Basic Syntax

This guide covers the fundamental syntax elements of MathFlow, a powerful mathematical expression parser and evaluator.

Overview

MathFlow's syntax is designed to be:

• Intuitive: Similar to standard mathematical notation
• Flexible: Supports various writing styles
• Forgiving: Handles different spacing and formatting
• Expressive: Rich set of operations and functions

Lexical Structure

Comments

Comments in MathFlow start with a hash symbol (#) and continue to the end of the line:

# This is a single line comment
2 + 3     # Calculate sum
x = 5     # Assign value to x

Whitespace

MathFlow is whitespace-insensitive. Spaces, tabs, and newlines are ignored except to separate tokens:

# These are equivalent:
2+3*4
2 + 3 * 4
2  +  3  *  4

# These are also equivalent:
sin(30)
sin (30)
sin ( 30 )

Numbers

MathFlow supports various numeric formats:

# Integers
42
-17

# Decimals
3.14
-0.001

# Scientific notation
1.23e4    # 12300
1.23e-4   # 0.000123

# Special values
Infinity
-Infinity

Operators

Arithmetic Operators

a + b    # Addition
a - b    # Subtraction
a * b    # Multiplication
a / b    # Division
a ^ b    # Exponentiation (power)
-a       # Negation (unary minus)

Assignment Operator

x = 5    # Assign 5 to variable x

Grouping

Use parentheses for grouping and controlling evaluation order:

2 * (3 + 4)     # 14 (not 10)
(1 + 2) * (3 + 4)  # 21

# Nested parentheses
((2 + 3) * 4) + 5  # 25

Expression Structure

Simple Expressions

# Basic arithmetic
2 + 3
4 * 5 - 1

# Using variables
x + y
2 * radius

# Using functions
sin(30)
sqrt(16)

Compound Expressions

# Multiple operations
2 * x + y / 4

# Function composition
sin(sqrt(x))

# Complex calculations
(-b + sqrt(b^2 - 4*a*c)) / (2*a)

Multiple Lines

# Sequential calculations
x = 5
y = 2 * x
z = x + y

# Functions with multiple arguments
point_distance(x1, y1, x2, y2)

# Multi-line expressions
(sin(x)^2 +
 cos(x)^2)

Implicit Multiplication

MathFlow supports implicit multiplication between:

• Numbers and variables: 2x = 2 * x
• Numbers and functions: 2sin(x) = 2 * sin(x)
• Variables: xy = x * y
• Parentheses: 2(x+y) = 2 * (x+y)

# These are equivalent:
2x + 3y
2 * x + 3 * y

# These are also equivalent:
2sin(30)
2 * sin(30)

Operator Precedence

Operators are evaluated in this order (highest to lowest):

1. Parentheses ()
2. Functions sin(), cos(), etc.
3. Exponentiation ^
4. Unary minus -
5. Multiplication * and Division /
6. Addition + and Subtraction -
7. Assignment =

# Examples of precedence:
2 + 3 * 4       # 14 (not 20)
-2^2            # -4 (not 4)
2^3 * 4         # 32 (not 64)
x = y = 5       # Assigns 5 to both x and y

Error Handling

MathFlow provides clear error messages for common syntax issues:

2 +             # Incomplete expression
2 * * 3         # Invalid operator sequence
(2 + 3          # Unmatched parenthesis
sin 30          # Missing parentheses

Style Guidelines

While MathFlow is flexible with syntax, these guidelines improve readability:

1. Use Spaces around operators:

   x = 2 * y + 5  # Good
   x=2*y+5        # Less readable

2. One Expression per Line:

   # Good
   x = 5
   y = 2 * x
   
   # Less readable
   x = 5; y = 2 * x

3. Use Parentheses for clarity:

   (a + b) * c    # Clear precedence
   a + b * c      # Less clear

4. Meaningful Variable Names:

   radius = 5          # Clear purpose
   r = 5              # Less clear

5. Add Comments for complex expressions:

   # Calculate discriminant
   b^2 - 4*a*c