It's not about any "given" AST, it's about having a computable representation of any code. For example, if I pass you a higher order mathematical function that calculates the first derivative of another function (f), you can create an algorithm that integrates the function symbolically, thus obtaining (another) primitive (related to the original f by a constant).
Note that I mean to symbolically calculate derivatives and integrals, not numerically. A homoiconic language can deconstruct any object representing code and can construct another object based on the underlying structure of the original, not based on any particular value of the original. The original doesn't even need to be invoked at all.
In mathematical parlance, a homoiconic language allows implementing functionals, as opposed to mere higher-oder functions (which is nothing more than function composition).
Please note that all this works with higher-order functions. You don't have to have a textual representation of the function. A.i. you don't parse your own source code.
LISP was actually invented to be able to implement functionals and symbolic calculations like this. The original paper demoed implementing function differentiation (among other things).
So, to understand what you are saying, is it true that in LISP, you can write a function F that can take any function object G, and turn it into an equivalent AST of G?
The spirit of your statement is true, but the precise formulation is incorrect. In LISPs, when you pass a function, you pass a list that defines the function. There is no special "turn into AST" step. Executable code is data, and you can create genuinely new executable code out of this data. There's no special "turn code into data" or "find the data corresponding to this code" step. Code just is data.
Note that I mean to symbolically calculate derivatives and integrals, not numerically. A homoiconic language can deconstruct any object representing code and can construct another object based on the underlying structure of the original, not based on any particular value of the original. The original doesn't even need to be invoked at all.
In mathematical parlance, a homoiconic language allows implementing functionals, as opposed to mere higher-oder functions (which is nothing more than function composition).
Please note that all this works with higher-order functions. You don't have to have a textual representation of the function. A.i. you don't parse your own source code.
LISP was actually invented to be able to implement functionals and symbolic calculations like this. The original paper demoed implementing function differentiation (among other things).