title | description |
---|---|
Unison language reference |
An informal reference for the Unison language |
This document is an informal reference for the Unison language meant as an aid for Unison programmers as well as authors of implementations of the language. This isn't meant to be a tutorial or introductory guide to the language; it's more like a dry and unexciting tome you consult when you have questions about some aspect of the language. 🧐
This language reference, like the language it describes, is a work in progress and will be improved over time (GitHub link). Contributions and corrections are welcome!
Unison is a language in which programs are not text. That is, the source of truth for a program is not its textual representation as source code, but its structured representation as an abstract syntax tree.
This document describes Unison in terms of its default (and currently, only) textual rendering into source code.
A top-level declaration can appear at the top level or outermost scope of a Unison file. It can be one of the following forms:
- A term declaration, like
x = 42
. - A type declaration, like
structural type Optional a = None | Some a
. - A use clause, like
use .base
oruse math sqrt
.
A Unison term declaration (or "term binding") consists of an optional type signature, and a term definition. For example:
timesTwo : Nat -> Nat
timesTwo x = x * 2
The first line in the above is a type signature. The type signature timesTwo : Nat -> Nat
declares that the term named timesTwo
is a function accepting an argument of type Nat
and computes a value of type Nat
. The type Nat
is the type of 64-bit natural numbers starting from zero. See Unison types for details.
The second line is the term definition. The =
sign splits the definition into a left-hand side, which is the term being defined, and the right-hand side, which is the definition of the term.
The general form of a term binding is:
name : Type
name p_1 p_2 … p_n = expression
name : Type
is a type signature, where name
is the name of the term being defined and Type
is a type for that term. The name
given in the type signature and the name
given in the definition must be the same.
Type signatures are optional. In the absence of a type signature, Unison will automatically infer the type of a term declaration. If a type signature is present, Unison will verify that the term has the type given in the signature.
A term definition has the form f p_1 p_2 … p_n = e
where f
is the name of the term being defined. The parameters p_1
through p_n
are the names of parameters, if any (if the term is a function), separated by spaces. The right-hand side of the =
sign is any Unison expression.
The names of the parameters as well as the name of the term are bound as local variables in the expression on the right-hand side (also known as the body of the function). When the function is called, the parameter names are bound to any arguments passed in the call. See function application for details on the call semantics of functions.
If the term takes no arguments, the term has the value of the fully evaluated expression on the right-hand side and is not a function.
The expression comprising the right-hand side can refer to the name given to the definition in the left-hand side. In that case, it’s a recursive definition. For example:
sumUpTo : Nat -> Nat
sumUpTo n =
if n < 2 then n
else n + sumUpTo (drop n 1)
The above defines a function sumUpTo
that recursively sums all the natural numbers less than some number n
. As an example, sumUpTo 3
is 1 + 2 + 3
, which is 6
.
Note: The expression drop n 1
on line 4 above subtracts one from the natural number n
. Since the natural numbers are not closed under subtraction (n - 1
is an Int
), we use the operation drop
which has the convention that drop 0 n = 0
for all natural numbers n
. Unison's type system saves us from having to deal with negative numbers here.
Operator identifiers are valid names for Unison definitions, but the syntax for defining them is slightly different. For example, we could define a binary operator **
:
(**) x y = Float.pow x y
Or we could define it using infix notation:
x ** y = Float.pow x y
If we want to give the operator a qualified name, we put the qualifier inside the parentheses:
(MyNamespace.**) x y = Float.pow x y
Or if defining it infix:
x MyNamespace.** y = Float.pow x y
The operator can be applied using either notation, no matter which way it's defined. See function application for details.
A user-defined data type is introduced with the type
keyword and a modifier unique
or structural
. The modifier indicates if the type is unique by its name, or if it is unique only by its structure. (See Types for an informal description of Unison's type system.)
For example:
structural type Optional a = None | Some a
or
unique type UserId = Email Text | Phone Nat
The =
sign splits the definition into a left-hand side and a right-hand side, much like term definitions.
The left-hand side is the data type being defined. It gives a name for the data type and declares a new type constructor with that name (here it’s named Optional
), followed by names for any type arguments (here there is one and it’s called a
). These names are bound as type variables in the right-hand side. The right-hand side may also refer to the name given to the type in the left-hand side, in which case it is a recursive type declaration. Note that the fully saturated type construction Optional Nat
is a type, whereas Optional
by itself is a type constructor, not a type (it requires a type argument in order to construct a type).
The right-hand side consists of zero or more data constructors separated by |
. These are data constructors for the type, or ways in which values of the type can be constructed. Each case declares a name for a data constructor (here the data constructors are None
and Some
), followed by the types of the arguments to the constructor.
When Unison compiles a type definition, it generates a term for each data constructor. Here they are the terms Optional.Some : a -> Optional a
, and Optional.None : Optional a
. It also generates patterns for matching on data (see Pattern Matching).
Note that these terms and patterns receive qualified names: if the type named x.y.Z
has a data constructor C
, the generated term and pattern for C
will be named x.y.Z.C
.
The general form of a type declaration is as follows:
<unique|structural<[<regular-identifier>]?>?> type TypeConstructor p1 p2 … pn
= DataConstructor_1
| DataConstructor_2
..
| DataConstructor_n
The structural
keyword specifies that the type being defined is a structural type. Structural types may have different names but are equivalent if they share the same data constructor and type constructor structure. In Unison the following are the same:
structural type Optional a = None | Some a
structural type Maybe x = None | Just x
They can be referenced by either name in a codebase.
The unique
keyword introduces a unique type, explained in the next section.
A type declaration gives a name to a type, but Unison does not uniquely identify a type by its name. Rather, the hash of a type's definition identifies the type. The hash is based on the structure of the type definition, with all identifiers removed.
For example, Unison considers these type declarations to declare the exact same type, even though they give different names to both the type constructor and the data constructors:
structural type Optional a = Some a | None
structural type Maybe a = Just a | Nothing
So a value Some 10
and a value Just 10
are in fact the same value and these two expressions have the same type. Even though one nominally has the type Optional Nat
and the other Maybe Nat
, Unison understands that as the type #5isltsdct9fhcrvu ##Nat
.
This is not always what you want. Sometimes you want to give meaning to a type that is more than just its structure. For example, it might be confusing that these two types are identical:
structural type Suit = Hearts | Spades | Diamonds | Clubs
structural type Direction = North | South | East | West
Unison will consider every unary type constructor with four nullary data constructors as identical to these declarations. So Unison will not stop us providing a Direction
where a Suit
is expected.
The unique
keyword solves this problem:
unique type Suit = Hearts | Spades | Diamonds | Clubs
unique type Direction = North | South | East | West
When compiling these declarations, Unison will generate a universally unique identifier for the type and use that identifier when generating the hash for the type. As a result, the type gets a hash that is universally unique.
In the type declarations discussed above, the arguments to each data constructor are nameless. For example:
structural type Point = Point Nat Nat
Here, the data type Point
has a constructor Point.Point
, with two arguments, both of type Nat
. The arguments have no name, so they are identified positionally, for example when creating a value of this type, like Point.Point 1 2
.
Types with a single data constructor can also be defined in the following style, in which case they are called record types.
type Point = { x : Nat, y : Nat }
This assigns names to each argument of the constructor. The effect of this is to generate some accessor methods, to help get, set, and modify each field.
Point.x : Point -> Nat
Point.x.modify : (Nat -> Nat) -> Point -> Point
Point.x.set : Nat -> Point -> Point
Point.y : Point -> Nat
Point.y.modify : (Nat -> Nat) -> Point -> Point
Point.y.set : Nat -> Point -> Point
👉 Note that
set
andmodify
are returning new, modified copies of the input record - there's no mutation of values in Unison.
There's currently no special syntax for creating or pattern matching on records. That works the same as for regular data types:
p = Point.Point 1 2
px = match p with
Point.Point x _ -> x
A user-defined ability declaration has the following general form:
unique|structural ability A p_1 p_2 … p_n where
Request_1 : Type_1
Request_2 : Type_2
Request_n : Type_n
This declares an ability type constructor A
with type parameters p_1
through p_n
, and request constructors Request_1
through Request_n
.
See Abilities and Ability Handlers for more on user-defined abilities.
This section describes the syntax and informal semantics of Unison expressions.
Unison's evaluation strategy for expressions is Applicative Order Call-by-Value. See Function application for details.
See the sections on:
- Identifiers, for example
foo
,foo.bar
, and+
. - Blocks and statements, for example:
x = 42
. - Literals, for example:
1
,"hello"
,[1,2,3]
. - Comments, for example
-- this is a comment
. - Pattern matching, for example
match (x,y) with (1, "hi") -> 42
.
Unison identifiers come in two flavors:
- Regular identifiers start with an alphabetic unicode character, emoji (which is any unicode character between 1F400 and 1FAFF inclusive), or underscore (
_
), followed by any number of alphanumeric characters, emoji, or the characters_
,!
, or'
. For example,foo
,_bar4
,qux'
, andset!
are valid regular identifiers. - Operators consist entirely of the characters
!$%^&*-=+<>.~\\/|:
. For example,+
,*
,<>
, and>>=
are valid operators.
The above describes unqualified identifiers. An identifier can also be qualified. A qualified identifier consists of a qualifier or namespace, followed by a .
, followed by either a regular identifier or an operator. The qualifier is one or more regular identifiers separated by .
. For example Foo.Bar.baz
is a qualified identifier where Foo.Bar
is the qualifier.
Namespace-qualified identifiers described above are relative to a “current” namespace, which the programmer can set (and defaults to the root of the global namespace). To ignore the current namespace, an identifier can have an absolute qualifier. An absolutely qualified name begins with a .
. For example, the name .base.List
always refers to the name .base.List
, regardless of the current namespace, whereas the name base.List
will refer to foo.base.List
if the current namespace is foo
.
Note that operator identifiers may contain the character .
. In order for this to not create ambiguity, the rule is as follows:
.
by itself is always an operator.- Any other identifier beginning with
.
is an absolutely qualified identifier. - A
.
immediately following a namespace is always a namespace separator. - Otherwise a
.
is treated as part of an operator identifier.
if .
is followed by whitespace or another operator character, the .
is treated like an operator character. If it's followed by a regular identifier character, it's treated as a namespace separator.
Any identifier, including a namespace-qualified one, can appear hash-qualified. A hash-qualified identifier has the form x#h
where x
is an identifier and #h
is a hash literal. The hash disambiguates names that may refer to more than one thing.
The following names are reserved by Unison and cannot be used as identifiers: =
, :
, ->
, '
, |
, !
, '
, if
, then
, else
, forall
, handle
, unique
, structural
, where
, use
, &&
, ||
, true
, false
, type
, ability
, alias
, let
, namespace
, cases
, match
, with
, termLink
, typeLink
.
During typechecking, Unison substitutes free variables in an expression by looking them up in an environment populated from a codebase of available definitions. A Unison codebase is a database of term and type definitions, indexed by hashes and names.
A name in the environment can refer to either terms or types, or both (a type name can never be confused with a term name).
If the list of segments of a name (base.List.map
has the segments [base,List,map]
) is a suffix of exactly one fully qualified name in the environment, Unison substitutes that name in the expression with a reference to the definition. For example, the fully qualified name .base.List.map
could be referenced via base.List.map
, List.map
as long as no other definitions end in base.List.map
or List.map
. This reduces the number of imports needed and cuts down on needing to remember the fully qualified names for definitions. ("Was it base.List.map
or util.List.map
?")
Hash literals in the program are substituted with references to the definitions in the environment whose hashes they match.
If a free term variable in the program cannot be found in the environment and is not the name of another term in scope in the program itself, or if an free variable matches more than one name (it’s ambiguous), Unison tries type-directed name resolution.
During typechecking, if Unison encounters a free term variable that is not a term name in the environment, Unison attempts type-directed name resolution, which:
- Finds term definitions in the environment whose unqualified name is the same as the free variable.
- If exactly one of those terms has a type that conforms to the expected type of the variable (the type system has always inferred this type already at this point), perform that substitution and resume typechecking.
If name resolution is unable to find the definition of a name, or is unable to disambiguate an ambiguous name, Unison reports an error.
A block is an expression that has the general form:
statement_1
statement_2
...
statement_n
expression
A block can have zero or more statements, and the value of the whole block is the value of the final expression
. A statement is either:
- A term definition which defines a term within the scope of the block. The definition is not visible outside this scope, and is bound to a local name. Unlike top-level definitions, a block-level definition does not result in a hash, and cannot be referenced with a hash literal.
- A Unison expression. In particular, blocks often contain action expressions, which are expressions evaluated solely for their effects. An action expression has type
{A} T
for some abilityA
(see Abilities and Ability Handlers) and some typeT
. - A
use
clause.
An example of a block (this evaluates to 16
):
x = 4
y = x + 2
f a = a + y
f 10
A number of language constructs introduce blocks. These are detailed in the relevant sections of this reference. Wherever Unison expects an expression, a block can be introduced with the let
keyword:
let <block>
Where <block>
denotes a block as described above.
The standard syntax expects statements to appear in a line-oriented layout, where whitespace is significant.
The opening keyword (let
, if
, then
, or else
, for example) introduces the block, and the position of the first character of the first statement in the block determines the top-left corner of the block. The beginning of each statement in the block must be lined up exactly with the left edge of the block. The first non-whitespace character that appears to the left of that edge (i.e. outdented) ends the block. Certain keywords also end blocks. For example, then
ends the block introduced by if
.
A statement or expression in a block can continue for more than one line as long as each line of the statement is indented further than the first character of the statement or expression.
For example, these are valid indentations for a block:
let
x = 1
y = 2
x + y
let x = 1
y = 2
x + y
Whereas these are incorrect:
let x = 1
y = 2
x + y
let x = 1
y = 2
x + y
Keywords that introduce blocks bind more tightly than function application. So f let x
is the same as f (let x)
and f if b then p else q
is the same as f (if b then p else q)
.
Block keywords bind more tightly than delayed computations syntax. So 'let x
is the same as _ -> let x
and !if b then p else q
is the same as (if b then p else q) ()
.
Blocks eagerly consume expressions, so if b then p else q + r
is the same as if b then p else (q + r)
.
A literal expression is a basic form of Unison expression. Unison has the following types of literals:
- A 64-bit unsigned integer of type
.base.Nat
(which stands for natural number) consists of digits from 0 to 9. The smallestNat
is0
and the largest is18446744073709551615
. - A 64-bit signed integer of type
.base.Int
consists of a natural number immediately preceded by either+
or-
. For example,4
is aNat
, whereas+4
is anInt
. The smallestInt
is-9223372036854775808
and the largest is+9223372036854775807
. - A 64-bit floating point number of type
.base.Float
consists of an optional sign (+
/-
), followed by two natural numbers separated by.
. Floating point literals in Unison are IEEE 754-1985 double-precision numbers. For example1.6777216
is a valid floating point literal. - A text literal of type
.base.Text
is any sequence of Unicode characters between pairs of"
. The escape character is\
, so a"
can be included in a text literal with the escape sequence\"
. The full list of escape sequences is given in the Escape Sequences section below. For example,"Hello, World!"
is a text literal. A text literal can span multiple lines. Newlines do not terminate text literals, but become part of the literal text. - A character literal of type
.base.Char
consists of a?
character marker followed by a single Unicode character, or a single escape sequence. For example,?a
,?🔥
or?\t
. - There are two Boolean literals:
true
andfalse
, and they have typeBoolean
. - A hash literal begins with the character
#
. See the section Hashes for details on the lexical form of hash literals. A hash literal is a reference to a term or type. The type or term that it references must have a definition whose hash digest matches the hash in the literal. The type of a hash literal is the same as the type of its referent.#a0v829
is an example of a hash literal. - A literal list has the general form
[v1, v2, ... vn]
wherev1
throughvn
are expressions. A literal list may be empty. For example,[]
,[x]
, and[1,2,3]
are list literals. The expressions that form the elements of the list all must have the same type. If that type isT
, then the type of the list literal is.base.List T
or[T]
. - A function literal or lambda has the form
p1 p2 ... pn -> e
, wherep1
throughpn
are regular identifiers ande
is a Unison expression (the body of the lambda). The variablesp1
throughpn
are local variables ine
, and they are bound to any values passed as arguments to the function when it’s called (see the section Function Application for details on call semantics). For examplex -> x + 2
is a function literal. - A tuple literal has the form
(v1,v2, ..., vn)
wherev1
throughvn
are expressions. A value(a,b)
has type(A,B)
ifa
has typeA
andb
has typeB
. The expression(a)
is the same as the expressiona
. The nullary tuple()
(pronounced “unit”) is of the trivial type()
. See tuple types for details on these types and more ways of constructing tuples.
Documentation blocks have type Doc
(documentation is a first-class value in the language).{{
starts a documentation block and }}
finishes it. For example:
List.take.apiDocs : Doc
List.take.apiDocs = {{
``List.take n [1,2,3]`` returns the first `n` elements of
a list. This is efficient and takes just `O(log n)` operations.
## Example
{{ examples.List.take.ex1 }}
## Also see
* The {type List} type and associated docs
* The {List.drop} function with signature @inlineSignature{List.drop}
* More about finger trees (used to implement {type List}) here: {fingerTrees.doc}
}}
More specifically, some important Doc features are:
- Links to definitions are done with single open and close braces.
{List.drop}
is a term link, and{type List}
is a type link. @signature{List.take}
or@inlineSignature{List.take}
expands to the type signature of List.take either as a block or inline, respectively.@source{List.map}
expands to the full source of List.map- To insert another Doc value into another Doc, use nested double braces.
{{I am a doc {{thisDocValueWillBeDisplayed}} }}
@eval{someDefinition}
expands to the result of evaluatingsomeDefinition
, which must be a pre-existing definition in the codebase (it can't be an arbitrary expression). You can evaluate multi-line codeblocks with the triple backtick syntax``` multipleLines ```
Text literals can include the following escape sequences:
\0
= null character\a
= alert (bell)\b
= backspace\f
= form feed\n
= new line\r
= carriage return\t
= horizontal tab\v
= vertical tab\s
= space\\
= literal\
character\'
= literal'
character\"
= literal"
character
A line comment starts with --
and is followed by any sequence of characters. A line that contains a comment can’t contain anything other than a comment and whitespace. Line comments are currently ignored by Unison.
Multi-line comments are supported by starting a comment block with {-
and ending it with -}
.
A line starting with ---
and containing no other characters is a fold. Any text below the fold is ignored by Unison.
A type annotation has the form e:T
where e
is an expression and T
is a type. This tells Unison that e
should be of type T
(or a subtype of type T
), and Unison will check whether this is true. It's a type error for the actual type of e
to be anything other than a type that conforms to T
.
Any expression can appear in parentheses, and an expression (e)
is the same as the expression e
. Parentheses can be used to delimit where an expression begins and ends. For example (f : P -> Q) y
is an application of the function f
of type P -> Q
to the argument y
. The parentheses are needed to tell Unison that y
is an argument to f
, not a part of the type annotation expression.
A function application f a1 a2 an
applies the function f
to the arguments a1
through an
.
The above syntax is valid where f
is a regular identifier. If the function name is an operator such as *
, then the syntax for application is infix : a1 * a2
. Any operator can be used in prefix position by surrounding it in parentheses: (*) a1 a2
. Any regular identifier can be used infix by surrounding it in backticks: a1 `f` a2
.
All Unison functions are of arity 1. That is, they take exactly one argument. An n-ary function is modeled either as a unary function that returns a further function (a partially applied function) which accepts the rest of the arguments, or as a unary function that accepts a tuple.
Function application associates to the left, so the expression f a b
is the same as (f a) b
. If f
has type T1 -> T2 -> Tn
then f a
is well typed only if a
has type T1
. The type of f a
is then T2 -> Tn
. The type constructor of function types, ->
, associates to the right. So T1 -> T2 -> Tn
parenthesizes as T1 -> (T2 -> TN)
.
The evaluation semantics of function application is applicative order Call-by-Value. In the expression f x y
, x
and y
are fully evaluated in left-to-right order, then f
is fully evaluated, then x
and y
are substituted into the body of f
, and lastly the body is evaluated.
An exception to the evaluation semantics is Boolean expressions, which have non-strict semantics.
Unison supports proper tail calls so function calls in tail position do not grow the call stack.
All operators and infix function applications currently have the same precedence, and are parsed left-associative. Use parentheses to obtain a different grouping. So for instance:
1 + 3 * 4
is parsed(1 + 3) * 4
. You can group it differently using parentheses:1 + (3 * 4)
a + b < c * d
is parsed as((a + b) < c) * d
. You can group it differently using parentheses:a + b < (c * d)
x `Nat.drop` 1 + 11
is parsed as(x `Nat.drop` 1) + 11
.
When your code is printed back to you by Unison, it will be displayed with minimal necessary parentheses, so if Unison's default syntax later supports operator precedence, old definitions written originally with more parentheses will get displayed with only the parentheses currently needed for the current precedence settings.
Prefix function application:
- Binds more tightly than infix operators. So
f x + g y
is the same as(f x) + (g y)
. - Binds less tightly than keywords that introduce blocks. So
f let x
is the same asf (let x)
andf if b then p else q
is the same asf (if b then p else q)
- Binds less tightly than
'
and!
(see delayed computations), so'f x y
is the same as(_ -> f) x y
and!f x y
is the same asf () x y
.
A Boolean expression has type Boolean
which has two values, true
and false
.
A conditional expression has the form if c then t else f
, where c
is an expression of type Boolean
, and t
and f
are expressions of any type, but t
and f
must have the same type.
Evaluation of conditional expressions is non-strict. The evaluation semantics of if c then t else f
are:
- The condition
c
is always evaluated. - If
c
evaluates totrue
, the expressiont
is evaluated andf
remains unevaluated. The whole expression reduces to the value oft
. - If
c
evaluates tofalse
, the expressionf
is evaluated andt
remains unevaluated. The whole expression reduces to the value off
.
The keywords if
, then
, and else
each introduce a Block as follows:
if
<block>
then
<block>
else
<block>
A Boolean conjunction expression is a Boolean
expression of the form a && b
where a
and b
are Boolean
expressions. Note that &&
is not a function, but built-in syntax.
The evaluation semantics of a && b
are equivalent to if a then b else false
.
A Boolean disjunction expression is a Boolean
expression of the form a || b
where a
and b
are Boolean
expressions. Note that ||
is not a function, but built-in syntax.
The evaluation semantics of a || b
are equivalent to if a then true else b
.
An expression can appear delayed as 'e
, which is the same as _ -> e
. If e
has type T
, then 'e
has type forall a. a -> T
.
If c
is a delayed computation, it can be forced with !c
, which is the same as c ()
. The expression c
must conform to a type () -> t
for some type t
, in which case !c
has type t
.
Delayed computations are important for writing expressions that require abilities. For example:
use io
program : '{IO} ()
program = 'let
printLine "What is your name?"
name = !readLine
printLine ("Hello, " ++ name)
This example defines a small I/O program. The type {IO} ()
by itself is not allowed as the type of a top-level definition, since the IO
ability must be provided by a handler, see abilities and ability handlers). Instead, program
has the type '{IO} ()
(note the '
indicating a delayed computation). Inside a handler for IO
, this computation can be forced with !program
.
Inside the program, !readLine
has to be forced, as the type of io.readLine
is '{IO} Text
, a delayed computation which, when forced, reads a line from standard input.
The reserved symbols '
and !
bind more tightly than function application, So 'f x
is the same as (_ -> f) x
and !x + y
is the same as (x ()) + y
.
These symbols bind less tightly than keywords that introduce blocks, so 'let x
is the same as _ -> let x
and !if b then p else q
is the same as (if b then p else q) ()
.
Additional '
and !
combine in the obvious way:
''x
is the same as(_ -> (_ -> x))
or(_ _ -> x)
.!!x
is the same asx () ()
.!'x
and'!x
are both the same asx
.
You can of course use parentheses to precisely control how '
and !
get applied.
A match expression has the general form:
match e with
pattern_1 -> block_1
pattern_2 -> block_2
...
pattern_n -> block_n
Where e
is an expression, called the scrutinee of the match expression, and each case has a pattern to match against the value of the scrutinee and a block to evaluate in case it matches.
The evaluation semantics of match expressions are as follows:
- The scrutinee is evaluated.
- The first pattern is evaluated and matched against the value of the scrutinee.
- If the pattern matches, any variables in the pattern are substituted into the block to the right of its
->
(called the match body) and the block is evaluated. If the pattern doesn’t match then the next pattern is tried and so on.
It's possible for Unison to actually evaluate cases in a different order, but such evaluation should always have the same observable behavior as trying the patterns in sequence.
It is an error if none of the patterns match. In this version of Unison, the error occurs at runtime. In a future version, this should be a compile-time error.
Unison provides syntactic sugar for match expressions in which the scrutinee is the sole argument of a lambda expression:
cases
pattern_1 -> block_1
pattern_2 -> block_1
...
pattern_n -> block_n
-- equivalent to
e -> match e with
pattern_1 -> block_1
pattern_2 -> block_1
...
pattern_n -> block_n
A pattern has one of the following forms:
A blank pattern has the form _
. It matches any expression without creating a variable binding.
For example:
match 42 with
_ -> "Always matches"
A literal pattern is a literal Boolean
, Nat
, Int
, Char
, or Text
. A literal pattern matches if the scrutinee has that exact value.
For example:
match 2 + 2 with
4 -> "Matches"
_ -> "Doesn't match"
A variable pattern is a regular identifier and matches any expression. The expression that it matches will be bound to that identifier as a variable in the match body.
For example, this expression evaluates to 3
:
match 1 + 1 with
x -> x + 1
An as-pattern has the form v@p
where v
is a regular identifier and p
is a pattern. This pattern matches if p
matches, and the variable v
will be bound in the body to the value matching p
.
For example, this expression evaluates to 3
:
match 1 + 1 with
x@4 -> x * 2
y@2 -> y + 1
_ -> 22
A constructor pattern has the form C p1 p2 ... pn
where C
is the name of a data constructor in scope, and p1
through pn
are patterns such that n
is the arity of C
. Note that n
may be zero. This pattern matches if the scrutinee reduces to a fully applied invocation of the data constructor C
and the patterns p1
through pn
match the arguments to the constructor.
For example, this expression uses Some
and None
, the constructors of the Optional
type, to return the 3rd element of the list xs
if present or 0
if there was no 3rd element.
match List.at 3 xs with
None -> 0
Some x -> x
A list pattern matches a List t
for some type t
and has one of three forms:
head +: tail
matches a list with at least one element. The patternhead
is matched against the first element of the list andtail
is matched against the suffix of the list with the first element removed.init :+ last
matches a list with at least one element. The patterninit
is matched against the prefix of the list with the last element removed, andlast
is matched against the last element of the list.- A literal list pattern has the form
[p1, p2, ... pn]
wherep1
throughpn
are patterns. The patternsp1
throughpn
are matched against the elements of the list. This pattern only matches if the length of the scrutinee is the same as the number of elements in the pattern. The pattern[]
matches the empty list. part1 ++ part2
matches a list which composed of the concatenation ofpart1
andpart2
. At least one ofpart1
orpart2
must be a pattern with a known list length, otherwise it's unclear where the list is being split. For instance,[x,y] ++ rest
is okay as isstart ++ [x,y]
, but justa ++ b
is not allowed.
Examples:
first : [a] -> Optional a
first as = match as with
h +: _ -> Some h
[] -> None
last : [a] -> Optional a
last as = match as with
_ :+ l -> Some l
[] -> None
exactlyOne : [a] -> Boolean
exactlyOne a = match a with
[_] -> true
_ -> false
lastTwo : [a] -> Optional (a,a)
lastTwo a = match a with
start ++ [a,a2] -> Some (a,a2)
_ -> None
firstTwo : [a] -> Optional (a,a)
firstTwo a = match a with
[a,a2] ++ rest -> Some (a,a2)
_ -> None
A tuple pattern has the form (p1, p2, ... pn)
where p1
through pn
are patterns. The pattern matches if the scrutinee is a tuple of the same arity as the pattern and p1
through pn
match against the elements of the tuple. The pattern (p)
is the same as the pattern p
, and the pattern ()
matches the literal value ()
of the trivial type ()
(both pronounced “unit”).
For example, this expression evaluates to 4
:
match (1,2,3) with
(a,_,c) -> a + c
An ability pattern only appears in an ability handler and has one of two forms (see Abilities and ability handlers for details):
{C p1 p2 ... pn -> k}
whereC
is the name of an ability constructor in scope, andp1
throughpn
are patterns such thatn
is the arity ofC
. Note thatn
may be zero. This pattern matches if the scrutinee reduces to a fully applied invocation of the ability constructorC
and the patternsp1
throughpn
match the arguments to the constructor. The scrutinee must be of typeRequest A T
for some ability{A}
and typeT
. The variablek
will be bound to the continuation of the program. If the scrutinee has typeRequest A T
andC
has typeX ->{A} Y
, thenk
has typeY -> {A} T
.{p}
wherep
is a pattern. This matches the case where the computation is pure (the value of typeRequest A T
calls none of the constructors of the ability{A}
). A pattern match on anRequest
is not complete unless this case is handled.
See the section on abilities and ability handlers for examples of ability patterns.
A guard pattern has the form p | g
where p
is a pattern and g
is a Boolean expression that may reference any variables bound in p
. The pattern matches if p
matches and g
evaluates to true
.
For example, the following expression evaluates to 6:
match 1 + 2 with
x | x == 4 -> 0
x | x + 1 == 4 -> 6
_ -> 42
A hash in Unison is a 512-bit SHA3 digest of a term or a type's internal structure, excluding all names. The textual representation of a hash is its base32Hex Unicode encoding.
Unison attributes a hash to every term and type declaration, and the hash may be used to unambiguously refer to that term or type in all contexts. As far as Unison is concerned, the hash of a term or type is its true name.
A term, type, data constructor, or ability constructor may be unambiguously referenced by hash. Literal hash references have the following structure:
- A term definition has a hash of the form
#x
wherex
is the base32Hex encoding of the hash of the term. For example#a0v829
. - A term or type definition that’s part of a cycle of mutually recursive definitions hashes to the form
#x.n
wherex
is the hash of the cycle andn
is the term or type’s index in its cycle. A cycle has a canonical order determined by sorting all the members of the cycle by their individual hashes (with the cycle removed). - A data constructor hashes to the form
#x#c
wherex
is the hash of the data type definition andc
is the index of that data constructor in the type definition. - A data constructor in a cyclic type definition hashes to the form
#x.n#c
where#x.n
is the hash of the data type andc
is the data constructor’s index in the type definition. - A built-in reference to a Unison built-in term or type
n
has a hash of the form##n
.##Nat
is an example of a built-in reference.
A hash literal may use a prefix of the base32Hex encoded SHA3 digest instead of the whole thing. For example the programmer may use a short hash like #r1mtr0
instead of the much longer 104-character representation of the full 512-bit hash. If the short hash is long enough to be unambiguous given the environment, Unison will substitute the full hash at compile time. When rendering code as text, Unison may calculate the minimum disambiguating hash length before rendering a hash.
This section describes informally the structure of types in Unison. See also the section titled User-defined types for detailed information on how to define new data types.
Formally, Unison’s type system is an implementation of the system described by Joshua Dunfield and Neelakantan R. Krishnaswami in their 2013 paper Complete and Easy Bidirectional Typechecking for Higher-Rank Polymorphism.
Unison extends that type system with, pattern matching, scoped type variables, ability types (also known as algebraic effects). See the section on Abilities for details on ability types.
Unison attributes a type to every valid expression. For example:
4 < 5
has typeBoolean
42 + 3
has typeNat
,"hello"
has typeText
- the list
[1,2,3]
has type[Nat]
- the function
(x -> x)
has typeforall a. a -> a
The meanings of these types and more are explained in the sections below.
A full treatise on types is beyond the scope of this document. In short, types help enforce that Unison programs make logical sense. Every expression must be well typed, or Unison will give a compile-time type error. For example:
[1,2,3]
is well typed, since lists require all elements to be of the same type.42 + "hello"
is not well typed, since the type of+
disallows adding numbers and text together.printLine "Hello, World!"
is well typed in some contexts and not others. It's a type error for instance to use I/O functions where anIO
ability is not provided.
Types are of the following general forms.
Type variables are regular identifiers beginning with a lowercase letter. For example a
, x0
, and foo
are valid type variables.
A universally quantified or polymorphic type has the form forall v1 v2 vn. t
, where t
is a type. The type t
may involve the variables v1
through vn
.
The symbol ∀
is an alias for forall
.
A type like forall x. F x
can be written simply as F x
(the forall x
is implied) as long as x
is free in F x
(it is not bound by an outer scope; see Scoped type variables below).
A polymorphic type may be instantiated at any given type. For example, the empty list []
has type forall x. [x]
. So it's a type-polymorphic value. Its type can be instantiated at Int
, for example, which binds x
to Int
resulting in [Int]
which is also a valid type for the empty list. In fact, we can say that the empty list []
is a value of type [x]
for all choices of element type e
, hence the type forall x. [x]
.
Likewise the identity function (x -> x)
, which simply returns its argument, has a polymorphic type forall t. t -> t
. It has type t -> t
for all choices of t
.
Type variables introduced by a type signature for a term remain in scope throughout the definition of that term.
For example in the following snippet, the type annotation temp:x
is telling Unison that temp
has the type x
which is bound in the type signature, so temp
and a
have the same type.
ex1 : x -> y -> x
ex1 a b =
-- refers to the type x in the outer scope
temp : x
temp = a
a
To explicitly shadow a type variable in scope, the variable can be reintroduced in the inner scope by a forall
binder, as follows:
ex2 : x -> y -> x
ex2 a b =
-- doesn’t refer to x in outer scope
id : ∀ x . x -> x
id v = v
temp = id 42
id a
Note that here the type variable x
in the type of id
gets instantiated to two different types. First id 42
instantiates it to Nat
, then id a
, instantiates it to the outer scope's type x
.
Just as values are built using data constructors, types are built from type constructors. Nullary type constructors like Nat
, Int
, Float
are already types, but other type constructors like List
and ->
(see built-in type constructors) take type parameters in order to yield types. List
is a unary type constructor, so it takes one type (the type of the list elements), and ->
is a binary type constructor. List Nat
is a type and Nat -> Int
is a type.
Types are to values as kinds are to type constructors. Unison attributes a kind to every type constructor, which is determined by its number of type parameters and the kinds of those type parameters.
A type must be well kinded, just like an expression must be well typed, and for the same reason. However, there is currently no syntax for kinds and they do not appear in Unison programs (this will certainly change in a future version of Unison).
Unison’s kinds have the following forms:
- A nullary type constructor or ordinary type has kind
Type
. - A type constructor has kind
k1 -> k2
wherek1
andk2
are kinds.
For example List
, a unary type constructor, has kind Type -> Type
as it takes a type and yields a type. A binary type constructor like ->
has kind Type -> Type -> Type
, as it takes two types (it actually takes a type and yields a partially applied unary type constructor that takes the other type). A type constructor of kind (Type -> Type) -> Type
is a higher-order type constructor (it takes a unary type constructor and yields a type).
A type constructor is applied to a type or another type constructor, depending on its kind, similarly to how functions are applied to arguments at the term level. C T
applies the type constructor C
to the type T
. Type application associates to the left, so the type A B C
is the same as the type (A B) C
.
The type X -> Y
is a type for functions that take arguments of type X
and yield results of type Y
. Application of the binary type constructor ->
associates to the right, so the type X -> Y -> Z
is the same as the type X -> (Y -> Z)
.
The type (A,B)
is a type for binary tuples (pairs) of values, one of type A
and another of type B
. The type (A,B,C)
is a triple, and so on.
The type (A)
is the same as the type A
and is not considered a tuple.
The nullary tuple type ()
is the type of the unique value also written ()
and is pronouced “unit”.
In the standard Unison syntax, tuples of arity 2 and higher are actually of a type Tuple a b
for some types a
and b
. For example, (X,Y)
is syntactic shorthand for the type Tuple X (Tuple Y ())
.
Tuples are either constructed with the syntactic shorthand (a,b)
(see tuple literals) or with the built-in Tuple.Cons
data constructor: Tuple.Cons a (Tuple.Cons b ())
.
Unison provides the following built-in types:
.base.Nat
is the type of 64-bit natural numbers, also known as unsigned integers. They range from 0 to 18,446,744,073,709,551,615..base.Int
is the type of 64-bit signed integers. They range from -9,223,372,036,854,775,808 to +9,223,372,036,854,775,807..base.Float
is the type of IEEE 754-1985 double-precision floating point numbers..base.Boolean
is the type of Boolean expressions whose value istrue
orfalse
..base.Bytes
is the type of arbitrary-length 8-bit byte sequences..base.Text
is the type of arbitrary-length strings of Unicode text..base.Char
is the type of a single Unicode character.- The trivial type
()
(pronounced “unit”) is the type of the nullary tuple. There is a single data constructor of type()
and it’s also written()
.
See literals for more on how values of some of these types are constructed.
Unison has the following built-in type constructors.
(->)
is the constructor of function types. A typeX -> Y
is the type of functions fromX
toY
.base.Tuple
is the constructor of tuple types. See tuple types for details on tuples..base.List
is the constructor of list types. A typeList T
is the type of arbitrary-length sequences of values of typeT
. The type[T]
is an alias forList T
..base.Request
is the constructor of requests for abilities. A typeRequest A T
is the type of values received by ability handlers for the abilityA
where current continuation requires a value of typeT
.
New types can be declared as described in detail in the User-defined types section. These include ordinary data types, unique types, and record types. A type declaration introduces a type, a corresponding type constructor, one or more data constructors that (collectively) construct all possible values of the type, and (in the case of record types) accessors for the named arguments of the type's single data constructor.
Unison provides a convenient feature called abilities which lets you use the same ordinary Unison syntax for programs that do (asynchronous) I/O, stream processing, exception handling, parsing, distributed computation, and lots more. Unison's system of abilities (often called "algebraic effects" in the literature) is based on the Frank language by Sam Lindley, Conor McBride, and Craig McLaughlin. Unison diverges slightly from the scheme detailed in this paper. In particular:
- Unison's ability polymorphism is provided by ordinary polymorphic types, and a Unison type with an empty ability set explicitly disallows any abilities. In Frank, the empty ability set implies an ability-polymorphic type.
- Unison doesn't overload function application syntax to do ability handling; instead it has a separate
handle
construct for this purpose.
The general form for a function type in Unison is I ->{A} O
, where I
is the input type of the function, O
is the output type, and A
is the set of ability requirements of the function. More generally, this can be any comma-separated list of types, like I ->{A1,A2,A3} O
.
A function type in Unison like A -> B
is really syntactic sugar for a type A ->{e} B
where e
is some set of abilities, possibly empty. A function that definitely requires no abilities has a type like A ->{} B
(it has an empty set of abilities).
The general typechecking rule used for abilities is this: calls to functions requiring abilities {A1,A2}
must be in a context where at least the abilities {A1,A2}
are available, otherwise the typechecker will complain with an ability check failure. Abilities can be made available using a handle
block (discussed below) or with a type signature: so for instance, within the body of a function Text ->{IO} Nat
, {IO}
is available and therefore:
- We can call a function
f : Nat ->{} Nat
, since the ability requirements of f are{}
which is a subset the available{IO}
abilities. - We can also call a function
g : Text ->{IO} ()
, since the requirements ofg
are{IO}
which is a subset of the available{IO}
abilities.
For functions accepting multiple arguments, it might seem we need a different rule, but the rule is the same: the body of the function can access the abilities attached to the corresponding function type in the signature. Here's an example that won't typecheck, since the function body must be pure according to the signature:
doesNotWork : Text ->{IO} Text ->{} Nat
doesNotWork arg1 arg2 =
printLine "Does not work!"
42
However, if we do the IO
before returning the pure function, it typechecks just fine:
doesWork : Text ->{IO} Text ->{} Nat
doesWork arg1 =
printLine "Works great!"
(arg2 -> 42) -- we return a pure `Text ->{} Nat`
For top-level definitions which aren't contained in a function body, they are required to be pure. For instance, this doesn't typecheck:
msg = printLine "hello"
But if we say msg = '(printLine "Hello")
that typechecks fine, since the printLine
is now inside a function body whose requirements inferred as {IO}
(try it!).
🤓 This restriction on top level definitions needing to be pure might lifted in a future version of Unison.
When inferring ability requirements for f
, the ability requirements become the union of all requirements for functions that can be called within the body of the function.
A user-defined ability is declared with an ability
declaration such as:
structural ability Store v where
get : v
put : v -> ()
Abilities need to be defined with either the structural
or unique
keyword. See the sections on unique types and structural-types for more detail on the difference.
This results in a new ability type constructor Store
which takes a type argument v
. It also create two value-level constructors named get
and put
. The idea is that get
provides the ability to "get" a value of type v
from somewhere, and put
allows "putting" a value of type v
somewhere. Where exactly these values of type v
will be kept depends on the handler.
The Store
constructors get
and put
have the following types:
get : forall v. {Store v} v
put : forall v. v ->{Store v} ()
The type {Store v}
means that the computation which results in that type requires a Store v
ability and cannot be executed except in the context of an ability handler that provides the ability.
A constructor {A} T
for some ability A
and some type T
(or a function which uses such a constructor), can only be used in a scope where the ability A
is provided. Abilities are provided by handle
expressions:
handle e with h
This expression gives e
access to abilities handled by the function h
. Specifically, if e
has type {A} T
and h
has type Request A T -> R
, then handle e with h
has type R
. The type constructor Request
is a special builtin provided by Unison which will pass arguments of type Request A T
to a handler for the ability A
. Note that h
must accept an argument of type Request A T
to handle e
of type {A} T
—ultimately, a type error will result if an ability is required in a scope where it is not provided by an enclosing handle expression.
The examples in the next section should help clarify how ability handlers work.
Each constructor of an ability corresponds with a pattern that can be used for pattern matching in ability handlers. The general form of such a pattern is:
{A.c p_1 p_2 p_n -> k}
Where A
is the name of the ability, c
is the name of the constructor, p_1
through p_n
are patterns matching the arguments to the constructor, and k
is a continuation for the program. If the value matching the pattern has type Request A T
and the constructor of that value had type X ->{A} Y
, then k
has type Y -> {A} T
.
The continuation will always be a function accepting the return value of the ability constructor, and the body of this function is the remainder of the handle .. with
block immediately following the call to the constructor. See below for an example.
A handler can choose to call the continuation or not, or to call it multiple times. For example, a handler can ignore the continuation in order to handle an ability that aborts the execution of the program:
ability Abort where
aborting : ()
-- Returns `a` immediately if the program `e` calls `abort`
abortHandler : a -> Request Abort a -> a
abortHandler a = cases
{ Abort.aborting -> _ } -> a
{ x } -> x
p : Nat
p = handle
x = 4
Abort.aborting
x + 2
with abortHandler 0
The program p
evaluates to 0
. If we remove the Abort.aborting
call, it evaluates to 6
.
Note that although the ability constructor is given the signature aborting : ()
, its actual type is {Abort} ()
.
The pattern { Abort.aborting -> _ }
matches when the Abort.aborting
call in p
occurs. This pattern ignores its continuation since it will not invoke it (which is how it aborts the program). The continuation at this point is the expression _ -> x + 2
.
The pattern { x }
matches the case where the computation is pure (makes no further requests for the Abort
ability and the continuation is empty). A pattern match on a Request
is not complete unless this case is handled.
When a handler calls the continuation, it needs describe how the ability is provided in the continuation of the program, usually with a recursive call, like this:
use .base Request
structural ability Store v where
get : v
put : v -> ()
storeHandler : v -> Request (Store v) a -> a
storeHandler storedValue = cases
{Store.get -> k} ->
handle k storedValue with storeHandler storedValue
{Store.put v -> k} ->
handle k () with storeHandler v
{a} -> a
Note that the storeHandler
has a with
clause that uses storeHandler
itself to handle the Request
s made by the continuation. So it’s a recursive definition. The initial "stored value" of type v
is given to the handler in its argument named storedValue
, and the changing value is captured by the fact that different values are passed to each recursive invocation of the handler.
In the pattern for Store.get
, the continuation k
expects a v
, since the return type of get
is v
. In the pattern for Store.put
, the continuation k
expects ()
, which is the return type of put
.
It's worth noting that this is a mutual recursion between storeHandler
and the various continuations (all named k
). This is no cause for concern, as they call each other in tail position and the Unison compiler performs tail call elimination.
An example use of the above handler:
modifyStore : (v -> v) ->{Store v} ()
modifyStore f =
v = Store.get
Store.put (f v)
Here, when the handler receives Store.get
, the continuation is v -> Store.put (f v)
. When the handler receives Store.put
, the continuation is _ -> ()
.
A use clause tells Unison to allow identifiers from a given namespace to be used unqualified in the lexical scope where the use clause appears.
In this example, the use .base.List
clause allows the definition that follows it to refer to .base.List.take
as simply take
:
use .base.List
oneTwo = take 2 [1,2,3]
The general form of use
clauses is as follows:
use namespace name_1 name_2 .. name_n
Where namespace
is the namespace from which we want to use names unqualified, and name_1
through name_n
are the names we want to use. If no names are given in the use
clause, Unison allows all the names from the namespace to be used unqualified. There's no performance penalty for this, as use
clauses are purely a syntactic convenience. When rendering code as text, Unison will insert precise use
clauses that mention exactly the names it uses, even if the programmer omitted the list of names.
See the section on identifiers for more on namespaces as well as qualified and unqualified names.