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Homework 08: Symbolic Evaluation of Boolean Expressions in Java

Due: 11:59pm Monday, Nov 16, 2020

200 points


Write a Java program  that reduces boolean expressions (represented in the input and output streams in Racket-like notation) to simplified form. For the purposes of this assignment, boolean expressions are Racket expressions constructed from:

  • the symbols T and F denoting the boolean values true and false ;
  • boolean variables (represented by symbols other than T, F, !, &, |, >, and ? that can be bound to either true or false .
  • the unary function ! meaning not .
  • the binary functions &, |, and > denoting and, or, and implies, respectively), and
  • the ternary function ? meaning if .

Note that the concrete (surface) syntax for boolean expressions differs from Assignment 5 because we are using the shorter names T, F, !, &, |, >, and ? are used instead of true, false, not, and, or, implies, and if for notational brevity, which matters in very large inputs.   You can write your Java code to perform boolean simplification using either the interpreter pattern of the visitor pattern.  The latter is perhaps slightly harder since there is more notational overhead, but it is valuable practice if you anticipate writing significant Java applications involving immutable inductively defined data

The course staff is providing

  • the Java "stub" files (where the functions in the simplifier are written using the visitor pattern) and (where the functions in the simplifier are written using that defines a composite hierarchy of "abstract syntax" tree classes rooted in the class Form representing boolean expressions;
  • a Java library file contain a class Parser with
    • a read() method that reads a boolean expression represented in concrete syntax ("Racket form"_ and returns the corresponding Java Form abstract syntax tree; and
    • a reduce() method that composes the visitors you must write in to reduce whatever formula the Parser instance contains to simplified form.
  • a Java "stub" test file that includes some rudimentary tests of the code in the (and similarly stub file.  

The stub files and also include comments showing you exactly what code you have to write to complete writing your simplifier. Of course, you also need to write corresponding tests and add them to the file

The file is provided primarily to enable you to test your solution on large inputs stored in files. includes two Parser constructors Parser(File file) and Parser(String form) for building parsers to parse the boolean expression (in concrete syntax form) in the specified File or String, respectively. Since the Java library class File is defined in the package, which is not imported by default (unlike java.lang), you need to insert either

Code Block

or more specifically

Code Block

at the head of a test file that uses the Parser class on the contents of a file.
To construct a Parser for the formula in a file <fileName> you can invoke

Code Block
new Parser(new File("<fileName>"));

If you omit the new File(...) wrapper around the String name of the file and simply use "<fileName>" instead, you will create a Parser for the String "<fileName>". which is then interpreted as a simple boolean variable. The File input medium is important because it enables us to conveniently apply your simplifier to formulas that are thousands of symbols long. As a result, for this assignment you only have to translate the Racket code in boolsimp.rkt into corresponding cleanly-written OO Java code by filling in the gaps in our Java stub file (or You are expected to appropriately use the composite, interpreter, singleton, and visitor patterns in the code that you write. Since the only stub files that you have to modify are (or and, simply upload working versions of these files to the Rice SVN repository to "turn in" your assignment. Warning: we will run your program on large inputs to determine if you wrote the code correctly. Try using the large test files provided on the course wiki.

All of the support files for this assignment are written standard Java rather than functional Java because the functional Java translator embedded no longer works well enough to write non-trivial programs like a boolean simplifier.   In principle, a very nice solution to this problem can be written in functional Java.  If I (with the help of students in Comp 402/501) manage to rewrite/repair the functional Java translator this spring, future editions of this assignment may be conducted entirely in functional Java.  We expect you to write functional code (mutation of data structures or the cells holding the bindings of variables).  If you use DrJava as your IDE, make sure that the language is set to "full Java".

The Racket file boolSimp.rkt includes Racket functions parse and unparse to translate Racket lists into abstract syntax trees and vice-versa. Racket provides a simple external syntax for lists (in homage to its LISP heritage) but Java does not. Hence the Java Parser class works on Java strings instead of lists. The Java visitor class Print in the file performs unparsing of the abstract syntax types Form and IfForm to type String.

As in Homework 5, the Racket parsing functions in boolSimp.rkt rely on the following Racket data definitions.


Code Block
(define-struct Not (arg))
(define-struct And (left right))
(define-struct Or (left right))
(define-struct Implies (left right))
(define-struct If (test conseq alt))

a boolExp is either:

  • a boolean constant true and false ;
  • a symbol S representing a boolean variable;
  • (make-Not X) where X is a boolExp ;
  • (make-And X Y) where =X and Y are boolExps;
  • (make-Or X Y) where =X and Y are boolExps;
  • (make-Implies X Y) where {{X and Y are boolExps; or
  • (make-If X Y Z) where X, Y, and Z are boolExps.


  1. The or operator must be written as \| in Racket instead of | because | is a metasymbol with a special meaning in Racket


  2. In essence, boolSimp.rkt is a solution to Homework 5.   The Java code in the file assumes the input in written in Racket notation, but with the following abbreviations to shorten the length of formulas:

    AbbreviationOriginal Symbol
  3. The Java abstract syntax classes include a separate composite hierarchy (called ifExp in boolSimp.rkt ). This representation includes only three concrete variant classes, making it much easier to write the visitors that perform normalization, evaluation, and convert-To-Bool.

Hints on Writing Your Java Code

The visitor pattern is a straightforward but notationally cumbersome alternative to the interpreter pattern. You can mechanically translate interpreter pattern code to visitor pattern code. (Perhaps IDEs like Eclipse should support such transformations.) The interpreter solution to this assignment is a bit easier to write than the visitor solution. If you are still learning Java mechanics, you are encouraged to write an interpreter solution first and perhaps translate it later to visitor form. A perfect visitor solution will be given 10 extra points over a perfect interpreter solutionu. If you submit an interpreter solution, your program must conform to class signatures given in the interpreter pattern support code below (just as a visitor solution must conform to the class signatures given in the visitor pattern code below).

The interpreter version of the support code replaces the ConvertToIf, Normalize, HeadNormalize, Evaluate, and Print visitors by methods named convertToIf, normalize, headNormalize, eval, and print.  The classes and contain references to these visitor class names and method names, respectively


Support Code

Here are the links for the files: is distinct from because the code for the reduce method embedded in the parser is different in the two versions.

Sample Input Files

The following files contain large formulas that can be reduced by your simplifier. Only the files named bigData x require a larger thread stack size than the JVM default on most platforms. NOTE: to handle the bigData x files, you must set JVM argument -Xss64M for the Interactions JVM using the DrJava Preferences command on the Edit menu. The JVM argument setting can be found on the last panel (called JVMs) in the Preferences categories tree.