You are aware you're asking to "mathematically formalize" algorithm constructs, right? Either you know nothing about the subject or are trolling this thread in spite of being completely removed from the field.
Algorithms are mathematical objects, and they sure as hell can be formalized. Alas, software design “patterns” aren't algorithms. And, so long as they resist formalization, they are non-ideas.
Accusations of trolling are completely unwarranted.
Accusations of trolling are completely unwarranted.