 1)) 2)
; expect Error
x
; expect 1

Here, an Error is raised because the operator does not evaluate to a procedure. However, if the operator is evaluated multiple times before raising an error, x will be bound to 2 instead of 1, causing the test to fail. Therefore, if your interpreter fails this test, you'll want to make sure you only evaluate the operator once in scheme_eval.

As you go through the project, you may want to think about other edge cases you can test. Here are a few ideas:

  • Do we check to see if the operator is a procedure before evaluating the operands?
  • Do we evaluate the expression in a define special form more than once?
  • Does the interpreter properly error when given an expression with the incorrect form, for example the expression (define x 2 y 4)?

Problem 6 (1 pt)

To complete the core functionality, let's implement quoting in our interpreter. In Scheme, you can quote expressions in two ways: with the quote special form or with the symbol '. Recall that the quote special form returns its operand expression without evaluating it:

scm> (quote hello)
hello
scm> '(cons 1 2)  ; Equivalent to (quote (cons 1 2))
(cons 1 2)

Read the Scheme Specifications to understand the behavior of the quote special form.

Let's take care of the quote special form first. Implement the do_quote_form function so that it simply returns the unevaluated operand to the special form.

After completing this function, you should be able to evaluate quoted expressions. Try out some of the following in your interpreter!

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

You do not need to worry about implementing do_quasiquote_form or do_unquote_form, as we have provided them for you.

Next, complete your implementation of scheme_read in scheme_reader.py by handling the case for ', `, and ,. First, notice that '<expr> translates to (quote <expr>), `<expr> translates to (quasiquote <expr>), and ,<expr> translates to (unquote <expr>). That means that we need to wrap the expression following one of these characters (which you can get by recursively calling scheme_read) into the appropriate special form, which, like all special forms, is really just a list.

For example, 'bagel should be represented as Pair('quote', Pair('bagel', nil))

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

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
scm> `(1 ,(+ 1 1) 3)
(1 2 3)

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 and quasiquote special forms,
  • Define symbols, and
  • Call built-in 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 7 (1 pt)

Read the Scheme Specifications to understand the behavior of the begin special form!

Change 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))
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)

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.

Problem 8 (1 pt)

Read the Scheme Specifications to understand the behavior of the lambda special form!

A LambdaProcedure represents a user-defined procedure. It has a list of formals (parameter names), a body of expressions to evaluate, and a parent frame env.

Implement the do_lambda_form function, which creates a LambdaProcedure instance. 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.

Problem 9 (1 pt)

Read the Scheme Specifications to understand the behavior of the define special form! In this problem, we'll finish defining the define form for procedures.

Currently, your Scheme interpreter is able to bind symbols to 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 named 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.

You should now find that defined procedures evaluate to LambdaProcedure instances. However, you can't call them yet - we'll implement that in the next two problems.

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

Problem 10 (1 pt)

Implement the make_child_frame method of the Frame class which will be used to create new call frames for user-defined procedures. This method takes in two arguments: formals, which is a Scheme list of symbols, and vals, which is a Scheme list of values. It should return a new child frame, binding the formal parameters to the values.

To do this:

  • Create a new Frame instance, the parent of which is self.
  • Bind each formal parameter to its corresponding argument value in the newly created frame. The first symbol in formals should be bound to the first value in vals, and so on. If the number of argument values does not match with the number of formal parameters, raise a SchemeError.
  • Return the new frame.

Hint: The define method of a Frame instance creates a binding in that frame.

Problem 11 (1 pt)

Implement the make_call_frame method in LambdaProcedure, which is needed by scheme_apply. It should create and return 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 dynamically scoped procedures in problem 15.

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.

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 scheme_builtins.py.

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. However when unlocking tests, use #t and #f.

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 12 (1 pt)

Read the Scheme Specifications to understand the behavior of the and and or special forms!

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 #f 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 #t.

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

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

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

Remember that you can use the provided Python functions scheme_truep and scheme_falsep to test boolean values.

Problem 13 (2 pt)

Read the Scheme Specifications to understand the behavior of the cond special form!

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))
hi
scm> (cond ((= 4 3) 'wat)
           ((= 4 4))
           (else 'hm))
#t
scm> (cond ((= 4 4) 'here (+ 40 2))
           (else 'wat 0))
42

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))
scm>

Problem 14 (2 pt)

Read the Scheme Specifications to understand the behavior of the let special form!

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

scm> (define x 5)
x
scm> (define y 'bye)
y
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. It takes in a list expr of expressions and a min and max length. If expr is not a proper list or does not have between min and max items inclusive, it raises an error.
  • 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 of the Frame class (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.

Problem 15 (1 pt)

Read the Scheme Specifications to understand the behavior of the mu special form!

All of the Scheme procedures we've seen so far use lexical scoping: the parent of the new call frame is the environment in which the procedure was defined. Another type of scoping, which is not standard in Scheme, is called dynamic scoping: the parent of the new call frame is the environment in which the procedure was evaluated. With dynamic scoping, calling the same procedure in different parts of your code can lead to different results (because of varying parent frames).

In this problem, we will implement the mu special form, a non-standard Scheme expression type representing a procedure that is dynamically scoped.

In the example below, we use the mu keyword instead of lambda to define a dynamically scoped procedure f:

scm> (define f (mu () (* a b)))
f
scm> (define g (lambda () (define a 4) (define b 5) (f)))
g
scm> (g)
20

The procedure f does not have an a or b defined; however, because f gets called within the procedure g, it has access to the a and b defined in g's frame.

Implement do_mu_form to evaluate the mu special form. 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.

In addition to filling out the body of do_mu_form, you'll need to complete the MuProcedure class so that when a call on such a procedure is executed, it is dynamically scoped. This means that when a MuProcedure created by a mu expression is called, 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.

Looking at LambdaProcedure should give you a clue about what needs to be done to MuProcedure to complete it. You will not need to modify any existing methods, but may wish to implement new ones.

One you have completed Part II, make sure you submit it to receive full credit for the checkpoint.

Congratulations! Your Scheme interpreter implementation is now complete!

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.

In addition, for this part of the project, you may find the built-in procedure reference very helpful if you ever have a question about the behavior of a built-in Scheme procedure, like the difference between pair? and list?.

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 editor and then try it in your own interpreter once you are confident your Scheme code is working.

Problem 16 (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 '())
()

Problem 17 (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 possibilities:

10
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, use the built-in map procedure. 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.

Problem 18 (2 pt)

In Scheme, source code is data. Every non-atomic expression is written as a Scheme list, so 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. Feel free to revisit Problem 15 as a refresher on how the let form works.

(let ((a 1) (b 2)) (+ a b))
;; Is equivalent to:
((lambda (a b) (+ a b)) 1 2)

These expressions can be represented by the following diagrams:

Let Lambda
let lambda

Use this rule to implement a procedure called let-to-lambda that rewrites all let special forms into lambda expressions. If we quote a let expression and pass it into this procedure, an equivalent lambda expression should be returned: pass it into this procedure:

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! As a reminder, atoms include numbers, booleans, nil, and symbols. You do not need to consider code that contains quasiquotation for this problem.

(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>)))

Hint: You may want to implement zip at the top of questions.scm and also use the built-in map procedure.

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

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

Note: During regular Office Hours and Project Parties, the staff will prioritize helping students with required questions. We will not be offering help with either extra credit problems unless the queue is empty.

Problem 19 (2 pt)

Complete the function optimize_tail_calls in scheme.py. It returns an alternative to scheme_eval that 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 a non-atomic expression in a tail context, then it returns an Thunk instance. Otherwise, it should repeatedly call original_scheme_eval until the result is a value, rather than a Thunk.

A successful implementation will require changes to several other functions, including some functions that we provided for you. All expressions throughout your interpreter that are in a tail context should be evaluated by calling scheme_eval with True as a third argument. Your goal is to determine which expressions are in a tail context throughout your code.

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

scheme_eval = optimize_tail_calls(scheme_eval)

Problem 20 (1 pt)

Macros allow the language itself to be extended by the user. Simple macros can be provided with the define-macro special form. This must be used like a procedure definition, and it creates a procedure just like define. However, this procedure has a special evaluation rule: it is applied to its arguments without first evaluating them. Then the result of this application is evaluated.

This final evaluation step takes place in the caller's frame, as if the return value from the macro was literally pasted into the code in place of the macro.

Here is a simple example:

scm> (define (map f lst) (if (null? lst) nil (cons (f (car lst)) (map f (cdr lst)))))
scm> (define-macro (for formal iterable body)
....     (list 'map (list 'lambda (list formal) body) iterable))
scm> (for i '(1 2 3)
....     (print (* i i)))
1
4
9
(None None None)

The code above defines a macro for that acts as a map except that it doesn't need a lambda around the body.

In order to implement define-macro, implement complete the implementation for do_define_macro, which should create a MacroProcedure and bind it to the given name as in do_define_form. Then, update scheme_eval so that calls to macro procedures are evaluated correctly.

Hint : Use the apply_macro method in the MacroProcedure class to apply a macro to the operands in its call expression. This procedure is written to interact well with tail call optimization.

Conclusion

Congratulations! You have just implemented an interpreter for an entire language! If you enjoyed this project and want to extend it further, you may be interested in looking at more advanced features, like let* and letrec, unquote splicing, error tracing, and continuations.