A polymorphic function is rather similar to a function template. However, the former is a first-class value in ATS while the latter is not. As an example, the following defined function swap_boxed is polymorphic:

The type variables a and b are often referred as static arguments while xy is a dynamic argument. For example, the following code makes use of the polymorphic function swap_boxed:val AB = (box("A"), box("B")) val BA1 = swap_boxed{boxstr,boxstr} (AB) val BA2 = swap_boxed (AB) // omitting type arguments may be fine

When calling a polymorphic function, we often omit passing static arguments explicitly and expect them to be synthesized by the compiler. However, there are also occasions, which are not uncommon, where static arguments need to be supplied explicitly as either they cannot be successfully synthesized or what is synthesized is not exactly what is expected by the programmer.

It is also possible to pass static arguments sequentially as is shown in the following style of implementation of a polymorphic function:

// fun swap2_boxed{a:type}{b:type} (xy: (a, b)): (b, a) = (xy.1, xy.0) // val AB = (box("A"), box("B")) val BA1 = swap2_boxed (AB) // both static arguments to be synthesized val BA2 = swap2_boxed{...} (AB) // both static arguments to be synthesized val BA3 = swap2_boxed{..}{boxstr} (AB) // 1st static argument to be synthesized val BA4 = swap2_boxed{boxstr}{..} (AB) // 2nd static argument to be synthesized val BA5 = swap2_boxed{..}{..} (AB) // both static arguments to be synthesized val BA6 = swap2_boxed{boxstr}{boxstr} (AB) // both static arguments are provided //

I have seen two kinds of errors involving polymorphic functions that are extremely common in practice.

The first kind is depicted in the following example:

Notice that the sort for type variables a and b is t@ype (instead of type). While this example can pass typechecking, its compilation results in a compile-time error that may seem mysterious to many programmers. The simple reason for this error is that the compiler cannot figure out the size of a and b when trying to generate code in C as the sort t@ype is for types of unspecified size.The second kind is depicted in the following example:

Strictly speaking, there is really no error in this case. If defined as such, swap_boxed is a function template instead of a polymorphic function. However, such a function template is severely restricted as it cannot be instantiated with types that are not boxed. While this could be intended, it is very unlikely.