Formal Description of Data Structures and Algorithms

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Math is (mostly) established on first-order formal logic. In computer science, the core study is about algorithms and data structures. I am wondering, if it is possible to describe algorithms and data structures in formal first-order logic, using object language. For example, can we see an algorithm as an object (a, say, in a formal system), and assert that there exists a time complexity function and a space complexity function associated with it. Further, can we use formal mathematical language to describe data structures such as linked lists, binary trees?