Project 3: Scheme Metacircular Evaluator

Optional checkpoint due Wednesday, Mar 9, 2022 at 8pm ET

Final deadline Monday, Mar 14, 2022 at 8pm ET

A PDF version of this document is located here.

In this project, you will implement an interpreter for a subset of the R5RS Scheme programming language, written in Scheme itself. The main purpose of this exercise is to gain further experience with functional programming, including recursion, higher-order functions, functional data abstraction, and message passing. A secondary goal is to achieve a basic understanding of interpretation, as well as the distinction between static and dynamic scope.

The project is divided into multiple suggested phases. The project will need to be completed in the order of the phases below.

You may work alone or with a partner. Please see the syllabus for partnership rules. As a reminder, you may not share any part of your solution outside of your partnership. This includes both code and test cases.

Reported Time to Complete the Project

The following is the time students reported they spent on the project in Winter 2021.

Time to complete project 1. 0% less than 5 hours, 0% 5-9 hours, 26% 10-14 hours, 43% 15-19 hours, 28% 20-24 hours, 2% 25-30 hours, 2% greater than 30 hours

These data are for planning purposes only. We do not consider the exact time spent on the project to be reflective of anyone’s learning or ability. Rather, completing the project regardless of how much time it takes is what is important to achieve the learning goals of the project.

Optional Checkpoint

The checkpoint consists of achieving at least 30% of the points on the public and private test cases before the checkpoint deadline. Your grade for the checkpoint will be computed as the better of:

  • \(min(0.3, score) / 0.3\), where \(score\) is the fraction of autograded points earned by your best submission before the checkpoint deadline.

  • \(finalScore\), where \(finalScore\) is the fraction of autograded points earned by your best submission before the final deadline.

Thus, completing the checkpoint is optional. However, doing it will work to your benefit, since you can guarantee full credit on the 20% of the project points dedicated to the checkpoint.


An interpreter follows a multistep procedure in processing code. In a program file, code is represented as raw character data, which isn’t suitable for interpreting directly. The first step then is to read the code and construct a more suitable internal representation that is more amenable to interpretation. This first step can be further subdivided into a lexing step, which chops the input data into individual tokens, and parsing, which generates program fragments from tokens. The end result of this reading process is a structured representation of a code fragment.

Once an input code fragment has been read, the interpreter proceeds to evaluate the expression that the fragment represents1. This evaluation process happens within the context of an environment that maps names to entities. Evaluation is recursive: subexpressions are themselves evaluated by the interpreter in order to produce a value.


An interpreter for an imperative language, such as Python, will execute the code fragment if it represents a statement. Scheme, however, only has expressions, so the interpreter only evaluates code.

Upon evaluating a code fragment, an interactive interpreter will proceed to print out a representation of the resulting value. It will then proceed to read the next code fragment from the input, repeating this process.

This iterative combination of steps is often referred to as a read-eval-print loop, or REPL for short. Interactive interpreters often provide a REPL with a prompt to read in a new expression, evaluating it and printing the result.

In this project, we are implementing a specific kind of interpreter called a metacircular evaluator. This is an interpreter in which the host language (the language in which the interpreter is implemented) is the same as the client language (the language that is being interpreted)2. The advantage of using the same language for writing the interpreter is that we can rely on the host interpreter to do most of the work. Thus, a metacircular evaluator is often a useful vehicle for exploring language extensions or optimizations, and systems such as PyPy use a similar strategy.


This is related to the concept of a self-hosting compiler, which is a compiler that compiles its own source code.

Most of the work in this project entails implementing data abstractions for the internals of an interpreter, as well as functionality involving evaluation, error checking, and special forms. We will rely on the built-in read procedure (or optionally, the read-datum procedure from the preceding project) for parsing. The result of parsing is Scheme-level representations of the code (in the form of pairs, numbers, symbols, and so on). Our interpreter performs the evaluation step on the resulting structured representations. For simplicity, we only support a subset of R5RS Scheme.

Distribution Code

Use the following commands to download and unpack the distribution code:

$ wget \
$ tar xzf starter-files.tar.gz

Start by looking over the distribution code, which consists of the following files:



Implementation of dictionary and environment abstract data types.


Implements the error procedure for signaling errors.


Top-level driver for the metacircular evaluator. Implements the read-eval-print loop.


Implements an abstract data type for primitive procedures, as well as error checking for those procedures.


Implements the core evaluation procedure, as well as data types for special forms and user-defined procedures.

The code you write will be in env.scm, primitives.scm, and core.scm. You will not modify driver.scm, unless you wish to use your Project 2 code for parsing. To do so, place distribution.scm, lexer.scm, and parser.scm in the project directory, and modify the use-project-parser global variable in driver.scm to be #t.

Test Files


Assertion procedures used in internal tests.


Basic internal tests for dictionaries and environments (Phase 1).


Internal tests of Phase 2 functions.


Internal tests of Phase 3 functions.


Basic tests for Phase 2.


Various tests for Phase 3.


Tests for the begin special form.


Tests for the define special form.


Error tests for Phase 3.


Tests for the if special form.


Tests for the lambda special form.


Tests for the quote special form.


Basic tests for the mu form (Phase 4).

In addition, the starter files include expected output files (*.expect) for the test files for Phases 2-4.

The provided tests can be run with the given Makefile. It contains the following targets:

  • all: run all tests for Phases 1-4

  • phase1, …, phase4: run the tests for an individual phase

  • phase3_all, phase3_begin, …: run an individual Phase 3 test, e.g. phase3_all_tests.scm, phase3_begin_tests.scm, and so on

Command-Line Interface

Start the Scheme interpreter with the following command:

$ plt-r5rs driver.scm

This will initialize the interpreter and place you in an interactive loop. You can exit with an EOF (Ctrl-D on Unix-based systems, Ctrl-Z on some other systems).

You can interpret all the code in a file using input redirection:

$ plt-r5rs driver.scm < phase2_tests.scm


$ cat phase2_tests.scm | plt-r5rs driver.scm

Error Detection

Your interpreter should never crash (except on parse errors if you are using the default read). Rather, it should detect erroneous Scheme code and report an error using the provided error procedure in error.scm. The procedure takes a string as its first argument, and it optionally takes an arbitrary Scheme datum as a second argument. The arguments are printed, and then the procedure invokes the continuation of the read-eval-print-loop to read and evaluate a new expression. The Makefile and autograder strip out the actual content of error messages before comparing output. Thus, the contents of an error message are up to you. We recommend providing a message that would be useful for a user.

Phase 1: Dictionaries and Environments

We start by building abstract data types for dictionaries and environments. We will build these abstractions using higher-order functions, specifically with message passing and dispatch functions. Messages will be represented as Scheme symbols.


R5RS Scheme does not have a built-in dictionary type, so we will construct our own. Implement the dictionary higher-order procedure in env.scm. The resulting object should support the following messages:

  • length, with no additional arguments: returns the number of key-value pairs in the dictionary

  • contains, with a key argument: returns whether the key is contained in the dictionary

  • get, with a key argument: returns the value associated with the given key

  • insert, with additional key and value arguments: associates the given key with the given value. If the key is already in the dictionary, this replaces the value associated with the key.

Here are some examples of creating and using a dictionary:

> (define d (dictionary))
> (d 'contains 'x)
> (d 'insert 'x 3)
> (not (d 'contains 'x))
> (d 'get 'x)
> (d 'insert 'x 4)
> (d 'get 'x)
> (d 'length)

Since different messages require different numbers of arguments, you will need to make use of variadic arguments. Read sections 4.1.4 and 5.2 in the R5RS spec for how to define variadic procedures.

You will need to use mutators to store and modify key-value pairs. You may use the set!, set-car!, and set-cdr! procedures within your dictionary implementation. Refer to the R5RS spec for details on these procedures.

You may implement your dictionary using any underlying representation. You do not have to use a hashtable or tree-based representation. You may find the built-in assoc procedure helpful.

Your dictionary abstraction does not need to perform any error checking.


An environment consists of a sequence of frames, each of which binds names to values. A natural representation of an environment is a linked list of individual frames, where each frame has a reference to its parent frame, and the top-level (global) frame has a null parent. Fill in the implementation for the higher-order frame procedure using this representation strategy. The resulting object should support the following messages:

  • contains, with a name argument: returns whether the name is bound in the environment, i.e. in the frame or any of its ancestors

  • get, with a name argument: returns the value bound to the given name in the closest frame that contains a binding for the name

  • insert, with additional name and value arguments: binds the given name to the given value in the current frame. If a binding already exists in the current frame, this replaces that binding.

Do not repeat code. Use the dictionary abstraction above to maintain the bindings for an individual frame. You can use the built-in apply procedure to forward variadic arguments. The following is an example of using apply:

> (apply + 1 2 '(3 4))

Refer to the R5RS spec for more details on apply.

We use an empty (null) list to represent a null parent. Refer to the documentation of the frame procedure for examples.

Your frame implementation does not need to perform any error checking.

When you are done with this phase, run the provided test with:

$ make phase1

Make sure to write additional tests of your own to cover all of the required behavior for dictionaries and environments.

Phase 2: Primitives and Evaluation

In this phase, you will implement basic features of the Scheme interpreter. Once this phase is complete, your interpreter should be able to evaluate basic Scheme expressions consisting of calls to primitive procedures, as well as compound expressions composed of these basic elements.

Primitive Procedures

Implement primitive-procedure in primitives.scm. This is a higher-order function that creates a wrapper object around a host-level implementation of a primitive procedure. The wrapper should take a message and any number of arguments. Given the call message, an environment, and any number of argument expressions, the wrapper should:

  1. Check whether the given number of argument expressions matches the expected number. Use the provided arity-error procedure to signal an error. We only support a fixed number of arguments to primitive procedures in this project.

  2. Evaluate the argument expressions in some arbitrary order in the given environment, using scheme-eval from core.scm.

  3. Invoke the underlying host implementation on the resulting argument values.

Do not repeat or write unnecessary code. Use the built-in map procedure for performing the map pattern rather than reimplementing it.

The following is an example of using primitive-procedure:

> (define proc (primitive-procedure 'cons 2 cons))
> (proc 'call (frame '()) 3 4)
(3 . 4)

A few more tests are in internal_phase2_tests.scm.

Refer to add-primitives for which primitive procedures we support in our interpreter.

Evaluating Symbols

The interpreter code we provide can evaluate primitive values (e.g. numbers and strings), as you can see by examining scheme-eval in core.scm. This procedure is the evaluator of the intepreter. It takes in a Scheme expression, in the form produced by the parser, and an environment, evaluates the expression in the given environment, and returns the result.

You can start the interpreter and type in primitive values, which evaluate to themselves:

$ plt-r5rs driver.scm
scm> 3
scm> "hello world"
"hello world"
scm> #t

Modify scheme-eval to support evaluating symbols in the current environment. This will allow you to evaluate symbols that are bound to primitive functions:

scm> =

The line number in the printout is dependent on your implementation. You do not have to match the output above.

If a symbol is undefined in the environment when it is evaluated, signal an error by invoking the error procedure defined in error.scm. This will print the provided message and optional additional argument and return the interpreter back to the REPL, as described in Error Detection. The following is an example of the resulting behavior:

scm> undefined
Error: unknown identifier undefined

You do not need to match this error message.

Evaluating Call Expressions

Modify scheme-eval so that it can evaluate a call expression (combination), which is comprised of a list. A list is evaluated by recursively evaluating the first operand. The result must be a callable object. In this project, all callable objects are represented by host procedures, so you should use the built-in procedure? predicate to check the result of evaluating the operand. If the result is a callable, then pass it the call message, the environment, and the remaining list elements.

If the first operand does not evaluate to a host procedure, your interpreter should signal an error with the error procedure.

You should now be able to evaluate calls to primitive procedures, such as:

scm> (boolean? #t)
scm> (not #t)
scm> (+ 1 (* 2 3))

Division Procedures

As mentioned in Error Detection, our interpreter is responsible for all error checking. This includes type checking for procedures that expect specific types. Take a look at the provided type-checked procedure, which wraps the implementation of a primitive with an adapter that performs type checking. Refer to add-primitives for how type-checked is used.

Division procedures not only require their arguments to be of the appropriate type, but they also require the second argument to be nonzero. Implement the divide-checked procedure, which wraps a division procedure with an adapter that does both type checking and value checking. Make use of the provided check-arg-types where appropriate.


When this phase is complete, you will be able to run the provided tests for the phase:

$ make phase2

Make sure to write your own tests as well, as only a few tests are provided for you.

Phase 3: Special Forms

Extend the evaluation procedure in your interpreter to handle special forms. A special form differs from a procedure in that it expects its arguments unevaluated, operating on the arguments as data instead.

First, complete the special-form wrapper in core.scm. This should be similar to primitive-procedure, but significantly simpler. Upon receiving the call message, a special-form object should invoke the underlying implementation with the subsequent arguments.

Next, proceed to actually implement the required functionality for the following forms. Fill in the scheme-* procedures (e.g. scheme-begin) to perform the correct actions for each individual form. Refer to the R5RS spec for full details about each form, including what constitutes an error.

  • Implement the begin form. This should just evaluate each of its arguments in order, and the result of the begin should be the result of the last argument expression.

    The R5RS spec allows begin to have zero arguments in some contexts, while it requires it to have at least one argument in others (see sections 7.1.3 and 7.1.6 in the spec for details). However, for this project, you should enforce that begin have at least one argument in all contexts.

  • Implement the if form. If the test yields a false value and there is no alternate, the result is unspecified. You do not need to do anything special for this case. (In other words, rely on the unspecified value produced by the host interpreter’s implementation of if or other forms.)

  • Implement the quote form, which simply returns its argument unevaluated.

User-Defined Procedures

A user-defined procedure can be introduced with the lambda special form. Start by implementing lambda-procedure, which returns an object representing a user-defined lambda procedure. This object keeps track of the formal parameters, body, and definition environment of a user-defined procedure – lambda procedures are statically scoped, so we need access to the definition environment when the procedure is actually called.

The object returned by lambda-procedure should accept the call message, accompanied by an environment argument and the arguments to the procedure call. Given the call message, it should:

  1. Check whether the given number of arguments matches the expected number. Keep in mind that internally, the procedure object also receives the environment as its first argument, in addition to the arguments provided by the user.

  2. Evaluate the arguments in some arbitrary order in the given (dynamic) environment.

  3. Extend the definition environment with a new frame.

  4. Bind the formal parameters to the argument values in the new frame.

  5. Evaluate the body in the new frame.

Do not repeat code. There are similarities to how primitive-procedure works, and you may need to do some refactoring to avoid code duplication.

We recommend testing your implementation before moving forward. You can do so by starting plt-r5rs (or DrRacket), loading driver.scm using the load procedure, exiting the interactive loop with an EOF, and then invoking procedures in driver.scm, core.scm, or primitives.scm manually. The following is an example:

> (load "driver.scm")
Welcome to the metacircular evaluator!
scm> ^D
> (define env (scheme-make-environment))
> (define p1 (lambda-procedure 'test '(x y) '((+ x y)) env))
> (p1 'call env 3 4)
> (p1 'call env 3)
Error: incorrect number of arguments to test: expected 2, got 1
scm> ^D

Notice that an error puts us back into our interactive loop, since it invokes the continuation for that loop. We can exit with another EOF.

You can also run the test cases in internal_phase3_tests.scm:

$ plt-r5rs internal_phase3_tests.scm

Note that this file has test code for the other special forms as well, so you may not yet pass all the test cases.

Once you are satisfied that lambda-procedure works correctly, proceed to actually implement scheme-lambda. You only have to support lambdas that take a fixed number of arguments (the first form mentioned in Section 4.1.4 of the Scheme spec).

Evaluating the lambda expression itself requires the following:

  • Check the format of the expression to make sure it is free of errors. Refer to the R5RS spec for the required format and what constitutes an error.

    For the purposes of this project (for both lambda and define), use the following rule for \(\langle\textrm{variable}\rangle\) rather than what is in section 7.1.1 of the R5RS spec:

    \[\langle\textrm{variable}\rangle \longrightarrow \langle\textrm{identifier}\rangle\]
  • Use lambda-procedure to create an object representing a user-defined procedure. You can pass it an arbitrary name, such as '<lambda>.

  • The resulting value of the lambda expression is the newly created procedure object.


You are required to implement the first two forms for define listed in Section 5.2 of the R5RS spec.

  • The first form binds a variable to the value of an expression. You will need to evaluate the expression in the current environment and bind the given name to the resulting value in the current frame.

  • The second form defines a procedure. You only have to handle a fixed number of parameters, so you need not consider the case where the formals contain a period. Do not repeat code; make use of what you have already written for lambda, and refactor if necessary to avoid duplication.

You do not have to check that define is at the top level or beginning of a body. For this project, the define form should evaluate to the name that was just defined:

scm> (define x 3)
scm> (define (foo x) (+ x 1))


Your implementation of each special form must check for errors where appropriate and invoke the error procedure in error.scm if an error occurs. Examples of errors include a variable definition that is provided more than one expression, a definition with an improper name, a procedure with multiple parameters with the same name, an if with less than two arguments, and so on. Specific examples of these:

(define x 3 4)
(define 4 5)
(lambda (x y x) 3)
(if #t)

Refer to the Scheme documentation for what constitutes erroneous cases for each special form.


When this phase is complete, you will be able to run the provided tests for the phase:

$ make phase3

You can also run an individual test file for this phase, as in the following:

$ make phase3_begin

Make sure to write your own tests as well.

Phase 4: Dynamic Scope

To illustrate the value of a metacircular evaluator, we will extend the Scheme language with a mu form that creates procedures that use dynamic rather than static scope. Recall that dynamic scope with shallow binding means that the parent environment of the newly created frame for a procedure call is the calling environment, rather than the definition environment. The following is an example of a mu procedure:

scm> (define y 5)
scm> (define foo (mu (x)
                   (+ x y)
scm> (foo 3)
scm> ((mu (y)
        (foo -3)

Here, we have defined foo to be a mu procedure that refers to a non-local variable y. When invoked from global scope, the dynamic environment is the global environment, so y evaluates to 5, reflecting its binding in the global frame. However, when foo is invoked from within another procedure with its own binding for y, then y evaluates to the value corresponding to that binding.

Start by implementing an analogue of lambda-procedure for procedures with dynamic scope. As always, avoid repeating code, refactoring if necessary.

Second, implement a scheme-mu procedure that handles evaluation of a mu expression, resulting in a newly created procedure object.

Finally, modify add-special-forms so that it adds a binding for the mu special form to the given environment.

When this phase is complete, you will be able to run the provided tests for the phase:

$ make phase4

Make sure to write your own tests as well.

Rules and Regulations

The goals of this project include obtaining experience in functional programming. As such, your code is subject to the following constraints:

  • You may not use any non-R5RS-standard code.

  • You may not use the built-in eval procedure, or similar procedures, except in testing.

  • You may not use any procedures or constructs with side effects. Included in the prohibited set are any mutators (procedures or constructs that end with a bang, e.g. set!), and you may only use define at the top level (i.e. at global scope). The only exception to this rule is that you may use set!, set-car!, and set-cdr! in env.scm.

  • You may not use any iteration constructs. Use recursion instead.

To facilitate checking the rules above, the following symbols may not appear in env.scm, primitives.scm, or core.scm:

  • read

  • eval

  • current-input-port

  • current-output-port

  • open-input-file

  • open-output-file

  • with-input-from-file

  • with-output-to-file

  • any symbol ending with !, except set!, set-car!, and set-cdr! in env.scm

  • define as the first item in a list, except at global scope

  • peek-char

  • read-char

  • do

  • for-each

  • syntax-rules

Any violations of the two sets of rules above will result in a score of 0.

In addition, the standard Engineering Honor Code rules apply. Thus, you may not share any artifact you produce for this project outside of your partnership, including code, test cases, and diagrams. This restriction continues to apply even after you leave the course. Violations will be reported to the Honor Council.


The grade breakdown for this project is as follows:

  • 20% checkpoint

  • 70% final deadline autograded

  • 10% final deadline hand graded

Hand grading will evaluate the comprehensiveness of your test cases as well as your programming practices, such as documentation, avoiding unnecessary repetition, defining appropriate ADTs, and making proper use of built-in Scheme procedures. In order to be eligible for hand grading, your solution must achieve at least half the points on the autograded, final-deadline portion of the project.


All code that you write for dictionaries and environments must be placed in env.scm. The remaining code you write for the interpreter must be placed in primitives.scm or core.scm. You may not change any part of the interface that is used by driver.scm.

Submit core.scm, env.scm, primitives.scm, and any of your own test files to the autograder before the deadline. We suggest including a README.txt describing how to run your test cases.


This project uses elements from the Structure and Interpretation of Computer Programs text by Abelson and Sussman, as well as the Scheme interpreter project in the Composing Programs text by John DeNero.