Scheme 代写-CSE-112
CSE-112 • Spring 2021 • Program 1 • Functionally Scheme 1 of 7
$Id:,v 1.19 2021-03-22 03:33:59-07 - - $
PWD: /afs/
1. Overview
Scheme is a dynamically typed (mostly) functional language with a very simple syn-
tax. In this assignment, you will write a Mini 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 function call stack overflow.
2. Examples Directory and Readme
Also look at the references in README.html or README.text in this directory for some
tutorials and references. When using google, be sure to look for references to Racket
and Mzscheme. There are other implementations of Scheme which are not neces-
sarily exactly compatible.
3. 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$ mzscheme
Welcome to Racket v7.4.
> (expt 2 128)
> (sqrt -1)
> (acos -1)
> ^D
To do this, be sure to put it in your $PATH. This can be done by putting the following
lines in your .bash_profile :
export PATH=$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.
To use the arrow keys on the keyboard to edit previous lines in interactive mode,
put the following line in a file $HOME/.racketrc :
(require readline)
Or, after starting mzscheme, enter the above command before any other interaction.
Or, put the following line in your .bash_profile :
alias wscheme=’rlwrap mzscheme’
Then start mzscheme with the command wscheme instead. This only works at the
command line, so don’t use it in the #! line of the program script. rlwrap is a pro-
gram that wraps another program in the readline utility, allowing use of common
terminal editing facilities, such as the use of the arrow keys.
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4. A Mini Basic Interpreter
mbir.scm — a Mini Basic Interpreter
mbir.scm [-d] filename
The mbir interpreter reads in an mbir 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 mbir 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.
Mini Basic is somewhat related. This description of the Mini Basic program-
ming language, assumes that certain things are intuitively obvious. There are
only two data types in the language : strings and numbers. Strings are used
only in print statements. There are no string variables. Variables are floating
point numbers.
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.
EWD manuscripts are archived at
This is a top-down definition of the mbir 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.
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(a) 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.
(a) Statement → ‘(’ ‘dim’ Arrayref ‘)’
Arrayref → ‘(’ ‘asub’ Variable Expression ‘)’
The dim statement creates an array given by the variable name and
inserts it into the array table, replacing any previous array already in
the array table. The dimension of the array is given by the expression.
All values in the array are initialized to 0.0 (as a real). The expression is
rounded to the nearest integer before being used as the bound, which
must be positive. Since the size of the vector must be an integer, use
(make-vector (exact-round size) 0.0) to create the array. A subscript i
must be in the range 0 ≤ i < n, where n is the dimension.
(b) 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.
(c) Statement → ‘(’ ‘goto’ Label ‘)’
Control transfers to the statement referred to by the Label. An error
occurs if the Label is not defined.
(d) 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
(e) Statement → ‘(’ ‘print’ { Printable }... ‘)’
Printable → String | Expression
Each of the operands is printed in sequence. A space is printed before
each expression in the list of values, but not before strings. Expresions
are evaluated to a number before being printed. A newline is output at
the end of the print statement. print statements are the only place
Strings may occur in mbir.
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(f) 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).
Counterintuitively, 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
or produces not a number (nan). The result of using complex numbers is unde-
(a) Expression → ‘(’ Binop Expression Expression ‘)’
Expression → ‘(’ Unop Expression ‘)’
Expression → ‘(’ Function Expression ‘)’
Expression → Constant
Expression → Memory
Binop → ‘+’ | ‘−’ | ‘*’ | ‘/’ | ‘^’
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
exponentiation (x y)
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, round, sin, sqrt, tan, trunc.
The following are part of the initial variable table :
nan = (/ 0.0 0.0) ; eof = 0.0 ; pi = (acos -1.0) ; e = (exp 1.0).
5. 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.
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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). Add 0.0 to all input num-
bers to ensure that they are converted to real numbers. Also look at the functions to
see which ones need special treatment.
You may ignore the directory mini-basic.d/mb-programs.d which contains source
code and a translator from Mini Basic to mbir. You may also ignore the directory
translator, which contains the mb to mbir translator itself, written in Ocaml.
6. 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 :
(a) *stmt-table* contains all of the individual statement interpreters. It is initial-
ized at the beginning of execution and thereafter never modified.
(b) *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).
(c) *variable-table* holds the value of all variables, and is updated as needed
during interpretation of the program. Whenever a variable in the symbol ta-
ble is not found, the value 0 is returned. The variable table is initialized with
the variables described in the section ‘‘builtin symbols’’.
(d) *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!.
(e) *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.
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7. Pseudocode Outline
The data structure consists of a recursively nested list :
(a) 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.
(b) 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?.
(c) A statement consists of a keyword followed by operands, mostly expressions.
(d) An expression uses prefix notation in standard Scheme format.
A suggested outline and description of some of the functions follows :
(a) 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).
(b) Write a function interpret-program takes the top level list as an argument and
checks to see if there is a statement.
(i) If there is no statement, call interpret-program recursively with the cdr
of the top level node as the continuation.
(ii) 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
(iii) This function should then call interpret-program with its continuation
for a statement that is not a control transfer, or for a statement that is a
control transfer that is not taken.
(iv) If this function has a control transfer, or if it is a statement that has a
control transfer that is taken, call interpret-program recursively with the
cdr, as explained above.
(c) Write separate functions interpret-statement for each one of the keyword in
the language.
(d) The function evaluate-expression is called by a statement interpreter.
(i) It looks up the function in the function table.
(ii) It uses map to call evaluate-expression for each of the arguments to the
(iii) Then use apply to apply the function to the list of results obtained.
(iv) Subscripting arrays will require a special case.
8. What to Submit
Submit files : README and mbir.scm. (And PARTNER if you are doing pair program-
ming.) mbir.scm must be runnable by using it as the command 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 following hashbang :
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#!/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 mbir.scm, but both
should submit the README and PARTNER files, as specified in the pair programming
guidelines. If you are not pair programming, read the section ‘‘Solo programming’’.
Be sure to use checksource to verify basic formatting. This script, and other scripts,
such as cid and elimcr, are in
which should also be put in your $PATH environment variable.
The .score/ subdirectory contains instructions to the graders. Be sure your pro-
gram runs with the test script. If your program runs when typed in manually from
the command line, but not using the script, you will receive no points for execution
and testing.
9. Debugging
To make it easier to debug, run the program interactively and call functions directly
from the interactive REPL (read eval print loop). This can be done in several ways :
(a) Use interactive mode in mzscheme and call individual functions interactively at
the prompt :
-bash$ mzscheme
> (load "mbir.scm")
> . . .
(b) Put the following line in your .bash_profile :
alias debug-mbir=’mzscheme -f mbir.scm -i -- -d’
Then, for debugging purposes only, you may use the command
debug-mbir program.mbir
to run the program. After loading mbir.scm, it turns on the *DEBUG* flag and
then runs the program. After that you see the interactive prompt for the
REPL (read eval print loop) which you can then use to call functions directly
from the command line.
(c) Another alternative is to put the definition of *DEBUG* in the file itself and com-
ment out the call to main. Then call main or other functions directly from the
When running the program in producton mode, call it directly from the command
line using the command mbir.scm, without using the name mzscheme at the command