Higher-order abstract syntax

Imagine you're playing with Lego bricks. You have little people figures, vehicles, and buildings that you can put together to create different scenes.

Now imagine that instead of just having those pre-made pieces, you can also make new types of pieces by using other pieces. For example, you could take two little people and put them together to make a bigger person. This is like creating a new type of Lego piece using existing ones.

Higher-order abstract syntax is kind of like that. It's a way to create new types of programming concepts by using other programming concepts. Instead of just using pre-existing programming structures like numbers and functions, you can create new types of structures by combining existing ones.

For example, if you have a function that takes in a number and returns another number, you could create a new "higher-order" function that takes in that first function as an input and returns a new function as an output. This new function could take in a number and then run the first function on it before returning the result.

In this way, higher-order abstract syntax allows for a lot more flexibility and creativity in programming. It lets you build new structures and ideas by combining and manipulating existing ones.