8. Compiler Error Index

Elaboration on type errors produced by the compiler. Many error messages contain links to the sections below.

8.1. Uniqueness errors

8.1.1. “Using x, but this was consumed at y.”

A core principle of uniqueness typing (see In-place Updates) is that after a variable is “consumed”, it must not be used again. For example, this is invalid, and will result in the error above:

let y = x with [0] = 0
in x

Several operations can consume a variable: array update expressions, calling a function with unique-typed parameters, or passing it as the initial value of a unique-typed loop parameter. When a variable is consumed, its aliases are also considered consumed. Aliasing is the possibility of two variables occupying the same memory at run-time. For example, this will fail as above, because y and x are aliased:

let y = x
let z = y with [0] = 0
in x

We can always break aliasing by using a copy expression:

let y = copy x
let z = y with [0] = 0
in x

8.1.2. “Would consume x, which is not consumable”

This error message occurs for programs that try to perform a consumption (such as an in-place update) on variables that are not consumable. For example, it would occur for the following program:

def f (a: []i32) =
  let a[0] = a[0]+1
  in a

Only arrays with a a unique array type can be consumed. Such a type is written by prefixing the array type with an asterisk. The program could be fixed by writing it like this:

def f (a: *[]i32) =
  let a[0] = a[0]+1
  in a

Note that this places extra obligations on the caller of the f function, since it now consumes its argument. See In-place Updates for the full details.

You can always obtain a unique copy of an array by using copy:

def f (a: []i32) =
  let a = copy a
  let a[0] = a[0]+1
  in a

But note that in most cases (although not all), this subverts the purpose of using in-place updates in the first place.

8.1.3. “Unique-typed return value of x is aliased to y, which is not consumable”

This can be caused by a function like this:

def f (xs: []i32) : *[]i32 = xs

We are saying that f returns a unique array - meaning it has no aliases - but at the same time, it aliases the parameter xs, which is not marked as being unique (see In-place Updates). This violates one of the core guarantees provided by uniqueness types, namely that a unique return value does not alias any value that might be used in the future. Imagine if this was permitted, and we had a program that used f:

let b = f a
let b[0] = x

The update of b is fine, but if b was allowed to alias a (hence occupying the same memory), then we would be modifying a as well, which is a violation of referential transparency.

As with most uniqueness errors, it can be fixed by using copy xs to break the aliasing. We can also change the type of f to take a unique array as input:

def f (xs: *[]i32) : *[]i32 = xs

This makes xs “consumable”, in the sense used by the error message.

8.1.4. “A unique-typed component of the return value of x is aliased to some other component”

Caused by programs like the following:

def main (xs: *[]i32) : (*[]i32, *[]i32) = (xs, xs)

While we are allowed to “consume” xs, as it is a unique parameter, this function is trying to return two unique values that alias each other. This violates one of the core guarantees provided by uniqueness types, namely that a unique return value does not alias any value that might be used in the future (see In-place Updates) - and in this case, the two values alias each other. We can fix this by inserting copies to break the aliasing:

def main (xs: *[]i32) : (*[]i32, *[]i32) = (xs, copy xs)

8.1.5. “Argument passed for consuming parameter is self-aliased.”

Caused by programs like the following:

def g (t: *([]i64, []i64)) = 0

def f n =
  let x = iota n
  in g (x,x)

The function g expects to consume two separate []i64 arrays, but f passes it a tuple containing two references to the same physical array. This is not allowed, as g must be allowed to assume that components of consuming record- or tuple parameters have no internal aliases. We can fix this by inserting copies to break the aliasing:

def f n =
  let x = iota n
  in g (copy (x,x))

Alternative, we could duplicate the expression producing the array:

def f n =
  g (iota n, iota n))

8.1.6. “Consuming parameter passed non-unique argument”

Caused by programs like the following:

def update (xs: *[]i32) = xs with [0] = 0

def f (ys: []i32) = update ys

The update function consumes its xs argument to perform an in-place update, as denoted by the asterisk before the type. However, the f function tries to pass an array that it is not allowed to consume (no asterisk before the type).

One solution is to change the type of f so that it also consumes its input, which allows it to pass it on to update:

def f (ys: *[]i32) = update ys

Another solution to copy the array that we pass to update:

def f (ys: []i32) = update (copy ys)

8.1.7. “Non-consuming higher-order parameter passed consuming argument.”

This error occurs when we have a higher-order function that expects a function that does not consume its arguments, and we pass it one that does:

def apply 'a 'b (f: a -> b) (x: a) = f x

def consume (xs: *[]i32) = xs with [0] = 0

def f (arr: *[]i32) = apply consume arr

We can fix this by changing consume so that it does not have to consume its argument, by adding a copy:

def consume (xs: []i32) = copy xs with [0] = 0

Or we can create a variant of apply that accepts a consuming function:

def apply 'a 'b (f: *a -> b) (x: *a) = f x

8.1.8. “Function result aliases the free variable x

Caused by definitions such as the following:

def x = [1,2,3]

def f () = x

To simplify the tracking of aliases, the Futhark type system requires that the result of a function may only alias the function parameters, not any free variables. Use copy to fix this:

def f () = copy x

8.1.9. “Size expression with binding is replaced by unknown size.”

To illustrate this error, consider the following program

def main (xs: *[]i64) =
  let a = iota (let n = 10 in n+n)
  in ...

Intuitively, the type of a should be [let n = 10 in n+n]i32, but this puts a binding into a size expression, which is invalid. Therefore, the type checker invents an unknown size variable, say l, and assigns a the type [l]i32.

8.1.10. “Size expression with consumption is replaced by unknown size.”

To illustrate this error, consider the following program

def consume (xs: *[]i64): i64 = xs[0]

def main (xs: *[]i64) =
  let a = iota (consume xs)
  in ...

Intuitively, the type of a should be [consume ys]i32, but this puts a consumption of the array ys into a size expression, which is invalid. Therefore, the type checker invents an unknown size variable, say l, and assigns a the type [l]i32.

8.1.11. “Parameter x refers to size y which will not be accessible to the caller

This happens when the size of an array parameter depends on a name that cannot be expressed in the function type:

def f (x: i64, y: i64) (A: [x]bool) = true

Intuitively, this function might have the following type:

val f : (x: i64, y: i64) -> [x]bool -> bool

But this is not currently a valid Futhark type. In a function type, each parameter can be named as a whole, but it cannot be taken apart in a pattern. In this case, we could fix it by splitting the tuple parameter into two separate parameters:

def f (x: i64) (y: i64) (A: [x]bool) = true

This gives the following type:

val f : (x: i64) -> (y: i64) -> [x]bool -> bool

Another workaround is to loosen the static safety, and use a size coercion to give A its expected size:

def f (x: i64, y: i64) (A_unsized: []bool) =
  let A = A_unsized :> [x]bool
  in true

This will produce a function with the following type:

val f [d] : (i64, i64) -> [d]bool -> bool

This does however lose the constraint that the size of the array must match one of the elements of the tuple, which means the program may fail at run-time.

The error is not always due to an explicit type annotation. It might also be due to size inference:

def f (x: i64, y: i64) (A: []bool) = zip A (iota x)

Here the type rules force A to have size x, leading to a problematic type. It can be fixed using the techniques above.

8.2. Size errors

8.2.1. “Size x unused in pattern.”

Caused by expressions like this:

def [n] (y: i32) = x

And functions like this:

def f [n] (x: i32) = x

Since n is not the size of anything, it cannot be assigned a value at runtime. Hence this program is rejected.

8.2.2. “Causality check”

Causality check errors occur when the program is written in such a way that a size is needed before it is actually computed. See Causality restriction for the full rules. Contrived example:

def f (b: bool) (xs: []i32) =
  let a = [] : [][]i32
  let b = [filter (>0) xs]
  in a[0] == b[0]

Here the inner size of the array a must be the same as the inner size of b, but the inner size of b depends on a filter operation that is executed after a is constructed.

There are various ways to fix causality errors. In the above case, we could merely change the order of statements, such that b is bound first, meaning that the size is available by the time a is bound. In many other cases, we can lift out the “size-producing” expressions into a separate let-binding preceding the problematic expressions.

8.2.3. “Unknown size x in parameter of y

This error occurs when you define a function that can never be applied, as it requires an input of a specific size, and that size is an unknown size. Somewhat contrived example:

def f (x: bool) =
  let n = if x then 10 else 20
  in \(y: [n]bool) -> ...

The above constructs a function that accepts an array of size 10 or 20, based on the value of x argument. But the type of f true by itself would be ?[n].[n]bool -> bool, where the n is unknown. There is no way to construct an array of the right size, so the type checker rejects this program. (In a fully dependently typed language, the type would have been [10]bool -> bool, but Futhark does not do any type-level computation.)

In most cases, this error means you have done something you didn’t actually mean to. However, in the case that that the above really is what you intend, the workaround is to make the function fully polymorphic, and then perform a size coercion to the desired size inside the function body itself:

def f (x: bool) =
  let n = if x then 10 else 20
  in \(y_any: []bool) ->
       let y = y_any :> [n]bool
       in true

This requires a check at run-time, but it is the only way to accomplish this in Futhark.

8.2.4. “Existential size would appear in function parameter of return type”

This occurs most commonly when we use function composition with one or more functions that return an existential size. Example:

filter (>0) >-> length

The filter function has this type:

val filter [n] 't : (t -> bool) -> [n]t -> ?[m].[m]t

That is, filter returns an array whose size is not known until the function actually returns. The length function has this type:

val length [n] 't : [n]t -> i64

Whenever length occurs (as in the composition above), the type checker must instantiate the [n] with the concrete symbolic size of its input array. But in the composition, that size does not actually exist until filter has been fully applied. For that matter, the type checker does not know what >-> does, and for all it knows it may actually apply filter many times to different arrays, yielding different sizes. This makes it impossible to uniquely instantiate the type of length, and therefore the program is rejected.

The common workaround is to use pipelining instead of composition whenever we use functions with existential return types:

xs |> filter (>0) |> length

This works because |> is left-associative, and hence the xs |> filter (>0) part will be fully evaluated to a concrete array before length is reached.

We can of course also write it as length (filter (>0) xs), with no use of either pipelining or composition.

8.2.5. “Existential size n not used as array size”

This error occurs for type expressions that bind an existential size for which there is no constructive use, such as in the following examples:


?[n].bool -> [n]bool

When we use existential quantification, we are required to use the size constructively within its scope, in particular it must not be exclusively as the parameter or return type of a function.

To understand the motivation behind this rule, consider that when we use an existential quantifier we are saying that there is some size. The size is not known statically, but must be read from some value (i.e. array) at runtime. In the first example above, the existential size n is not used at all, so the actual value cannot be determined at runtime. In the second example, while an array [n]bool does exist, it is part of a function type, and at runtime functions are black boxes and don’t “carry” the size of their parameter or result types.

The workaround is to actually use the existential size. This can be as simple as adding a witness array of type [n]():


?[n].([n](), bool -> [n]bool)

Such an array will take up no space at runtime.

8.2.6. “Type abbreviation contains an anonymous size not used constructively as an array size.”

This error occurs for type abbreviations that use anonymous sizes, such as the following:

type^ t = []bool -> bool

Such an abbreviation is actually shorthand for

type^ t = ?[n].[n]bool -> bool

which is erroneous, but with workarounds, as explained in “Existential size n not used as array size”.

8.2.7. “Parameter x used as size would go out of scope.”

This error tends to happen when higher-order functions are used in a way that causes a size requirement to become impossible to express. Real programs that encounter this issue tend to be complicated, but to illustrate the problem, consider the following contrived function:

def f (n: i64) (m: i64) (b: [n][m]bool) = b[0,0]

We have the following type:

val f : (n: i64) -> (m: i64) -> (b: [n][m]bool) -> bool

Now suppose we say:

def g = uncurry f

What should be the type of g? Intuitively, something like this:

val g : (n: i64, m: i64) -> (b: [n][m]bool) -> bool

But this is not expressible in the Futhark type system - and even if it were, it would not be easy to infer this in general, as it depends on exactly what uncurry does, which the type checker does not know.

As a workaround, we can use explicit type annotation and size coercions to give g an acceptable type:

def g [a][b] (n,m) (b: [a][b]bool) = f n m (b :> [n][m]bool)

Another workaround, which is often the right one in cases not as contrived as above, is to modify f itself to produce a witness of the constraint, in the form of an array of shape [n][m]:

def f (n: i64) (m: i64) : ([n][m](), [n][m]bool -> bool) =
  (replicate n (replicate m ()), \b -> b[0,0])

Then uncurry f works just fine and has the following type:

(i64, i64) -> ?[n][m].([n][m](), [n][m]bool -> bool)

Programming with such explicit size witnesses is a fairly advanced technique, but often necessary when writing advanced size-dependent code.

8.2.8. “Parameter types x and y are incompatible regarding consuming their arguments

This error occurs when you provide a function that does consume its argument in a context that expects a function that does not allow a function that consumes its argument.

As a simple example, consider the following contrived function that does consume its argument:

def f (xs: *[]f32) : f32 = 0f32

Now we define another function that is merely f, but with a type annotation that tries to hide the consumption:

def g : []f32 -> f32 = f

Allowing this would permit us to hide the fact that f consumes its argument, which would not be sound, so the type checker complains.

8.2.9. “Ambiguous size x

There are various sources for this error, but they all have the same ultimate cause: the type checker cannot figure out how some symbolic size name should be resolved to a concrete size. The simplest example, although contrived, is probably this:

let [n][m] (xss: [n][m]i64) = []

The type checker can infer that n should be zero, but how can it possibly figure out the shape of the (non-existent) rows of the two-dimensional array? This can be fixed in many ways, but adding a type ascription to the array is one of them: [] : [0][2]i64.

Another common case arises when using holes. For an expression length ???, how would the type checker figure out the intended size of the array that the hole represents? Again, this can be solved with a type ascription: length (??? : [10]bool).

Finally, ambiguous sizes can also occur for functions that use size parameters only in “non-witnessing” position, meaning sizes that are not actually uses as sizes of real arrays. An example:

def f [n] (g: [n]i64 -> i64) : i64 = n

def main = f (\xs -> xs[0])

Note that f is a higher order function, and that the size parameter n is only used in the type of the g function. Futhark’s value model is such that given a value of type [n]i64 -> i64, we cannot extract an n from it. Using a function such as f is only valid when n can be inferred from the usage, which is not the case here. Again, we can fix it by adding a type ascription to disambiguate:

def main = f (\(xs:[1]i64) -> xs[0])

8.3. Module errors

8.3.1. “Module x is a parametric module

A parametric module is a module-level function:

module PM (P: {val x : i64}) = {
  def y = x + 2

If we directly try to access the component of PM, as PM.y, we will get an error. To use PM we must first apply it to a module of the expected type:

module M = PM { val x = 2 : i64 }

Now we can say M.y. See Modules for more.

8.4. Other errors

8.4.1. “Literal out of bounds”

This occurs for overloaded constants such as 1234 that are inferred by context to have a type that is too narrow for their value. Example:

257 : u8

It is not an error to have a non-overloaded numeric constant whose value is too large for its type. The following is perfectly cromulent:


In such cases, the behaviour is overflow (so this is equivalent to 1u8).

8.4.2. “Type is ambiguous”

There are various cases where the type checker is unable to infer the full type of something. For example:

def f r = r.x

We know that r must be a record with a field called x, but maybe the record could also have other fields as well. Instead of assuming a perhaps too narrow type, the type checker signals an error. The solution is always to add a type annotation in one or more places to disambiguate the type:

def f (r: {x:bool, y:i32}) = r.x

Usually the best spot to add such an annotation is on a function parameter, as above. But for ambiguous sum types, we often have to put it on the return type. Consider:

def f (x: bool) = #some x

The type of this function is ambiguous, because the type checker must know what other possible contructors (apart from #some) are possible. We fix it with a type annotation on the return type:

def f (x: bool) : (#some bool | #none) = #just x

See Type Abbreviations for how to avoid typing long types in several places.

8.4.3. “The x operator may not be redefined”

The && and || operators have magical short-circuiting behaviour, and therefore may not be redefined. There is no way to define your own short-circuiting operators.

8.4.4. “Unmatched cases in match expression”

Futhark requires match expressions to be exhaustive - that is, cover all possible forms of the value being matched. Example:

def f (x: i32) =
  match x case 0 -> false
          case 1 -> true

Usually this is an actual bug, and you fix it by adding the missing cases. But sometimes you know that the missing cases will never actually occur at run-time. To satisfy the type checker, you can turn the final case into a wildcard that matches anything:

def f (x: i32) =
  match x case 0 -> false
          case _ -> true

Alternatively, you can add a wildcard case that explicitly asserts that it should never happen:

def f (x: i32) =
  match x case 0 -> false
          case 1 -> true
          case _ -> assert false false

See here for details on how to use assert.

8.4.5. “Refutable pattern not allowed here”

This occurs when you try to use a refutable pattern in a let binding or function parameter. A refutable pattern is a pattern that is not guaranteed to match a well-typed value. For example, this expression tries to bind an arbitrary tuple value x a pattern that requires the first element is 2:

let (2, y) = x in 0

What should happen at run-time if x is not 2? Refutable patterns are only allowed in match expressions, where the failure to match can be handled. For example:

match x
case (2, y) ->  0
case _ -> ... -- do something else

8.4.6. “Full type of x is not known at this point”

When performing a record update, the type of the field we are updating must be known. This restriction is based on a limitation in the type type checker, so the notion of “known” is a bit subtle:

def f r : {x:i32} = r with x = 0

Even though the return type annotation disambiguates the type, this program still fails to type check. This is because the return type is not consulted until after the body of the function has been checked. The solution is to put a type annotation on the parameter instead:

def f (r : {x:i32}) = r with x = 0

8.5. Entry points

8.5.1. “Entry points may not be declared inside modules.”

This occurs when the program uses the entry keyword inside a module:

module m = {
  entry f x = x + 1

Entry points can only be declared at the top level of a file. When we wish to make a function from inside a module available as an entry point, we must define a wrapper function:

module m = {
  def f x = x + 1

entry f = m.f

8.5.2. “Entry point functions may not be polymorphic.”

Entry points are Futhark functions that can be called from other languages, and are therefore limited how advanced their types can be. In this case, the problem is that an entry point may not have a polymorphic type, for example:

entry dup 't (x: t) : (t,t) = x

This is an invalid entry point because it uses a type parameter 't. This error occurs frequently when we want to test a polymorphic function. In such cases, the solution is to define one or more monomorphic entry points, each for a distinct type. For example, to we can define a variety of monomorphic entry points that call the built-in function scan:

entry scan_i32 (xs: []i32) = scan (+) 0 xs

entry scan_f32 (xs: []i32) = scan (*) 1 xs

8.5.3. “Entry point functions may not be higher-order.”

Entry points are Futhark functions that can be called from other languages, and are therefore limited how advanced their types can be. In this case, the problem is that an entry point may use functions as input or output. For example:

entry apply (f: i32 -> i32) (x: i32) = f x

There is no simple workaround for such cases. One option is to manually defunctionalise to use a non-functional encoding of the functional values, but this can quickly get very elaborate. Following up on the example above, if we know that the only functions that would ever be passed are (+y) or (*y) for some y, we could do something like the following:

type function = #add i32 | #mul i32

entry apply (f: function) (x: i32) =
  match f
  case #add y -> x + y
  case #mul y -> x + y

Although in many cases, the best solution is simply to define a handful of simpler entry points instead of a single complicated one.

8.5.4. “Entry point functions must not be size-polymorphic in their return type.”

This somewhat rare error occurs when an entry point returns an array that can have an arbitrary size chosen by its caller. Contrived example:

-- Entry point taking no parameters.
entry f [n] : [0][n]i32 = []

The size n is chosen by the caller. Note that the n might be inferred and invisible, as in this example:

entry g : [0][]i32 = []

When calling functions within a Futhark program, size parameters are handled by type inference, but entry points are called from the outside world, which is not subject to type inference. If you really must have entry points like this, turn the size parameter into an ordinary parameter:

entry f (n: i64) : [0][n]i32 = []

8.5.5. “Entry point size parameter [n] only used non-constructively.”

This error occurs for programs such as the following:

.. code-block:: futhark

entry main [x] (A: [x+1]i32) = …

The size parameter [x] is only used in an size expression x+1, rather than directly as an array size. This is allowed for ordinary functions, but not for entry points. The reason is that entry points are not subject to ordinary type inference, as they are called from the external world, meaning that the value of the size parameter [x] will have to be determined from the size of the array A. This is in principle not a problem for simple sizes like x+1, as it is obvious that x == length A - 1, but in the general case it would require computing function inverses that might not exist. For this reason, entry points require that all size parameters are used constructively.

As a workaround, you can rewrite the entry point as follows:

entry main [n] (A: [n]i32) =
  let x = n-1
  let A = A :> [x+1]i32

Or by passing the x explicitly:

entry main (x: i64) (A: [x+1]i32) = ...