# Language quick reference

This section serves as a technical reference for the previous chapters and has specific technical information for readers with specific interests. For example, this section provides technical details of interest to the following audiences:

• Authors providing the higher-level documentation about the Motoko programming language.

• Compiler experts interested in the details of Motoko and its compiler.

The language quick reference is intended to provide complete reference information about Motoko, but this section does not provide explanatory text or usage information. Therefore, this section is typically not suitable for readers who are new to programming languages or who are looking for a general introduction to using Motoko.

Throughout, we use the term canister to refer to an Internet Computer canister smart contract.

## Basic language syntax​

This section describes the basic language conventions you need to know for programming in Motoko.

### Whitespace​

Space, newline, horizontal tab, carriage return, line feed and form feed are considered as whitespace. Whitespace is ignored but used to separate adjacent keywords, identifiers and operators.

In the definition of some lexemes, the quick reference uses the symbol ␣ to denote a single whitespace character.

Single line comments are all characters following // until the end of the same line.

// single line commentx = 1

Single or multi-line comments are any sequence of characters delimited by /* and */:

/* multi-line comments   look like this, as in C and friends */

Comments delimited by /* and */ may be nested, provided the nesting is well-bracketed.

/// I'm a documentation comment/// for a function

Documentation comments start with /// followed by a space until the end of line, and get attached to the definition immediately following them.

Deprecation comments start with /// @deprecated followed by a space until the end of line, and get attached to the definition immediately following them. They are only recognized in front of public declarations.

All comments are treated as whitespace.

### Keywords​

The following keywords are reserved and may not be used as identifiers:

actor and assert async await break case catch class continue debugdebug_show do else flexible false for from_candid func if ignore importin module not null object or label let loop private public query returnshared stable switch system throw to_candid true try type var while

### Identifiers​

<id>   ::= Letter (Letter | Digit | _)*Letter ::= A..Z | a..zDigit  ::= 0..9

### Integers​

Integers are written as decimal or hexadecimal, Ox-prefixed natural numbers. Subsequent digits may be prefixed a single, semantically irrelevant, underscore.

digit ::= ['0'-'9']hexdigit ::= ['0'-'9''a'-'f''A'-'F']num ::= digit ('_'? digit)*hexnum ::= hexdigit ('_'? hexdigit)*nat ::= num | "0x" hexnum

Negative integers may be constructed by applying a prefix negation - operation.

### Floats​

Floating point literals are written in decimal or Ox-prefixed hexadecimal scientific notation.

let frac = numlet hexfrac = hexnumlet float =    num '.' frac?  | num ('.' frac?)? ('e' | 'E') sign? num  | "0x" hexnum '.' hexfrac?  | "0x" hexnum ('.' hexfrac?)? ('p' | 'P') sign? num

The 'e' (or 'E') prefixes a base 10, decimal exponent; 'p' (or 'P') prefixes a base 2, binary exponent. In both cases, the exponent is in decimal notation.

note

the use of decimal notation, even for the base 2 exponent, is in keeping with the established hexadecimal floating point literal syntax of the C language.

### Characters​

A character is a single quote (') delimited:

• Unicode character in UTF-8,

• \-escaped newline, carriage return, tab, single or double quotation mark

• \-prefixed ASCII character (TBR),

• or \u{ hexnum } enclosed valid, escaped Unicode character in hexadecimal (TBR).

ascii ::= ['\x00'-'\x7f']ascii_no_nl ::= ['\x00'-'\x09''\x0b'-'\x7f']utf8cont ::= ['\x80'-'\xbf']utf8enc ::=    ['\xc2'-'\xdf'] utf8cont  | ['\xe0'] ['\xa0'-'\xbf'] utf8cont  | ['\xed'] ['\x80'-'\x9f'] utf8cont  | ['\xe1'-'\xec''\xee'-'\xef'] utf8cont utf8cont  | ['\xf0'] ['\x90'-'\xbf'] utf8cont utf8cont  | ['\xf4'] ['\x80'-'\x8f'] utf8cont utf8cont  | ['\xf1'-'\xf3'] utf8cont utf8cont utf8contutf8 ::= ascii | utf8encutf8_no_nl ::= ascii_no_nl | utf8encescape ::= ['n''r''t''\\''\'''\"']character ::=  | [^'"''\\''\x00'-'\x1f''\x7f'-'\xff']  | utf8enc  | '\\'escape  | '\\'hexdigit hexdigit  | "\\u{" hexnum '}'char := '\'' character '\''

### Text​

A text literal is "-delimited sequence of characters:

text ::= '"' character* '"'

### Literals​

<lit> ::=                                     literals  <nat>                                         natural  <float>                                       float  <char>                                        character  <text>                                        Unicode text

Literals are constant values. The syntactic validity of a literal depends on the precision of the type at which it is used.

## Operators and types​

To simplify the presentation of available operators, operators and primitive types are classified into basic categories:

AbbreviationCategorySupported opertions
AArithmeticarithmetic operations
LLogicallogical/Boolean operations
BBitwisebitwise and wrapping operations
OOrderedcomparison
TTextconcatenation

Some types have several categories. For example, type Int is both arithmetic (A) and ordered (O) and supports both arithmetic addition (+) and relational less than (<) (amongst other operations).

### Unary operators​

<unop>Category
-Anumeric negation
+Anumeric identity
^Bbitwise negation
!null break

### Relational operators​

<relop>Category
==equals
!=not equals
␣<␣Oless than (must be enclosed in whitespace)
␣>␣Ogreater than (must be enclosed in whitespace)
<=Oless than or equal
>=Ogreater than or equal

Note that equality (==) and inequality (!=) do not have categories. Instead, equality and inequality are applicable to arguments of all shared types, including non-primitive, compound types such as immutable arrays, records, and variants.

Equality and inequality are structural and based on the observable content of their operands (as determined by their static type).

### Numeric binary operators​

<binop>Category
+Aaddition
-Asubtraction
*Amultiplication
/Adivision
%Amodulo
**Aexponentiation

### Bitwise and wrapping binary operators​

<binop>Category
&Bbitwise and
\|Bbitwise or
^Bexclusive or
<<Bshift left
␣>>Bshift right (must be preceded by whitespace)
<<>Brotate left
<>>Brotate right
+%Aaddition (wrap-on-overflow)
-%Asubtraction (wrap-on-overflow)
*%Amultiplication (wrap-on-overflow)
**%Aexponentiation (wrap-on-overflow)

### Text operators​

<binop>Category
#Tconcatenation

### Assignment operators​

:=, <unop>=, <binop>=Category
:=*assignment (in place update)
+=Ain place add
-=Ain place subtract
*=Ain place multiply
/=Ain place divide
%=Ain place modulo
**=Ain place exponentiation
&=Bin place logical and
\|=Bin place logical or
^=Bin place exclusive or
<<=Bin place shift left
>>=Bin place shift right
<<>=Bin place rotate left
<>>=Bin place rotate right
+%=Bin place add (wrap-on-overflow)
-%=Bin place subtract (wrap-on-overflow)
*%=Bin place multiply (wrap-on-overflow)
**%=Bin place exponentiation (wrap-on-overflow)
#=Tin place concatenation

The category of a compound assignment <unop>=/<binop>= is given by the category of the operator <unop>/<binop>.

### Operator and keyword precedence​

The following table defines the relative precedence and associativity of operators and tokens, ordered from lowest to highest precedence. Tokens on the same line have equal precedence with the indicated associativity.

PrecedenceAssociativityToken
LOWESTnoneif _ _ (no else), loop _ (no while)
(higher)noneelse, while
(higher)right:=, +=, -=, *=, /=, %=, **=, #=, &=, \|=, ^=, <<=, >>=, <<>=, <>>=, +%=, -%=, *%=, **%=
(higher)left:
(higher)leftor
(higher)leftand
(higher)none==, !=, <, >, <=, >, >=
(higher)left+, -, #, +%, -%
(higher)left*, /, %, *%
(higher)left\|
(higher)left&
(higher)left^
(higher)none<<, >>, <<>, <>>
HIGHESTleft**, **%

### Programs​

The syntax of a program <prog> is as follows:

<prog> ::=             programs  <imp>;* <dec>;*

A program is a sequence of imports <imp>;* followed by a sequence of declarations <dec>;* that ends with an optional actor or actor class declaration. The actor or actor class declaration determines the main actor, if any, of the program.

For now, compiled programs must obey the following additional restrictions (not imposed on interpreted programs):

• a shared function can only appear as a public field of an actor or actor class;

• a program may contain at most one actor or actor class declaration, i.e. the final main actor or actor class; and

• any main actor class declaration should be anonymous; if named, the class name should not be used as a value within the class and will be reported as an unavailable identifier.

The last two restrictions are designed to forbid programmatic actor class recursion, pending compiler support.

Note that the parameters (if any) of an actor class must have shared type (see Sharability). The parameters of a program’s final actor class provide access to the corresponding canister installation argument(s); the Candid type of this argument is determined by the Candid projection of the Motoko type of the class parameter.

### Imports​

The syntax of an import <imp> is as follows:

<imp> ::= imports  import <pat> =? <url><url> ::=  "<filepath>"                      import module from relative <filepath>.mo  "mo:<package-name>/<filepath>"    import module from package  "canister:<canisterid>"           import external actor by <canisterid>  "canister:<name>"                 import external actor by <name>

An import introduces a resource referring to a local source module, module from a package of modules, or canister (imported as an actor). The contents of the resource are bound to <pat>.

Though typically a simple identifier, <id>, <pat> can also be any composite pattern binding selective components of the resource.

The pattern must be irrefutable.

### Libraries​

The syntax of a library (that can be referenced in an import) is as follows:

<lib> ::=                                               library  <imp>;* module <id>? <obj-body>                         module  <imp>;* <shared-pat>? actor class                       actor class    <id> <typ-params>? <pat> (: <typ>)? <class-body>

A library <lib> is a sequence of imports <imp>;* followed by:

• a named or anonymous (module) declaration; or

• a named actor class declaration.

Libraries stored in .mo files may be referenced by import declarations.

In a module library, the optional name <id>? is only significant within the library and does not determine the name of the library when imported. Instead, the imported name of a library is determined by the import declaration, giving clients of the library the freedom to choose library names (e.g. to avoid clashes).

An actor class library, because it defines both a type constructor and a function with name <id>, is imported as a module defining both a type and a function named <id>. The name <id> is mandatory and cannot be omitted. An actor class constructor is always asynchronous, with return type async T where T is the inferred type of the class body. Because actor construction is asynchronous, an instance of an imported actor class can only be created in an asynchronous context (i.e. in the body of a (non-query) shared function or async expression).

### Declaration syntax​

The syntax of a declaration is as follows:

<dec> ::=                                                               declaration  <exp>                                                                  expression  let <pat> = <exp>                                                      immutable  var <id> (: <typ>)? = <exp>                                            mutable  <sort> <id>? =? <obj-body>                                             object  <shared-pat>? func <id>? <typ-params>? <pat> (: <typ>)? =? <exp>       function  type <id> <typ-params>? = <typ>                                        type  <shared-pat>? <sort>? class                                            class    <id>? <typ-params>? <pat> (: <typ>)? <class-body><obj-body> ::=           object body  { <dec-field>;* }       field declarations<class-body> ::=         class body  = <id>? <obj-body>     object body, optionally binding <id> to 'this' instance  <obj-body>             object body

The syntax of a shared function qualifier with call-context pattern is as follows:

<shared-pat> ::=  shared query? <pat>?

For <shared-pat>, an absent <pat>? is shorthand for the wildcard pattern _.

<dec-field> ::=                                object declaration fields  <vis>? <stab>? <dec>                           field<vis> ::=                                      field visibility  public  private  system<stab> ::=                                     field stability (actor only)  stable  flexible

The visibility qualifier <vis>? determines the accessibility of every field <id> declared by <dec>:

• An absent <vis>? qualifier defaults to private visibility.

• Visibility private restricts access to <id> to the enclosing object, module or actor.

• Visibility public extends private with external access to <id> using the dot notation <exp>.<id>.

• Visibility system extends private with access by the run-time system.

• Visibility system may only appear on func declarations that are actor fields, and must not appear anywhere else.

The stability qualifier <stab> determines the upgrade behaviour of actor fields:

• A stability qualifier should appear on let and var declarations that are actor fields. An absent stability qualifier defaults to flexible.

• <stab> qualifiers must not appear on fields of objects or modules.

• The pattern in a stable let <pat> = <exp> declaration must be simple where, a pattern pat is simple if it (recursively) consists of

• a variable pattern <id>, or

• an annotated simple pattern <pat> : <typ>, or

• a parenthesized simple pattern ( <pat> ).

### Expression syntax​

The syntax of an expression is as follows:

<exp> ::=                                      expressions  <id>                                           variable  <lit>                                          literal  <unop> <exp>                                   unary operator  <exp> <binop> <exp>                            binary operator  <exp> <relop> <exp>                            binary relational operator  ( <exp>,* )                                    tuple  <exp> . <nat>                                  tuple projection  ? <exp>                                        option injection  { <exp-field>;* }                              object  { <exp> (and <exp>)* (with <exp-field>;+)? }   object combination/extension  # id <exp>?                                    variant injection  <exp> . <id>                                   object projection/member access  <exp> := <exp>                                 assignment  <unop>= <exp>                                  unary update  <exp> <binop>= <exp>                           binary update  [ var? <exp>,* ]                               array  <exp> [ <exp> ]                                array indexing  <shared-pat>? func <func_exp>                  function expression  <exp> <typ-args>? <exp>                        function call  not <exp>                                      negation  <exp> and <exp>                                conjunction  <exp> or <exp>                                 disjunction  if <exp> <block-or-exp> (else <block-or-exp>)? conditional  switch <exp> { (case <pat> <block-or-exp>;)+ } switch  while <exp> <block-or-exp>                     while loop  loop <block-or-exp> (while <exp>)?             loop  for ( <pat> in <exp> ) <block-or-exp>          iteration  label <id> (: <typ>)? <block-or-exp>           label  break <id> <exp>?                              break  continue <id>                                  continue  return <exp>?                                  return  async <block-or-exp>                           async expression  await <block-or-exp>                           await future (only in async)  throw <exp>                                    raise an error (only in async)  try <block-or-exp> catch <pat> <block-or-exp>  catch an error (only in async)  assert <block-or-exp>                          assertion  <exp> : <typ>                                  type annotation  <dec>                                          declaration  ignore <block-or-exp>                          ignore value  do <block>                                     block as expression  do ? <block>                                   option block  <exp> !                                        null break  debug <block-or-exp>                           debug expression  actor <exp>                                    actor reference  to_candid ( <exp>,* )                          Candid serialization  from_candid <exp>                              Candid deserialization  (system <exp> . <id>)                          System actor class constructor  ( <exp> )                                      parentheses<block-or-exp> ::=  <block>  <exp><block> ::=  { <dec>;* }

### Patterns​

The syntax of a pattern is as follows:

<pat> ::=                                      patterns  _                                              wildcard  <id>                                           variable  <unop>? <lit>                                  literal  ( <pat>,* )                                    tuple or brackets  { <pat-field>;* }                              object pattern  # <id> <pat>?                                  variant pattern  ? <pat>                                        option  <pat> : <typ>                                  type annotation  <pat> or <pat>                                 disjunctive pattern<pat-field> ::=                                object pattern fields  <id> (: <typ>) = <pat>                         field  <id> (: <typ>)                                 punned field

## Type syntax​

Type expressions are used to specify the types of arguments, constraints (a.k.a bounds) on type parameters, definitions of type constructors, and the types of sub-expressions in type annotations.

<typ> ::=                                     type expressions  <path> <typ-args>?                            constructor  <sort>? { <typ-field>;* }                     object  { <typ-tag>;* }                               variant  { # }                                         empty variant  [ var? <typ> ]                                array  Null                                          null type  ? <typ>                                       option  <shared>? <typ-params>? <typ> -> <typ>        function  async <typ>                                   future  ( ((<id> :)? <typ>),* )                       tuple  Any                                           top  None                                          bottom  <typ> and <typ>                               intersection  <typ> or <typ>                                union  Error                                         errors/exceptions  ( <typ> )                                      parenthesized type<sort> ::= (actor | module | object)<shared> ::=                                 shared function type qualifier  shared query?<path> ::=                                   paths  <id>                                         type identifier  <path> . <id>                                projection

An absent <sort>? abbreviates object.

### Primitive types​

Motoko provides the following primitive type identifiers, including support for Booleans, signed and unsigned integers and machine words of various sizes, characters and text.

The category of a type determines the operators (unary, binary, relational and in-place update via assignment) applicable to values of that type.

IdentifierCategoryDescription
BoolLBoolean values true and false and logical operators
CharOUnicode characters
TextT, OUnicode strings of characters with concatenation _ # _ and iteration
FloatA, O64-bit floating point values
IntA, Osigned integer values with arithmetic (unbounded)
Int8A, Osigned 8-bit integer values with checked arithmetic
Int16A, Osigned 16-bit integer values with checked arithmetic
Int32A, Osigned 32-bit integer values with checked arithmetic
Int64A, Osigned 64-bit integer values with checked arithmetic
NatA, Onon-negative integer values with arithmetic (unbounded)
Nat8A, Onon-negative 8-bit integer values with checked arithmetic
Nat16A, Onon-negative 16-bit integer values with checked arithmetic
Nat32A, Onon-negative 32-bit integer values with checked arithmetic
Nat64A, Onon-negative 64-bit integer values with checked arithmetic
BlobObinary blobs with iterators
PrincipalOprincipals
Error(opaque) error values

Although many of these types have linguistic support for literals and operators, each primitive type also has an eponymous base library providing related functions and values (see Motoko Base Library). For example, the Text library provides common functions on Text values.

### Type Bool​

The type Bool of category L (Logical) has values true and false and is supported by one and two branch if _ <exp> (else <exp>)?, not <exp>, _ and _ and _ or _ expressions. Expressions if, and and or are short-circuiting.

### Type Char​

A Char of category O (Ordered) represents a character as a code point in the Unicode character set.

Base library function Char.toNat32(c) converts a Char value, c to its Nat32 code point. Function Char.fromNat32(n) converts a Nat32 value, n, in the range 0x0..xD7FF or 0xE000..0x10FFFF of valid code points to its Char value; this conversion traps on invalid arguments. Function Char.toText(c) converts the Char c into the corresponding, single character Text value.

### Type Text​

The type Text of categories T and O (Text, Ordered) represents sequences of Unicode characters (i.e. strings). Function t.size returns the number of characters in Text value t. Operations on text values include concatenation (_ # _) and sequential iteration over characters via t.chars as in for (c : Char in t.chars()) { …​ c …​ }.

### Type Float​

The type Float represents 64-bit floating point values of categories A (Arithmetic) and O (Ordered).

The semantics of Float and its operations is in accordance with standard IEEE 754-2019 (See References).

Common functions and values are defined in base library "base/Float".

### Types Int and Nat​

The types Int and Nat are signed integral and natural numbers of categories A (Arithmetic) and O (Ordered).

Both Int and Nat are arbitrary precision, with only subtraction - on Nat trapping on underflow.

The subtype relation Nat <: Int holds, so every expression of type Nat is also an expression of type Int (but not vice versa). In particular, every value of type Nat is also a value of type Int, without change of representation.

### Bounded integers Int8, Int16, Int32 and Int64​

The types Int8, Int16, Int32 and Int64 represent signed integers with respectively 8, 16, 32 and 64 bit precision. All have categories A (Arithmetic), B (Bitwise) and O (Ordered).

Operations that may under- or overflow the representation are checked and trap on error.

The operations +%, -%, *% and **% provide access to wrap-around, modular arithmetic.

As bitwise types, these types support bitwise operations and (&), or (|) and exclusive-or (^). Further, they can be rotated left (<<>), right (<>>), and shifted left (<<), right (>>). The right-shift preserves the two’s-complement sign. All shift and rotate amounts are considered modulo the numbers’s bit width n.

Bounded integer types are not in subtype relationship with each other or with other arithmetic types, and their literals need type annotation if the type cannot be inferred from context, e.g. (-42 : Int16).

The corresponding module in the base library provides conversion functions: Conversion to Int, checked and wrapping conversions from Int and wrapping conversion to the bounded natural type of the same size.

### Bounded naturals Nat8, Nat16, Nat32 and Nat64​

The types Nat8, Nat16, Nat32 and Nat64 represent unsigned integers with respectively 8, 16, 32 and 64 bit precision. All have categories A (Arithmetic), B (Bitwise) and O (Ordered).

Operations that may under- or overflow the representation are checked and trap on error.

The operations +%, -%, *% and **% provide access to the modular, wrap-on-overflow operations.

As bitwise types, these types support bitwise operations and (&), or (|) and exclusive-or (^). Further, they can be rotated left (<<>), right (<>>), and shifted left (<<), right (>>). The right-shift is logical. All shift and rotate amounts are considered modulo the number’s bit width n.

The corresponding module in the base library provides conversion functions: Conversion to Int, checked and wrapping conversions from Int and wrapping conversion to the bounded natural type of the same size.

### Type Blob​

The type Blob of category O (Ordered) represents binary blobs or sequences of bytes. Function b.size returns the number of characters in Blob value b. Operations on blob values include sequential iteration over bytes via function b.vals as in for (v : Nat8 in b.vals()) { …​ v …​ }.

### Type Principal​

The type Principal of category O (Ordered) represents opaque principals such as canisters and users that can, for example, be used to identify callers of shared functions and used for simple authentication. Although opaque, principals may be converted to binary Blob values for more efficient hashing and other applications (see module Principal from the base library).

### Error type​

Assuming base library import,

import E "mo:base/Error";

Errors are opaque values constructed and examined with operations:

• E.reject : Text -> Error

• E.code : Error -> E.ErrorCode

• E.message : Error -> Text

Type E.ErrorCode is equivalent to variant type:

type ErrorCode = {  // Fatal error.  #system_fatal;  // Transient error.  #system_transient;  // Destination invalid.  #destination_invalid;  // Explicit reject by canister code.  #canister_reject;  // Canister trapped.  #canister_error;  // Future error code (with unrecognized numeric code)  #future : Nat32;};

A constructed error e = E.reject(t) has E.code(e) = #canister_reject and E.message(e) = t.

Error values can be thrown and caught within an async expression or shared function (only). See Throw and Try.

Errors with codes other than #canister_reject (i.e. system errors) may be caught and thrown, but not user-constructed.

note

Exiting an async block or shared function with a non-#canister-reject system error exits with a copy of the error with revised code #canister_reject and the original Text message. This prevents programmatic forgery of system errors.

### Constructed types​

<path> <typ-args>? is the application of a type identifier or path, either built-in (i.e. Int) or user defined, to zero or more type arguments. The type arguments must satisfy the bounds, if any, expected by the type constructor’s type parameters (see Well-formed types).

Though typically a type identifier, more generally, <path> may be a .-separated sequence of actor, object or module identifiers ending in an identifier accessing a type component of a value (for example, Acme.Collections.List).

### Object types​

<sort>? { <typ-field>;* } specifies an object type by listing its zero or more named type fields.

Within an object type, the names of fields must be distinct (both by name and hash value).

Object types that differ only in the ordering of the fields are equivalent.

When <sort>? is actor, all fields have shared function type (specifying messages).

### Variant types​

{ <typ-tag>;* } specifies a variant type by listing its variant type fields as a sequence of <typ-tag>s.

Within a variant type, the tags of its variants must be distinct (both by name and hash value).

Variant types that differ only in the ordering of their variant type fields are equivalent.

{ # } specifies the empty variant type.

### Array types​

[ var? <typ> ] specifies the type of arrays with elements of type <typ>.

Arrays are immutable unless specified with qualifier var.

### Null type​

The Null type has a single value, the literal null. Null is a subtype of the option ? T, for any type T.

### Option types​

? <typ> specifies the type of values that are either null or a proper value of the form ? <v> where <v> has type <typ>.

### Function types​

Type <shared>? <typ-params>? <typ1> -> <typ2> specifies the type of functions that consume (optional) type parameters <typ-params>, consume a value parameter of type <typ1> and produce a result of type <typ2>.

Both <typ1> and <typ2> may reference type parameters declared in <typ-params>.

If <typ1> or <typ2> (or both) is a tuple type, then the length of that tuple type determines the argument or result arity of the function type.

The optional <shared> qualifier specifies whether the function value is shared, which further constrains the form of <typ-params>, <typ1> and <typ2> (see Sharability below).

(Note that a <shared> function may itself be shared or shared query, determining the persistence of its state changes.)

### Async types​

async <typ> specifies a future producing a value of type <typ>.

Future types typically appear as the result type of a shared function that produces an await-able value.

### Tuple types​

( ((<id> :)? <typ>),* ) specifies the type of a tuple with zero or more ordered components.

The optional identifier <id>, naming its components, is for documentation purposes only and cannot be used for component access. In particular, tuple types that differ only in the names of components are equivalent.

The empty tuple type () is called the unit type.

### Any type​

Type Any is the top type, i.e. the super-type of all types. All values have type Any.

### None type​

Type None is the bottom type, a subtype of all other types. No value has type None.

As an empty type, None can be used to specify the impossible return value of an infinite loop or unconditional trap.

### Intersection type​

The type expression <typ1> and <typ2> denotes the syntactic intersection between its two type operands, that is, the greatest type that is a subtype of both. If both types are incompatible, the intersection is None.

The intersection is syntactic, in that it does not consider possible instantiations of type variables. The intersection of two type variables is None, unless they are equal, or one is declared to be a (direct or indirect) subtype of the other.

### Union type​

The type expression <typ1> or <typ2> denotes the syntactic union between its two type operands, that is, the smallest type that is a supertype of both. If both types are incompatible, the union is Any.

The union is syntactic, in that it does not consider possible instantiations of type variables. The union of two type variables is the union of their bounds, unless the variables are equal, or one is declared to be a (direct or indirect) subtype of the other.

### Parenthesized type​

A function that takes an immediate, syntactic tuple of length n >= 0 as its domain or range is a function that takes (respectively returns) n values.

When enclosing the argument or result type of a function, which is itself a tuple type, ( <tuple-typ> ) declares that the function takes or returns a single (boxed) value of type <tuple-type>.

In all other positions, ( <typ> ) has the same meaning as <typ>.

### Type fields​

<typ-field> ::=                               object type fields  <id> : <typ>                                  immutable  var <id> : <typ>                              mutable  <id> <typ-params>? <typ1> : <typ2>            function (short-hand)

A type field specifies the name and type of a field of an object. The field names within a single object type must be distinct and have non-colliding hashes.

<id> : <typ> specifies an immutable field, named <id> of type <typ>.

var <id> : <typ> specifies a mutable field, named <id> of type <typ>.

### Variant type fields​

<typ-tag> ::=                                 variant type fields  # <id> : <typ>                                tag  # <id>                                        unit tag (short-hand)

A variant type field specifies the tag and type of a single variant of an enclosing variant type. The tags within a single variant type must be distinct and have non-colliding hashes.

# <id> : <typ> specifies an (immutable) field, named <id> of type <typ>. # <id> is sugar for an (immutable) field, named <id> of type ().

### Sugar​

When enclosed by an actor object type, <id> <typ-params>? <typ1> : <typ2> is syntactic sugar for an immutable field named <id> of shared function type shared <typ-params>? <typ1> → <typ2>.

When enclosed by a non-actor object type, <id> <typ-params>? <typ1> : <typ2> is syntactic sugar for an immutable field named <id> of ordinary function type <typ-params>? <typ1> → <typ2>.

### Type parameters​

<typ-params> ::=                              type parameters  < typ-param,* ><typ-param>  <id> <: <typ>                               constrained type parameter  <id>                                        unconstrained type parameter

A type constructors, function value or function type may be parameterised by a vector of comma-separated, optionally constrained, type parameters.

<id> <: <typ> declares a type parameter with constraint <typ>. Any instantiation of <id> must subtype <typ> (at that same instantiation).

Syntactic sugar <id> declares a type parameter with implicit, trivial constraint Any.

The names of type parameters in a vector must be distinct.

All type parameters declared in a vector are in scope within its bounds.

### Type arguments​

<typ-args> ::=                                type arguments  < <typ>,* >

Type constructors and functions may take type arguments.

The number of type arguments must agree with the number of declared type parameters of the type constructor.

For a function, the number of type arguments, when provided, must agree with the number of declared type parameters of the function’s type. Note that type arguments in function applications can typically be omitted and inferred by the compiler.

Given a vector of type arguments instantiating a vector of type parameters, each type argument must satisfy the instantiated bounds of the corresponding type parameter.

### Well-formed types​

A type T is well-formed only if (recursively) its constituent types are well-formed, and:

• if T is async U then U is shared, and

• if T is shared query? U -> V, U is shared and V == () or V == async W with W shared, and

• if T is C<T0, …​, Tn> where:

• a declaration type C<X0 <: U0, Xn <: Un> = …​ is in scope, and

• Ti <: Ui[ T0/X0, …​, Tn/Xn ], for each 0 <= i <= n.

• if T is actor { …​ } then all fields in …​ are immutable and have shared function type.

### Subtyping​

Two types T, U are related by subtyping, written T <: U, whenever, one of the following conditions is true:

• T equals U (reflexivity).

• U equals Any.

• T equals None.

• T is a type parameter X declared with constraint U.

• T is Nat and U is Int.

• T is a tuple (T0, …​, Tn), U is a tuple (U0, …​, Un), and for each 0 <= i <= n, Ti <: Ui.

• T is an immutable array type [ V ], U is an immutable array type [ W ] and V <: W.

• T is a mutable array type [ var V ], U is a mutable array type [ var W ] and V == W.

• T is Null and U is an option type ? W for some W.

• T is ? V, U is ? W and V <: W.

• T is a future async V, U is a future async W, and V <: W.

• T is an object type sort0 { fts0 }, U is an object type sort1 { fts1 } and

• sort0 == sort1, and, for all fields,

• if field id : V is in fts0 then id : W is in fts1 and V <: W, and

• if mutable field var id : V is in fts0 then var id : W is in fts1 and V == W.

(That is, object type T is a subtype of object type U if they have same sort, every mutable field in U super-types the same field in T and every mutable field in U is mutable in T with an equivalent type. In particular, T may specify more fields than U.)

• T is a variant type { fts0 }, U is a variant type { fts1 } and

• if field # id : V is in fts0 then # id : W is in fts1 and V <: W.

(That is, variant type T is a subtype of variant type U if every field of T subtypes the same field of U. In particular, T may specify fewer variants than U.)

• T is a function type <shared>? <X0 <: V0, ..., Xn <: Vn> T1 -> T2, U is a function type <shared>? <X0 <: W0, ..., Xn <: Wn> U1 -> U2 and

• T and U are either both equivalently <shared>?, and

• assuming constraints X0 <: W0, …​, Xn <: Wn then

• for all i, Wi == Vi, and

• U1 <: T1, and

• T2 <: U2.

(That is, function type T is a subtype of function type U if they have same <shared>? qualification, they have the same type parameters (modulo renaming) and assuming the bounds in U, every bound in T supertypes the corresponding parameter bound in U (contra-variance), the domain of T supertypes the domain of U (contra-variance) and the range of T subtypes the range of U (co-variance).)

• T (respectively U) is a constructed type C<V0, …​, Vn> that is equal, by definition of type constructor C, to W, and W <: U (respectively U <: W).

• For some type V, T <: V and V <: U (transitivity).

### Sharability​

A type T is shared if it is

• Any or None, or

• a primitive type other than Error, or

• an option type ? V where V is shared, or

• a tuple type (T0, …​, Tn) where all Ti are shared, or

• an immutable array type [V] where V is shared, or

• an object type where all fields are immutable and have shared type, or

• a variant type where all tags have shared type, or

• a shared function type, or

• an actor type.

### Stability​

Stability extends sharability to include mutable types. More precisely:

A type T is stable if it is

• Any or None, or

• a primitive type other than Error, or

• an option type ? V where V is stable, or

• a tuple type (T0, …​, Tn) where all Ti are stable, or

• a (mutable or immutable) array type [var? V] where V is stable, or

• an object type where all fields have stable type, or

• a variant type where all tags have stable type, or

• a shared function type, or

• an actor type.

This definition implies that every shared type is a stable type. The converse does not hold: there are types that are stable but not shared (notably types with mutable components).

The types of actor fields declared with the stable qualifier must have stable type.

The (current) value of such a field is preserved upon upgrade, whereas the values of other fields are reinitialized after an upgrade.

## Static and dynamic semantics​

Below, we give a detailed account of the semantics of Motoko programs.

For each expression form and each declaration form, we summarize its semantics, both in static terms (based on typing) and dynamic terms (based on program evaluation).

### Programs​

A program <imp>;* <dec>;* has type T provided:

• <dec>;* has type T under the static environment induced by the imports in <imp>;*.

All type and value declarations within <dec>;* are mutually-recursive.

A program evaluates by (transitively) evaluating the imports, binding their values to the identifiers in <imp>;* and then evaluating the sequence of declarations in <dec>;*.

### Libraries​

Restrictions on the syntactic form of modules means that libraries can have no side-effects.

The imports of a library are local and not re-exported in its interface.

Multiple imports of the same library can be safely deduplicated without loss of side-effects.

#### Module libraries​

A library <imp>;* module <id>? <obj-body> is a sequence of imports <import>;* followed by a single module declaration.

A library has module type T provided

• module <id>? <obj-body> has (module) type T under the static environment induced by the imports in <import>;*.

A module library evaluates by (transitively) evaluating its imports, binding their values to the identifiers in <imp>;* and then evaluating module <id>? <obj-body>.

#### Actor class libraries​

The actor class library <imp>;* <dec> where <dec> is of the form <shared-pat>? actor class <id> <typ-params>? <pat> (: <typ>)? <class-body> has type:

module {  type <id> = T;  <id> : (U1,...,Un) -> async T}

provided that:

• the actor class declaration <dec> has function type (U1, ...​, Un) -> async T under the static environment induced by the imports in <import>;*.

Notice that the imported type of the function <id> must be asynchronous.

An actor class library evaluates by (transitively) evaluating its imports, binding their values to the identifiers in <imp>;*, and evaluating the (derived) module:

module {  <dec>}

On the Internet Computer, if this library is imported as identifier Lib, then calling await Lib.<id>(<exp1>, ..., <expn>), installs a fresh instance of the actor class as an isolated IC canister, passing the values of <exp1>, ...​, <expn> as installation arguments, and returns a reference to a (remote) actor of type Lib.<id>, that is, T. Installation is (necessarily) asynchronous.

#### Actor class management​

On the Internet Computer, the primary constructor of an imported actor class always creates a new principal and installs a fresh instance of the class as the code for that principal. While that is one way to install a canister on the IC, it is not the only way.

To provide further control over the installation of actor classes, Motoko endows each imported actor class with an extra, secondary constructor, for use on the Internet Computer. This constructor takes an additional first argument that tailors the installation. The constructor is only available via special syntax that stresses its system functionality.

Given some actor class constructor:

Lib.<id> : (U1, ...​, Un) -> async T

Its secondary constructor is accessed as (system Lib.<id>) with typing:

(system Lib.<id>) :  { #new : CanisterSettings;    #install : Principal;    #reinstall : actor {} ;    #upgrade : actor {} }  ->    (U1, ...​, Un) -> async T

where

  type CanisterSettings = {     settings : ?{        controllers : ?[Principal];        compute_allocation : ?Nat;        memory_allocation : ?Nat;        freezing_threshold : ?Nat;     }  }

Calling (system Lib.<id>)(<exp>)(<exp1>, ...​, <expn>) uses the first argument <exp>, a variant value, to control the installation of the canister further. Arguments (<exp1>, ..., <expn>) are just the user-declared constructor arguments of types U1, ..., Un that would also be passed to the primary constructor.

If <exp> is

• #new s, where s has type CanisterSettings: the call creates a fresh Internet Computer principal p, with settings s, and installs the instance to principal p.
• #install p, where p has type Principal, the call installs the actor to an already created Internet Computer principal p. The principal must be empty (have no previously installed code) or the call will return an error.
• #upgrade a, where a has type (or supertype) actor {}, the call installs the instance as an upgrade of actor a, using its current stable storage to initialize stable variables and stable memory of the new instance.
• #reinstall a, where a has type (or supertype) actor {}, reinstalls the instance over the existing actor a, discarding its stable variables and stable memory.
note

On the Internet Computer, calling the primary constructor Lib.<id> is equivalent to calling the secondary constructor (system Lib.<id>) with argument (#new {settings = null}) (i.e. using default settings).

note

On the Internet Computer, calls to Lib.<id> and (system Lib.<id>)(#new ...) must be provisioned with enough cycles for the creation of a new principal. Other call variants will use the cycles of the already allocated principal or actor.

danger

The use of #upgrade a may be unsafe. Motoko will currently not verify that the upgrade is compatible with the code currently installed at a. (A future extension may verify compatibilty with a dynamic check.)

The use of #reinstall a may be unsafe. Motoko cannot verify that the reinstall is compatible with the code currently installed in actor a (even with a dynamic check). A change in interface may break any existing clients of a. The current state of a will be lost.

### Imports and Urls​

An import import <pat> =? <url> declares a pattern <pat> bound to the contents of the text literal <url>.

<url> is a text literal that designates some resource: a local library specified with a relative path, a named module from a named package, or an external canister, referenced either by numeric canister id or by a named alias, and imported as a Motoko actor.

In detail, if <url> is of the form:

• "<filepath>" then <pat> is bound to the library module defined in file <filepath>.mo. <filepath> is interpreted relative to the absolute location of the enclosing file. Note the .mo extension is implicit and should not be included in <url>. For example, import U "lib/Util" defines U to reference the module in local file ./lib/Util.

• "mo:<package-name>/<path>" then <pat> is bound to the library module defined in file <package-path>/<path>.mo in directory <package-path> referenced by package alias <package-name>. The mapping from <package-name> to <package-path> is determined by a compiler command-line argument --package <package-name> <package-path>. For example, import L "mo:base/List" defines L to reference the List library in package alias base.

• "ic:<canisterid>" then <pat> is bound to a Motoko actor whose Motoko type is determined by the canister’s IDL interface. The IDL interface of canister <canisterid> must be found in file <actorpath>/<canisterid>.did. The compiler assumes that <actorpath> is specified by command line argument --actor-idl <actorpath> and that file <actorpath>/<canisterid>.did exists. For example, import C "ic:lg264-qjkae" defines C to reference the actor with canister id lg264-qjkae and IDL file lg264-qjkae.did.

• "canister:<name>" is a symbolic reference to canister alias <name>. The compiler assumes that the mapping of <name> to <canisterid> is specified by command line argument --actor-alias <name> ic:<canisterid>. If so, "canister:<name>" is equivalent to "ic:<cansterid>" (see above). For example, import C "canister:counter" defines C to reference the actor otherwise known as counter.

The case sensitivity of file references depends on the host operating system so it is recommended not to distinguish resources by filename casing alone.

(Remark: when building multi-canister projects with the DFINITY Canister SDK, Motoko programs can typically import canisters by alias (e.g. import C "canister:counter"), without specifying low-level canister ids (e.g. import C "ic:lg264-qjkae"). The SDK tooling takes care of supplying the appropriate command-line arguments to the Motoko compiler.)

(Remark: sensible choices for <pat> are identifiers, such as Array, or object patterns like { cons; nil = empty }, which allow selective importing of individual fields, under original or other names.)

### Declaration fields​

A declaration field <vis>? <stab>? <dec> defines zero or more fields of an actor or object, according to the set of variables defined by <dec>.

Any identifier bound by a public declaration appears in the type of enclosing object, module or actor and is accessible via the dot notation.

An identifier bound by a private or system declaration is excluded from the type of the enclosing object, module or actor and thus inaccessible.

The declaration field has type T provided:

• <dec> has type T;

• if <stab>? is stable then T must be a stable type (see Stability).

(Actor fields declared flexible (implicitly or explicitly) can have any type, but will not be preserved across upgrades.)

Sequences of declaration fields are evaluated in order by evaluating their constituent declarations, with the following exception:

During an upgrade only, the value of a stable declaration is obtained as follows:

• if the stable declaration was previously declared stable in the retired actor, its initial value is inherited from the retired actor.

• if the stable declaration was not declared stable in the retired actor, and is thus new, its value is obtained by evaluating <dec>.

For an upgrade to be safe:

• every stable identifier declared with type T in the retired actor and declared stable and of type U in the replacement actor, must satisfy T <: U.

This condition ensures that every stable variable is either fresh, requiring initialization, or its value can be safely inherited from the retired actor. Note that stable variables may be removed across upgrades, or may simply be deprecated by an upgrade to type Any.

#### System fields​

The declaration <dec> of a system field must be a manifest func declaration with one of the following names and types:

nametypedescription
heartbeat() -> async ()heartbeat action
inspect{ caller : Principal; msg : <Variant>; arg : Blob } -> Boolmessage predicate
preupgrade() -> ()pre upgrade action
postupgrade() -> ()post upgrade action
• heartbeat, when declared, is called on every Internet Computer subnet heartbeat, scheduling an asynchronous call to the heartbeat function. Due to its async return type, a heartbeat function may send messages and await results. The result of a heartbeat call, including any trap or thrown error, is ignored. The implicit context switch means that the time the heartbeat body is executed may be later than the time the heartbeat was issued by the subnet.

• inspect, when declared, is called as a predicate on every Internet Computer ingress message (with the exception of HTTP query calls). The return value, a Bool, indicates whether to accept or decline the given message. The argument type depends on the interface of the enclosing actor (see Inspect).

• preupgrade, when declared, is called during an upgrade, immediately before the (current) values of the (retired) actor’s stable variables are transferred to the replacement actor.

• postupgrade, when declared, is called during an upgrade, immediately after the (replacement) actor body has initialized its fields (inheriting values of the retired actors' stable variables), and before its first message is processed.

These preupgrade and postupgrade system methods provide the opportunity to save and restore in-flight data structures (e.g. caches) that are better represented using non-stable types.

During an upgrade, a trap occurring in the implicit call to preupgrade() or postupgrade() causes the entire upgrade to trap, preserving the pre-upgrade actor.

##### inspect​

Given a record of message attributes, this function produces a Bool that indicates whether to accept or decline the message by returning true or false. The function is invoked (by the system) on each ingress message (excluding non-replicated queries). Similar to a query, any side-effects of an invocation are transient and discarded. A call that traps due to some fault has the same result as returning false (message denial).

The argument type of inspect depends on the interface of the enclosing actor. In particular, the formal argument of inspect is a record of fields of the following types:

• caller : Principal: the principal, possibly anonymous, of the caller of the message;

• arg : Blob: the raw, binary content of the message argument;

• msg : <variant>: a variant of decoding functions, where <variant> == {…​; #<id>: () → T; …​} contains one variant per shared function, <id>, of the actor. The variant’s tag identifies the function to be called; The variant’s argument is a function that, when applied, returns the (decoded) argument of the call as a value of type T.

Using a variant, tagged with #<id>, allows the return type, T, of the decoding function to vary with the argument type (also T) of the shared function <id>.

The variant’s argument is a function so that one can avoid the expense of message decoding (when appropriate).

danger

An actor that fails to declare system field inspect will simply accept all ingress messages.

### Sequence of declarations​

A sequence of declarations <dec>;* occurring in a block, a program or embedded in the <dec-field>;* sequence of an object body has type T provided:

• <dec>;* is empty and T == (); or

• <dec>;* is non-empty and:

• all value identifiers bound by <dec>;* are distinct, and

• all type identifiers bound by <dec>;* are distinct, and

• under the assumption that each value identifier <id> in <dec>;* has type var_id? Tid, and assuming the type definitions in <dec>;*:

• each declaration in <dec>;* is well-typed, and

• each value identifier <id> in bindings produced by <dec>;* has type var_id? Tid, and

• all but the last <dec> in <dec>;* of the form <exp> has type ();

• the last declaration in <dec>;* has type T.

Declarations in <dec>;* are evaluated sequentially. The first declaration that traps causes the entire sequence to trap. Otherwise, the result of the declaration is the value of the last declaration in <dec>;*. In addition, the set of value bindings defined by <dec>;* is the union of the bindings introduced by each declaration in <dec>;*.

It is a compile-time error if any declaration in <dec>;* might require the value of an identifier declared in <dec>;* before that identifier’s declaration has been evaluated. Such use-before-define errors are detected by a simple, conservative static analysis not described here.

### Patterns​

Patterns bind function parameters, declare identifiers and decompose values into their constituent parts in the cases of a switch expression.

Matching a pattern against a value may succeed, binding the corresponding identifiers in the pattern to their matching values, or fail. Thus the result of a match is either a successful binding, mapping identifiers of the pattern to values, or failure.

The consequences of pattern match failure depends on the context of the pattern.

• In a function application or let-binding, failure to match the formal argument pattern or let-pattern causes a trap.

• In a case branch of a switch expression, failure to match that case’s pattern continues with an attempt to match the next case of the switch, trapping only when no such case remains.

### Wildcard pattern​

The wildcard pattern _ matches a single value without binding its contents to an identifier.

### Identifier pattern​

The identifier pattern <id> matches a single value and binds it to the identifier <id>.

### Literal pattern​

The literal pattern <unop>? <lit> matches a single value against the constant value of literal <lit> and fails if they are not (structurally) equal values.

For integer literals only, the optional <unop> determines the sign of the value to match.

### Tuple pattern​

The tuple pattern ( <pat>,* ) matches a n-tuple value against an n-tuple of patterns (both the tuple and pattern must have the same number of items). The set of identifiers bound by each component of the tuple pattern must be distinct.

The empty tuple pattern () is called the unit pattern.

Pattern matching fails if one of the patterns fails to match the corresponding item of the tuple value. Pattern matching succeeds if every pattern matches the corresponding component of the tuple value. The binding returned by a successful match is the disjoint union of the bindings returned by the component matches.

### Object pattern​

The object pattern { <pat-field>;* } matches an object value, a collection of named field values, against a sequence of named pattern fields. The set of identifiers bound by each field of the object pattern must be distinct. The names of the pattern fields in the object pattern must be distinct.

Object patterns support punning for concision. A punned field <id> is shorthand for <id> = <id>; Similarly, a typed, punned field <id> : <typ> is short-hand for <id> = <id> : <typ>. Both bind the matched value of the field named <id> to the identifier <id>.

Pattern matching fails if one of the pattern fields fails to match the corresponding field value of the object value. Pattern matching succeeds if every pattern field matches the corresponding named field of the object value. The binding returned by a successful match is the union of the bindings returned by the field matches.

The <sort> of the matched object type must be determined by an enclosing type annotation or other contextual type information.

### Variant pattern​

The variant pattern # <id> <pat>? matches a variant value (of the form # <id'> v) against a variant pattern. An absent <pat>? is shorthand for the unit pattern (()). Pattern matching fails if the tag <id'> of the value is distinct from the tag <id> of the pattern (i.e. <id> \<> <id'>); or the tags are equal but the value v does not match the pattern <pat>?. Pattern matching succeeds if the tag of the value is <id> (i.e. <id'> = <id>) and the value v matches the pattern <pat>?. The binding returned by a successful match is just the binding returned by the match of v against <pat>?.

### Annotated pattern​

The annotated pattern <pat> : <typ> matches value of v type <typ> against the pattern <pat>.

<pat> : <typ> is not a dynamic type test, but is used to constrain the types of identifiers bound in <pat>, e.g. in the argument pattern to a function.

### Option pattern​

The option ? <pat> matches a value of option type ? <typ>.

The match fails if the value is null. If the value is ? v, for some value v, then the result of matching ? <pat> is the result of matching v against <pat>.

Conversely, the null literal pattern may be used to test whether a value of option type is the value null and not ? v for some v.

### Or pattern​

The or pattern <pat1> or <pat2> is a disjunctive pattern.

The result of matching <pat1> or <pat2> against a value is the result of matching <pat1>, if it succeeds, or the result of matching <pat2>, if the first match fails.

(Note, statically, neither <pat1> nor <pat2> may contain identifier (<id>) patterns so a successful match always binds zero identifiers.)

### Expression declaration​

The declaration <exp> has type T provided the expression <exp> has type T . It declares no bindings.

The declaration <exp> evaluates to the result of evaluating <exp> (typically for <exp>'s side-effect).

Note that if <exp> appears within a sequence of declarations, but not as the last declaration of that sequence, then T must be ().

### Let declaration​

The let declaration let <pat> = <exp> has type T and declares the bindings in <pat> provided:

• <exp> has type T.

• <pat> has type T.

The declaration let <pat> = <exp> evaluates <exp> to a result r. If r is trap, the declaration evaluates to trap. If r is a value v then evaluation proceeds by matching the value v against <pat>. If matching fails, then the result is trap. Otherwise, the result is v and the binding of all identifiers in <pat> to their matching values in v.

All bindings declared by a let (if any) are immutable.

### Var declaration​

The variable declaration var <id> (: <typ>)? = <exp> declares a mutable variable <id> with initial value <exp>. The variable’s value can be updated by assignment.

The declaration var <id> has type () provided:

• <exp> has type T; and

• If the annotation (:<typ>)? is present, then T == <typ>.

Within the scope of the declaration, <id> has type var T (see Assignment).

Evaluation of var <id> (: <typ>)? = <exp> proceeds by evaluating <exp> to a result r. If r is trap, the declaration evaluates to trap. Otherwise, the r is some value v that determines the initial value of mutable variable <id>. The result of the declaration is () and <id> is bound to a fresh location that contains v.

### Type declaration​

The declaration type <id> <typ-params>? = <typ> declares a new type constructor <id>, with optional type parameters <typ-params> and definition <typ>.

The declaration type C< X0 <: T0, …​, Xn <: Tn > = U is well-formed provided:

• type parameters X0, …​, Xn are distinct, and

• assuming the constraints X0 <: T0, …​, Xn <: Tn:

• constraints T0, …​, Tn are well-formed.

• definition U is well-formed.

• it is productive (see Productivity).

• it is non-expansive (see Expansiveness).

In scope of the declaration type C< X0<:T0, …​, Xn <: Tn > = U, any well-formed type C< U0, …​, Un > is equivalent to its expansion U [ U0/X0, …​, Un/Xn ]. Distinct type expressions that expand to identical types are inter-changeable, regardless of any distinction between type constructor names. In short, the equivalence between types is structural, not nominal.

#### Productivity​

A type is productive if recursively expanding any outermost type constructor in its definition eventually produces a type other than the application of a type constructor.

Motoko requires all type declarations to be productive.

For example, the type definitions:

  type Person = { first : Text; last : Text };  type List<T> = ?(T, List<T>);  type Fst<T, U> = T;  type Ok<T> = Fst<Any, Ok<T>>;

are all productive and legal.

But the type definitions,

  type C = C;  type D<T, U> = D<U, T>;  type E<T> = F<T>;  type F<T> = E<T>;  type G<T> = Fst<G<T>, Any>;

are all non-productive, since each definition will enter a loop after one or more expansions of its body.

#### Expansiveness​

A set of mutually recursive type or class declarations will be rejected if the set is expansive.

Expansiveness is a syntactic criterion. To determine whether a set of singly or mutually recursive type definitions, say

  type C<...,Xi,...> = T;  ...  type D<...,Yj,...> = U;

is expansive, construct a directed graph whose vertices are the formal type parameters (identified by position), C#i, with the following {0,1}-labeled edges:

• For each occurrence of parameter C#i as immediate, j-th argument to type D<…​,C#i,…​>, add a non-expansive, 0-labeled edge,C#i -0-> D#j.

• For each occurrence of parameter C#i as a proper sub-expression of the j-th argument to type D<…​,T[C#i],..> add an expansive 1-labeled edge, C#i -1-> D#j.

The graph is expansive if, and only if, it contains a cycle with at least one expansive edge.

For example, the type definition:

  type List<T> = ?(T, List<T>);

that recursively instantiates List at the same parameter T, is non-expansive and accepted, but the similar looking definition:

  type Seq<T> = ?(T, Seq<[T]>);

that recursively instantiates Seq with a larger type, [T], containing T, is expansive and rejected.

• Type List<T> is non-expansive because its graph, { List#0 -0-> List#0 }, though cyclic, has no expansive edge.

• Type Seq<T>, on the other hand, is expansive, because its graph, { Seq#0 -1-> Seq#0 }, has a cycle that includes an expansive edge.

### Object declaration​

Declaration <sort> <id>? <obj-body>, where <obj_body> is of the form =? { <dec-field>;* }, declares an object with optional identifier <id> and zero or more fields <dec-field>;*. Fields can be declared with public or private visibility; if the visibility is omitted, it defaults to private.

The qualifier <sort> (one of actor, module or object) specifies the sort of the object’s type. The sort imposes restrictions on the types of the public object fields.

Let T = <sort> { [var0] id0 : T0, …​ , [varn] idn : T0 } denote the type of the object. Let <dec>;* be the sequence of declarations embedded in <dec-field>;*. The object declaration has type T provided that:

1. type T is well-formed for sort sort, and

2. under the assumption that <id> : T,

• the sequence of declarations <dec>;* has type Any and declares the disjoint sets of private and public identifiers, Id_private and Id_public respectively, with types T(id) for id in Id == Id_private union Id_public, and

• { id0, …​, idn } == Id_public, and

• for all i in 0 <= i <= n, [vari] Ti == T(idi).

3. If <sort> is module, then the declarations in <dec>;* must be static (see Static declarations).

Note that requirement 1. imposes further constraints on the field types of T. In particular, if the sort is actor then:

• all public fields must be non-var (immutable) shared functions (the public interface of an actor can only provide asynchronous messaging via shared functions);

Because actor construction is asynchronous, an actor declaration can only occur in an asynchronous context (i.e. in the body of a (non-query) shared function or async expression).

Evaluation of <sort>? <id>? =? { <dec-field>;* } proceeds by binding <id> (if present), to the eventual value v, and evaluating the declarations in <dec>;*. If the evaluation of <dec>;* traps, so does the object declaration. Otherwise, <dec>;* produces a set of bindings for identifiers in Id. let v0, …​, vn be the values or locations bound to identifiers <id0>, …​, <idn>. The result of the object declaration is the object v == sort { <id0> = v1, …​, <idn> = vn}.

If <id>? is present, the declaration binds <id> to v. Otherwise, it produces the empty set of bindings.

danger

Actor declaration is (implicitly) asynchronous and the state of the enclosing actor may change due to concurrent processing of other incoming actor messages. It is the programmer’s responsibility to guard against non-synchronized state changes.

#### Static declarations​

A declaration is static if it is:

• a type declaration, or

• a class declaration, or

• a let declaration with a static pattern and a static expression, or

• a module, function or object declaration that desugars to a static let declaration, or

• a static expression.

An expression is static if it is:

• a literal expression, or

• a tuple of static expressions, or

• an object of static expressions, or

• a variant or option with a static expression, or

• an immutable array, or

• field access and projection from a static expression, or

• a module expression, or

• a function expression, or

• a static declaration, or

• an ignore of a static expression, or

• a block, all of whose declarations are static, or

• a type annotation with a static expression.

A pattern is static if it is:

• an identifier, or

• a wildcard, or

• a tuple of static patterns, or

• type annotation with a static pattern.

Static phrases are designed to be side-effect free, allowing the coalescing of duplicate library imports (a.k.a deduplication).

### Function declaration​

The function declaration <shared-pat>? func <id>? <typ-params>? <pat> (: <typ>)? =? <exp> is syntactic sugar for a named let or anonymous declaration of a function expression.

That is, when <id>? is present and the function is named:

<shared-pat>? func <id> <typ-params>? <pat> (: <typ>)? =? <block-or-exp> :=  let <id> = <shared-pat>? func <typ-params>? <pat> (: <typ>)? =? <block-or-exp>

But when <id>? is absent and the function is anonymous:

<shared-pat>? func <typ-params>? <pat> (: <typ>)? =? <block-or-exp> :=  <shared-pat>? func <typ-params>? <pat> (: <typ>)? =? <block-or-exp>

Named function definitions support recursion (a named function can call itself).

note

In compiled code, shared functions can only appear as public actor fields.

### Class declaration​

The class declaration <shared-pat>? <sort>? class <id>? <typ-params>? <pat> (: <typ>)? <class-body> is sugar for pair of a type and function declaration:

<shared-pat>? <sort>? class <id> <typ-params>? <pat> (: <typ>)? <class-body> :=  type <id> <typ-params> = <sort> { <typ-field>;* };  <shared-pat>? func <id> <typ-params>? <pat> : async? <id> <typ-args> =    async? <sort> <id_this>? <obj-body>

where:

• <shared-pat>?, when present, requires <sort> == actor, and provides access to the caller of an actor constructor, and

• <typ-args>? is the sequence of type identifiers bound by <typ-params>? (if any), and

• <typ-field>;* is the set of public field types inferred from <dec-field>;*.

• <obj-body> is the object body of <class-body>.

• <id_this>? is the optional this (a.k.a self), parameter of <class-body>.

• async? is present, if only if, <sort> == actor.

Note <shared-pat>? must not be of the form shared query <pat>?: a constructor, unlike a function, cannot be a query.

An absent <shared-pat>? defaults to shared when sort = actor.

If sort is actor, then:

• <typ-args>? must be absent or empty (actor classes cannot have type parameters);

• <pat>'s type must be shared (see Sharability).

• (: <typ>)?, if present, must be of the form : async T for some actor type T (actor instantiation is asynchronous).

If (: <typ>) is present, then the type <async?> <sort> { <typ_field>;* } must be a subtype of the annotation <typ>. In particular, the annotation is used only to check, but not affect, the inferred type of function <id>.

The class declaration has the same type as function <id> and evaluates to the function value <id>.

### Identifiers​

The identifier expression <id> has type T provided <id> is in scope, defined and declared with explicit or inferred type T.

The expression <id> evaluates to the value bound to <id> in the current evaluation environment.

### Literals​

A literal has type T only when its value is within the prescribed range of values of type T.

The literal (or constant) expression <lit> evaluates to itself.

### Unary operators​

The unary operator <unop> <exp> has type T provided:

• <exp> has type T, and

• The category of <unop> is a category of T.

The unary operator expression <unop> <exp> evaluates <exp> to a result. If the result is a value v, it returns the result of <unop> v. If the result is trap, the entire expression results in trap.

### Binary operators​

The binary operator expression <exp1> <binop> <exp2> has type T provided:

• <exp1> has type T, and

• <exp2> has type T, and

• The category of <binop> is a category of T.

The binary operator expression <exp1> <binop> <exp2> evaluates exp1 to a result r1. If r1 is trap, the expression results in trap.

Otherwise, exp2 is evaluated to a result r2. If r2 is trap, the expression results in trap.

Otherwise, r1 and r2 are values v1 and v2 and the expression returns the result of v1 <binop> v2.

### Relational operators​

The relational expression <exp1> <relop> <exp2> has type Bool provided:

• <exp1> has type T, and

• <exp2> has type T, and

• <relop> is equality == or inequality !=, T is shared, and T is the least type such that <exp1> and <exp2> have type T;

• the category O (Ordered) is a category of T and <relop>; or

The binary operator expression <exp1> <relop> <exp2> evaluates <exp1> to a result r1. If r1 is trap, the expression results in trap.

Otherwise, exp2 is evaluated to a result r2. If r2 is trap, the expression results in trap.

Otherwise, r1 and r2 are values v1 and v2 and the expression returns the Boolean result of v1 <relop> v2.

For equality and inequality, the meaning of v1 <relop> v2 depends on the compile-time, static choice of T (not the run-time types of v1 and v2, which, due to subtyping, may be more precise).

### Tuples​

Tuple expression (<exp1>, …​, <expn>) has tuple type (T1, …​, Tn), provided <exp1>, …​, <expn> have types T1, …​, Tn.

The tuple expression (<exp1>, …​, <expn>) evaluates the expressions exp1 …​ expn in order, trapping as soon as some expression <expi> traps. If no evaluation traps and exp1, …​, <expn> evaluate to values v1,…​,vn then the tuple expression returns the tuple value (v1, …​ , vn).

The tuple projection <exp> . <nat> has type Ti provided <exp> has tuple type (T1, …​, Ti, …​, Tn), <nat> == i and 1 <= i <= n.

The projection <exp> . <nat> evaluates <exp> to a result r. If r is trap, then the result is trap. Otherwise, r must be a tuple (v1,…​,vi,…​,vn) and the result of the projection is the value vi.

The empty tuple expression () is called the unit value.

### Option expressions​

The option expression ? <exp> has type ? T provided <exp> has type T.

The literal null has type Null. Since Null <: ? T for any T, literal null also has type ? T and signifies the "missing" value at type ? T.

### Variant injection​

The variant injection # <id> <exp> has variant type {# id T} provided:

• <exp> has type T.

The variant injection # <id> is just syntactic sugar for # <id> ().

The variant injection # <id> <exp> evaluates <exp> to a result r. If r is trap, then the result is trap. Otherwise, r must be a value v and the result of the injection is the tagged value # <id> v.

The tag and contents of a variant value can be tested and accessed using a variant pattern.

### Objects​

Objects can be written in literal form { <exp-field>;* }, consisting of a list of expression fields:

<exp-field> ::=                                object expression fields  var? <id> (: <typ>) = <exp>                    field  var? <id> (: <typ>)                            punned field

Such an object literal, sometimes called a record, is equivalent to the object declaration object { <dec-field>;* } where the declaration fields are obtained from the expression fields by prefixing each of them with public let, or just public in case of var fields. However, unlike declarations, the field list does not bind each <id> as a local name within the literal, i.e., the field names are not in scope in the field expressions.

Object expressions support punning for concision. A punned field <id> is shorthand for <id> = <id>; Similarly, a typed, punned field <id> : <typ> is short-hand for <id> = <id> : <typ>. Both associate the field named <id> with the value of the identifier <id>.

### Object combination/extension​

Objects can be combined and/or extended using the and and with keywords.

A record expression { <exp> (and <exp>)* (with <exp-field>;+)? } merges the objects (or modules) specified as base expressions, and augments the result to also contain the specified fields. The with <exp-field>;+ clause can be omitted when at least two bases appear and none have common field labels. Thus the field list serves to:

• disambiguate field labels occurring more than once in the bases,
• define new fields,
• override existing fields and their types, and
• add new var fields
• redefine existing var fields from some base to prevent aliasing.

The resulting type is determined by the bases' (and explicitly given fields') static type.

Any var field from some base must be overwritten in the explicit field list. This prevents introducing aliases of var fields.

The record expression { <exp1> and ... <expn> with <exp-field1>; ... <exp_fieldn>; } has type T provided:

• The record { <exp-field1>; ... <exp_fieldm>; } has record type { field_tys } == { var? <id1> : U1; ... var? <idm> : Um }.

• Let newfields == { <id1> , ..., <idm> } be the set of new field names.

• Considering value fields:

• Base expression <expi> has object or module type sorti { field_tysi } == sorti { var? <idi1> : Ti1, …​, var? <idik> : Tik } where sorti <> Actor.

Let fields(i) == { <idi1>, ..., <idik> } be the set of static field names of base i. Then

• fields(i) is disjoint from newfields (possibly by applying subtyping to the type of <expi>);
• no field in field_tysi is a var field;
• fields(i) is disjoint from fields(j) for j < i.
• Considering type fields:

• Base expression <expi> has object or module type sorti { typ_fieldsi } == sorti { type <idj1> = … , …, type <idik> = … } where sorti <> Actor.
• typ_fieldsi agrees with typ_fieldsj for j < i.
• T is { typ_fieldsi fields_tys1 ... typ_fieldsm fields_tysm field_tys }.

Here, two sequences of type fields agree only when any two type fields of the same name in each sequence have equivalent definitions.

The record expression { <exp1> and ... <expn> with <exp-field1>; ... <exp_fieldm>; } evaluates records <exp1> through <expn> and { exp-field1; ... <exp_fieldm } to results r1 through rn and r, trapping on the first result that is a trap. If none of the expressions produces a trap, the results are objects sort1 { f1 }, sortn { fn } and object { f }, where f1 ... fn and f are maps from identifiers to values or mutable locations.

The result of the entire expression is the value object { g } where g is the partial map with domain fields(1) union fields(n) union newfields mapping identifiers to unique values or locations such that g(<id>) = fi(<id>) if <id> is in fields(i), for some i, or f(<id>) if <id> is in newfields.

### Object projection (member access)​

The object projection <exp> . <id> has type var? T provided <exp> has object type sort { var1? <id1> : T1, …​, var? <id> : T, …​, var? <idn> : Tn } for some sort sort.

The object projection <exp> . <id> evaluates <exp> to a result r. If r is trap, then the result is trap. Otherwise, r must be an object value { <id1> = v1,…​, id = v, …​, <idm> = vm } and the result of the projection is the value w obtained from value or location v in field id.

If var is absent from var? T then the value w is just the value v of immutable field <id>, otherwise:

• if the projection occurs as the target of an assignment expression then w is just v, the mutable location in field <id>.

• otherwise, w (of type T) is the value currently stored at the mutable location v in field <id>.

### Special member access​

The iterator access <exp> . <id> has type T provided <exp> has type U, and U,<id> and T are related by a row of the following table:

U<id>TDescription
TextsizeNatsize (or length) in characters
Textchars{ next: () -> Char? }character iterator, first to last
BlobsizeNatsize in bytes
Blobvals{ next: () -> Nat8? }byte iterator, first to last
[var? T]sizeNatnumber of elements
[var? T]getNat -> Tindexed read function
[var? T]keys{ next: () -> Nat? }index iterator, by ascending index
[var? T]vals{ next: () -> T? }value iterator, by ascending index
[var T]put(Nat, T) -> ()indexed write function (mutable arrays only)

The projection <exp> . <id> evaluates <exp> to a result r. If r is trap, then the result is trap. Otherwise, r must be a value of type U and the result of the projection is a value of type T whose semantics is given by the Description column of the previous table.

note

the chars, vals, keys and vals members produce stateful iterator objects than can be consumed by for expressions (see For).

### Assignment​

The assignment <exp1> := <exp2> has type () provided:

• <exp1> has type var T, and

• <exp2> has type T.

The assignment expression <exp1> := <exp2> evaluates <exp1> to a result r1. If r1 is trap, the expression results in trap.

Otherwise, exp2 is evaluated to a result r2. If r2 is trap, the expression results in trap.

Otherwise r1 and r2 are (respectively) a location v1 (a mutable identifier, an item of a mutable array or a mutable field of an object) and a value v2. The expression updates the current value stored in v1 with the new value v2 and returns the empty tuple ().

### Unary compound assignment​

The unary compound assignment <unop>= <exp> has type () provided:

• <exp> has type var T, and

• <unop>'s category is a category of T.

The unary compound assignment <unop>= <exp> evaluates <exp> to a result r. If r is trap the evaluation traps, otherwise r is a location storing value v and r is updated to contain the value <unop> v.

### Binary compound assignment​

The binary compound assignment <exp1> <binop>= <exp2> has type () provided:

• <exp1> has type var T, and

• <exp2> has type T, and

• <binop>'s category is a category of T.

For binary operator <binop>, the compound assignment expression <exp1> <binop>= <exp2> evaluates <exp1> to a result r1. If r1 is trap, the expression results in trap. Otherwise, exp2 is evaluated to a result r2. If r2 is trap, the expression results in trap.

Otherwise r1 and r2 are (respectively) a location v1 (a mutable identifier, an item of a mutable array or a mutable field of object) and a value v2. The expression updates the current value, w stored in v1 with the new value w <binop> v2 and returns the empty tuple ().

### Arrays​

The expression [ var? <exp>,* ] has type [var? T] provided each expression <exp> in the sequence <exp>,* has type T.

The array expression [ var <exp0>, …​, <expn> ] evaluates the expressions exp0 …​ expn in order, trapping as soon as some expression <expi> traps. If no evaluation traps and exp0, …​, <expn> evaluate to values v0,…​,vn then the array expression returns the array value [var? v0, …​ , vn] (of size n+1).

### Array indexing​

The array indexing expression <exp1> [ <exp2> ] has type var? T provided:

• <exp> has (mutable or immutable) array type [var? T1].

The expression <exp1> [ <exp2> ] evaluates exp1 to a result r1. If r1 is trap, then the result is trap.

Otherwise, exp2 is evaluated to a result r2. If r2 is trap, the expression results in trap.

Otherwise, r1 is an array value, var? [v0, …​, vn], and r2 is a natural integer i. If i > n the index expression returns trap.

Otherwise, the index expression returns the value v, obtained as follows:

If var is absent from var? T then the value v is the constant value vi.

Otherwise,

• if the indexing occurs as the target of an assignment expression then v is the i-th mutable location in the array;

• otherwise, v is vi, the value currently stored in the i-th location of the array.

### Function calls​

The function call expression <exp1> <T0,…​,Tn>? <exp2> has type T provided:

• the function <exp1> has function type <shared>? < X0 <: V0, ..., Xn <: Vn > U1-> U2; and

• if <T0,…​,Tn>? is absent but n > 0 then there exists minimal T0, …​, Tn (inferred by the compiler) such that:

• each type argument satisfies the corresponding type parameter’s bounds: for each 1 <= i <= n, Ti <: [T0/X0, …​, Tn/Xn]Vi; and

• the argument <exp2> has type [T0/X0, …​, Tn/Xn]U1, and

• T == [T0/X0, …​, Tn/Xn]U2.

The call expression <exp1> <T0,…​,Tn>? <exp2> evaluates exp1 to a result r1. If r1 is trap, then the result is trap.

Otherwise, exp2 is evaluated to a result r2. If r2 is trap, the expression results in trap.

Otherwise, r1 is a function value, <shared-pat>? func <X0 <: V0, …​, n <: Vn> <pat1> { <exp> } (for some implicit environment), and r2 is a value v2. If <shared-pat> is present and of the form shared query? <pat> then evaluation continues by matching the record value {caller = p} against <pat>, where p is the Principal invoking the function (typically a user or canister). Matching continues by matching v1 against <pat1>. If pattern matching succeeds with some bindings, then evaluation returns the result of <exp> in the environment of the function value (not shown) extended with those bindings. Otherwise, some pattern match has failed and the call results in trap.

note

The exhaustiveness side condition on shared function expressions ensures that argument pattern matching cannot fail (see Functions).

### Functions​

The function expression <shared-pat>? func < X0 <: T0, …​, Xn <: Tn > <pat1> (: U2)? =? <block-or-exp> has type <shared>? < X0 <: T0, ..., Xn <: Tn > U1-> U2 if, under the assumption that X0 <: T0, …​, Xn <: Tn:

• <shared-pat>? is of the form shared query? <pat> if and only if <shared>? is shared query? (the query modifiers must agree);

• all the types in T0, …​, Tn and U2 are well-formed and well-constrained;

• pattern <pat> has context type { caller : Principal };

• pattern <pat1> has type U1;

• if the function is shared then <pat> and <pat1> must be exhaustive;

• expression <block-or-exp> has type return type U2 under the assumption that <pat1> has type U1.

<shared-pat>? func <typ-params>? <pat1> (: <typ>)? =? <block-or-exp> evaluates to a function value (a.k.a. closure), denoted <shared-pat>? func <typ-params>? <pat1> = <exp>, that stores the code of the function together with the bindings from the current evaluation environment (not shown) needed to evaluate calls to the function value.

Note that a <shared-pat> function may itself be shared <pat> or shared query <pat>:

• A shared <pat> function may be invoked from a remote caller. Unless causing a trap, the effects on the callee persist beyond completion of the call.

• A shared query <pat> function may be also be invoked from a remote caller, but the effects on the callee are transient and discarded once the call has completed with a result (whether a value or error).

In either case, <pat> provides access to a context value identifying the caller of the shared (query) function.

note

The context type is a record to allow extension with further fields in future releases.

### Blocks​

The block expression { <dec>;* } has type T provided the last declaration in the sequence <dec>;* has type T. All identifiers declared in block must be distinct type identifiers or distinct value identifiers and are in scope in the definition of all other declarations in the block.

The bindings of identifiers declared in { dec;* } are local to the block.

The type system ensures that a value identifier cannot be evaluated before its declaration has been evaluated, precluding run-time errors at the cost of rejection some well-behaved programs.

Identifiers whose types cannot be inferred from their declaration, but are used in a forward reference, may require an additional type annotation (see Annotated pattern) to satisfy the type checker.

The block expression { <dec>;* } evaluates each declaration in <dec>;* in sequence (program order). The first declaration in <dec>;* that results in a trap causes the block to result in trap, without evaluating subsequent declarations.

### Do​

The do expression do <block> allows the use of a block as an expression, in positions where the syntax would not directly allow a block.

The expression do <block> has type T provided <block> has type T.

The do expression evaluates by evaluating <block> and returning its result.

### Option block​

The option block do ? <block> introduces scoped handling of null values.

The expression do ? <block> has type ?T provided <block> has type T.

The do ? <block> expression evaluates <block> and returns its result as an optional value.

Within <block> the null break expression <exp1> ! exits the nearest enclosing do ? block with value null whenever <exp1> has value null, or continues evaluation with the contents of <exp1>'s option value. (See Null break.)

Option blocks nest with the target of a null break determined by the nearest enclosing option block.

### Null break​

The null break expression <exp> ! invokes scoped handling of null values and returns the contents of an option value or changes control-flow when the value is null.

It has type T provided:

• the expression appears in the body, <block>, of an enclosing option block of the form do ? <block> (see Option block).

• <exp> has option type ? T.

The expression <exp> ! evaluates <exp> to a result r. If r is trap, then the result is trap; if r is null, execution breaks with value null from the nearest enclosing option block of form do ? <block>; otherwise, r is ? v and execution continues with value v.

### Not​

The not expression not <exp> has type Bool provided <exp> has type Bool.

If <exp> evaluates to trap, the expression returns trap. Otherwise, <exp> evaluates to a Boolean value v and the expression returns not v, (the Boolean negation of v).

### And​

The and expression <exp1> and <exp2> has type Bool provided <exp1> and <exp2> have type Bool.

The expression <exp1> and <exp2> evaluates exp1 to a result r1. If r1 is trap, the expression results in trap. Otherwise r1 is a Boolean value v. If v == false the expression returns the value false (without evaluating <exp2>). Otherwise, the expression returns the result of evaluating <exp2>.

### Or​

The or expression <exp1> or <exp2> has type Bool provided <exp1> and <exp2> have type Bool.

The expression <exp1> and <exp2> evaluates exp1 to a result r1. If r1 is trap, the expression results in trap. Otherwise r1 is a Boolean value v. If v == true the expression returns the value true (without evaluating <exp2>). Otherwise, the expression returns the result of evaluating <exp2>.

### If​

The expression if <exp1> <exp2> (else <exp3>)? has type T provided:

• <exp1> has type Bool

• <exp2> has type T

• <exp3> is absent and () <: T, or

• <exp3> is present and has type T.

The expression evaluates <exp1> to a result r1. If r1 is trap, the result is trap. Otherwise, r1 is the value true or false. If r1 is true, the result is the result of evaluating <exp2>. Otherwise, r1 is false and the result is () (if <exp3> is absent) or the result of <exp3> (if <exp3> is present).

### Switch​

The switch expression switch <exp> { (case <pat> <block-or-exp>;)+ } has type T provided:

• exp has type U; and

• for each case case <pat> <block-or-exp> in the sequence (case <pat> <block-or-exp>;)+ :

• pattern <pat> has type U; and,

• expression <block-or-exp> has type T

The expression evaluates <exp> to a result r. If r is trap, the result is trap. Otherwise, r is some value v. Let case <pat> <block-or-exp>; be the first case in (case <pat> <block-or-exp>;)+ such that <pat> matches v for some binding of identifiers to values. Then result of the switch is the result of evaluating <block-or-exp> under that binding. If no case has a pattern that matches v, the result of the switch is trap.

### While​

The expression while <exp1> <exp2> has type () provided:

• <exp1> has type Bool, and

• <exp2> has type ().

The expression evaluates <exp1> to a result r1. If r1 is trap, the result is trap. Otherwise, r1 is the value true or false. If r1 is true, the result is the result of re-evaluating while <exp1> <exp2>. Otherwise, the result is ().

### Loop​

The expression loop <block-or-exp> has type None provided <block-or-exp> has type ().

The expression evaluates <block-or-exp> to a result r1. If r1 is trap, the result is trap. Otherwise, the result is the result of (re-)evaluating loop <block-or-exp>.

### Loop-while​

The expression loop <block-or-exp1> while <exp2> has type () provided:

• <block-or-exp1> has type (), and

• <exp2> has type Bool.

The expression evaluates <block-or-exp1> to a result r1. If r1 is trap, the result is trap. Otherwise, evaluation continues with <exp2>, producing result r2. If r2 is trap the result is trap. Otherwise, if r2 is true, the result is the result of re-evaluating loop <block-or-exp1> while <exp2>. Otherwise, r2 is false and the result is ().

### For​

The iterator expression for ( <pat> in <exp1> ) <block-or-exp2> has type () provided:

• <exp1> has type { next : () → ?T },

• pattern <pat> has type T, and

• expression <block-or-exp2> has type () (in the environment extended with the bindings of <pat>).

The for-expression is syntactic sugar for

for ( <pat> in <exp1> ) <block-or-exp2> :=  {    let x = <exp1>;    label l loop {      switch (x.next()) {        case (? <pat>) <block-or-exp2>;        case (null) break l;      }    }  }

where x and l are fresh identifiers.

In particular, the for loop will trap if evaluation of <exp1> traps; as soon as x.next() traps, or the value of x.next() does not match pattern <pat>, or when <block-or-exp2> traps.

note

Although general purpose, for loops are commonly used to consume iterators produced by Special member access to, for example, loop over the indices (a.keys()) or values (a.vals()) of some array (here a).

### Label​

The label-expression label <id> (: <typ>)? <block-or-exp> has type T provided:

• (: <typ>)? is absent and T is unit; or (: <typ>)? is present and T == <typ>;

• <block-or-exp> has type T in the static environment extended with label l : T.

The result of evaluating label <id> (: <typ>)? <block-or-exp> is the result of evaluating <block-or-exp>.

### Labeled loops​

If <exp> in label <id> (: <typ>)? <exp> is a looping construct:

• while (exp2) <block-or-exp1>,

• loop <block-or-exp1> (while (<exp2>))?, or

• for (<pat> in <exp2>) <block-or-exp1>

the body, <exp1>, of the loop is implicitly enclosed in label <id_continue> (…​) allowing early continuation of the loop by the evaluation of expression continue <id>.

<id_continue> is fresh identifier that can only be referenced by continue <id> (through its implicit expansion to break <id_continue>).

### Break​

The expression break <id> is equivalent to break <id> ().

The expression break <id> <exp> has type None provided:

• The label <id> is declared with type label <id> : T.

• <exp> has type T.

The evaluation of break <id> <exp> evaluates exp to some result r. If r is trap, the result is trap. If r is a value v, the evaluation abandons the current computation up to dynamically enclosing declaration label <id> …​ using the value v as the result of that labelled expression.

### Continue​

The expression continue <id> is equivalent to break <id_continue>, where <id_continue> is implicitly declared around the bodies of <id>-labelled looping constructs (see Labeled loops).

### Return​

The expression return is equivalent to return ().

The expression return <exp> has type None provided:

• <exp> has type T and

• T is the return type of the nearest enclosing function (with no intervening async expression), or

• async T is the type of the nearest enclosing (perhaps implicit) async expression (with no intervening function declaration)

The return expression exits the corresponding dynamic function invocation or completes the corresponding dynamic async expression with the result of <exp>.

### Async​

The async expression async <block-or-exp> has type async T provided:

• <block-or-exp> has type T;

• T is shared.

Any control-flow label in scope for async <block-or-exp> is not in scope for <block-or-exp>. However, <block-or-exp> may declare and use its own, local, labels.

The implicit return type in <block-or-exp> is T. That is, the return expression, <exp0>, (implicit or explicit) to any enclosed return <exp0>? expression, must have type T.

Evaluation of async <block-or-exp> queues a message to evaluate <block-or-exp> in the nearest enclosing or top-level actor. It immediately returns a future of type async T that can be used to await the result of the pending evaluation of <exp>.

### Await​

The await expression await <exp> has type T provided:

• <exp> has type async T,

• T is shared,

• the await is explicitly enclosed by an async-expression or appears in the body of a shared function.

Expression await <exp> evaluates <exp> to a result r. If r is trap, evaluation returns trap. Otherwise r is a future. If the future is incomplete, that is, its evaluation is still pending, await <exp> suspends evaluation of the neared enclosing async or shared-function, adding the suspension to the wait-queue of the future. Execution of the suspension is resumed once the future is completed (if ever). If the future is complete with value v, then await <exp> suspends evaluation and schedules resumption of execution with value v. If the future is complete with (thrown) error value e, then await <exp> suspends evaluation and schedules resumption of execution by re-throwing the error e.

Note: suspending computation on await, regardless of the dynamic status of the future, ensures that all tentative state changes and message sends prior to the await are committed and irrevocable.

danger

Between suspension and resumption of a computation, the state of the enclosing actor may change due to concurrent processing of other incoming actor messages. It is the programmer’s responsibility to guard against non-synchronized state changes.

### Throw​

The throw expression throw <exp> has type None provided:

• <exp> has type Error,

• the throw is explicitly enclosed by an async-expression or appears in the body of a shared function.

Expression throw <exp> evaluates <exp> to a result r. If r is trap, evaluation returns trap. Otherwise r is an error value e. Execution proceeds from the catch clause of the nearest enclosing try <block-or-exp1> catch <pat> <block-or-exp2> whose pattern <pat> matches value e. If there is no such try expression, e is stored as the erroneous result of the async value of the nearest enclosing async expression or shared function invocation.

### Try​

The try expression try <block-or-exp1> catch <pat> <block-or-exp2> has type T provided:

• <block-or-exp1> has type T,

• <pat> has type Error and <block-or-exp2> has type T in the context extended with <pat>, and

• the try is explicitly enclosed by an async-expression or appears in the body of a shared function.

Expression try <block-or-exp1> catch <pat> <block-or-exp2> evaluates <block-or-exp1> to a result r. If evaluation of <block-or-exp1> throws an uncaught error value e, the result of the try is the result of evaluating <block-or-exp2> under the bindings determined by the match of e against pat.

note

Because the Error type is opaque, the pattern match cannot fail (typing ensures that <pat> is an irrefutable wildcard or identifier pattern).

See Error type.

### Assert​

The assert expression assert <exp> has type () provided <exp> has type Bool.

Expression assert <exp> evaluates <exp> to a result r. If r is trap evaluation returns trap. Otherwise r is a Boolean value v. The result of assert <exp> is:

• the value (), when v is true; or

• trap, when v is false.

### Type annotation​

The type annotation expression <exp> : <typ> has type T provided:

• <typ> is T, and

• <exp> has type U where U <: T.

Type annotation may be used to aid the type-checker when it cannot otherwise determine the type of <exp> or when one wants to constrain the inferred type, U of <exp> to a less-informative super-type T provided U <: T.

The result of evaluating <exp> : <typ> is the result of evaluating <exp>.

note

Type annotations have no-runtime cost and cannot be used to perform the (checked or unchecked) down-casts available in other object-oriented languages.

### Candid Serialization​

The Candid serialization expression to_candid ( <exp>,*) has type Blob provided:

• (<exp>,*) has type (T1,…​,Tn), and each Ti is shared.

Expression to_candid ( <exp>,* ) evaluates the expression sequence ( <exp>,* ) to a result r. If r is trap, evaluation returns trap. Otherwise, r is a sequence of Motoko values vs. The result of evaluating to_candid ( <exp>,* ) is some Candid blob b = encode((T1,...,Tn))(vs), encoding vs.

The Candid deserialization expression from_candid <exp> has type ?(T1,…​,Tn) provided:

• ?(T1,…​,Tn) is the expected type from the context;

• <exp> has type Blob; and

• ?(T1,…​,Tn) is shared.

Expression from_candid <exp> evaluates <exp> to a result r. If r is trap, evaluation returns trap. Otherwise r is a binary blob b. If b Candid-decodes to Candid value sequence Vs of type ea((T1,...,Tn)) then the result of from_candid is ?v where v = decode((T1,...,Tn))(Vs). If b Candid-decodes to a Candid value sequence Vs that is not of Candid type ea((T1,...,Tn)) (but well-formed at some other type) then the result is null. If b is not the encoding of any well-typed Candid value, but some arbitrary binary blob, then the result of from_candid is a trap.

(Informally, here ea(_) is the Motoko-to-Candid type sequence translation and encode/decode((T1,...,Tn))(_) are type-directed Motoko-Candid value translations.)

note

Operation from_candid returns null when the argument is a valid Candid encoding of the wrong type. It traps if the blob is not a valid Candid encoding at all.

note

Operations to_candid and from_candid are syntactic operators, not first-class functions, and must be fully applied in the syntax.

danger

The Candid encoding of a value as a blob is not unique and the same value may have many different Candid representations as a blob. For this reason, blobs should never be used to, for instance, compute hashes of values or determine equality, whether across compiler versions or even just different programs.

### Declaration​

The declaration expression <dec> has type T provided the declaration <dec> has type T.

Evaluating the expression <dec> proceeds by evaluating <dec>, returning the result of <dec> but discarding the bindings introduced by <dec> (if any).

(The expression <dec> is actually shorthand for the block expression { <dec> }.)

### Ignore​

The expression ignore <exp> has type () provided the expression <exp> has type Any .

The expression ignore <exp> evaluates <exp> (typically for some side-effect) but discards its value.

Ignore is useful for evaluating an expression within a sequence of declarations when that expression has non-unit type (and the simpler <exp> declaration would be ill-typed). Then the semantics is equivalent to let _ = <exp> : Any.

### Debug​

The debug expression debug <block-or-exp> has type () provided the expression <block-or-exp> has type ().

When the program is compiled or interpreted with (default) flag --debug, evaluating the expression debug <exp> proceeds by evaluating <block-or-exp>, returning the result of <block-or-exp>.

When the program is compiled or interpreted with flag --release, evaluating the expression debug <exp> immediately returns the unit value (). The code for <block-or-exp> is never executed, nor is its code included in the compiled binary.

### Actor references​

The actor reference actor <exp> has expected type T provided:

• the expression is used in a context expecting an expression of type T (typically as the subject of a type annotation, typed declaration or function argument); and

• T is an some actor type actor { …​ }; and

• <exp> has type Text.

The argument <exp> must be, or evaluate to, the textual format of an IC canister identifier (specified elsewhere), otherwise the expression traps. The result of the expression is an actor value representing that canister.

The validity of the canister identifier and its asserted type T are promises and taken on trust.

An invalid canister identifier or type may manifest itself, if at all, as a later dynamic failure when calling a function on the actor’s proclaimed interface, which will either fail or be rejected.

note

The argument to actor should not include the ic: resource locator used to specify an import. For example, use actor "lg264-qjkae", not actor "ic:lg264-qjkae".

danger

Although they do not compromise type safety, actor references can easily introduce latent, dynamic errors. Accordingly, actor references should be used sparingly and only when needed.

### Parentheses​

The parenthesized expression ( <exp> ) has type T provided <exp> has type T.

The result of evaluating ( <exp> ) is the result of evaluating <exp>.

### Subsumption​

Whenever <exp> has type T and T <: U (T subtypes U) then by virtue of implicit subsumption, <exp> also has type U (without extra syntax).

In general, this means that an expression of a more specific type may appear wherever an expression of a more general type is expected, provided the specific and general types are related by subtyping. This static change of type has no runtime cost.

## References​

• IEEE Standard for Floating-Point Arithmetic, in IEEE Std 754-2019 (Revision of IEEE 754-2008), vol., no., pp.1-84, 22 July 2019, doi: 10.1109/IEEESTD.2019.8766229.