hobdrive-docs

Dynamic Expressions: Core Syntax

The expression evaluator is based on an Excel-like implementation. It can parse mathematical expressions with support for the most commonly used functions.

Examples:

4*(24/2-5)+14
cos(Pi/4)*sin(Pi/6)^2
1-1/E^(0.5^2)
min(5;2;9;10;42;35)

Data Types

Five data types are supported:

Type	Description
`double`	Floating-point number (default for all calculations)
`int`	Integer. Use the `int()` function to convert explicitly
`hexadecimal`	Hexadecimal number. Converted to `double` in calculations
`string`	Text string
`boolean`	Logical value (`true` / `false`)

Note: Integers and hexadecimals are always converted to double when used in calculations. Use int() to convert to integer explicitly.

Built-in Constants

Constant	Description
`Pi`	The number π ≈ 3.14159…
`E`	Euler’s number e ≈ 2.71828…

Function Reference

Math Functions

Function	Description	Example
`Abs(x)`	Absolute value	`Abs(-5)` → `5`
`Acos(x)`	Arc cosine (inverse cosine)	`Acos(0)` → `1.5708`
`Asin(x)`	Arc sine (inverse sine)	`Asin(1)` → `1.5708`
`Atan(x)`	Arc tangent (inverse tangent)	`Atan(1)` → `0.7854`
`Atan2(y;x)`	Arc tangent of y/x, using signs to determine quadrant	`Atan2(1;1)` → `0.7854`
`Ceiling(x)`	Rounds up to the nearest integer	`Ceiling(4.1)` → `5`
`Cos(x)`	Cosine	`Cos(0)` → `1`
`Cosh(x)`	Hyperbolic cosine	`Cosh(0)` → `1`
`Exp(x)`	e raised to the power x	`Exp(1)` → `2.7183`
`Fact(x)`	Factorial	`Fact(5)` → `120`
`Floor(x)`	Rounds down to the nearest integer	`Floor(4.9)` → `4`
`Ln(x)`	Natural logarithm (base e)	`Ln(E)` → `1`
`Log(x)`	Common logarithm (base 10)	`Log(100)` → `2`
`Pow(x;y)`	x raised to the power y	`Pow(2;10)` → `1024`
`Round(x)`	Rounds to the nearest integer	`Round(4.5)` → `5`
`Sign(x)`	Returns the sign: −1, 0, or 1	`Sign(-42)` → `-1`
`Sin(x)`	Sine	`Sin(Pi/2)` → `1`
`Sinh(x)`	Hyperbolic sine	`Sinh(1)` → `1.1752`
`Sqr(x)`	Square (x²)	`Sqr(5)` → `25`
`Sqrt(x)`	Square root	`Sqrt(25)` → `5`
`Trunc(x)`	Truncates to integer (removes decimal part)	`Trunc(4.9)` → `4`

Aggregate / Statistics Functions

Function	Description	Example
`Avg(…)`	Average of values	`Avg(2;4;6)` → `4`
`Max(…)`	Maximum value	`Max(5;2;9)` → `9`
`Min(…)`	Minimum value	`Min(5;2;9)` → `2`
`StDev(…)`	Standard deviation	`StDev(2;4;6)`
`Var(…)`	Variance	`Var(2;4;6)`

Logic Functions

Function	Description	Example
`And(a;b)`	Logical AND	`And(true;false)` → `false`
`Or(a;b)`	Logical OR	`Or(true;false)` → `true`
`Not(x)`	Logical NOT	`Not(true)` → `false`
`If(cond;then;else)`	Conditional: returns `then` if `cond` is true, otherwise `else`	`If(5>6;"yes";"no")` → `"no"`

String Functions

Function	Description	Example
`Format(x;fmt)`	Formats a value using a format string	`Format(Pi;"0.00")` → `"3.14"`
`Hex(x)`	Converts a number to hexadecimal string	`Hex(255)` → `"FF"`
`Left(s;n)`	Returns the first `n` characters	`Left("hello";3)` → `"hel"`
`Right(s;n)`	Returns the last `n` characters	`Right("hello";3)` → `"llo"`
`Mid(s;start;n)`	Returns `n` characters starting at `start`	`Mid("hello";2;3)` → `"ell"`
`Len(s)`	Returns the length of a string	`Len("hello")` → `5`
`Lower(s)`	Converts to lowercase	`Lower("HELLO")` → `"hello"`
`Upper(s)`	Converts to uppercase	`Upper("hello")` → `"HELLO"`
`Val(s)`	Converts a string to a number	`Val("42")` → `42`

Utility Functions

Function	Description
`About`	Displays version information
`Clear`	Clears all user-defined variables and functions
`Help`	Displays help information

String Operations

The & operator concatenates strings:

"Hello " & "world"          // → "Hello world"
"Pi = " & Pi                // → "Pi = 3.14159265358979"
Len("hello world")          // → 11

Boolean Operators and Conditionals

true != false               // → true
5 > 6 ? "hello" : "world"  // → "world"
If(5 > 6;"hello";"world")  // → "world"

Variable and Function Declaration

Use := to declare variables and functions:

x := 42
f(x) := x^2
f(x) := sin(x) / cos(x)    // declare dynamic functions using built-in functions

Recursion and Scope

Functions can call themselves recursively. Variables declared as function parameters are local to that function; other variables are resolved from the global scope.

fac(n) := (n = 0) ? 1 : fac(n-1)*n
// fac calls itself with different parameters

f(x) := x * Y
// x is in function scope, Y is in global scope

Operator Precedence

From highest to lowest priority:

Priority	Operator	Description
1	`( )`, `f(x)`	Grouping, function calls
2	`!` `~` `-` `+`	Unary operators
3	`^`	Exponentiation (Excel rule: `a^b^c` → `(a^b)^c`)
4	`*` `/` `%`	Multiplication, division, modulo
5	`+` `-`	Addition, subtraction
6	`&`	String concatenation
7	`<` `<=` `>` `>=`	Comparison operators
8	`=` `!=` `<>`	Equality and inequality
9	`&&`	Logical AND
10	`\\|\\|`	Logical OR
11	`?:`	Ternary conditional
12	`:=`	Assignment