Program 1 • Functionally Scheme Solution



1. Overview

Scheme is a dynamically typed (mostly) functional language with a very simple syn-tax. In this assignment, you will write a Silly Basic language interpreter in Scheme. The interpreter will read in an intermediate language program, parse it, and then interpret it. No looping constructs may be used, so it is critical that cer-tain parts use proper tail-recursion to avoid nuking the function call stack.

2. A Silly Basic Interpreter


sbi.scm — a Silly Basic Interpreter


sbi.scm filename


The SB interpreter reads in an SBIR program from the file whose name is specified in the argument list, stores it in a list, and then interprets that inter-mediate representation. During interpretation, numbers are read from the standard input and results written to the standard output.

Error messages are printed to the standard error. The first error, whether dur-ing compilation or interpretation, causes a message to be printed and the pro-gram to exit with an exit code of 1.




The single filename argument specifies an SBIR program to be run.


If the program completes without error, 0 is returned. If not, 1 is returned.


BASIC (Beginner’s All-purpose Symbolic Instruction Code) was designed at Dartmouth College, NH, by John Kemeny and Thomas Kurtz in 1965. A vari-ation of that language was ROM BASIC, distributed by IBM on their original PC in 1980.

(People used to spell the names of programming languages in all upper case because keypunches, such as the IBM 026 and 029, did not have lower case. Also, most printers usually had only upper case letters mounted, such as the IBM LN print train. A request to get upper and lower case, as with the IBM TN print train, would cause the job to go into an overnight queue.)

This version of basic is somewhat related, but no attempt is made to make it exactly the same. This description of the Silly Basic programming language, assumes that certain things are intuitively obvious. There are only two data types in the language : strings and real or complex numbers. Strings are used only in print statements. There are no string variables. All variables are real

CMPS-112 • • Program 1 • Functionally Scheme

2 of 7



And don’t forget about what Dijkstra said about this language :

Edsger W. Dijkstra : ‘‘It is practically impossible to teach good programming to students that have had a prior exposure to BASIC : as potential programmers they are mentally mutilated beyond hope of regeneration.’’ — EWD498.

The EWD manuscript archive is at THE SBIR LANGUAGE

This is a top-down definition of the SBIR language, specified using a variation of Backus-Naur Form (BNF), the format used to specify Algol-60, yet another one of the ancient languages. In the metanotation, brackets indicate that what they enclose is optional, braces indicate that what they enclose is repeated zero or more times, and a bar indicates alternation. Italics indicate nonterminal symbols and token classes, while quoted courier bold indicates lit-eral tokens.

  1. Program (’ { ‘( Linenr [ Label ] [ Statement ] ‘)’ }… ‘)

A program consists of zero or more statements, each of which might be identified by a label. Labels are kept in a namespace separate from the Variable namespace and do not conflict with each other. The program terminates when control flows off the last statement. A statement with neither a label nor a statement is considered just a comment and not put into the statement list.


Statements are the only organizational structure in the language and are exe-cuted one by one in sequence, except when a control transfer occurs. There is no block structure or nesting.

  1. Statement (’ ‘dim Arrayref )

Arrayref (’ ‘asub Variable Expression )

The dim statement creates an array given by the variable name and inserts it into the Symbol table, replacing any previous variable, array, or function already in the Symbol table. The dimension of the array is given by the expression. All values in the array are initialized to 0.

Unlike C, the lower bound of the array is 1 and the upper bound is the dimension, which may be an arbitrary expression. The expression is rounded to the nearest integer before being used as the bound, which must be positive.

  1. Statement (’ ‘let Memory Expression ) Memory Arrayref | Variable

A let statement makes an assignment to a variable. The expression is first evaluated. For a Variable, its value is stored into the Symbol table, replacing whatever was there previously. For an Arrayref , the store mes-sage is sent to the vector representing the array. If the Symbol table entry is not an array, an error occurs.

CMPS-112 • • Program 1 • Functionally Scheme

3 of 7

  1. Statement (’ ‘goto Label )

Control transfers to the statement referred to by the Label. An error occurs if the Label is not defined.

  1. Statement (’ ‘if’ ‘( Relop Expression Expression ) Label )

Relop =’ | ‘<’ | ‘>’ | ‘<>’ | ‘>=’ | ‘<=

The two Expressions are compared according to the given Relop, and if the comparison is true, control transfers to the statement, as for the goto statement. Note : <> is the symbol for not equal. The others should be obvious.

  1. Statement (’ ‘print’ { Printable }… ‘) Printable String | Expression

Each of the operands is printed in sequence, with a space before Expres-sion values. A newline is output at the end of the print statement. print statements are the only place Strings may occur in SBIR.

  1. Statement (’ ‘input Memory { Memory }… ‘)

Numeric values are read in and assigned to the input variables in sequence. Arguments might be elements of an array. For each value read into a Memory, the value is inserted into the Symbol table under that variable’s key. For arrays, the array must already exist and the sub-script not be out of bounds.

If an invalid value (anything that is not a number?) is read, the value returned is nan. If end of file is encountered, the value returned is nan and the variable eof is entered into the symbol table with the value 1. The value of nan can be computed using the expression (/ 0.0 0.0). The expression (= nan nan) is false.


Expressions consistitute the computational part of the language. All values dealt with at the expression level are real numbers. Invalid computations, such as division by zero and infinite results do not cause computation to stop. The value just propagates according to the rules of real or complex arithmetic.

  1. Expression ( Binop Expression Expression ) Expression ( Unop Expression ) Expression ( Function Expression ) Expression Constant

Expression Memory

Binop Unop | ‘*’ | ‘/’ | ‘%’ | ‘^ Unop +’ | ‘

Constants are numbers. Names of Functions, Arrayref s, and Variables all look like identifiers and their meaning is given by context.

    • (% x y) is equivalent to (- x (* (trunc (/ x y)) y))

    • (^ a b) is exponentiation (ab)

CMPS-112 • • Program 1 • Functionally Scheme

4 of 7


Comments being with a semi-colon and end at the end of a line. Strings are delimited by double-quote marks (). Numbers consist of digits, an optional decimal point, and an optional exponent. Keywords and Variable names are atoms. All of this is taken care of by Scheme’s builtin read.


In addition to the operators that are part of the language, the following func-tions are part of the function table : abs, acos, asin, atan, ceil, cos, exp, floor, log, log10, log2, round, sin, sqrt, tan, trunc. There is no facility for the user to add functions to the function table.

The following are part of the initial variable table :

  • nan is (/ 0.0 0.0)

  • eof is 0

  • pi is (acos -1.0)

  • e is (exp 1.0)

Thus, if you like, you can follow the law in Indiana, according to House Bill No. 246, Indiana State Legislature, 1897, which purportedly attempted to set the value of π to 3 [].

3. Program Structure

The program will be read in by Scheme’s read function, and represented internally as a list of statements, each statement having its own structure. After reading in the program, all labels must be put into a hash table, the key being the label itself and the value being the particular statement it refers to.

Interpretation will then proceed down the list from the first statement to the last. The interpreter stops when it runs off the end of the list. A control transfer is exe-cuted by fetching the address of a statement from the label table.

All variables are either real numbers or vectors of real numbers. Another hash ta-ble is used whose keys are variable names and whose values are real numbers, vec-tors of real numbers, or single parameter functions. An array subscript operation and a function call are syntactically ambiguous, but are disambiguated at run time by checking the symbol table. An uninitialized variable should be treated as 0.

Your program should not crash, no matter what the input. If a detectable unforseen condition happens due to user error, a message should be printed, giving the name of the file and the statement number.

The usual arithmetic results for infinities are printed by the runtime system, and these should be generated wherever possible. Division by zero, for example, should produce one of these quantities (+inf.0, -inf.0, +nan.0). Make sure to add 0.0 to the denominator to ensure that you have a real number. Also look at the functions to see which ones need special treatment. While there is no way to input a complex number, Some computations, such as sqrt(-1), may produce them, and thus will be written out in MzScheme’s complex number notation.

You may ignore the directory src-sb, which contains source code and a translator from Basic to SBIR. You may also ignore the directory sbtran, which contains the SB to SBIR translator itself, written in Ocaml.

CMPS-112 • • Program 1 • Functionally Scheme

5 of 7

4. Functional Style

Programming should be done in entirely functional style, except for maintenance of the symbol tables. That means do not use any imperative functions except as out-lined below. In Scheme, imperative functions end with a bang (!) to indicate that an assignment is being made. Symbol tables are created with make-hash and updated with hash-set!. The symbol tables are as follows :

  1. *function-table* is used to hold all of the functions, which include the opera-tors. This is initialized when the program begins using a for-each loop con-taining a lambda. (See the example symbols.scm).

  1. *variable-table* holds the value of all variables, including pi and e and is updated as needed during interpretation of the program. The variable eof is initialized to 0. Whenever a variable in the symbol table is not found, the value 0 is returned.

  1. *array-table* is used to hold all arrays defined in the program. Arrays and variables are in separate namespaces. Arrays are created with make-vector and updated with vector-set!.

  1. *label-table* is used to hold addresses of each line, one level up from state-ments. This is initialized by scanning the list returned by (read) when the program begins.

Except for hash-set! and vector-set! as outlined above, no imperative functions are permitted. Use functional style only.

5. Pseudocode Outline

The data structure consists of a recursively nested list :

  1. The top level list consists of a sequence of lines. Each line is pointed at by the car of a cell in the top level list.

  1. Each line consists of a line number, an optional label, which is always a sym-bol?, and an optional statement, which is always a pair?. Use null? to deter-mine whether not something exists. Do not use list?.

  1. A statement consists of a keyword followed by operands, mostly expressions.

  1. An expression uses prefix notation in standard Scheme format.

A suggested outline and description of some of the functions follows :

  1. After reading in the program, make one pass over the top level, checking for a label in each line. Each label should be inserted into the label hash with a pointer to the top level node (not the line).

  1. Write a function interpret-program takes the top level list as an argument and checks to see if there is a statement.

    1. If there is no statement, call interpret-program recursively with the cdr of the top level node.

    1. If there is a statement, look up the keyword in the statement hash and call interpret-statement, where statement is the keyword found in the statement.

CMPS-112 • • Program 1 • Functionally Scheme

6 of 7

      1. This funcion should return null for a statement that is not a control transfer, or for a statement that is a control transfer that is not taken.

      1. If this function returns a null then call interpret-program recursively with the cdr, as explained above.

      1. If this function is a successful control transfer, it should return the label to which to transfer, and then interpret-program calls itself recursively with the associated line.

    1. Write separate functions interpret-statement for each one of the keyword in the language.

    1. The function evaluate-expression is called by a statement interpreter.

      1. It looks up the function in the function table.

      1. It uses map to call evaluate-expression for each of the arguments to the function.

      1. Then use apply to apply the function to the list of results obtained.

      1. Subscripting arrays will require a special case.

  1. Examples Directory


7. Running mzscheme Interactively

It will be very convenient for you to run mzscheme interactively for testing purposes simply by invoking it from the command line, as in :

-bash-1$ mzscheme

Welcome to Racket v6.1.

  • (expt 2 128) 340282366920938463463374607431768211456

  • ^D

To do this, be sure to put it in your $PATH. This can be done by putting the following lines in your .bashrc or .bash_profile :

export PATH=$PATH:/afs/

Of course, you may prefer to collapse these multiple shell commands into a single line. If you use a different shell, then setting your $PATH will be done differently.

8. What to Submit

Submit two files : README and sbi.scm. It must be runnable by using it as the com-mand word of any shell command, and hence the execute bit must be turned on (chmod +x). It will be run as a shell script, and hence the first line must be the fol-lowing hashbang :

#!/afs/ -qr

Make sure that the Unix command which mzscheme responds with the same exe-cutable. Important note : This must be the fiRST line in your script, and your id should be after it. Be sure there are no carriage return characters in the file.

If you are doing pair programming, one partner should submit sbi.scm, but both

CMPS-112 • • Program 1 • Functionally Scheme

7 of 7

should submit the README and PARTNER files, as specified in the pair programming guidelines.

Be sure to use checksource to verify basic formatting. If you do something silly like edit using a M*cr*$*ft editor, be sure to delete the carriage return characters before porting to Unix. This script, and other scripts, such as cid and elimcr, are in the directory


which should also be put in your $PATH environment variable.

The .score/ subdirectory contains instructions to the graders. Be sure your pro-gram runs with the test script. If your program runs when typed in manually from the command line, but not using the script, you will receive no points for execution and testing.

error: Content is protected !!