Introduction to Programming in ATS:
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Function Interface

The interface for a function specifies the type assigned to the function. It offers a means to describe a function that is both efficient and informative. Given a binary function foo of the type (T1, T2) -> T3, its interface can be written as follows: 

fun foo (arg1: T1, arg2: T2): T3

where arg1 and arg2 may be replaced with any other legal identifiers for function arguments. For functions of more or fewer arguments, interfaces can be written in a similar fashion. For instance, we have the following interfaces for various functions on integers: 

fun succ_int (x: int): int // successor
fun pred_int (x: int): int // predecessor

fun add_int_int (x: int, y: int): int // +
fun sub_int_int (x: int, y: int): int // -
fun mul_int_int (x: int, y: int): int // *
fun div_int_int (x: int, y: int): int // /

fun mod_int_int (x: int, y: int): int // modulo
fun gcd_int_int (x: int, y: int): int // greatest common divisor

fun lt_int_int (x: int, y: int): bool // <
fun lte_int_int (x: int, y: int): bool // <=
fun gt_int_int (x: int, y: int): bool // >
fun gte_int_int (x: int, y: int): bool // >=
fun eq_int_int (x: int, y: int): bool // =
fun neq_int_int (x: int, y: int): bool // <>

fun max_int_int (x: int, y: int): int // maximum
fun min_int_int (x: int, y: int): int // minimum

fun print_int (x: int): void
fun tostring_int (x: int): string

For now, I mostly use function interfaces for the purpose of presenting functions. I will show later how a function definition can be separated into two parts: a function interface and an implementation that implements the function interface. Note that separation as such is pivotal for constructing (large) programs in a modular style.

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