You can think of the semantics (i.e., specification) of any CRDT as a function that inputs the operation history DAG and outputs the resulting user-facing state. However, algorithms and implementations usually have a more programmatic description, like "here is a function `(internal state, new operation) -> new internal state`", both for efficiency (update speed; storing less info than the full history) and because DAGs are hard to reason about. But you do see the function-of-history approach in the paper "Pure Operation-Based Replicated Data Types" [1].

[1] https://arxiv.org/abs/1710.04469