Represent code in math equations

[comment]: # 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