Grammar

Grammar#

This page describes the grammar of function expressions in FuncSketch.

Types#

FuncSketch supports the following types of values:

Type

Description

Integer

32-bit signed integers.

Real

Double-precision floating-point numbers.

When you write a number in a function expression, it is automatically recognized as follows:

  • Integer if it is an integer number without a decimal point (e.g. 1, -12, 0)

  • Real if it is a number with a decimal point and/or an exponent (e.g. 1.0, -12.34, 1e+6)

Note

Future implementation may support boolean and complex numbers.

Implicit Conversions#

  • Integer can be implicitly converted to Real. This conversion is done automatically when an Integer value is used with a Real value in binary operations (e.g. 1 + 2.0), or when an Integer value is passed to a function that takes a Real argument.

Operators#

The following operators are supported:

Operator

Description

-x

Negation

x + y

Addition

x - y

Subtraction

x * y

Multiplication

x / y

Division

x ** y

Power \(x^y\) (Works the same as pow)

Note

** is right-associative (e.g. 2 ** 3 ** 4 is parsed as 2 ** (3 ** 4)).

Note

The right operand of ** cannot be directly preceded by - unless it is a number literal (e.g. 2 ** -3 is valid). To negate an identifier, a function call, or a parenthesized expression, wrap it in parentheses (e.g. 2 ** (-x) instead of 2 ** -x).

Operator Precedence#

Operators have the following precedence (from highest to lowest):

  1. ** (power)

  2. - (negation)

  3. *, / (multiplication, division)

  4. +, - (addition, subtraction)

You can use parentheses () to change the order of evaluation.

Identifiers#

In function expressions, the following identifiers exist:

  • Parameter of the function. Currently x is the only parameter name.

  • Constants. (e.g. pi, e)

  • Functions. (e.g. sin, exp)

Identifiers before ( are treated as function names, and other identifiers are treated as parameters or constants. For example,

  • When exp(x) is parsed, FuncSketch searches for a function named exp.

  • When x + 1 is parsed, FuncSketch searches for a constant or a parameter named x.

For built-in names of constants and functions, see Built-in Constants and Built-in Functions.