# The CUE Language Specification

## Introduction

This is a reference manual for the CUE data constraint language. CUE, pronounced cue or Q, is a general-purpose and strongly typed constraint-based language. It can be used for data templating, data validation, code generation, scripting, and many other applications involving structured data. The CUE tooling, layered on top of CUE, provides a general purpose scripting language for creating scripts as well as simple servers, also expressed in CUE.

CUE was designed with cloud configuration, and related systems, in mind, but is not limited to this domain. It derives its formalism from relational programming languages. This formalism allows for managing and reasoning over large amounts of data in a straightforward manner.

The grammar is compact and regular, allowing for easy analysis by automatic tools such as integrated development environments.

This document is maintained by mpvl@golang.org. CUE has a lot of similarities with the Go language. This document draws heavily from the Go specification as a result.

CUE draws its influence from many languages. Its main influences were BCL/ GCL (internal to Google), LKB (LinGO), Go, and JSON. Others are Swift, Typescript, Javascript, Prolog, NCL (internal to Google), Jsonnet, HCL, Flabbergast, Nix, JSONPath, Haskell, Objective-C, and Python.

## Notation

The syntax is specified using Extended Backus-Naur Form (EBNF):

Production  = production_name "=" [ Expression ] "." .
Expression  = Alternative { "|" Alternative } .
Alternative = Term { Term } .
Term        = production_name | token [ "…" token ] | Group | Option | Repetition .
Group       = "(" Expression ")" .
Option      = "[" Expression "]" .
Repetition  = "{" Expression "}" .


Productions are expressions constructed from terms and the following operators, in increasing precedence:

|   alternation
()  grouping
[]  option (0 or 1 times)
{}  repetition (0 to n times)


Lower-case production names are used to identify lexical tokens. Non-terminals are in CamelCase. Lexical tokens are enclosed in double quotes "” or back quotes .

The form a … b represents the set of characters from a through b as alternatives. The horizontal ellipsis … is also used elsewhere in the spec to informally denote various enumerations or code snippets that are not further specified. The character … (as opposed to the three characters …) is not a token of the CUE language.

## Source code representation

Source code is Unicode text encoded in UTF-8. Unless otherwise noted, the text is not canonicalized, so a single accented code point is distinct from the same character constructed from combining an accent and a letter; those are treated as two code points. For simplicity, this document will use the unqualified term character to refer to a Unicode code point in the source text.

Each code point is distinct; for instance, upper and lower case letters are different characters.

Implementation restriction: For compatibility with other tools, a compiler may disallow the NUL character (U+0000) in the source text.

Implementation restriction: For compatibility with other tools, a compiler may ignore a UTF-8-encoded byte order mark (U+FEFF) if it is the first Unicode code point in the source text. A byte order mark may be disallowed anywhere else in the source.

### Characters

The following terms are used to denote specific Unicode character classes:

newline        = /* the Unicode code point U+000A */ .
unicode_char   = /* an arbitrary Unicode code point except newline */ .
unicode_letter = /* a Unicode code point classified as "Letter" */ .
unicode_digit  = /* a Unicode code point classified as "Number, decimal digit" */ .


In The Unicode Standard 8.0, Section 4.5 “General Category” defines a set of character categories. CUE treats all characters in any of the Letter categories Lu, Ll, Lt, Lm, or Lo as Unicode letters, and those in the Number category Nd as Unicode digits.

### Letters and digits

The underscore character _ (U+005F) is considered a letter.

letter        = unicode_letter | "_" .
decimal_digit = "0" … "9" .
octal_digit   = "0" … "7" .
hex_digit     = "0" … "9" | "A" … "F" | "a" … "f" .


## Lexical elements

Comments serve as program documentation. CUE supports line comments that start with the character sequence // and stop at the end of the line.

A comment cannot start inside a string literal or inside a comment. A comment acts like a newline.

### Tokens

Tokens form the vocabulary of the CUE language. There are four classes: identifiers, keywords, operators and punctuation, and literals. White space, formed from spaces (U+0020), horizontal tabs (U+0009), carriage returns (U+000D), and newlines (U+000A), is ignored except as it separates tokens that would otherwise combine into a single token. Also, a newline or end of file may trigger the insertion of a comma. While breaking the input into tokens, the next token is the longest sequence of characters that form a valid token.

### Commas

The formal grammar uses commas “,” as terminators in a number of productions. CUE programs may omit most of these commas using the following two rules:

When the input is broken into tokens, a comma is automatically inserted into the token stream immediately after a line’s final token if that token is

• an identifier
• null, true, false, bottom, or an integer, floating-point, or string literal
• one of the characters ), ], or }

Although commas are automatically inserted, the parser will require explicit commas between two list elements.

To reflect idiomatic use, examples in this document elide commas using these rules.

### Identifiers

Identifiers name entities such as fields and aliases. An identifier is a sequence of one or more letters (which includes _ and $) and digits, optionally preceded by # or _#. It may not be _ or $. The first character in an identifier, or after an # if it contains one, must be a letter. Identifiers starting with a # or _ are reserved for definitions and hidden fields.

identifier  = [ "#" | "_#" ] letter { letter | unicode_digit } .

a
_x9
fieldName
αβ


Some identifiers are predeclared.

### Keywords

CUE has a limited set of keywords. In addition, CUE reserves all identifiers starting with __(double underscores) as keywords. These are typically targets of pre-declared identifiers.

All keywords may be used as labels (field names). Unless noted otherwise, they can also be used as identifiers to refer to the same name.

#### Values

The following keywords are values.

null         true         false


These can never be used to refer to a field of the same name. This restriction is to ensure compatibility with JSON configuration files.

#### Preamble

The following keywords are used at the preamble of a CUE file. After the preamble, they may be used as identifiers to refer to namesake fields.

package      import


#### Comprehension clauses

The following keywords are used in comprehensions.

for          in           if           let


#### Arithmetic

The following pseudo keywords can be used as operators in expressions.

div          mod          quo          rem


### Operators and punctuation

The following character sequences represent operators and punctuation:

+     div   &&    ==    <     =     (     )
-     mod   ||    !=    >     :     {     }
*     quo   &     =~    <=    ?     [     ]     ,
/     rem   |     !~    >=    !     _|_   ...   .


### Integer literals

An integer literal is a sequence of digits representing an integer value. An optional prefix sets a non-decimal base: 0o for octal, 0x or 0X for hexadecimal, and 0b for binary. In hexadecimal literals, letters a-f and A-F represent values 10 through 15. All integers allow interstitial underscores “_"; these have no meaning and are solely for readability.

Decimal integers may have a SI or IEC multiplier. Multipliers can be used with fractional numbers. When multiplying a fraction by a multiplier, the result is truncated towards zero if it is not an integer.

int_lit     = decimal_lit | si_lit | octal_lit | binary_lit | hex_lit .
decimal_lit = ( "1" … "9" ) { [ "_" ] decimal_digit } .
decimals    = decimal_digit { [ "_" ] decimal_digit } .
si_it       = decimals [ "." decimals ] multiplier |
"." decimals  multiplier .
binary_lit  = "0b" binary_digit { binary_digit } .
hex_lit     = "0" ( "x" | "X" ) hex_digit { [ "_" ] hex_digit } .
octal_lit   = "0o" octal_digit { [ "_" ] octal_digit } .
multiplier  = ( "K" | "M" | "G" | "T" | "P" ) [ "i" ]

float_lit   = decimals "." [ decimals ] [ exponent ] |
decimals exponent |
"." decimals [ exponent ].
exponent    = ( "e" | "E" ) [ "+" | "-" ] decimals .

42
1.5Gi
170_141_183_460_469_231_731_687_303_715_884_105_727
0o755
0b0101_0001


### Decimal floating-point literals

A decimal floating-point literal is a representation of a decimal floating-point value (a float). It has an integer part, a decimal point, a fractional part, and an exponent part. The integer and fractional part comprise decimal digits; the exponent part is an e or E followed by an optionally signed decimal exponent. One of the integer part or the fractional part may be elided; one of the decimal point or the exponent may be elided.

decimal_lit = decimals "." [ decimals ] [ exponent ] |
decimals exponent |
"." decimals [ exponent ] .
exponent  = ( "e" | "E" ) [ "+" | "-" ] decimals .

0.
72.40
072.40  // == 72.40
2.71828
1.e+0
6.67428e-11
1E6
.25
.12345E+5


### String and byte sequence literals

A string literal represents a string constant obtained from concatenating a sequence of characters. Byte sequences are a sequence of bytes.

String and byte sequence literals are character sequences between, respectively, double and single quotes, as in "bar" and 'bar'. Within the quotes, any character may appear except newline and, respectively, unescaped double or single quote. String literals may only be valid UTF-8. Byte sequences may contain any sequence of bytes.

Several escape sequences allow arbitrary values to be encoded as ASCII text. An escape sequence starts with an escape delimiter, which is \ by default. The escape delimiter may be altered to be \ plus a fixed number of hash symbols # by padding the start and end of a string or byte sequence literal with this number of hash symbols.

There are four ways to represent the integer value as a numeric constant: \x followed by exactly two hexadecimal digits; \u followed by exactly four hexadecimal digits; \U followed by exactly eight hexadecimal digits, and a plain backslash \ followed by exactly three octal digits. In each case the value of the literal is the value represented by the digits in the corresponding base. Hexadecimal and octal escapes are only allowed within byte sequences (single quotes).

Although these representations all result in an integer, they have different valid ranges. Octal escapes must represent a value between 0 and 255 inclusive. Hexadecimal escapes satisfy this condition by construction. The escapes \u and \U represent Unicode code points so within them some values are illegal, in particular those above 0x10FFFF. Surrogate halves are allowed, but are translated into their non-surrogate equivalent internally.

The three-digit octal (\nnn) and two-digit hexadecimal (\xnn) escapes represent individual bytes of the resulting string; all other escapes represent the (possibly multi-byte) UTF-8 encoding of individual characters. Thus inside a string literal \377 and \xFF represent a single byte of value 0xFF=255, while ÿ, \u00FF, \U000000FF and \xc3\xbf represent the two bytes 0xc3 0xbf of the UTF-8 encoding of character U+00FF.

\a   U+0007 alert or bell
\b   U+0008 backspace
\f   U+000C form feed
\n   U+000A line feed or newline
\r   U+000D carriage return
\t   U+0009 horizontal tab
\v   U+000b vertical tab
\/   U+002f slash (solidus)
\\   U+005c backslash
\'   U+0027 single quote  (valid escape only within single quoted literals)
\"   U+0022 double quote  (valid escape only within double quoted literals)


The escape \( is used as an escape for string interpolation. A \( must be followed by a valid CUE Expression, followed by a ).

All other sequences starting with a backslash are illegal inside literals.

escaped_char     = \ { # } ( "a" | "b" | "f" | "n" | "r" | "t" | "v" | "/" | \ | "'" | " ) .
byte_value       = octal_byte_value | hex_byte_value .
octal_byte_value = \ octal_digit octal_digit octal_digit .
hex_byte_value   = \ "x" hex_digit hex_digit .
little_u_value   = \ "u" hex_digit hex_digit hex_digit hex_digit .
big_u_value      = \ "U" hex_digit hex_digit hex_digit hex_digit
hex_digit hex_digit hex_digit hex_digit .
unicode_value    = unicode_char | little_u_value | big_u_value | escaped_char .
interpolation    = "\(" Expression ")" .

string_lit       = simple_string_lit |
multiline_string_lit |
simple_bytes_lit |
multiline_bytes_lit |
# string_lit # .

simple_string_lit    = " { unicode_value | interpolation } " .
simple_bytes_lit     = ' { unicode_value | interpolation | byte_value } ' .
multiline_string_lit = """ newline
{ unicode_value | interpolation | newline }
newline """ .
multiline_bytes_lit  = "'''" newline
{ unicode_value | interpolation | byte_value | newline }
newline "'''" .


Carriage return characters (\r) inside string literals are discarded from the string value.

'a\000\xab'
'\007'
'\377'
'\xa'        // illegal: too few hexadecimal digits
"\n"
"\""
'Hello, world!\n'
"Hello, \( name )!"
"日本語"
"\u65e5本\U00008a9e"
"\xff\u00FF"
"\uD800"             // illegal: surrogate half (TODO: probably should allow)
"\U00110000"         // illegal: invalid Unicode code point

#"This is not an \(interpolation)"#
#"This is an \#(interpolation)"#
#"The sequence "\U0001F604" renders as \#U0001F604."#


These examples all represent the same string:

"日本語"                                 // UTF-8 input text
'日本語'                                 // UTF-8 input text as byte sequence
日本語                                 // UTF-8 input text as a raw literal
"\u65e5\u672c\u8a9e"                    // the explicit Unicode code points
"\U000065e5\U0000672c\U00008a9e"        // the explicit Unicode code points
"\xe6\x97\xa5\xe6\x9c\xac\xe8\xaa\x9e"  // the explicit UTF-8 bytes


If the source code represents a character as two code points, such as a combining form involving an accent and a letter, the result will appear as two code points if placed in a string literal.

Strings and byte sequences have a multiline equivalent. Multiline strings are like their single-line equivalent, but allow newline characters.

Multiline strings and byte sequences respectively start with a triple double quote (""") or triple single quote ('''), immediately followed by a newline, which is discarded from the string contents. The string is closed by a matching triple quote, which must be by itself on a newline, preceded by optional whitespace. The newline preceding the closing quote is discarded from the string contents. The whitespace before a closing triple quote must appear before any non-empty line after the opening quote and will be removed from each of these lines in the string literal. A closing triple quote may not appear in the string. To include it is suffices to escape one of the quotes.

"""
lily:
out of the water
out of itself

bass
picking bugs
off the moon
— Nick Virgilio, Selected Haiku, 1988
"""


This represents the same string as:

"lily:\nout of the water\nout of itself\n\n" +
"bass\npicking bugs\noff the moon\n" +
"    — Nick Virgilio, Selected Haiku, 1988"


## Values

In addition to simple values like "hello" and 42.0, CUE has structs. A struct is a map from labels to values, like {a: 42.0, b: "hello"}. Structs are CUE’s only way of building up complex values; lists, which we will see later, are defined in terms of structs.

All possible values are ordered in a lattice, a partial order where every two elements have a single greatest lower bound. A value a is an instance of a value b, denoted a ⊑ b, if b == a or b is more general than a, that is if a orders before b in the partial order (⊑ is not a CUE operator). We also say that b subsumes a in this case. In graphical terms, b is “above” a in the lattice.

At the top of the lattice is the single ancestor of all values, called top, denoted _ in CUE. Every value is an instance of top.

At the bottom of the lattice is the value called bottom, denoted _|_. A bottom value usually indicates an error. Bottom is an instance of every value.

An atom is any value whose only instances are itself and bottom. Examples of atoms are 42.0, "hello", true, null.

A value is concrete if it is either an atom, or a struct all of whose field values are themselves concrete, recursively.

CUE’s values also include what we normally think of as types, like string and float. But CUE does not distinguish between types and values; only the relationship of values in the lattice is important. Each CUE “type” subsumes the concrete values that one would normally think of as part of that type. For example, “hello” is an instance of string, and 42.0 is an instance of float. In addition to string and float, CUE has null, int, bool and bytes. We informally call these CUE’s “basic types”.

false ⊑ bool
true  ⊑ bool
true  ⊑ true
5.0   ⊑ float
bool  ⊑ _
_|_   ⊑ _
_|_   ⊑ _|_

_     ⋢ _|_
_     ⋢ bool
int   ⋢ bool
bool  ⋢ int
false ⋢ true
true  ⋢ false
float ⋢ 5.0
5     ⋢ 6


### Unification

The unification of values a and b is defined as the greatest lower bound of a and b. (That is, the value u such that u ⊑ a and u ⊑ b, and for any other value v for which v ⊑ a and v ⊑ b it holds that v ⊑ u.) Since CUE values form a lattice, the unification of two CUE values is always unique.

These all follow from the definition of unification:

• The unification of a with itself is always a.
• The unification of values a and b where a ⊑ b is always a.
• The unification of a value with bottom is always bottom.

Unification in CUE is a binary expression, written a & b. It is commutative and associative. As a consequence, order of evaluation is irrelevant, a property that is key to many of the constructs in the CUE language as well as the tooling layered on top of it.

### Disjunction

The disjunction of values a and b is defined as the least upper bound of a and b. (That is, the value d such that a ⊑ d and b ⊑ d, and for any other value e for which a ⊑ e and b ⊑ e, it holds that d ⊑ e.) This style of disjunctions is sometimes also referred to as sum types. Since CUE values form a lattice, the disjunction of two CUE values is always unique.

These all follow from the definition of disjunction:

• The disjunction of a with itself is always a.
• The disjunction of a value a and b where a ⊑ b is always b.
• The disjunction of a value a with bottom is always a.
• The disjunction of two bottom values is bottom.

Disjunction in CUE is a binary expression, written a | b. It is commutative, associative, and idempotent.

The unification of a disjunction with another value is equal to the disjunction composed of the unification of this value with all of the original elements of the disjunction. In other words, unification distributes over disjunction.

(a_0 | ... |a_n) & b ==> a_0&b | ... | a_n&b.

Expression                Result
({a:1} | {b:2}) & {c:3}   {a:1, c:3} | {b:2, c:3}
(int | string) & "foo"    "foo"
("a" | "b") & "c"         _|_


A disjunction is normalized if there is no element a for which there is an element b such that a ⊑ b.

#### Default values

Any element of a disjunction can be marked as a default by prefixing it with an asterisk *. Intuitively, when an expression needs to be resolved for an operation other than unification or disjunctions, non-starred elements are dropped in favor of starred ones if the starred ones do not resolve to bottom.

More precisely, any value v may be associated with a default value d, denoted (v, d) (not CUE syntax), where d must be in instance of v (d ⊑ v). The rules for unifying and disjoining such values are as follows:

U1: (v1, d1) & v2       => (v1&v2, d1&v2)
U2: (v1, d1) & (v2, d2) => (v1&v2, d1&d2)

D1: (v1, d1) | v2       => (v1|v2, d1)
D2: (v1, d1) | (v2, d2) => (v1|v2, d1|d2)


Default values may be introduced within disjunctions by marking terms of a disjunction with an asterisk * (a unary expression). The default value of a disjunction with marked terms is the disjunction of those marked terms, applying the following rules for marks:

M1: *v        => (v, v)
M2: *(v1, d1) => (v1, d1)


In general, any operation f in CUE involving default values proceeds along the following lines

O1: f((v1, d1), ..., (vn, dn))  => (f(v1, ..., vn), f(d1, ..., dn))


where, with the exception of disjunction, a value v without a default value is promoted to (v, v).

Expression               Value-default pair      Rules applied
*"tcp" | "udp"           ("tcp"|"udp", "tcp")    M1, D1
string | *"foo"          (string, "foo")         M1, D1

*1 | 2 | 3               (1|2|3, 1)              M1, D1

(*1|2|3) | (1|*2|3)      (1|2|3, 1|2)            M1, D1, D2
(*1|2|3) | *(1|*2|3)     (1|2|3, 1|2)            M1, D1, M2, D2
(*1|2|3) | (1|*2|3)&2    (1|2|3, 1|2)            M1, D1, U1, D2

(*1|2) & (1|*2)          (1|2, _|_)              M1, D1, U2

(*1|2) + (1|*2)          ((1|2)+(1|2), 3)        M1, D1, O1


The rules of subsumption for defaults can be derived from the above definitions and are as follows.

(v2, d2) ⊑ (v1, d1)  if v2 ⊑ v1 and d2 ⊑ d1
(v1, d1) ⊑ v         if v1 ⊑ v
v ⊑ (v1, d1)         if v ⊑ d1

Expression                       Resolves to
"tcp" | "udp"                    "tcp" | "udp"
*"tcp" | "udp"                   "tcp"
float | *1                       1
*string | 1.0                    string

(*1|2|3) | (1|*2|3)              1|2
(*1|2|3) & (1|*2|3)              1|2|3 // default is _|_

(* >=5 | int) & (* <=5 | int)    5

(*"tcp"|"udp") & ("udp"|*"tcp")  "tcp"
(*"tcp"|"udp") & ("udp"|"tcp")   "tcp"
(*"tcp"|"udp") & "tcp"           "tcp"
(*"tcp"|"udp") & (*"udp"|"tcp")  "tcp" | "udp" // default is _|_

(*true | false) & bool           true
(*true | false) & (true | false) true

{a: 1} | {b: 1}                  {a: 1} | {b: 1}
{a: 1} | *{b: 1}                 {b:1}
*{a: 1} | *{b: 1}                {a: 1} | {b: 1}
({a: 1} | {b: 1}) & {a:1}        {a:1} // after eliminating {a:1,b:1} by normalization
({a:1}|*{b:1}) & ({a:1}|*{b:1})  {b:1} // after eliminating {a:1,b:1} by normalization


### Bottom and errors

Any evaluation error in CUE results in a bottom value, respresented by the token _|_. Bottom is an instance of every other value. Any evaluation error is represented as bottom.

Implementations may associate error strings with different instances of bottom; logically they all remain the same value.

### Top

Top is represented by the underscore character _, lexically an identifier. Unifying any value v with top results v itself.

Expr        Result
_ &  5        5
_ &  _        _
_ & _|_      _|_
_ | _|_       _


### Null

The null value is represented with the keyword null. It has only one parent, top, and one child, bottom. It is unordered with respect to any other value.

null_lit   = "null"

null & 8     _|_
null & _     null
null & _|_   _|_


### Boolean values

A boolean type represents the set of Boolean truth values denoted by the keywords true and false. The predeclared boolean type is bool; it is a defined type and a separate element in the lattice.

boolean_lit = "true" | "false"

bool & true          true
true & true          true
true & false         _|_
bool & (false|true)  false | true
bool & (true|false)  true | false


### Numeric values

The integer type represents the set of all integral numbers. The decimal floating-point type represents the set of all decimal floating-point numbers. They are two distinct types. Both are instances instances of a generic number type.

The predeclared number, integer, decimal floating-point types are number, int and float; they are defined types.

A decimal floating-point literal always has type float; it is not an instance of int even if it is an integral number.

Integer literals are always of type int and don’t match type float.

Numeric literals are exact values of arbitrary precision. If the operation permits it, numbers should be kept in arbitrary precision.

Implementation restriction: although numeric values have arbitrary precision in the language, implementations may implement them using an internal representation with limited precision. That said, every implementation must:

• Represent integer values with at least 256 bits.
• Represent floating-point values, with a mantissa of at least 256 bits and a signed binary exponent of at least 16 bits.
• Give an error if unable to represent an integer value precisely.
• Give an error if unable to represent a floating-point value due to overflow.
• Round to the nearest representable value if unable to represent a floating-point value due to limits on precision. These requirements apply to the result of any expression except for builtin functions for which an unusual loss of precision must be explicitly documented.

### Strings

The string type represents the set of UTF-8 strings, not allowing surrogates. The predeclared string type is string; it is a defined type.

The length of a string s (its size in bytes) can be discovered using the built-in function len.

### Bytes

The bytes type represents the set of byte sequences. A byte sequence value is a (possibly empty) sequence of bytes. The number of bytes is called the length of the byte sequence and is never negative. The predeclared byte sequence type is bytes; it is a defined type.

### Bounds

A bound, syntactically a unary expression, defines an infinite disjunction of concrete values than can be represented as a single comparison.

For any comparison operator op except ==, op a is the disjunction of every x such that x op a.

2 & >=2 & <=5           // 2, where 2 is either an int or float.
2.5 & >=1 & <=5         // 2.5
2 & >=1.0 & <3.0        // 2.0
2 & >1 & <3.0           // 2.0
2.5 & int & >1 & <5     // _|_
2.5 & float & >1 & <5   // 2.5
int & 2 & >1.0 & <3.0   // _|_
2.5 & >=(int & 1) & <5  // _|_
>=0 & <=7 & >=3 & <=10  // >=3 & <=7
!=null & 1              // 1
>=5 & <=5               // 5


### Structs

A struct is a set of elements called fields, each of which has a name, called a label, and value.

We say a label is defined for a struct if the struct has a field with the corresponding label. The value for a label f of struct a is denoted a.f. A struct a is an instance of b, or a ⊑ b, if for any label f defined for b, label f is also defined for a and a.f ⊑ b.f. Note that if a is an instance of b it may have fields with labels that are not defined for b.

The (unique) struct with no fields, written {}, has every struct as an instance. It can be considered the type of all structs.

{a: 1} ⊑ {}
{a: 1, b: 1} ⊑ {a: 1}
{a: 1} ⊑ {a: int}
{a: 1, b: 1} ⊑ {a: int, b: float}

{} ⋢ {a: 1}
{a: 2} ⋢ {a: 1}
{a: 1} ⋢ {b: 1}


A field may be required or optional. The successful unification of structs a and b is a new struct c which has all fields of both a and b, where the value of a field f in c is a.f & b.f if f is in both a and b, or just a.f or b.f if f is in just a or b, respectively. If a field f is in both a and b, c.f is optional only if both a.f and b.f are optional. Any references to a or b in their respective field values need to be replaced with references to c. The result of a unification is bottom (_|_) if any of its non-optional fields evaluates to bottom, recursively.

Syntactically, a field is marked as optional by following its label with a ?. The question mark is not part of the field name. A struct literal may contain multiple fields with the same label, the result of which is a single field with the same properties as defined as the unification of two fields resulting from unifying two structs.

Expression                             Result (without optional fields)
{a: int, a: 1}                         {a: 1}
{a: int} & {a: 1}                      {a: 1}
{a: >=1 & <=7} & {a: >=5 & <=9}        {a: >=5 & <=7}
{a: >=1 & <=7, a: >=5 & <=9}           {a: >=5 & <=7}

{a: 1} & {b: 2}                        {a: 1, b: 2}
{a: 1, b: int} & {b: 2}                {a: 1, b: 2}

{a: 1} & {a: 2}                        _|_


A struct may define constraints that apply to fields that are added when unified with another struct using pattern or default constraints.

A pattern constraint, denoted [pattern]: value, defines a pattern, which is a value of type string, and a value to unify with fields whose label match that pattern. When unifying structs a and b, a pattern constraint [p]: v declared in a defines that the value v should unify with any field in the resulting struct c whose label unifies with pattern p and for which there exists no field in a with the same label.

Additionally, a default constraint, denoted ...value, defines a value to unify with any field for which there is no other declaration in a struct. When unifying structs a and b, a default constraint ...v declared in a defines that the value v should unify with any field in the resulting struct c whose label does not unify with any of the patterns of the pattern constraints defined for a and for which there exists no field in a with that label. The token ... is a shorthand for ..._.

a: {
foo:    string  // foo is a string
["^i"]: int     // all other fields starting with i are integers
["^b"]: bool    // all other fields starting with b are booleans
...string       // all other fields must be a string
}

b: a & {
i3:    3
bar:   true
other: "a string"
}


Concrete field labels may be an identifier or string, the latter of which may be interpolated. Fields with identifier labels can be referred to within the scope they are defined, string labels cannot. References within such interpolated strings are resolved within the scope of the struct in which the label sequence is defined and can reference concrete labels lexically preceding the label within a label sequence.

StructLit       = "{" { Declaration "," } "}" .
Declaration     = Field | Ellipsis | Embedding | LetClause | attribute .
Ellipsis        = "..." [ Expression ] .
Embedding       = Comprehension | AliasExpr .
Field           = Label ":" { Label ":" } Expression { attribute } .
Label           = [ identifier "=" ] LabelExpr .
LabelExpr       = LabelName [ "?" ] | "[" AliasExpr "]" .
LabelName       = identifier | simple_string_lit  .

attribute       = "@" identifier "(" attr_tokens ")" .
attr_tokens     = { attr_token |
"(" attr_tokens ")" |
"[" attr_tokens "]" |
"{" attr_tokens "}" } .
attr_token      = /* any token except '(', ')', '[', ']', '{', or '}' */

Expression                             Result (without optional fields)
a: { foo?: string }                    {}
b: { foo: "bar" }                      { foo: "bar" }
c: { foo?: *"bar" | string }           {}

d: a & b                               { foo: "bar" }
e: b & c                               { foo: "bar" }
f: a & c                               {}
g: a & { foo?: number }                {}
h: b & { foo?: number }                _|_
i: c & { foo: string }                 { foo: "bar" }

intMap: [string]: int
intMap: {
t1: 43
t2: 2.4  // error: 2.4 is not an integer
}

nameMap: [string]: {
firstName: string
nickName:  *firstName | string
}

nameMap: hank: { firstName: "Hank" }


The optional field set defined by nameMap matches every field, in this case just hank, and unifies the associated constraint with the matched field, resulting in:

nameMap: hank: {
firstName: "Hank"
nickName:  "Hank"
}


#### Closed structs

By default, structs are open to adding fields. Instances of an open struct p may contain fields not defined in p. This is makes it easy to add fields, but can lead to bugs:

S: {
field1: string
}

S1: S & { field2: "foo" }

// S1 is { field1: string, field2: "foo" }

A: {
field1: string
field2: string
}

A1: A & {
feild1: "foo"  // "field1" was accidentally misspelled
}

// A1 is
//    { field1: string, field2: string, feild1: "foo" }
// not the intended
//    { field1: "foo", field2: string }


A closed struct c is a struct whose instances may not have regular fields with a name that does not match the name of a regular or optional field or the pattern of a pattern constraint defined in c. A struct that is the result of unifying any struct with a ... declaration is defined for all fields. Recursively closing a struct is equivalent to adding ..._|_ to its its root and any of its substructures that are not defined for all fields.

Syntactically, structs are recursively closed explicitly with the close builtin or implicitly by definitions.

A: close({
field1: string
field2: string
})

A1: A & {
feild1: string
} // _|_ feild1 not defined for A

A2: A & {
for k,v in { feild1: string } {
k: v
}
}  // _|_ feild1 not defined for A

C: close({
[_]: _
})

C2: C & {
for k,v in { thisIsFine: string } {
"\(k)": v
}
}

D: close({
// Values generated by comprehensions are treated as embeddings.
for k,v in { x: string } {
"\(k)": v
}
})


#### Embedding

A struct may contain an embedded value, an operand used as a declaration, which must evaluate to a struct. An embedded value of type struct is unified with the struct in which it is embedded, but disregarding the restrictions imposed by closed structs. A struct resulting from such a unification is closed if either of the involved structs were closed.

At the top level, an embedded value may be any type. In this case, a CUE program will evaluate to the embedded value and the CUE program may not have top-level regular or optional fields (definitions and aliases are allowed).

Syntactically, embeddings may be any expression.

S1: {
a: 1
b: 2
{
c: 3
}
}
// S1 is { a: 1, b: 2, c: 3 }

S2: close({
a: 1
b: 2
{
c: 3
}
})
// same as close(S1)

S3: {
a: 1
b: 2
close({
c: 3
})
}
// same as S2


#### Definitions and hidden fields

A field is a definition if its identifier starts with # or _#. A field is hidden if its starts with a _. Definitions and hidden fields are not emitted when converting a CUE program to data and are never required to be concrete.

Referencing a definition will implicitely close it. A struct that embeds a referenced definition will itself be closed after first allowing any other fields or embedded structs to unify. The result of { #A } is #A for any #A.

If referencing a definition would always result in an error, implementations may report this inconsistency at the point of its declaration.

#MyStruct: {
sub: field:    string
}

#MyStruct: {
sub: enabled?: bool
}

myValue: #MyStruct & {
sub: feild:   2     // error, feild not defined in #MyStruct
sub: enabled: true  // okay
}

#D: {
#OneOf

c: int // adds this field.
}

#OneOf: { a: int } | { b: int }

D1: #D & { a: 12, c: 22 }  // { a: 12, c: 22 }
D2: #D & { a: 12, b: 33 }  // _|_ // cannot define both a and b


#### Attributes

Attributes allow associating meta information with values. Their primary purpose is to define mappings between CUE and other representations. Attributes do not influence the evaluation of CUE.

An attribute associates an identifier with a value, a balanced token sequence, which is a sequence of CUE tokens with balanced brackets ((), [], and {}). The sequence may not contain interpolations.

Fields, structs and packages can be associated with a set of attributes. Attributes accumulate during unification, but implementations may remove duplicates that have the same source string representation. The interpretation of an attribute, including the handling of multiple attributes for a given identifier, is up to the consumer of the attribute.

Field attributes define additional information about a field, such as a mapping to a protocol buffer tag or alternative name of the field when mapping to a different language.

// Package attribute
@protobuf(proto3)

myStruct1: {
// Struct attribute:
@jsonschema(id="https://example.org/mystruct1.json")

// Field attributes
field: string @go(Field)
attr:  int    @xml(,attr) @go(Attr)
}

myStruct2: {
field: string @go(Field)
attr:  int    @xml(a1,attr) @go(Attr)
}

Combined: myStruct1 & myStruct2
// field: string @go(Field)
// attr:  int    @xml(,attr) @xml(a1,attr) @go(Attr)


#### Aliases

Aliases name values that can be referred to within the scope in which they are declared. The name of an alias must be unique within its scope.

AliasExpr  = Expression | identifier "=" Expression .


Aliases can appear in several positions:

In front of a Label (X=label: value):

• binds the identifier to the same value as label would be bound to if it were a valid identifier.
• for optional fields (foo?: bar and [foo]: bar), the bound identifier is only visible within the field value (bar).

Inside a bracketed label ([X=expr]: value):

• binds the identifier to the the concrete label that matches expr within the instances of the field value (value).

Before a list element ([ X=value, X+1 ]) (Not yet implemented)

• binds the identifier to the list element it precedes within the scope of the list expression.
// An alias declaration
Alias = 3
a: Alias  // 3

// A field alias
foo: X  // 4
X="not an identifier": 4

// A label alias
[Y=string]: { name: Y }
foo: { value: 1 } // outputs: foo: { name: "foo", value: 1 }


#### Let declarations

Let declarations bind an identifier to an expression. The identifier is visible within the scope in which it is declared. The identifier must be unique within its scope.

let x = expr

a: x + 1
b: x + 2


#### Shorthand notation for nested structs

A field whose value is a struct with a single field may be written as a colon-separated sequence of the two field names, followed by a colon and the value of that single field.

job: myTask: replicas: 2


expands to

job: {
replicas: 2
}
}


### Lists

A list literal defines a new value of type list. A list may be open or closed. An open list is indicated with a ... at the end of an element list, optionally followed by a value for the remaining elements.

The length of a closed list is the number of elements it contains. The length of an open list is the its number of elements as a lower bound and an unlimited number of elements as its upper bound.

ListLit       = "[" [ ElementList [ "," [ Ellipsis ] ] [ "," ] "]" .
ElementList   = Embedding { "," Embedding } .


Lists can be thought of as structs:

List: *null | {
Elem: _
Tail: List
}


For closed lists, Tail is null for the last element, for open lists it is *null | List, defaulting to the shortest variant. For instance, the open list [ 1, 2, … ] can be represented as:

open: List & { Elem: 1, Tail: { Elem: 2 } }


and the closed version of this list, [ 1, 2 ], as

closed: List & { Elem: 1, Tail: { Elem: 2, Tail: null } }


Using this representation, the subsumption rule for lists can be derived from those of structs. Implementations are not required to implement lists as structs. The Elem and Tail fields are not special and len will not work as expected in these cases.

## Declarations and Scopes

### Blocks

A block is a possibly empty sequence of declarations. The braces of a struct literal { ... } form a block, but there are others as well:

• The universe block encompasses all CUE source text.
• Each package has a package block containing all CUE source text in that package.
• Each file has a file block containing all CUE source text in that file.
• Each for and let clause in a comprehension is considered to be its own implicit block.

Blocks nest and influence [scoping].

### Declarations and scope

A declaration may bind an identifier to a field, alias, or package. Every identifier in a program must be declared. Other than for fields, no identifier may be declared twice within the same block. For fields an identifier may be declared more than once within the same block, resulting in a field with a value that is the result of unifying the values of all fields with the same identifier. String labels do not bind an identifier to the respective field.

The scope of a declared identifier is the extent of source text in which the identifier denotes the specified field, alias, or package.

CUE is lexically scoped using blocks:

1. The scope of a predeclared identifier is the universe block.
2. The scope of an identifier denoting a field declared at top level (outside any struct literal) is the package block.
3. The scope of an identifier denoting an alias declared at top level (outside any struct literal) is the file block.
4. The scope of the package name of an imported package is the file block of the file containing the import declaration.
5. The scope of a field, alias or let identifier declared inside a struct literal is the innermost containing block.

An identifier declared in a block may be redeclared in an inner block. While the identifier of the inner declaration is in scope, it denotes the entity declared by the inner declaration.

The package clause is not a declaration; the package name does not appear in any scope. Its purpose is to identify the files belonging to the same package and to specify the default name for import declarations.

### Predeclared identifiers

CUE predefines a set of types and builtin functions. For each of these there is a corresponding keyword which is the name of the predefined identifier, prefixed with __.

Functions
len       required  close     open

Types
null      The null type and value
bool      All boolean values
int       All integral numbers
float     All decimal floating-point numbers
string    Any valid UTF-8 sequence
bytes     Any valid byte sequence

Derived   Value
number    int | float
uint      >=0
uint8     >=0 & <=255
int8      >=-128 & <=127
uint16    >=0 & <=65536
int16     >=-32_768 & <=32_767
rune      >=0 & <=0x10FFFF
uint32    >=0 & <=4_294_967_296
int32     >=-2_147_483_648 & <=2_147_483_647
uint64    >=0 & <=18_446_744_073_709_551_615
int64     >=-9_223_372_036_854_775_808 & <=9_223_372_036_854_775_807
uint128   >=0 & <=340_282_366_920_938_463_463_374_607_431_768_211_455
int128    >=-170_141_183_460_469_231_731_687_303_715_884_105_728 &
<=170_141_183_460_469_231_731_687_303_715_884_105_727
float32   >=-3.40282346638528859811704183484516925440e+38 &
<=3.40282346638528859811704183484516925440e+38
float64   >=-1.797693134862315708145274237317043567981e+308 &
<=1.797693134862315708145274237317043567981e+308


### Exported identifiers

An identifier of a package may be exported to permit access to it from another package. All identifiers not starting with _ (so all regular fields and definitions starting with #) are exported. Any identifier starting with _ is not visible outside the package and resides in a separate namespace than namesake identifiers of other packages.

package mypackage

foo:   string  // visible outside mypackage
"bar": string  // visible outside mypackage

#Foo: {      // visible outside mypackage
a:  1    // visible outside mypackage
_b: 2    // not visible outside mypackage

#C: {    // visible outside mypackage
d: 4 // visible outside mypackage
}
_#E: foo // not visible outside mypackage
}


### Uniqueness of identifiers

Given a set of identifiers, an identifier is called unique if it is different from every other in the set, after applying normalization following Unicode Annex #31. Two identifiers are different if they are spelled differently or if they appear in different packages and are not exported. Otherwise, they are the same.

### Field declarations

A field associates the value of an expression to a label within a struct. If this label is an identifier, it binds the field to that identifier, so the field’s value can be referenced by writing the identifier. String labels are not bound to fields.

a: {
b: 2
"s": 3

c: b   // 2
d: s   // _|_ unresolved identifier "s"
e: a.s // 3
}


If an expression may result in a value associated with a default value as described in default values, the field binds to this value-default pair.

### Let declarations

Within a struct, a let clause binds an identifier to the given expression.

Within the scope of the identifier, the identifier refers to the locally declared expression. The expression is evaluated in the scope it was declared.

## Expressions

An expression specifies the computation of a value by applying operators and built-in functions to operands.

Expressions that require concrete values are called incomplete if any of their operands are not concrete, but define a value that would be legal for that expression. Incomplete expressions may be left unevaluated until a concrete value is requested at the application level.

### Operands

Operands denote the elementary values in an expression. An operand may be a literal, a (possibly qualified) identifier denoting field, alias, or let declaration, or a parenthesized expression.

Operand     = Literal | OperandName | "(" Expression ")" .
Literal     = BasicLit | ListLit | StructLit .
BasicLit    = int_lit | float_lit | string_lit |
null_lit | bool_lit | bottom_lit | top_lit .
OperandName = identifier | QualifiedIdent .


### Qualified identifiers

A qualified identifier is an identifier qualified with a package name prefix.

QualifiedIdent = PackageName "." identifier .


A qualified identifier accesses an identifier in a different package, which must be [imported]. The identifier must be declared in the [package block] of that package.

math.Sin    // denotes the Sin function in package math


### References

An identifier operand refers to a field and is called a reference. The value of a reference is a copy of the expression associated with the field that it is bound to, with any references within that expression bound to the respective copies of the fields they were originally bound to. Implementations may use a different mechanism to evaluate as long as these semantics are maintained.

a: {
place:    string
greeting: "Hello, \(place)!"
}

b: a & { place: "world" }
c: a & { place: "you" }

d: b.greeting  // "Hello, world!"
e: c.greeting  // "Hello, you!"


### Primary expressions

Primary expressions are the operands for unary and binary expressions.


Slice: indices must be complete
([0, 1, 2, 3] | [2, 3])[0:2]   => [0, 1] | [2, 3]

([0, 1, 2, 3] | *[2, 3])[0:2]   => [0, 1] | [2, 3]
([0,1,2,3]|[2,3], [2,3])[0:2]   => ([0,1]|[2,3], [2,3])

Index
a: (1|2, 1)
b: ([0,1,2,3]|[2,3], [2,3])[a]   => ([0,1,2,3]|[2,3][a], 3)

Binary operation
A binary is only evaluated if its operands are complete.

Input          Maximum allowed evaluation
a: string      string
b: 2           2
c: a * b       a * 2

An error in a struct is if the evaluation of any expression results in
bottom, where an incomplete expression is not considered bottom.

PrimaryExpr =
Operand |
PrimaryExpr Selector |
PrimaryExpr Index |
PrimaryExpr Slice |
PrimaryExpr Arguments .

Selector       = "." (identifier | simple_string_lit) .
Index          = "[" Expression "]" .
Argument       = Expression .
Arguments      = "(" [ ( Argument { "," Argument } ) [ "," ] ] ")" .

x
2
(s + ".txt")
f(3.1415, true)
m["foo"]
s[i : j + 1]
obj.color
f.p[i].x


### Selectors

For a primary expression x that is not a package name, the selector expression

x.f


denotes the element of a struct x identified by f.

f must be an identifier or a string literal identifying

any definition or regular non-optional field. The identifier f is called the field selector.

If x is a package name, see the section on qualified identifiers.

Otherwise, if x is not a struct, or if f does not exist in x, the result of the expression is bottom (an error). In the latter case the expression is incomplete. The operand of a selector may be associated with a default.

T: {
x:     int
y:     3
"x-y": 4
}

a: T.x     // int
b: T.y     // 3
d: T."x-y" // 4

e: {a: 1|*2} | *{a: 3|*4}
f: e.a  // 4 (default value)


### Index expressions

A primary expression of the form

a[x]


denotes the element of a list or struct a indexed by x. The value x is called the index or field name, respectively. The following rules apply:

If a is not a struct:

• a is a list (which need not be complete)
• the index x unified with int must be concrete.
• the index x is in range if 0 <= x < len(a), where only the explicitly defined values of an open-ended list are considered, otherwise it is out of range

The result of a[x] is

for a of list type:

• the list element at index x, if x is within range
• bottom (an error), otherwise

for a of struct type:

• the index x unified with string must be concrete.
• the value of the regular and non-optional field named x of struct a, if this field exists
• bottom (an error), otherwise
[ 1, 2 ][1]     // 2
[ 1, 2 ][2]     // _|_
[ 1, 2, ...][2] // _|_


Both the operand and index value may be a value-default pair.

va[vi]              =>  va[vi]
va[(vi, di)]        =>  (va[vi], va[di])
(va, da)[vi]        =>  (va[vi], da[vi])
(va, da)[(vi, di)]  =>  (va[vi], da[di])

Fields                  Result
x: [1, 2] | *[3, 4]     ([1,2]|[3,4], [3,4])
i: int | *1             (int, 1)

v: x[i]                 (x[i], 4)


### Operators

Operators combine operands into expressions.

Expression = UnaryExpr | Expression binary_op Expression .
UnaryExpr  = PrimaryExpr | unary_op UnaryExpr .

binary_op  = "|" | "&" | "||" | "&&" | "==" | rel_op | add_op | mul_op  .
rel_op     = "!=" | "<" | "<=" | ">" | ">=" | "=~" | "!~" .
add_op     = "+" | "-" .
mul_op     = "*" | "/" | "div" | "mod" | "quo" | "rem" .
unary_op   = "+" | "-" | "!" | "*" | rel_op .


Comparisons are discussed elsewhere. For any binary operators, the operand types must unify.

Operands of unary and binary expressions may be associated with a default using the following

Field               Resulting Value-Default pair
a: *1|2             (1|2, 1)
b: -a               (-a, -1)

c: a + 2            (a+2, 3)
d: a + a            (a+a, 2)


#### Operator precedence

Unary operators have the highest precedence.

There are eight precedence levels for binary operators. Multiplication operators binds strongest, followed by addition operators, comparison operators, && (logical AND), || (logical OR), & (unification), and finally | (disjunction):

Precedence    Operator
7             *  / div mod quo rem
6             +  -
5             ==  !=  <  <=  >  >= =~ !~
4             &&
3             ||
2             &
1             |


Binary operators of the same precedence associate from left to right. For instance, x / y * z is the same as (x / y) * z.

+x
23 + 3*x[i]
x <= f()
f() || g()
x == y+1 && y == z-1
2 | int
{ a: 1 } & { b: 2 }


#### Arithmetic operators

Arithmetic operators apply to numeric values and yield a result of the same type as the first operand. The three of the four standard arithmetic operators (+, -, *) apply to integer and decimal floating-point types; + and * also apply to lists and strings. / only applies to decimal floating-point types and div, mod, quo, and rem only apply to integer types.

+    sum                    integers, floats, lists, strings, bytes
-    difference             integers, floats
*    product                integers, floats, lists, strings, bytes
/    quotient               floats
div  division               integers
mod  modulo                 integers
quo  quotient               integers
rem  remainder              integers


For any operator that accepts operands of type float, any operand may be of type int or float, in which case the result will be float if any of the operands is float or int otherwise. For / the result is always float.

#### Integer operators

For two integer values x and y, the integer quotient q = x div y and remainder r = x mod y  implement Euclidean division and satisfy the following relationship:

r = x - y*q  with 0 <= r < |y|


where |y| denotes the absolute value of y.

 x     y    x div y   x mod y
5     3       1         2
-5     3      -2         1
5    -3      -1         2
-5    -3       2         1


For two integer values x and y, the integer quotient q = x quo y and remainder r = x rem y  implement truncated division and satisfy the following relationship:

x = q*y + r  and  |r| < |y|


with x quo y truncated towards zero.

 x     y    x quo y   x rem y
5     3       1         2
-5     3      -1        -2
5    -3      -1         2
-5    -3       1        -2


A zero divisor in either case results in bottom (an error).

For integer operands, the unary operators + and - are defined as follows:

+x                          is 0 + x
-x    negation              is 0 - x


#### Decimal floating-point operators

For decimal floating-point numbers, +x is the same as x, while -x is the negation of x. The result of a floating-point division by zero is bottom (an error).

An implementation may combine multiple floating-point operations into a single fused operation, possibly across statements, and produce a result that differs from the value obtained by executing and rounding the instructions individually.

#### List operators

Lists can be concatenated using the + operator. Opens list are closed to their default value beforehand.

[ 1, 2 ]      + [ 3, 4 ]       // [ 1, 2, 3, 4 ]
[ 1, 2, ... ] + [ 3, 4 ]       // [ 1, 2, 3, 4 ]
[ 1, 2 ]      + [ 3, 4, ... ]  // [ 1, 2, 3, 4 ]


Lists can be multiplied with a non-negativeint using the * operator to create a repeated the list by the indicated number.

3*[1,2]         // [1, 2, 1, 2, 1, 2]
3*[1, 2, ...]   // [1, 2, 1, 2, 1 ,2]
[byte]*4        // [byte, byte, byte, byte]
0*[1,2]         // []


#### String operators

Strings can be concatenated using the + operator:

s: "hi " + name + " and good bye"


String addition creates a new string by concatenating the operands.

A string can be repeated by multiplying it:

s: "etc. "*3  // "etc. etc. etc. "

##### Comparison operators

Comparison operators compare two operands and yield an untyped boolean value.

==    equal
!=    not equal
<     less
<=    less or equal
>     greater
>=    greater or equal
=~    matches regular expression
!~    does not match regular expression


In any comparison, the types of the two operands must unify or one of the operands must be null.

The equality operators == and != apply to operands that are comparable. The ordering operators <, <=, >, and >= apply to operands that are ordered. The matching operators =~ and !~ apply to a string and regular expression operand. These terms and the result of the comparisons are defined as follows:

• Null is comparable with itself and any other type. Two null values are always equal, null is unequal with anything else.
• Boolean values are comparable. Two boolean values are equal if they are either both true or both false.
• Integer values are comparable and ordered, in the usual way.
• Floating-point values are comparable and ordered, as per the definitions for binary coded decimals in the IEEE-754-2008 standard.
• Floating point numbers may be compared with integers.
• String and bytes values are comparable and ordered lexically byte-wise.
• Struct are not comparable.
• Lists are not comparable.
• The regular expression syntax is the one accepted by RE2, described in https://github.com/google/re2/wiki/Syntax, except for \C.
• s =~ r is true if s matches the regular expression r.
• s !~ r is true if s does not match regular expression r.
3 < 4       // true
3 < 4.0     // true
null == 2   // false
null != {}  // true
{} == {}    // _|_: structs are not comparable against structs

"Wild cats" =~ "cat"   // true
"Wild cats" !~ "dog"   // true

"foo" =~ "^[a-z]{3}$" // true "foo" =~ "^[a-z]{4}$"  // false


#### Logical operators

Logical operators apply to boolean values and yield a result of the same type as the operands. The right operand is evaluated conditionally.

&&    conditional AND    p && q  is  "if p then q else false"
||    conditional OR     p || q  is  "if p then true else q"
!     NOT                !p      is  "not p"


### Calls

Calls can be made to core library functions, called builtins. Given an expression f of function type F,

f(a1, a2, … an)


calls f with arguments a1, a2, … an. Arguments must be expressions of which the values are an instance of the parameter types of F and are evaluated before the function is called.

a: math.Atan2(x, y)


In a function call, the function value and arguments are evaluated in the usual order. After they are evaluated, the parameters of the call are passed by value to the function and the called function begins execution. The return parameters of the function are passed by value back to the calling function when the function returns.

### Comprehensions

Lists and fields can be constructed using comprehensions.

Comprehensions define a clause sequence that consists of a sequence of for, if, and let clauses, nesting from left to right. The sequence must start with a for or if clause. The for and let clauses each define a new scope in which new values are bound to be available for the next clause.

The for clause binds the defined identifiers, on each iteration, to the next value of some iterable value in a new scope. A for clause may bind one or two identifiers. If there is one identifier, it binds it to the value of a list element or struct field value. If there are two identifiers, the first value will be the key or index, if available, and the second will be the value.

For lists, for iterates over all elements in the list after closing it. For structs, for iterates over all non-optional regular fields.

An if clause, or guard, specifies an expression that terminates the current iteration if it evaluates to false.

The let clause binds the result of an expression to the defined identifier in a new scope.

A current iteration is said to complete if the innermost block of the clause sequence is reached. Syntactically, the comprehension value is a struct. A comprehension can generate non-struct values by embedding such values within this struct.

Within lists, the values yielded by a comprehension are inserted in the list at the position of the comprehension. Within structs, the values yielded by a comprehension are embedded within the struct. Both structs and lists may contain multiple comprehensions.

Comprehension       = Clauses StructLit .

Clauses             = StartClause { [ "," ] Clause } .
StartClause         = ForClause | GuardClause .
Clause              = StartClause | LetClause .
ForClause           = "for" identifier [ "," identifier ] "in" Expression .
GuardClause         = "if" Expression .
LetClause           = "let" identifier "=" Expression .

a: [1, 2, 3, 4]
b: [ for x in a if x > 1 { x+1 } ]  // [3, 4, 5]

c: {
for x in a
if x < 4
let y = 1 {
"\(x)": x + y
}
}
d: { "1": 2, "2": 3, "3": 4 }


### String interpolation

String interpolation allows constructing strings by replacing placeholder expressions with their string representation. String interpolation may be used in single- and double-quoted strings, as well as their multiline equivalent.

A placeholder consists of “(” followed by an expression and a “)". The expression is evaluated within the scope within which the string is defined.

a: "World"
b: "Hello \( a )!" // Hello World!


## Builtin Functions

Built-in functions are predeclared. They are called like any other function.

### len

The built-in function len takes arguments of various types and return a result of type int.

Argument type    Result

string            string length in bytes
bytes             length of byte sequence
list              list length, smallest length for an open list
struct            number of distinct data fields, including optional

Expression           Result
len("Hellø")         6
len([1, 2, 3])       3
len([1, 2, ...])     >=2


### close

The builtin function close converts a partially defined, or open, struct to a fully defined, or closed, struct.

### and

The built-in function and takes a list and returns the result of applying the & operator to all elements in the list. It returns top for the empty list.

Expression:          Result
and([a, b])          a & b
and([a])             a
and([])              _


### or

The built-in function or takes a list and returns the result of applying the | operator to all elements in the list. It returns bottom for the empty list.

Expression:          Result
or([a, b])           a | b
or([a])              a
or([])               _|_


## Cycles

Implementations are required to interpret or reject cycles encountered during evaluation according to the rules in this section.

### Reference cycles

A reference cycle occurs if a field references itself, either directly or indirectly.

// x references itself
x: x

// indirect cycles
b: c
c: d
d: b


Implementations should report these as an error except in the following cases:

#### Expressions that unify an atom with an expression

An expression of the form a & e, where a is an atom and e is an expression, always evaluates to a or bottom. As it does not matter how we fail, we can assume the result to be a and validate after the field in which the expression occurs has been evaluated that a == e.

// Config            Evaluates to (requiring concrete values)
x: {                  x: {
a: b + 100            a: _|_ // cycle detected
b: a - 100            b: _|_ // cycle detected
}                     }

y: x & {              y: {
a: 200                a: 200 // asserted that 200 == b + 100
b: 100
}                     }


#### Field values

A field value of the form r & v, where r evaluates to a reference cycle and v is a value, evaluates to v. Unification is idempotent and unifying a value with itself ad infinitum, which is what the cycle represents, results in this value. Implementations should detect cycles of this kind, ignore r, and take v as the result of unification.

Configuration    Evaluated
//    c           Cycles in nodes of type struct evaluate
//  ↙︎   ↖         to the fixed point of unifying their
// a  →  b        values ad infinitum.

a: b & { x: 1 }   // a: { x: 1, y: 2, z: 3 }
b: c & { y: 2 }   // b: { x: 1, y: 2, z: 3 }
c: a & { z: 3 }   // c: { x: 1, y: 2, z: 3 }

// resolve a             b & {x:1}
// substitute b          c & {y:2} & {x:1}
// substitute c          a & {z:3} & {y:2} & {x:1}
// eliminate a (cycle)   {z:3} & {y:2} & {x:1}
// simplify              {x:1,y:2,z:3}


This rule also applies to field values that are disjunctions of unification operations of the above form.

a: b&{x:1} | {y:1}  // {x:1,y:3,z:2} | {y:1}
b: {x:2} | c&{z:2}  // {x:2} | {x:1,y:3,z:2}
c: a&{y:3} | {z:3}  // {x:1,y:3,z:2} | {z:3}

// resolving a           b&{x:1} | {y:1}
// substitute b          ({x:2} | c&{z:2})&{x:1} | {y:1}
// simplify              c&{z:2}&{x:1} | {y:1}
// substitute c          (a&{y:3} | {z:3})&{z:2}&{x:1} | {y:1}
// simplify              a&{y:3}&{z:2}&{x:1} | {y:1}
// eliminate a (cycle)   {y:3}&{z:2}&{x:1} | {y:1}
// expand                {x:1,y:3,z:2} | {y:1}


Note that all nodes that form a reference cycle to form a struct will evaluate to the same value. If a field value is a disjunction, any element that is part of a cycle will evaluate to this value.

### Structural cycles

CUE disallows infinite structures. Implementations must report an error when encountering such declarations.

// Disallowed: a list of infinite length with all elements being 1.
list: {
tail: list
}

// Disallowed: another infinite structure (a:{b:{d:{b:{d:{...}}}}}, ...).
a: {
b: c
}
c: {
d: a
}


It is allowed for a value to define an infinite set of possibilities without evaluating to an infinite structure itself.

// List defines a list of arbitrary length (default null).
List: *null | {
tail: List
}


## Modules, instances, and packages

CUE configurations are constructed combining instances. An instance, in turn, is constructed from one or more source files belonging to the same package that together declare the data representation. Elements of this data representation may be exported and used in other instances.

### Source file organization

Each source file consists of an optional package clause defining collection of files to which it belongs, followed by a possibly empty set of import declarations that declare packages whose contents it wishes to use, followed by a possibly empty set of declarations.

Like with a struct, a source file may contain embeddings. Unlike with a struct, the embedded expressions may be any value. If the result of the unification of all embedded values is not a struct, it will be output instead of its enclosing file when exporting CUE to a data format

SourceFile = [ PackageClause "," ] { ImportDecl "," } { Declaration "," } .

"Hello \(place)!"

place: "world"

// Outputs "Hello world!"


### Package clause

A package clause is an optional clause that defines the package to which a source file the file belongs.

PackageClause  = "package" PackageName .
PackageName    = identifier .


The PackageName must not be the blank identifier or a definition identifier.

package math


### Modules and instances

A module defines a tree of directories, rooted at the module root.

All source files within a module with the same package belong to the same package.

A module may define multiple packages.

An instance of a package is any subset of files belonging to the same package.

It is interpreted as the concatenation of these files.

An implementation may impose conventions on the layout of package files to determine which files of a package belongs to an instance. For example, an instance may be defined as the subset of package files belonging to a directory and all its ancestors.

### Import declarations

An import declaration states that the source file containing the declaration depends on definitions of the imported package (§Program initialization and execution) and enables access to exported identifiers of that package. The import names an identifier (PackageName) to be used for access and an ImportPath that specifies the package to be imported.

ImportDecl       = "import" ( ImportSpec | "(" { ImportSpec "," } ")" ) .
ImportSpec       = [ PackageName ] ImportPath .
ImportLocation   = { unicode_value } .
ImportPath       = " ImportLocation [ ":" identifier ] " .


The PackageName is used in qualified identifiers to access exported identifiers of the package within the importing source file. It is declared in the file block. It defaults to the identifier specified in the package clause of the imported package, which must match either the last path component of ImportLocation or the identifier following it.

The interpretation of the ImportPath is implementation-dependent but it is typically either the path of a builtin package or a fully qualifying location of a package within a source code repository.

An ImportLocation must be a non-empty strings using only characters belonging Unicode’s L, M, N, P, and S general categories (the Graphic characters without spaces) and may not include the characters !"#\$%&'()*,:;<=>?[]^{|} or the Unicode replacement character U+FFFD.

Assume we have package containing the package clause “package math”, which exports function Sin at the path identified by “lib/math”. This table illustrates how Sin is accessed in files that import the package after the various types of import declaration.

Import declaration          Local name of Sin

import   "lib/math"         math.Sin
import   "lib/math:math"    math.Sin
import m "lib/math"         m.Sin
`

An import declaration declares a dependency relation between the importing and imported package. It is illegal for a package to import itself, directly or indirectly, or to directly import a package without referring to any of its exported identifiers.

TODO