According to the Java Language Specification for Java 8, a Functional Interface in Java is:

A functional interface is an interface that has just one abstract method (aside from the methods of Object), and thus represents a single function contract. This "single" method may take the form of multiple abstract methods with override-equivalent signatures inherited from superinterfaces; in this case, the inherited methods logically represent a single method.

For an interface I, let M be the set of abstract methods that are members of I that do not have the same signature as any public instance method of the class Object. Then, I is a functional interface if there exists a method m in M for which both of the following are true:

• The signature of m is a subsignature (§8.4.2) of every method's signature in M.
• m is return-type-substitutable (§8.4.5) for every method in M.

Source

ZenScript, being a Java-like programming language that interacts with a Java backend, has a similar definition.

The above definition is overly precise and complicated, which has to be expected from a formal language specification. A way more simplified version for the developer could be the following:

An interface I is called a functional interface if it defines only a single abstract method.

This definition is also accepted by ZenScript itself.

Up until now, the above documentation has more relied on "what" rather than "why". Functional interfaces may seem like a gimmick, but they're particularly useful, since in ZenScript they allow Pure Functions (i.e. the things you create with function) to be passed to Java code without requiring weird shenanigans. This is something that we define as "lambda".

Examples of applications of these interfaces are the Recipe Functions that can be passed to recipes to change the output or input dynamically: IRecipeFunction and IRecipeAction are in fact two functional interfaces.

The Functional Interfaces that are available in the ZenScript language are all overly specific. On one hand, this allows finely crafted functions for certain parameters; on the other hand, this severely limits the possibilities of what can be done by the developer.

For this reason, the ZenScriptX Project decided to provide a set of general purpose functional interfaces that can receive a set amount of input parameters and output something else, allowing for easier interoperability with Java-based APIs. A full list of the functional interfaces that are available can be found on this page, along with all their arguments and return types.

Note that in this documentation we have referred mainly to interoperability between ZenScript and Java. This is because ZenScript already provides support for higher-order functions (i.e. storing functions in a variable, calling them, passing them as parameters etc.) without requiring any functional interface in-between. For this reason the following code would be invalid in ZenScript:

ZenScript
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val fun as Function = function (input as IIngredient) as IItemStack {
    if (input instanceof IItemStack) return input as IItemStack;
    return null;
} as Function;

print(fun.apply(<minecraft:stick>).commandString); # doesn't compile

This happens because the functional methods aren't exposed to ZenScript, but only to the Java backend. To find an example of a real usage of such functional interfaces, refer to the Sequences documentation page.