You will be writing a C++ program that reads a string, determines whether it is a syntactically correct Boolean expression, and, if so, determines its value. For a grade of 100, This program will be due on Thursday, Sept 28. Each week or part of a week thereafter counts off 10%. The program must pass all of the test cases created by the grader to receive credit. Programs that do not pass all test cases may be resubmitted the following week.

1. Data model

A symbol is one of the following nine strings: "T", "F", "^", "v", "~", "=>", "<=>", "(", ")". Intuitively, these are interpreted as true, false, and, or, not, implies, if-and-only-if, and left and right parentheses.

A symbol string is the concatenation of zero or more symbols and/or spaces. For example, the following are symbol strings:

"T "

"=> Tv~ F(( F"

"T => F ^ (F v F)"

""

" "

and the following are not symbols strings

"T X "

" F= > T"

"TF p*^)"

A Boolean expression is a C++ vector of strings satisfying certain conditions. We will write C++ vectors by writing their elements, separated in commas and enclosed in brackets; for example, we will write [10 ,20] for the vector of length 2 whose first element is 10 and whose second element is 20.. "Followed by" means concatenated with. For example, ["F"] followed by ["^", "T"] is the vector ["F","^","T]. The rules for forming Boolean expressions of various sorts are given below.

A Boolean constant is ["T"] or ["F"].

An unbreakable expression is either a Boolean constant, or ["("] followed by a Boolean expression followed by [")"].

A negation is either an unbreakable expression, or ["~"] followed by a negation.

A conjunction is either a negation, or a conjunction followed by ["^"] followed by a negation.

A disjunction is either a conjunction, or a disjunction followed by ["v"] followed by a conjunction.

An implication is either a disjunction, or a disjunction followed by ["=>"] followed by an implication.

A Boolean expression is either an implication, or an implication followed by ["<=>"] followed by a Boolean expression.

This grammar can be formalized in BNF notation as follows:

Const "T" | "F"

U Const | "(" B ")" // note, this rule has been corrected

N U | "~" N

C N | C "^" N

D C | D "v" C // note, this rule has been corrected

I D | D "=>" I

B I | I "<=>" B

An AST (short for abstract syntax tree, the standard name for what the book calls an expression tree) is defined below. This follows the pattern for defining trees given in the Aho & Ullman book in Chapter 5, p. 232. We will use AST's as a data structure to store the semantic structure of Boolean expressions.

typedef struct AST* pNODE;

struct AST {string info; pNODE children[2];};

The info member of an AST is a symbol, as defined above. If info is "T" or "F" then both children are NULL. If info is "~" then children[1] is NULL. Otherwise, both children are non-NULL. Sample code illustrating the use of this data structure can be found here.

A tokRslt is a struct with two fields:

success, a bool

syms, a C++ vector of strings.

A parseRslt is a struct with two fields:

success, a bool

ast, an AST

A TPERslt is a struct with two fields:

val, a bool

msg, a string

2. Functions

Implement the following five functions in a single C++ file:

tokRslt tokenize(string s)

If s is a string, tokenize(s).success is true if s is a string of symbols, and false otherwise.

If s is a string of symbols, then tokenize(s).syms is a vector of the symbols occurring in s, in order. For example, if s = "T vv =>" then tokenize(s).syms = ["T","v","v","=>"]

parseRslt parse(vector V)

If V is a Boolean expression, then parse(V).success is true and parse(V).ast is the abstract syntax tree of V according to the standard grammar of Boolean expressions.

Otherwise, parse(V).success if false.

bool eval(AST T)

eval(T) is the value of T according to the standard semantics of Boolean expressions.

TPERslt TPE(string s) (tokenize, parse, and evaluate)

If s is a string of symbols whose tokenization is a Boolean expression, then TPE.msg is "success" and TPE(s).val is the value of that Boolean expression.

If s is a string of symbols whose tokenization is not a Boolean expression, then TPE.msg is "grammar error".

If s is not a string of symbols, then TPE.msg is "symbol error".

string TPEOut(string s)

If s is a string of symbols whose tokenization is a Boolean expression, then TPEOut(s) is the value of that expression, converted to a string, which is either "true" or "false".

If s is a string of symbols whose tokenization is not a Boolean expression, then TPEOut(s) is "grammar error".

If s is not a string of symbols, then TPEOut(s) is "symbol error".

For example,

If s = "T v F ^ T", then TPEOut(s) is "true"

If s = "T => (F X T", then TPEOut(s) is "symbol error"

If s = "T T (F & T => F)", then TPEOut(s) is "grammar error"

Academic Integrity

Students are allowed to discuss this assignment verbally with each other, search the Web for useful source code, and download and use code if it helps you (though I doubt one can find code that will use the same data structures we use). The following are prohibited:

Looking at another student's code

Sharing code with another student

Asking another person to write code for you or to see their code.

Violations of 1-3 will result in a request to withdraw from the class with a W, if done before the last day to drop. After this date, it will result in a withdrawal from the class with a WF. If those options are not acceptable, the result will be a university-level academic honesty proceeding, with the aim of expulsion from the university.