| slug |
|---|
typing |
(For the motivations behind typing and a high-level overview of contracts and types, first read the correctness section.)
By default, Nickel code is dynamically typed. For example:
{
name = "hello",
version = "0.1.1",
fullname =
if std.is_number version then
"hello-v%{std.string.from_number version}"
else
"hello-%{version}",
}
As long as we operate on basic data (numbers, strings, etc.), dynamic type error can be sufficient. Let us introduce an error on the last line of the previous example:
{
name = "hello",
version = "0.1.1",
fullname =
if std.is_number version then
"hello-v%{std.string.from_number version}"
else
"hello-%{version + 1}",
}
version is a string, and can't be added to a number. If we try to export this
configuration using nickel export, we get a reasonable error message:
error: type error
┌─ repl-input-0:8:16
│
3 │ version = "0.1.1",
│ ------- evaluated to this
·
8 │ "hello-%{version + 1}",
│ ^^^^^^^ this expression has type String, but Number was expected
│
= +, 1st argument
While dynamic typing is fine for configuration code, the trouble begins once we are using functions. Say we want to filter over an array of elements:
let filter = fun pred l =>
std.array.fold_left (fun acc x => if pred x then acc @ [x] else acc) [] l in
filter (fun x => if x % 2 == 0 then x else -1) [1,2,3,4,5,6]
Result:
error: type error
┌─ repl-input-3:2:40
│
2 │ std.array.fold_left (fun acc x => if pred x then acc @ [x] else acc) [] l in
│ ^^^^^^ this expression has type Number, but Bool was expected
3 │ filter (fun x => if x % 2 == 0 then x else -1) [1,2,3,4,5,6]
│ -- evaluated to this
│
= if
This example illustrates how dynamic typing delays type errors, making them
harder to diagnose. Here, filter is fine, but the error still points to inside
its implementation. The actual issue is that the caller provided an argument of
the wrong type: the filtering function should return a boolean, but the above
one returns either the original element or -1, both numbers. This is a tiny
example, so debugging is still doable here. In a real code base (where filter
could come from an external library), you might have a harder time diagnosing
the issue from the error report.
The filter example is the poster child for static typing. The typechecker will
catch the error early, because the type expected by filter and the return type
of the filtering function passed as the argument don't match.
To call the typechecker to the rescue, use : to introduce a type annotation.
This annotation turns on the typechecker inside the annotated expression. A
type annotation can appear inline on any expression, or be attached to a
let-binding or a record field. We will refer to the annotated expression as a
statically typed block.
Example:
# Let binding
let f : Number -> Bool = fun x => x % 2 == 0 in
# Record field
let r = {
count : Number = 2354.45 * 4 + 100,
} in
# Inline
1 + ((if f 10 then 1 else 0) : Number)
Let us try on the filter example. We want the call to be inside the statically typechecked block. The easiest way is to capture the whole expression by adding a type annotation at the top-level:
(let filter = fun pred l =>
std.array.fold_left (fun acc x => if pred x then acc @ [x] else acc) [] l in
filter (fun x => if x % 2 == 0 then x else -1) [1,2,3,4,5,6]) : Array Number
Result:
error: incompatible types
┌─ repl-input-6:3:18
│
3 │ filter (fun x => if x % 2 == 0 then x else -1) [1,2,3,4,5,6]) : Array Number
│ ^^^^^^^^^^^^^^^^^^^^^^^^^^^^ this expression
│
= The type of the expression was expected to be `Bool`
= The type of the expression was inferred to be `Number`
= These types are not compatible
This is already better! The error now points at the call site, and inside our
anonymous function, telling us it is expected to return a boolean instead of a
number. Notice how we just had to give the top-level annotation Array Number.
Nickel performs type inference, so that you don't have to write the type for
filter, the filtering function nor the array.
You can use a type wildcard, written _, when you want the typechecker to
infer the part of a type for you:
# will infer `Array String`
let foo : Array _ = ["hello", "there"] in
# will infer `{first: Number, second: Bool}`
let r : {first: _, second: _} = {first = 0 + 1, second = 1 < 2} in
# will infer String
std.array.first foo : _
For debugging purpose, the quickest way to have the typechecker kick in is
simply to slap a : _ on a problematic expression.
Nickel is gradually typed, meaning you can mix both static typing and dynamic
typing. The default is dynamic typing. The static typechecker kicks in when
using a type annotation exp : Type, which delimits a statically typed block.
Nickel also has type inference, sparing you from writing unnecessary type
annotations. You can use _ anywhere in a type to ask the typechecker to
infer this part for you.
Let us now have a quick tour of the type system. The basic types are:
Dyn: the dynamic type. This is the type given to most expressions outside a typed block. A value of typeDyncan be pretty much anything.Number: the only number type. Currently, implemented as arbitrary precision rationals. Common arithmetic operations are exact. The power function using a non-integer exponent is computed on floating point values, which might incur rounding errors.String: a string, which must always be valid UTF8.Bool: a boolean, that is eithertrueorfalse.
The following type constructors are available:
-
Array:
Array T. An array of elements of typeT.Example:
let x : Array (Array Number) = [[1,2], [3,4]] in std.array.flatten x : Array Number -
Record:
{field1: T1, .., fieldn: Tn}. A record whose field names are known statically asfield1, ..,fieldn, respectively of typeT1, ..,Tn.Example:
let pair : {fst: Number, snd: String} = {fst = 1, snd = "a"} in pair.fst : Number -
Dictionary:
{_: T}. A record whose field names are statically unknown but are all of the typeT.Example:
let occurrences : {_: Number} = {a = 1, b = 3, c = 0} in std.record.map (fun char count => count + 1) occurrences : {_ : Number} -
Enum:
[| 'tag1, .., 'tagn |]: an enumeration comprised of alternativestag1, ..,tagn. An enumeration literal is prefixed with a single quote and serialized as a string. It is useful to encode finite alternatives. The advantage over strings is that the typechecker handles them more finely: it is able to detect incomplete matches, for example.Example:
let protocol : [| 'http, 'ftp, 'sftp |] = 'http in (protocol |> match { 'http => 1, 'ftp => 2, 'sftp => 3 }) : Number -
Arrow (function):
S -> T. A function taking arguments of typeSand returning a value of typeT. For multi-parameters functions, just iterate the arrow constructor.Example:
{ increment : Number -> Number = fun x => x + 1, make_path : String -> String -> String -> String = fun basepath filename ext => "%{basepath}/%{filename}.%{ext}", }
Usually, a function like filter would be defined in a library. In this case,
it is good practice to write a type annotation for it, if only to provide the
consumers of this library with an explicit interface. What should be the type
annotation for filter?
In our initial filter example, we are filtering on an array of numbers. But the
code of filter is agnostic with respect to the type of elements of the array.
That is, filter is generic. Genericity is expressed in Nickel through
polymorphism. A polymorphic type is a type that contains the keyword forall,
which introduces type variables that can later be substituted for any concrete
type. Here is our polymorphic type annotation for filter:
{
filter : forall a. (a -> Bool) -> Array a -> Array a = ...,
}
Now, filter can be used not only on numbers as in the initial example, but on strings as well:
{
foo : Array String = filter (fun s => std.string.length s > 2) ["a","ab","abcd"],
bar : Array Number = filter (fun x => x % 2 == 0) [1,2,3,4,5,6],
}
You can use as many parameters as you need:
let fst : forall a b. a -> b -> a = fun x y => x in
let snd : forall a b. a -> b -> b = fun x y => y in
{ n = fst 1 "a", s = snd 1 "a" } : {n: Number, s: String}
Let's go back to our first statically typed filter, without the polymorphic
annotation. If we try to add a call to filter on an array of strings, the
typechecker surprisingly rejects our code:
(let filter = ... in
let result = filter (fun x => x % 2 == 0) [1,2,3,4,5,6] in
let dummy = filter (fun s => std.string.length s > 2) ["a","ab","abcd"] in
result) : Array Number
Result:
error: incompatible types
┌─ repl-input-1:5:48
│
5 │ let dummy = filter (fun s => std.string.length s > 2) ["a","ab","abcd"] in
│ ^ this expression
│
= The type of the expression was expected to be `String`
= The type of the expression was inferred to be `Number`
= These types are not compatible
The reason is that without an explicit polymorphic annotation, the typechecker
will always infer non-polymorphic types. If you need polymorphism, you have to
write a type annotation. Here, filter is inferred to be of type (Number -> Bool) -> Array Number -> Array Number, guessed from the application in the
right hand side of result.
Note:
if you are a more type-inclined reader, you may wonder why the typechecker is
not capable of inferring a polymorphic type for filter by itself. Indeed,
Hindley-Milner
type-inference can precisely infer heading foralls, such that the previous
rejected example would be accepted. We chose to abandon this so-called automatic
generalization, because doing so just makes things simpler with respect to the
implementation, the design and the extensibility of the language and the type
system. Requiring annotation of polymorphic functions seems like a good practice
and a small price to pay in return, in a non type-heavy configuration language
like Nickel.
In a configuration language, you will often find yourself handling records of various kinds. In a simple type system, you can hit the following issue:
(
let add_total : { total : Number } -> { total : Number } -> Number
= fun r1 r2 => r1.total + r2.total
in
let r1 = { jan = 200, feb = 300, march = 10, total = jan + feb } in
let r2 = { aug = 50, sept = 20, total = aug + sept } in
let r3 = { may = 1300, june = 400, total = may + june } in
{
partial1 = add_total r1 r2,
partial2 = add_total r2 r3,
}
) : { partial1 : Number, partial2 : Number }
error: type error: extra row `jan`
┌─ src.ncl:9:25
│
9 │ partial1 = add_total r1 r2,
│ ^^ this expression
│
= The type of the expression was expected to be `{total: Number}`, which does not contain the field `jan`
= The type of the expression was inferred to be `{jan: Number, march: Number, feb: Number, total: Number}`, which contai
ns the extra field `jan`
The problem here is that for this code to run fine, the requirement of
add_total should be that both arguments have a field total: Number, but could
very well have other fields, for all we care. Unfortunately, we don't know right
now how to express this constraint. The current annotation is too restrictive,
because it imposes that arguments have exactly one field total: Number, and
nothing more.
To express such constraints, Nickel features row polymorphism. The idea is similar to polymorphism, but instead of substituting a parameter for a single type, we can substitute a parameter for a whole sequence of field declarations, also referred to as rows:
(
let add_total : forall a b. { total : Number; a } -> { total : Number; b } -> Number
= fun r1 r2 => r1.total + r2.total
in
let r1 = { jan = 200, feb = 300, march = 10, total = jan + feb } in
let r2 = { aug = 50, sept = 20, total = aug + sept } in
let r3 = { may = 1300, june = 400, total = may + june } in
{
partial1 = add_total r1 r2,
partial2 = add_total r2 r3,
}
) : { partial1 : Number, partial2 : Number }
Result:
{ partial1 = 570, partial2 = 1770 }
In the type of add_total, the part {total: Number ; a} expresses exactly what
we wanted: the argument must have a field total: Number, but the tail (the
rest of the record type) is polymorphic, and a may be substituted for
arbitrary fields (such as jan: Number, feb: Number). We used two different
generic parameters a and b, to express that the tails of the arguments may
differ. If we used a in both places, as in forall a. {total: Number ; a} -> {total: Number ; a} -> Number, we could still write add_total {total = 1, foo = 1} {total = 2, foo = 2} but not add_total {total = 1, foo = 1} {total = 2, bar = 2}. Using distinct parameters a and b gives us maximum flexibility.
What comes before the tail may include several fields, is in e.g. forall a. {total: Number, subtotal: Number ; a} -> Number.
Note that row polymorphism also works with enums, with the same intuition of a tail that can be substituted for something else. For example:
{
port_of : forall a. [| 'http, 'ftp; a |] -> Number = match {
'http => 80,
'ftp => 21,
_ => 8000,
}
}
Because the match statement has a catch-all case _, this function is indeed
able to handle other tags than http and ftp, as expressed by its polymorphic
type.
The type system of Nickel has the primitive types (Dyn, Number, String,
and Bool) and type constructors for arrays, records and functions. Nickel
features generics via polymorphism, introduced by the forall keyword. A type
can not only be generic in other types, but record types can also be generic in
their tail. The tail is delimited by ;.
In the previous section, we've been focusing solely on the static typing side. We'll now explore how typed and untyped code interact.
Until now, we have written the statically typed filter examples using
statically typed blocks that enclosed both the definition of filter and the
call sites. More realistically, filter would be a statically typed library
function (it is actually part of the standard library as std.array.filter) and
likely be called from dynamically typed configuration files. In this situation,
the call site escapes the typechecker. Thus, without an additional mechanism,
static typing would only ensure that the implementation of filter doesn't
violate the typing rules, but wouldn't prevent an ill-formed call from
dynamically typed code. At first sight, static typing hasn't solved the
original issue of delayed dynamic type errors at all! Remember, the typical
problem is the caller passing a value of the wrong type that eventually raises
an error from within filter.
Fortunately, Nickel does have a mechanism to prevent this from happening and to
provide good error reporting in this situation. Let us see that by ourselves by
calling to the statically typed std.array.filter from dynamically typed code:
std.array.filter (fun x => if x % 2 == 0 then x else null) [1,2,3,4,5,6]
Result:
error: contract broken by the caller
┌─ <stdlib/std.ncl>:333:25
│
333 │ : forall a. (a -> Bool) -> Array a -> Array a
│ ---- expected return type of a function provided by the caller
│
┌─ repl-input-24:1:54
│
1 │ std.array.filter (fun x => if x % 2 == 0 then x else -1) [1,2,3,4,5,6]
│ -- evaluated to this expression
│
┌─ <unknown> (generated by evaluation):1:1
│
1 │ -1
│ -- evaluated to this value
│
= This error may happen in the following situation:
1. A function `f` is bound by a contract: e.g. `(Number -> Number) -> Number`.
2. `f` takes another function `g` as an argument: e.g. `f = fun g => g 0`.
3. `f` is called by with an argument `g` that does not respect the contract: e.g. `f (fun x => false)`.
= Either change the contract accordingly, or call `f` with a function that returns a value of the right type.
= Note: this is an illustrative example. The actual error may involve deeper nested functions calls.
note:
┌─ repl-input-24:1:1
│
1 │ std.array.filter (fun x => if x % 2 == 0 then x else -1) [1,2,3,4,5,6]
│ ---------------------------------------------------------------------- (1) calling filter
We call filter from a dynamically typed location, but still get a spot-on
error. To precisely avoid dynamically code injecting values of the wrong type
inside statically typed functions, the interpreter protects said blocks by a
contract. Contracts are a principled runtime verification scheme. Please refer
to the dedicated manual section for more details, but for now,
you can just remember that any type annotation (wherever it is) gives rise at
runtime to a corresponding contract application. In other words, foo: T and
foo | T behave exactly the same at runtime.
Thanks to this guard, you can statically type your library functions and use them from dynamically typed code while still enjoying good error messages.
In the other direction, we face a different issue. Because dynamically typed
code just get assigned the Dyn type most of the time, we can't use a
dynamically typed value inside a statically typed block directly:
let x = 0 + 1 in
(1 + x : Number)
Result:
error: Incompatible types
┌─ repl-input-6:1:6
│
1 │ (1 + x : Number)
│ ^ this expression
│
= The type of the expression was expected to be `Number`
= The type of the expression was inferred to be `Dyn`
= These types are not compatible
We could add a type annotation to x. But sometimes we don't want to, or we
can't. Maybe x is an expression that we know correctly evaluates to a number
but is rejected by the typechecker because it uses dynamic idioms. In this case,
we can trade a type annotation for a contract application:
Example:
let x | Number = if true then 0 else "a" in
(1 + x : Number)
Here, x is clearly always a number, but it is not well-typed (the then and
else branches of an if must have the same type). Nonetheless, this program
is accepted! Because we inserted a contract application, the typechecker can be
sure that if x is not a number, the program will fail early with a detailed
contract error. Thus, if we reach 1 + x, at this point x is necessarily a
number and won't cause any type mismatch. In a way, the contract application
acts like a type cast, but whose verification is delayed to run-time.
Dually to a static type annotation, a contract application also turns the typechecker off again. You are back in the dynamic world. Even in a statically typed block, a contract application can thus serve to embed dynamically typed code that you know is correct but wouldn't typecheck:
(1 + ((if true then 0 else "a" | Number)) : Number
The typechecker accepts the code above, while it rejects a fully statically typed version because of the type mismatch between the if branches:
(1 + (if true then 0 else "a")) : Number
Result:
error: Incompatible types
┌─ repl-input-46:1:27
│
1 │ (1 + (if true then 0 else "a")) : Number
│ ^^^ this expression
│
= The type of the expression was expected to be `Number`
= The type of the expression was inferred to be `String`
= These types are not compatible
Apparent type: As a side note, annotations are not always needed to use dynamically typed code inside a statically typed block. The following example is accepted:
let x = 1 in
(1 + x : Number)
The typechecker tries to respect the intent of the programmer. If one doesn't
use annotations, then the code shouldn't be typechecked, whatever the reason is.
If you want x to be statically typed, you should annotate it.
That being said, the typechecker still avoids being too rigid: it is obvious in
the previous example case that 1 is of type Number. This information is
cheap to gather. When encountering a binding outside a typed block, the
typechecker determines the apparent type of the definition. The rationale is
that determining the apparent type shouldn't recurse arbitrarily inside the
expression or do anything non-trivial. Typically, replacing 1 with a compound
expression 0 + 1 changes the type of x type to Dyn and makes the example
fail. For now, the typechecker determines an apparent type that is not Dyn
only for literals (numbers, strings, booleans), arrays, variables, imports and
annotated expressions. Otherwise, the typechecker falls back to Dyn. It may do
more in the future (assign Dyn -> Dyn to functions, {_: Dyn} to records,
etc).
When calling to typed code from untyped code, Nickel automatically inserts
contract checks at the boundary to enjoy clearer and earlier error reporting. In
the other direction, an expression exp | Type is blindly accepted to be of
type Type by the typechecker. This is a way of using untyped values inside
typed code by telling the typechecker "trust me on this one, and if I'm wrong
there will be a contract error anyway". While a type annotation switches the
typechecker on, a contract annotation switches it back off.
Type annotations and contracts share the same syntax. This means that you can technically use custom contracts as any other type inside a static type annotation.
let Port = std.contract.from_predicate (fun value =>
std.is_number value
&& value % 1 == 0
&& value >= 0
&& value <= 65535) in
(10 - 1 : Port)
But this program is unfortunately rejected by the typechecker:
Result:
error: Incompatible types
┌─ repl-input-0:7:2
│
7 │ (10 : Port)
│ ^^ this expression
│
= The type of the expression was expected to be `Port`
= The type of the expression was inferred to be `Number`
= These types are not compatible
It turns out statically ensuring that an arbitrary expression will eventually
satisfy a user-written predicate is a really hard problem even in simple cases
(technically, it is even undecidable in the general case). The typechecker
doesn't have a clue about the relation between numbers and ports. So, what can
it do with annotations like Port? There is one situation when the typechecker
can be sure that something will eventually be a port number, or will fail with
the correct error message: when using a contract application.
(let p | Port = 10 - 1 in
let id = fun x => x in
id p
) : Port
A custom contract hence acts like an opaque type (sometimes called abstract type
as well) for the typechecker. The typechecker doesn't really know much about it
except that the only way to construct a value of type Port is to use contract
application. You also need an explicit contract application to cast back a
Port to a Number: (p | Number) + 1 : Number.
Because of the rigidity of opaque types, using custom contracts inside static type annotations is not very useful right now. We just had to give them a reasonable meaning at typechecking time because types and contracts share the same specification syntax, and they can thus appear inside types.
When to use type annotation, a contract application, or none of those? This is what the guide Type versus contracts: when to? is for.