FuncCalc

Term Project

Uni: MIREA – Russian Technological University

Field of study: Applied Mathematics and Informatics, Master's Degree

Subject: Functional Programming

Requirements

Non-functional requirements

• Programming Language: Swift
• Use some fuctional programing patterns: closures, pure finctions, higher-order functions (i.e. map, filter, reduce), etc.

Functional requirements

Defining functions with numbers and simple arithmetic operations (+, -, *, /, ^) in infix notation

>f1(x) = x^2
f1(x) = x^2

>f2(x) = 3*x
f2(x) = 3*x

Defining functions via previosly defined functions

>f1(x) = x^2
f1(x) = x^2

>f2(x) = 3*x
f2(x) = 3*x

>f3(x) = f1(x) + f2(x)
f3(x) = x^2 + 3*x

Calculation of the function value

>f3(x) = x^2 + 3*x
f3(x) = x^2 + 3*x

>f3(10)
f3(10) = 130

Taking symbolic derivative

>f3(x) = x^2 + 3*x
f3(x) = x^2 + 3*x

>f3’
f3’(x) = 2x + 3

Tasks to accomplish functional requirements

• Get rid of all spaces inside entered string
• Write regular expressions to indentify command type (expression f1(x) = x^2, calculation f3(10) or invalid)
• Parse expression-commands via regex and save results to Dictionary, where key is a name of a function (e.g. f) and value is struct containing symbol (e.g. x) and mathematical expression (e.g. x^2 + 3*x). So f(x) will overwrite f(y) and that's good, because when we calculate the function value, we don't use any symbol, only function name: f(10)
• Transform functions defined by previosly defined functions into original representation (e.g. f1(x) + f2(x) -> x^2 + 3*x)
• Do research into sumbolic derivation techniques
• Study Shunting_yard algorithm to translate Infix notation to Reverse Polish Notation
• Implement Stack data structure
• Check for parentheses balance
• Detect numbers with many digits and decimal point as single token
• Replace symbol of function (e.g. 'x' in 'f(x)') with number while function value calculation (e.g. 'f(10)') before using Shunting_yard algorithm
• Implement token detection
• Implement Shunting_yard algorithm
• Implement Expression Tree creation from Postfix Notation
• Implement evaluation of Expression Tree
• Implement symbolic differentiation
• Refactor