Represent code in math equations

Introduce

The article shows a way to use math equations to represent code's logical.

Key ideas

logical first

Get readers to see the logical first, so prefer to keep a 'where' section to describe variables separately.

Pure function conception

I am thinking, in a function, whether we can just use

• Only has a 'if/else' statement
• Only has a 'switch/case' statement
• Only has a 'for' statement
• Only has a 'foreach' statement
• Only has a 'while' statement
• Only has statements without 'if/else', 'switch/case', 'for', 'foreach' or 'while'.

Decision Structures

• Decision structure - simple
  \[
  result =
  \begin{cases}
  statement_1, & {condition}_1 \\
  statement_2, & {condition}_2 \\
  statement_3 & \text{otherwise}
  \end{cases}
  \]

• Decision structure (if ... then) - if, else
  \[
  result =
  \begin{cases}
  statement_1, & \text{if}\ {condition}_1 \\
  statement_2, & \text{if}\ {condition}_2 \\
  statement_3 & \text{otherwise}
  \end{cases}
  \]

• Decision structure (if ... then) - if, else with multiple lines
  \[
  \text{if (constant-expression)} \\
  \{ \\
  \qquad statement_1 \\
  \qquad statement_2 \\
  \}
  \]

• Decision structure(selection) - switch, case, default, goto, break
  \[
  result = (switch : {expression})
  \begin{cases}
  statement_1, & \text{case}\ {constant-expression}_1 \\
  statement_2, & \text{case}\ {constant-expression}_2 \\
  statement_3 & \text{otherwise}
  \end{cases}
  \]

• Loop structure (conditional) - while, continue
  First check the condition to determine if enter the loop.
  \[
  {while}_\text{condition} \text{statement}
  \]

• Loop structure (conditional) - do, while, continue
  First execute the statement, then check the condition to determine if enter the next loop.
  \[
  {while}^\text{condition} \text{statement}
  \]

• Loop structure (iteration) - for
  \[
  {for}_\text{i = 1}^\text{ i < n} \text{statement}
  \]

• Loop structure (iteration) - for with step
  \[
  {for}_\text{i = 1}^\text{ i < n; i += 2} \text{statement}
  \]

• Loop structure (iteration) - foreach
  \[
  {foreach}_\text{item}^\text{items} \text{statement}
  \]

Keywords

• break
  \(\bigotimes\)
• continue
  \(\bigodot\)

function

\[
\text{(variable_1 [, ..., variable_n]) function_name(parameter_1 [, ..., parameter_k])} = \\
[\{] \\
\qquad statement_1 \\
\qquad statement_2 \\
\qquad ... \\
\qquad statement_n \\
where \\
\qquad variable_1 = ... \\
\qquad ... \\
\qquad variable_m = ... \\
[\}]
\]

function in one body

\[
\text{(variable_1 [, ..., variable_n]) function_name(parameter_1 [, ..., parameter_l])} = \\
\qquad \begin{cases}
statement_1 \\
statement_2 \\
where \\
\qquad variable_1 = ... \\
\qquad ... \\
\qquad variable_m = ... \\
\end{cases} \\
\]

class

\[
\text{class class_name[(inherited class name)]} = \\
[\{] \\
[where] \\
\qquad field_1 = ... \\
\qquad ... \\
\qquad field_m = ... \\
[functions]\\
\qquad function_1 \\
\qquad function_2 \\
\qquad ... \\
\qquad function_n \\
[\}]
\]

Comment - single line

\[
\text{ # input some comments} \\
\text{ : input some comments}
\]

Comment - multiple lines

\[
''' \\
\text{ this is} \\
\text{ multiple lines comments} \\
'''
\]

Comment - multiple lines 2

\[
""" \\
\text{ this is} \\
\text{ multiple lines comments} \\
"""
\]

Sample

\[
\text{class firstclass} = \\
\qquad field1 = 1 \\
\qquad field2 = true \\
\qquad \\
\qquad func1(param1, y) \\
\qquad \{ \\
\qquad \qquad var1,\ var2 = func2(1,\ 2) = \\
\qquad \qquad func3(var1) \\
\qquad \qquad y^{(mean)} = f4(y) \\
\qquad where \\
\qquad \qquad var1 \text{ # return value 1}\\
\qquad \qquad var2 \text{ # return value 2}\\
\qquad \qquad y \text{ : result data of training data.} \\
\qquad \qquad y^{(mean)} \text{ : the arithmetic mean along the y.} \\
\qquad \} \\
\qquad \\
\qquad (result1,\ result2)\ func2(param1,\ param2) = \\
\qquad \{ \\
\qquad \qquad result1 =
\begin{cases}
1, & \text{param1 > 0} \\
-1 & \text{otherwise}
\end{cases} \\
\qquad \qquad var2 = 100 \text{ # it is a variable defined in body. }\\
\qquad \qquad result2 = var1 + var2 + param2 \\
\qquad where \\
\qquad \qquad result1 \text{ # return value 1} \\
\qquad \qquad result2 = 0 \text{ # return value 2} \\
\qquad \qquad var1 = 10 \text{ # it is a variable. } \\
\qquad \} \\
\qquad \\
\qquad func3(param1) = \\
\qquad \begin{cases}
\text{# do something ...} \\
\text{# do something ...} \\
\text{# do something ...} \\
\text{# do something ...} \\
\text{# do something ...} \\
\text{# do something ...} \\
\end{cases} \\
\qquad \\
\qquad f4(y) = \frac{sum(y)}{count(y)} \\
\qquad \\
\qquad
\]

References

• Help:Displaying a formula
• LaTeX Wiki
• List of LaTeX symbols
• LaTeX documentation