Latest 0.9.3
License MIT
Platforms ios 8.0, osx 10.10, tvos 9.0, watchos 2.0, requires ARC

Swift 3.2
Swift 4.0



Expression is a library for Mac and iOS for evaluating numeric expressions at runtime.

It is similar to Foundation’s built-in Expression class, but with better support for custom operators, a more Swift-friendly API, and a focus on performance.


There are many situations where it is useful to be able to evaluate a simple expression at runtime. Some are demonstrated in the example apps included with the library:

  • A scientific calculator
  • A CSS color string parser
  • A basic layout engine, similar to AutoLayout

But there are other possible applications, e.g.

  • A spreadsheet app
  • Configuration (e.g. using expressions in a config file to avoid data duplication)
  • The basis for simple scripting language

(If you find any other use cases, let me know and I’ll add them)

Normally these kind of calculations would involve embedding a heavyweight interpreted language such as JavaScript or Lua into your app. Expression avoids that overhead, and is also more secure, as it reduces the risk of arbitrary code injection or crashes due to infinite loops, buffer overflows, etc.

Expression is fast, lightweight, well-tested, and written entirely in Swift.


Expression works by parsing an expression string into a tree of symbols, which can then be evaluated at runtime. Each symbol maps to a Swift closure (function) which is executed during evaluation. There are built-in functions representing common math operations, or you can provide your own custom ones.



The entire Expression API is encapsulated in a single file, and everything public is prefixed or namespaced, so you can simply drag the Expression.swift file into your project to use it. If you prefer, there’s a framework for Mac and iOS that you can import, or you can use CocoaPods, Carthage, or Swift Package Manager on Linux.

To install Expression using CocoaPods, add the following to your Podfile:

pod 'Expression', '~> 0.9.0'


You create an Expression instance by passing a string containing your expression, and (optionally) any or all of the following:

  • A set of configuration options – used to enabled or disable certain features
  • A dictionary of named constants – this is the simplest and most efficient way to specify predefined constants
  • A dictionary of named array constants – this is the simplest and most efficient way to specify predefined arrays of related values
  • A dictionary of symbols and callback functions – this is the most efficient way to provide custom functions or operators
  • A custom Evaluator function – this is the most flexible solution, and can support dynamic variable or function names

You can then calculate the result by calling the Expression.evaluate() function.

By default, Expression already implements most standard math functions and operators, so you only need to provide a custom symbol dictionary or evaluator function if your app needs to support additional functions or variables. You can mix and match implementations, so if you have some custom constants or arrays and some custom functions or operators, you can provide separate constants and symbols dictionaries.

Here are some examples:

// Basic usage:
// Only using built-in math functions

let expression = Expression("5 + 6")
let result = try! expression.evaluate() // 11

// Intermediate usage:
// Custom constants and functions

let expression = Expression("foo + bar(5) + rnd()", constants: [
    "foo": 5,
], symbols: [
    .function("bar", arity: 1): { args in args[0] + 1 },
    .function("rnd", arity: 0): { _ in arc4random() },
let result = try! expression.evaluate()

// Advanced usage:
// Using a custom Evaluator to decode hex color literals

let hexColor = "#FF0000FF" // rrggbbaa
let expression = Expression(hexColor) { symbol, args in
    if case .variable(let name), name.hasPrefix("#") { {
        let hex = String(name.characters.dropFirst())
        return Double("0x" + hex)
    return nil // pass to default evaluator
let color: UIColor = {
    let rgba = UInt32(try! expression.evaluate())
    let red = CGFloat((rgba & 0xFF000000) >> 24) / 255
    let green = CGFloat((rgba & 0x00FF0000) >> 16) / 255
    let blue = CGFloat((rgba & 0x0000FF00) >> 8) / 255
    let alpha = CGFloat((rgba & 0x000000FF) >> 0) / 255
    return UIColor(red: red, green: green, blue: blue, alpha: alpha)

Note that the evaluate() function can throw an error. An error will be thrown during evaluation if the expression was malformed, or if it references an unknown symbol.

For a simple, hard-coded expression like the first example, there is no possibility of an error being thrown. If you accept user-entered expressions, you must always ensure that you catch and handle errors. The error messages produced by Expression are detailed and human-readable (but not localized, currently).

do {
    let result = try expression.evaluate()
    print("Result: (result)")
} catch {
    print("Error: (error)")

When using the constants, arrays and symbols dictionaries, error message generation is handled automatically by the Expression library. If you need to support dynamic symbol decoding (as in the hex color example earlier), you can use a custom Evaluator function, which is a little bit more complex.

Your custom Evaluator function can return either a Double or nil or it can throw an error. If you do not recognize a symbol, you should return nil so that it can be handled by the default evaluator.

In some cases you may be certain that a symbol is incorrect, and this is an opportunity to provide a more useful error message. The following example matches a function bar with an arity of 1 (meaning that it takes one argument). This will only match calls to bar that take a single argument, and will ignore calls with zero or multiple arguments.

switch symbol {
case .function("bar", arity: 1):
    return args[0] + 1
    return nil // pass to default evaluator

Since bar is a custom function, we know that it should only take one argument, so it’s more helpful to throw an error if it is called with the wrong number of arguments, rather than returning nil to indicate that the function doesn’t exist. That would look something like this:

switch symbol {
case .function("bar", let arity):
    guard arity == 1 else { throw Expression.Error.arityMismatch(symbol) }
    return args[0] + 1
    return nil // pass to default evaluator

Note that you can check the arity of the function either using pattern matching (as we did above), or just by checking args.count. These will always match.

For dynamic symbols, a more performant (but more complex) alternative to using a custom Evaluator function is to pre-parse the expression to discover the specific symbols that it’s actually using, then calculate the values in advance. Here is how that would work for the hex colors example:

// Expert usage:
// Pre-parsing to get the symbols, then initializing Expression with
// precalculated hex color constants to improve evaluation performance

let hexColor = "#FF0000FF" // rrggbbaa
let parsedExpression = Expression.parse(hexColor)
var constants = [String: Double]()
for symbol in parsedExpression.symbols {
    if case .variable(let name), name.hasPrefix("#") { {
        let hex = String(name.characters.dropFirst())
        if let value = Double("0x" + hex) {
            constants[name] = value
let expression = Expression(parsedExpression, constants: constants)
let color: UIColor = {
    let rgba = UInt32(try! expression.evaluate())
    let red = CGFloat((rgba & 0xFF000000) >> 24) / 255
    let green = CGFloat((rgba & 0x00FF0000) >> 16) / 255
    let blue = CGFloat((rgba & 0x0000FF00) >> 8) / 255
    let alpha = CGFloat((rgba & 0x000000FF) >> 0) / 255
    return UIColor(red: red, green: green, blue: blue, alpha: alpha)


Expressions are formed from a mixture of numeric literals and symbols, which are instances of the Expression.Symbol enum type. The built-in math and boolean libraries define a number of standard symbols, but you are free to define your own.

The Expression.Symbol enum supports the following symbol types:



This is an alphanumeric identifier representing a constant or variable in an expression. Identifiers can be any sequence of letters and numbers, beginning with a letter, underscore (_), dollar symbol ($), at sign (@) or hash/pound sign (#).

Like Swift, Expression allows unicode characters in identifiers, such as emoji and scientific symbols. Unlike Swift, Expression’s identifiers may also contain periods (.) as separators, which is useful for name-spacing (as demonstrated in the Layout example app).

The parser also accepts quoted strings as identifiers. Single quotes (‘) , double quotes (") , or backticks (`) may be used. Since Expression only deals with numeric values, it’s up to your application to map these string indentifiers to numbers. Unlike regular identifiers, quoted identifiers can contain any unicode character, including spaces. Newlines, quotes and other special characters can be escaped using a backslash (). Escape sequences are decoded for you, but the outer quotes are retained so you can distinguish strings from other identifiers.

Finally, unquoted identifiers are permitted to end with a single quote (‘), as this is a common notation used in mathematics to indicate modified values. A quote at any other point in the identifier will be treated as the end of the name.

To verify that a given string is safe for use as an identifier, you can use the Expression.isValidIdentifier() method.



These symbols represent operators. Operators can be one or more characters long, and can contain almost any symbol that wouldn’t conflict with a valid identifier name, with some caveats:

  • Comma (,) is a valid operator on its own, but cannot form part of a longer character sequence
  • The bracket characters [, ‘(‘, ‘{‘, and their counterparts are reserved and cannot be used as operators
  • An operator may begin with one or more dots (.) or hyphens (-), but a dot or hyphen cannot appear after any other character. The following are permitted:

    ..., ..<, ., -, --, -=, -->

    but the following are not:

    +., >.<, *-, -+-, <--, .-, -.

To verify that a given character sequence is safe for use as an operator, you can use the Expression.isValidOperator() method.

You can overload existing infix operators with a post/prefix variant, or vice-versa. Disambiguation depends on the white-space surrounding the operator (which is the same approach used by Swift).

Any valid identifier may also be used as an infix operator, by placing it between two operands, or as a postfix operator, by placing it after an operand. For example, you could define m and cm as postfix operators when handling distance logic, or use and as a more readable alternative to the boolean && operator.

Operator precedence follows standard BODMAS order, with multiplication/division given precedence over addition/subtraction. Prefix operators take precedence over postfix operators, which take precedence over infix ones. There is currently no way to specify precedence for custom operators – they all have equal priority to addition/subtraction.

Standard boolean operators are supported, and follow the normal precidence rules, with the caveat that short-circuiting (where the right-hand argument(s) may not be evaluated, depending on the left-hand-side) is not supported. The parser will also recognize the ternary ?: operator, treating a ? b : c as a single infix operator with three arguments.


.function(String, arity: Int)

A function symbol is defined with a name and an "arity", which is the number of arguments that it expects. Functions are called in an expression by using their name followed by a comma-delimited sequence of arguments in parentheses. Functions can be overloaded to support different argument counts, but it is up to you to handle argument validation in your evaluator function.



Array symbols represent a sequence of values that can be accessed by index. Array symbols are referenced in an expression by using their name followed by an index argument in square brackets.



By default, Expression caches parsed expressions. The expression cache is unlimited in size. In most applications this is very unlikely to ever be a problem – expressions are tiny, and even the most complex expression you can imagine is probably well under 1KB, so it would take a lot of them to cause memory pressure – But if for some reason you do ever need to reclaim the memory used by cached expressions, you can do so by calling the flushCache() method:


The flushCache() method takes an optional string argument, so you can also remove a specific expression from the cache without clearing others:

Expression.flushCache(for: "foo + bar"))

If you’d prefer even more fine-grained control of caching, you can pre-parse the expression without caching it, then create the Expression instance from the pre-parsed expression, as follows:

let expressionString = "foo + bar"
let parsedExpression = Expression.parse(expressionString, usingCache: false)
let expression = Expression(parsedExpression, constants: ["foo": 4, "bar": 5])

By setting the usingCache argument to false in the code above, we avoid adding the expression to the global cache. You are also free to implement your own caching by storing the parsed expression and re-using it, which may be more efficient than the built-in cache in some cases (e.g. by avoiding thread management if your code is single-threaded).

A second variant of the Expression.parse() method accepts a String.UnicodeScalarView.SubSequence and optional list of terminating delimiter strings. This can be used to match an expression embedded inside a longer string, and leaves the startIndex of the character sequence in the right place to continue parsing once the delimiter is reached:

let expressionString = "lorem ipsum {foo + bar} dolor sit"
var characters = String.UnicodeScalarView.SubSequence(expression.unicodeScalars)
while characters.popFirst() != "{" {} // Read up to start of expression
let parsedExpression = Expression.parse(&characters, upTo: "}")
let expression = Expression(parsedExpression, constants: ["foo": 4, "bar": 5])


By default, expressions are optimized where possible to make evaluation more efficient. Common optimizations include replacing constants with their literal values, and replacing pure functions or operators with their result when all arguments are constant.

The optimizer reduces evaluation time at the cost of increased initialization time, and for an expression that will only be evaluated once or twice, this tradeoff may not be worth it, in which case you can disable optimization using the options argument, as follows:

let expression = Expression("foo + bar", options: .noOptimize, ...)

On the other hand, if your expressions are being evaluated hundreds or thousands of times, you will want to take full advantage of the optimizer to improve your application’s performance. To ensure you are getting the best out of Expression’s optimizer, follow these guidelines:

  • Always pass constant values via the constants argument instead of as a variable in the symbols dictionary or evaluator function. Constant values can be inlined, whereas variables must be re-computed each time the function is evaluated in case they have changed.

  • If your custom functions and operators are all pure – i.e. they have no side effects, and always return the same output for a given set of argument values – then you should set the pureSymbols option for your expression. This option tells the optimizer that it’s safe to inline any functions or operators in the symbols dictionary if all their arguments are constant. Note that the pureSymbols option does not affect variables (which are never inlined), nor any symbols matched by the evaluator function.

  • Wherever possible, use the symbols dictionary to specify custom variables, operators or functions, instead of an evaluator function. Just having an evaluator function (even one that returns nil for everything) introduces an overhead to both initialization and the first evaluation, so if you don’t need it, don’t include it. The exception to this is if you have a mix of pure and impure symbols, in which case it’s better to put the pure symbols in the symbols dictionary (and set the pureSymbols option), then put the impure ones in the evaluator function.

  • If your expressions may contain values which are constant, but where not all possible values can be computed in advance – e.g. encoded values such as in the hex colors example, or arbitrary keypaths that must be looked up in a deep object graph – you can use the parse() function to get access to the list of symbols that are actually used in the expression. This allows you to decode or look up just the specific values that are needed, and then pass them as constants to the Expression at initialization time, without needing to use an evaluator function (see the "Expert usage" example in the Integration section above).

Standard Library

Math Symbols

By default, Expression supports a number of basic math functions, operators, and constants that are generally useful independent of a particular application.

If you use a custom symbol dictionary, you can override any default symbol, or overload default functions with a different number of arguments (arity). Any symbols from the standard library that you do not explicitly override will still be available.

To explicitly disable individual symbols from the standard library, you can override them and throw an exception:

let expression = Expression("pow(2,3)", symbols: [
    .function("pow", arity: 2): { _ in throw Expression.Error.undefinedSymbol(.function("pow", arity: 2)) }
try expression.evaluate() // this will throw an error because pow() has been undefined

If you have provided a custom Evaluator function, you can fall back to the standard library functions and operators by returning nil for unrecognized symbols. If you do not want to provide access to the standard library functions in your expression, throw an Error for unrecognized symbols instead of returning nil.

let expression = Expression("3 + 4") { symbol, args in
    switch symbol {
    case .function("foo", arity: 1):
        return args[0] + 1
        throw Expression.Error.undefinedSymbol(symbol)
try expression.evaluate() // this will throw an error because no standard library operators are supported, including +

Here are the currently supported math symbols:



infix operators

+ - / * %

prefix operators





Boolean Symbols

In addition to math, Expression also supports boolean logic, following the C convention that zero is false and any nonzero value is true. The standard boolean symbols are not enabled by default, but you can enable them using the .boolSymbols option:

let expression = Expression("foo ? bar : baz", options: .boolSymbols, ...)

As with the math symbols, all standard boolean operators can be individually overriden or disabled for a given expression using the symbols or evaluator constructor arguments.

Here are the currently supported boolean symbols:



infix operators


prefix operators


ternary operator


Example Projects


Not much to say about this. It’s a calculator. You can type expressions into it, and it will evaluate them and produce a result (or an error, if what you typed was invalid).


The Colors example demonstrates how to use Expression to create a (mostly) CSS-compliant color parser. It takes a string containing a named color, hex color or rgb() function call, and returns a UIColor object.

Using Expression to parse colors is a bit of a hack, as it only works because it’s possible to encode a color as a UInt32, which itself can be stored inside the Double returned by the Expression evaluator. Still, it’s a neat trick.


This is where things get interesting: The Layout example demonstrates a crude-but-usable layout system, which supports arbitrary expressions for the coordinates of the views.

It’s conceptually similar to AutoLayout, but with some important differences:

  • The expressions can be as simple or as complex as you like. In AutoLayout, every constraint uses a choice between a few fixed formulae, where only the operands are interchangeable.
  • Instead of applying an arbitrary number of constraints between properties of views, each view just has four fixed properties that can be calculated however you like.
  • Layout is deterministic. There is no weighting system used for resolving conflicts, and circular references are forbidden. Despite that, weighted relationships can be achieved using explicit multipliers.

Default layout values for the example views have been set in the Storyboard, but you can edit them live in the app by tapping a view and typing in new values.

Here are some things to note:

  • Every view has a top, left, width and height expression to define its coordinates on the screen.
  • Views have an optional key (like a tag, but string-based) that can be used to reference their properties from another view.
  • Any expression-based property of any view can reference any other property (of the same view, or any other view), and can even reference multiple properties.
  • Every view has a bottom and right property. These are computed, and cannot be set directly, but they can be used in expressions.
  • Circular references (a property whose value depends on itself) are forbidden, and will be detected by the system.
  • The width and height properties can use the auto variable, which does nothing useful for ordinary views, but can be used with text labels to calculate the optimal height for a given width, based on the amount of text.
  • Numeric values are measured in screen points. Percentage values are relative to the superview’s width or height property.
  • Remember you can use functions like min() and max() to ensure that relative values don’t go above or below a fixed threshold.

This is just a toy example, but if you like the concept, check out the Layout framework on Github.

Latest podspec

    "name": "Expression",
    "version": "0.9.3",
    "license": {
        "type": "MIT",
        "file": ""
    "summary": "Mac and iOS library for evaluating numeric expressions at runtime.",
    "homepage": "",
    "authors": "Nick Lockwood",
    "source": {
        "git": "",
        "tag": "0.9.3"
    "source_files": "Sources",
    "requires_arc": true,
    "platforms": {
        "ios": "8.0",
        "osx": "10.10",
        "tvos": "9.0",
        "watchos": "2.0"
    "pushed_with_swift_version": "4.0"

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