[zmonx]

For one particular example where homoiconicity makes reasoning about programs easier, consider an important reasoning method called abstract interpretation:

https://en.wikipedia.org/wiki/Abstract_interpretation

Using abstract interpretation, you can derive interesting program properties. The uniformity and simplicity of Prolog code, as well as its built-in language constructs like unification and backtracking, make it especially easy to write abstract interpreters for Prolog.

Here is a paper that applies this idea to derive several interesting facts about programs and their meaning:

Michael Codish and Harald Søndergaard, Meta-circular Abstract Interpretation in Prolog (2002) https://link.springer.com/chapter/10.1007%2F3-540-36377-7_6

Abstract interpretation is also applicable to other programming languages. However, it is much easier to apply to homoiconic languages like Prolog.

[kd0amg]

Abstract interpretation is entirely about the semantics of programs and has nothing to do with their surface syntax.

[zmonx]

Yes, indeed!

Please note that what makes this reasoning method so easily applicable in this case is uniformity of the abstract syntax, not of the surface syntax, which is also called concrete syntax.

Homoiconicity is a relation between the concrete and abstract syntax tree (AST) of programs and the language's built-in data structures.

[catnaroek]

No idea about you, but when I reason about programs, I spend very little time manipulating syntax. Most of the time is spent manipulating semantic objects, like predicates on the program state, whose representation is independent from even the abstract syntax of a programming language.