Parser Combinator

Functional expressions

• Developed functions constant, variable, add, subtract, multiply, divide, med and avg, that take an arbitrary number of arguments
• An expression parser has been developed that reads expressions in the standard Clojure form

For example:
Expression 2x-3 representation:

  (def expr
   (subtract
    (multiply
      (constant 2)
      (variable "x"))
    (constant 3)))

(parseFunction "(- (* 2 x) 3)") is equivalent to expr.

Object Expressions

• Developed constructors Constant, Variable, Add, Subtract, Multiply и Divide to represent expressions with variables.
• A function evaluate has been developed, that calculates an expression if the values of the variables are known
• A function toString has been developed, that displays an expression in the standard Clojure form
• A function parseObject has been developed, that parses expressions in the standard Clojure form
• A function diff has been developed, that returns an expression representing the derivative with respect to a given variable.

Examples:

;; 2x - 3
(def expr
  (Subtract
    (Multiply
      (Constant 2)
      (Variable "x"))
    (Const 3)))
    
(evaluate expr {"x" 2}) ;; 1

(toString expr) ;; "(- (* 2 x) 3)"

(parseObject "(- (* 2 x) 3)") ;; expr

(diff expr "x") ;; (Constant 2),

Combinatorial parser

• A function parseObjectInfix has been developed that parses expressions written in infix form.
• A function toStringInfix has been developed, that displays an expression in infix form
• The system of operator priorities has been implemented, as well as left-associative and right-associative operations.

Examples:

(toStringInfix (parseObjectInfix "2 * x - 3")) ;; "((2.0 * x) - 3.0)"

(toStringInfix (parseObjectInfix "2 * x + 3 * z")) ;; "((2.0 * x) - (3.0 * z))"

(toStringInfix (parseObjectInfix "2 ** 3 ** 4")) ;; "(2.0 ** (3.0 ** 4.0))"

(toStringInfix (parseObjectInfix "2 + 3 + 4")) ;; "((2.0 + 3.0) + 4.0)"