--- slug: typing --- # Typing in Nickel (For the motivations behind typing and a high-level overview of contracts and types, first read the [correctness](./correctness.md) section.) ## Typing modes ### Dynamic typing By default, Nickel code is dynamically typed. For example: ```nickel { 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: ```nickel { 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: ```text 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: ```nickel 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: ```text 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. ### Static typing 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: ```nickel # 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: ```nickel (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: ```text 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: ```nickel # 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. ### Take-away 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. ## Type system 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 type `Dyn` can 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 either `true` or `false`. The following type constructors are available: - **Array**: `Array T`. An array of elements of type `T`. Example: ```nickel 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 as `field1`, .., `fieldn`, respectively of type `T1`, .., `Tn`. Example: ```nickel 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 type `T`. Example: ```nickel 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 alternatives `tag1`, .., `tagn`. An enumeration literal is prefixed with a backtick 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: ```nickel 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 type `S` and returning a value of type `T`. For multi-parameters functions, just iterate the arrow constructor. Example: ```nickel { increment : Number -> Number = fun x => x + 1, make_path : String -> String -> String -> String = fun basepath filename ext => "%{basepath}/%{filename}.%{ext}", } ``` ### Polymorphism #### Type polymorphism 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`: ```nickel { 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: ```nickel { 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: ```nickel 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} ``` #### Type inference and polymorphism 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: ```nickel (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: ```text 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](https://en.wikipedia.org/wiki/Hindley%E2%80%93Milner_type_system) 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. #### Row polymorphism 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: ```nickel ( 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 } ``` ```text 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: ```nickel ( 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: ```nickel { 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: ```nickel { 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. ### Take-away 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 `;`. ## Interaction between statically typed and dynamically typed code In the previous section, we've been focusing solely on the static typing side. We'll now explore how typed and untyped code interact. ### Using statically typed code inside dynamically code 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: ```nickel std.array.filter (fun x => if x % 2 == 0 then x else null) [1,2,3,4,5,6] ``` Result: ```text error: contract broken by the caller ┌─ :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 │ ┌─ (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](./contracts.md) 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. ### Using dynamically typed code inside statically typed code 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: ```nickel let x = 0 + 1 in (1 + x : Number) ``` Result: ```text 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: ```nickel 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: ```nickel (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: ```nickel (1 + (if true then 0 else "a")) : Number ``` Result: ```text 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: ```nickel 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). ### Take-away 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. ## Using contracts as types 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. ```nickel 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: ```text 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. ```nickel (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. ## Typing in practice When to use type annotation, a contract application, or none of those? This is what the guide [Type versus contracts: when to?](./types-vs-contracts.md) is for.