pigeon

README

pigeon - a PEG parser generator for Go

The pigeon command generates parsers based on a parsing expression grammar (PEG). Its grammar and syntax is inspired by the PEG.js project, while the implementation is loosely based on the parsing expression grammar for C# 3.0 article. It parses Unicode text encoded in UTF-8.

See the godoc page for detailed usage. Also have a look at the Pigeon Wiki for additional information about Pigeon and PEG in general.

Releases

• v1.0.0 is the tagged release of the original implementation.
• Work has started on v2.0.0 with some planned breaking changes.

Github user @mna created the package in April 2015, and @breml is the package's maintainer as of May 2017.

Release policy

Starting of June 2023, the backwards compatibility support for pigeon is changed to follow the official Go Security Policy.

Over time, the Go ecosystem is evolving.

On one hand side, packages like golang.org/x/tools, which are critical dependencies of pigeon, do follow the official Security Policy and with pigeon not following the same guidelines, it was no longer possible to include recent versions of these dependencies and with this it was no longer possible to include critical bugfixes. On the other hand there are changes to what is considered good practice by the greater community (e.g. change from interface{} to any). For users following (or even enforcing) these good practices, the code generated by pigeon does no longer meet the bar of expectations. Last but not least, following the Go Security Policy over the last years has been a smooth experience and therefore updating Go on a regular bases feels like duty that is reasonable to be put on users of pigeon.

This observations lead to the decision to follow the same Security Policy as Go.

Installation

Provided you have Go correctly installed with the $GOPATH and $GOBIN environment variables set, run:

$ go get -u github.com/mna/pigeon

This will install or update the package, and the pigeon command will be installed in your $GOBIN directory. Neither this package nor the parsers generated by this command require any third-party dependency, unless such a dependency is used in the code blocks of the grammar.

Basic usage

$ pigeon [options] [PEG_GRAMMAR_FILE]

By default, the input grammar is read from stdin and the generated code is printed to stdout. You may save it in a file using the -o flag.

Example

Given the following grammar:

{
// part of the initializer code block omitted for brevity

var ops = map[string]func(int, int) int {
    "+": func(l, r int) int {
        return l + r
    },
    "-": func(l, r int) int {
        return l - r
    },
    "*": func(l, r int) int {
        return l * r
    },
    "/": func(l, r int) int {
        return l / r
    },
}

func toAnySlice(v any) []any {
    if v == nil {
        return nil
    }
    return v.([]any)
}

func eval(first, rest any) int {
    l := first.(int)
    restSl := toAnySlice(rest)
    for _, v := range restSl {
        restExpr := toAnySlice(v)
        r := restExpr[3].(int)
        op := restExpr[1].(string)
        l = ops[op](l, r)
    }
    return l
}
}


Input <- expr:Expr EOF {
    return expr, nil
}

Expr <- _ first:Term rest:( _ AddOp _ Term )* _ {
    return eval(first, rest), nil
}

Term <- first:Factor rest:( _ MulOp _ Factor )* {
    return eval(first, rest), nil
}

Factor <- '(' expr:Expr ')' {
    return expr, nil
} / integer:Integer {
    return integer, nil
}

AddOp <- ( '+' / '-' ) {
    return string(c.text), nil
}

MulOp <- ( '*' / '/' ) {
    return string(c.text), nil
}

Integer <- '-'? [0-9]+ {
    return strconv.Atoi(string(c.text))
}

_ "whitespace" <- [ \n\t\r]*

EOF <- !.

The generated parser can parse simple arithmetic operations, e.g.:

18 + 3 - 27 * (-18 / -3)

=> -141

More examples can be found in the examples/ subdirectory.

See the package documentation for detailed usage.

Contributing

See the CONTRIBUTING.md file.

License

The BSD 3-Clause license. See the LICENSE file.

Documentation

Overview

Command pigeon generates parsers in Go from a PEG grammar.

From Wikipedia [0]:

A parsing expression grammar is a type of analytic formal grammar, i.e.
it describes a formal language in terms of a set of rules for recognizing
strings in the language.

Its features and syntax are inspired by the PEG.js project [1], while the implementation is loosely based on [2]. Formal presentation of the PEG theory by Bryan Ford is also an important reference [3]. An introductory blog post can be found at [4].

[0]: http://en.wikipedia.org/wiki/Parsing_expression_grammar
[1]: http://pegjs.org/
[2]: http://www.codeproject.com/Articles/29713/Parsing-Expression-Grammar-Support-for-C-Part
[3]: http://pdos.csail.mit.edu/~baford/packrat/popl04/peg-popl04.pdf
[4]: http://0value.com/A-PEG-parser-generator-for-Go

Command-line usage

The pigeon tool must be called with PEG input as defined by the accepted PEG syntax below. The grammar may be provided by a file or read from stdin. The generated parser is written to stdout by default.

pigeon [options] [GRAMMAR_FILE]

The following options can be specified:

-cache : cache parser results to avoid exponential parsing time in
pathological cases. Can make the parsing slower for typical
cases and uses more memory (default: false).

-debug : boolean, print debugging info to stdout (default: false).

-nolint: add '// nolint: ...' comments for generated parser to suppress
warnings by gometalinter (https://github.com/alecthomas/gometalinter) or
golangci-lint (https://golangci-lint.run/).

-no-recover : boolean, if set, do not recover from a panic. Useful
to access the panic stack when debugging, otherwise the panic
is converted to an error (default: false).

-o=FILE : string, output file where the generated parser will be
written (default: stdout).

-optimize-basic-latin : boolean, if set, a lookup table for the first 128
characters of the Unicode table (Basic Latin) is generated for each character
class matcher. This speeds up the parsing, if parsed data mainly consists
of characters from this range (default: false).

-optimize-grammar : boolean, (EXPERIMENTAL FEATURE) if set, several performance
optimizations on the grammar are performed, with focus to the reduction of the
grammar depth.
Optimization:
	* removal of unreferenced rules
	* replace rule references with a copy of the referenced Rule, if the
	  referenced rule it self has no references.
	* resolve nested choice expressions
	* resolve choice expressions with only one alternative
	* resolve nested sequences expression
	* resolve sequence expressions with only one element
	* combine character class matcher and literal matcher, where possible
The resulting grammar is usually more memory consuming, but faster for parsing.
The optimization of the grammar is done in multiple rounds (optimize until no
more optimizations have applied). This process takes some time, depending on the
optimization potential of the grammar.

-optimize-parser : boolean, if set, the options Debug, Memoize and Statistics are
removed	from the resulting parser. The global "state" is optimized as well by
either removing all related code if no state change expression is present in the
grammar or by removing the restoration of the global "state" store after action
and predicate code blocks. This saves a few cpu cycles, when using the generated
parser (default: false).

-x : boolean, if set, do not build the parser, just parse the input grammar
(default: false).

-receiver-name=NAME : string, name of the receiver variable for the generated
code blocks. Non-initializer code blocks in the grammar end up as methods on the
*current type, and this option sets the name of the receiver (default: c).

-alternate-entrypoints=RULE[,RULE...] : string, comma-separated list of rule names
that may be used as alternate entrypoints for the parser, in addition to the
default entrypoint (the first rule in the grammar) (default: none).
Such entrypoints can be specified in the call to Parse by passing an
Entrypoint option that specifies the alternate rule name to use. This is only
necessary if the -optimize-parser flag is set, as some rules may be optimized
out of the resulting parser.

-support-left-recursion : boolean, (EXPERIMENTAL FEATURE) if set, add support
for left recursion rules, including those with indirect recursion
(default: false).
E.g.:
	expr = expr '*' term / expr '+' term

If the code blocks in the grammar (see below, section "Code block") are golint- and go vet-compliant, then the resulting generated code will also be golint- and go vet-compliant.

The generated code doesn't use any third-party dependency unless code blocks in the grammar require such a dependency.

PEG syntax

The accepted syntax for the grammar is formally defined in the grammar/pigeon.peg file, using the PEG syntax. What follows is an informal description of this syntax.

Identifiers, whitespace, comments and literals follow the same notation as the Go language, as defined in the language specification (http://golang.org/ref/spec#Source_code_representation):

// single line comment
/* multi-line comment */
'x' (single quotes for single char literal)
"double quotes for string literal"
`backtick quotes for raw string literal`
RuleName (a valid identifier)

The grammar must be Unicode text encoded in UTF-8. New lines are identified by the \n character (U+000A). Space (U+0020), horizontal tabs (U+0009) and carriage returns (U+000D) are considered whitespace and are ignored except to separate tokens.

Rules

A PEG grammar consists of a set of rules. A rule is an identifier followed by a rule definition operator and an expression. An optional display name - a string literal used in error messages instead of the rule identifier - can be specified after the rule identifier. E.g.:

RuleA "friendly name" = 'a'+ // RuleA is one or more lowercase 'a's

The rule definition operator can be any one of those:

=, <-, ← (U+2190), ⟵ (U+27F5)

Expressions

A rule is defined by an expression. The following sections describe the various expression types. Expressions can be grouped by using parentheses, and a rule can be referenced by its identifier in place of an expression.

Choice expression

The choice expression is a list of expressions that will be tested in the order they are defined. The first one that matches will be used. Expressions are separated by the forward slash character "/". E.g.:

ChoiceExpr = A / B / C // A, B and C should be rules declared in the grammar

Because the first match is used, it is important to think about the order of expressions. For example, in this rule, "<=" would never be used because the "<" expression comes first:

BadChoiceExpr = "<" / "<="

Sequence expression

The sequence expression is a list of expressions that must all match in that same order for the sequence expression to be considered a match. Expressions are separated by whitespace. E.g.:

SeqExpr = "A" "b" "c" // matches "Abc", but not "Acb"

Labeled expression

A labeled expression consists of an identifier followed by a colon ":" and an expression. A labeled expression introduces a variable named with the label that can be referenced in the code blocks in the same scope. The variable will have the value of the expression that follows the colon. E.g.:

LabeledExpr = value:[a-z]+ {
	fmt.Println(value)
	return value, nil
}

The variable is typed as an empty interface, and the underlying type depends on the following:

For terminals (character and string literals, character classes and the any matcher), the value is []byte. E.g.:

Rule = label:'a' { // label is []byte }

For predicates (& and !), the value is always nil. E.g.:

Rule = label:&'a' { // label is nil }

For a sequence, the value is a slice of empty interfaces, one for each expression value in the sequence. The underlying types of each value in the slice follow the same rules described here, recursively. E.g.:

Rule = label:('a' 'b') { // label is []any }

For a repetition (+ and *), the value is a slice of empty interfaces, one for each repetition. The underlying types of each value in the slice follow the same rules described here, recursively. E.g.:

Rule = label:[a-z]+ { // label is []any }

For a choice expression, the value is that of the matching choice. E.g.:

Rule = label:('a' / 'b') { // label is []byte }

For the optional expression (?), the value is nil or the value of the expression. E.g.:

Rule = label:'a'? { // label is nil or []byte }

Of course, the type of the value can be anything once an action code block is used. E.g.:

RuleA = label:'3' {
	return 3, nil
}
RuleB = label:RuleA { // label is int }

And and not expressions

An expression prefixed with the ampersand "&" is the "and" predicate expression: it is considered a match if the following expression is a match, but it does not consume any input.

An expression prefixed with the exclamation point "!" is the "not" predicate expression: it is considered a match if the following expression is not a match, but it does not consume any input. E.g.:

AndExpr = "A" &"B" // matches "A" if followed by a "B" (does not consume "B")
NotExpr = "A" !"B" // matches "A" if not followed by a "B" (does not consume "B")

The expression following the & and ! operators can be a code block. In that case, the code block must return a bool and an error. The operator's semantic is the same, & is a match if the code block returns true, ! is a match if the code block returns false. The code block has access to any labeled value defined in its scope. E.g.:

CodeAndExpr = value:[a-z] &{
	// can access the value local variable...
	return true, nil
}

Repeating expressions

An expression followed by "*", "?" or "+" is a match if the expression occurs zero or more times ("*"), zero or one time "?" or one or more times ("+") respectively. The match is greedy, it will match as many times as possible. E.g.

ZeroOrMoreAs = "A"*

Literal matcher

A literal matcher tries to match the input against a single character or a string literal. The literal may be a single-quoted single character, a double-quoted string or a backtick-quoted raw string. The same rules as in Go apply regarding the allowed characters and escapes.

The literal may be followed by a lowercase "i" (outside the ending quote) to indicate that the match is case-insensitive. E.g.:

LiteralMatch = "Awesome\n"i // matches "awesome" followed by a newline

Character class matcher

A character class matcher tries to match the input against a class of characters inside square brackets "[...]". Inside the brackets, characters represent themselves and the same escapes as in string literals are available, except that the single- and double-quote escape is not valid, instead the closing square bracket "]" must be escaped to be used.

Character ranges can be specified using the "[a-z]" notation. Unicode classes can be specified using the "[\pL]" notation, where L is a single-letter Unicode class of characters, or using the "[\p{Class}]" notation where Class is a valid Unicode class (e.g. "Latin").

As for string literals, a lowercase "i" may follow the matcher (outside the ending square bracket) to indicate that the match is case-insensitive. A "^" as first character inside the square brackets indicates that the match is inverted (it is a match if the input does not match the character class matcher). E.g.:

NotAZ = [^a-z]i

Any matcher

The any matcher is represented by the dot ".". It matches any character except the end of file, thus the "!." expression is used to indicate "match the end of file". E.g.:

AnyChar = . // match a single character
EOF = !.

Code block

Code blocks can be added to generate custom Go code. There are three kinds of code blocks: the initializer, the action and the predicate. All code blocks appear inside curly braces "{...}".

The initializer must appear first in the grammar, before any rule. It is copied as-is (minus the wrapping curly braces) at the top of the generated parser. It may contain function declarations, types, variables, etc. just like any Go file. Every symbol declared here will be available to all other code blocks. Although the initializer is optional in a valid grammar, it is usually required to generate a valid Go source code file (for the package clause). E.g.:

{
	package main

	func someHelper() {
		// ...
	}
}

Action code blocks are code blocks declared after an expression in a rule. Those code blocks are turned into a method on the "*current" type in the generated source code. The method receives any labeled expression's value as argument (as any) and must return two values, the first being the value of the expression (an any), and the second an error. If a non-nil error is returned, it is added to the list of errors that the parser will return. E.g.:

RuleA = "A"+ {
	// return the matched string, "c" is the default name for
	// the *current receiver variable.
	return string(c.text), nil
}

Predicate code blocks are code blocks declared immediately after the and "&" or the not "!" operators. Like action code blocks, predicate code blocks are turned into a method on the "*current" type in the generated source code. The method receives any labeled expression's value as argument (as any) and must return two opt, the first being a bool and the second an error. If a non-nil error is returned, it is added to the list of errors that the parser will return. E.g.:

RuleAB = [ab]i+ &{
	return true, nil
}

State change code blocks are code blocks starting with "#". In contrast to action and predicate code blocks, state change code blocks are allowed to modify values in the global "state" store (see below). State change code blocks are turned into a method on the "*current" type in the generated source code. The method is passed any labeled expression's value as an argument (of type any) and must return a value of type error. If a non-nil error is returned, it is added to the list of errors that the parser will return, note that the parser does NOT backtrack if a non-nil error is returned. E.g:

Rule = [a] #{
	c.state["a"]++
	if c.state["a"] > 5 {
		return fmt.Errorf("we have seen more than 5 a's") // parser will not backtrack
	}
	return nil
}

The "*current" type is a struct that provides four useful fields that can be accessed in action, state change, and predicate code blocks: "pos", "text", "state" and "globalStore".

The "pos" field indicates the current position of the parser in the source input. It is itself a struct with three fields: "line", "col" and "offset". Line is a 1-based line number, col is a 1-based column number that counts runes from the start of the line, and offset is a 0-based byte offset.

The "text" field is the slice of bytes of the current match. It is empty in a predicate code block.

The "state" field is a global store, with backtrack support, of type "map[string]any". The values in the store are tied to the parser's backtracking, in particular if a rule fails to match then all updates to the state that occurred in the process of matching the rule are rolled back. For a key-value store that is not tied to the parser's backtracking, see the "globalStore". The values in the "state" store are available for read access in action and predicate code blocks, any changes made to the "state" store will be reverted once the action or predicate code block is finished running. To update values in the "state" use state change code blocks ("#{}").

IMPORTANT:

• In order to properly roll back the state if a rule fails to match the parser must clone the state before trying to match a rule.
• The default clone mechanism makes a "shallow" copy of each value in the "state", this implies that pointers, maps, slices, channels, and structs containing any of the previous types are not properly copied.
• To support theses cases pigeon offers the "Cloner" interface which consists of a single method "Clone". If a value stored in the "state" store implements this interface, the "Clone" method is used to obtain a proper copy.
• If a general solution is needed, external libraries which provide deep copy functionality may be used in the "Clone" method (e.g. https://github.com/mitchellh/copystructure).

The "globalStore" field is a global store of type "map[string]any", which allows to store arbitrary values, which are available in action and predicate code blocks for read as well as write access. It is important to notice, that the global store is completely independent from the backtrack mechanism of PEG and is therefore not set back to its old state during backtrack. The initialization of the global store may be achieved by using the GlobalStore function (http://godoc.org/github.com/mna/pigeon/test/predicates#GlobalStore). Be aware, that all keys starting with "_pigeon" are reserved for internal use of pigeon and should not be used nor modified. Those keys are treated as internal implementation details and therefore there are no guarantees given in regards of API stability.

Left recursion

With options -support-left-recursion pigeon supports left recursion. E.g.:

expr = expr '*' term

Supports indirect recursion:

A = B / D
B = A / C

The implementation is based on the [Left-recursive PEG Grammars][9] article that links to [Left Recursion in Parsing Expression Grammars][10] and [Packrat Parsers Can Support Left Recursion][11] papers.

References:

[9]: https://medium.com/@gvanrossum_83706/left-recursive-peg-grammars-65dab3c580e1
[10]: https://arxiv.org/pdf/1207.0443.pdf
[11]: http://web.cs.ucla.edu/~todd/research/pepm08.pdf

Failure labels, throw and recover

pigeon supports an extension of the classical PEG syntax called failure labels, proposed by Maidl et al. in their paper "Error Reporting in Parsing Expression Grammars" [7]. The used syntax for the introduced expressions is borrowed from their lpeglabel [8] implementation.

This extension allows to signal different kinds of errors and to specify, which recovery pattern should handle a given label.

With labeled failures it is possible to distinguish between an ordinary failure and an error. Usually, an ordinary failure is produced when the matching of a character fails, and this failure is caught by ordered choice. An error (a non-ordinary failure), by its turn, is produced by the throw operator and may be caught by the recovery operator.

In pigeon, the recovery expression consists of the regular expression, the recovery expression and a set of labels to be matched. First, the regular expression is tried. If this fails with one of the provided labels, the recovery expression is tried. If this fails as well, the error is propagated. E.g.:

FailureRecoveryExpr = RegularExpr //{FailureLabel1, FailureLabel2} RecoveryExpr

To signal a failure condition, the throw expression is used. E.g.:

ThrowExpr = %{FailureLabel1}

For concrete examples, how to use throw and recover, have a look at the examples "labeled_failures" and "thrownrecover" in the "test" folder.

The implementation of the throw and recover operators work as follows: The failure recover expression adds the recover expression for every failure label to the recovery stack and runs the regular expression. The throw expression checks the recovery stack in reversed order for the provided failure label. If the label is found, the respective recovery expression is run. If this expression is successful, the parser continues the processing of the input. If the recovery expression is not successful, the parsing fails and the parser starts to backtrack.

If throw and recover expressions are used together with global state, it is the responsibility of the author of the grammar to reset the global state to a valid state during the recovery operation.

[7]: https://arxiv.org/pdf/1405.6646v3.pdf
[8]: https://github.com/sqmedeiros/lpeglabel

Using the generated parser

The parser generated by pigeon exports a few symbols so that it can be used as a package with public functions to parse input text. The exported API is:

• Parse(string, []byte, ...Option) (any, error)
• ParseFile(string, ...Option) (any, error)
• ParseReader(string, io.Reader, ...Option) (any, error)
• AllowInvalidUTF8(bool) Option
• Debug(bool) Option
• Entrypoint(string) Option
• GlobalStore(string, any) Option
• MaxExpressions(uint64) Option
• Memoize(bool) Option
• Recover(bool) Option
• Statistics(*Stats) Option

See the godoc page of the generated parser for the test/predicates grammar for an example documentation page of the exported API: http://godoc.org/github.com/mna/pigeon/test/predicates.

Like the grammar used to generate the parser, the input text must be UTF-8-encoded Unicode.

The start rule of the parser is the first rule in the PEG grammar used to generate the parser. A call to any of the Parse* functions returns the value generated by executing the grammar on the provided input text, and an optional error.

Typically, the grammar should generate some kind of abstract syntax tree (AST), but for simple grammars it may evaluate the result immediately, such as in the examples/calculator example. There are no constraints imposed on the author of the grammar, it can return whatever is needed.

Error reporting

When the parser returns a non-nil error, the error is always of type errList, which is defined as a slice of errors ([]error). Each error in the list is of type *parserError. This is a struct that has an "Inner" field that can be used to access the original error.

So if a code block returns some well-known error like:

{
	return nil, io.EOF
}

The original error can be accessed this way:

_, err := ParseFile("some_file")
if err != nil {
	list := err.(errList)
	for _, err := range list {
		pe := err.(*parserError)
		if pe.Inner == io.EOF {
			// ...
		}
	}
}

By defaut the parser will continue after an error is returned and will cumulate all errors found during parsing. If the grammar reaches a point where it shouldn't continue, a panic statement can be used to terminate parsing. The panic will be caught at the top-level of the Parse* call and will be converted into a *parserError like any error, and an errList will still be returned to the caller.

The divide by zero error in the examples/calculator grammar leverages this feature (no special code is needed to handle division by zero, if it happens, the runtime panics and it is recovered and returned as a parsing error).

Providing good error reporting in a parser is not a trivial task. Part of it is provided by the pigeon tool, by offering features such as filename, position, expected literals and rule name in the error message, but an important part of good error reporting needs to be done by the grammar author.

For example, many programming languages use double-quotes for string literals. Usually, if the opening quote is found, the closing quote is expected, and if none is found, there won't be any other rule that will match, there's no need to backtrack and try other choices, an error should be added to the list and the match should be consumed.

In order to do this, the grammar can look something like this:

StringLiteral = '"' ValidStringChar* '"' {
	// this is the valid case, build string literal node
	// node = ...
	return node, nil
} / '"'  ValidStringChar* !'"' {
	// invalid case, build a replacement string literal node or build a BadNode
	// node = ...
	return node, errors.New("string literal not terminated")
}

This is just one example, but it illustrates the idea that error reporting needs to be thought out when designing the grammar.

Because the above mentioned error types (errList and parserError) are not exported, additional steps have to be taken, ff the generated parser is used as library package in other packages (e.g. if the same parser is used in multiple command line tools). One possible implementation for exported errors (based on interfaces) and customized error reporting (caret style formatting of the position, where the parsing failed) is available in the json example and its command line tool: http://godoc.org/github.com/mna/pigeon/examples/json

API stability

Generated parsers have user-provided code mixed with pigeon code in the same package, so there is no package boundary in the resulting code to prevent access to unexported symbols. What is meant to be implementation details in pigeon is also available to user code - which doesn't mean it should be used.

For this reason, it is important to precisely define what is intended to be the supported API of pigeon, the parts that will be stable in future versions.

The "stability" of the version 1.0 API attempts to make a similar guarantee as the Go 1 compatibility [5]. The following lists what part of the current pigeon code falls under that guarantee (features may be added in the future):

• The pigeon command-line flags and arguments: those will not be removed and will maintain the same semantics.

• The explicitly exported API generated by pigeon. See [6] for the documentation of this API on a generated parser.

• The PEG syntax, as documented above.

• The code blocks (except the initializer) will always be generated as methods on the *current type, and this type is guaranteed to have the fields pos (type position) and text (type []byte). There are no guarantees on other fields and methods of this type.

• The position type will always have the fields line, col and offset, all defined as int. There are no guarantees on other fields and methods of this type.

• The type of the error value returned by the Parse* functions, when not nil, will always be errList defined as a []error. There are no guarantees on methods of this type, other than the fact it implements the error interface.

• Individual errors in the errList will always be of type *parserError, and this type is guaranteed to have an Inner field that contains the original error value. There are no guarantees on other fields and methods of this type.

The above guarantee is given to the version 1.0 (https://github.com/mna/pigeon/releases/tag/v1.0.0) of pigeon, which has entered maintenance mode (bug fixes only). The current master branch includes the development toward a future version 2.0, which intends to further improve pigeon. While the given API stability should be maintained as far as it makes sense, breaking changes may be necessary to be able to improve pigeon. The new version 2.0 API has not yet stabilized and therefore changes to the API may occur at any time.

References:

[5]: https://golang.org/doc/go1compat
[6]: http://godoc.org/github.com/mna/pigeon/test/predicates