Examples of reversible computations Irreversible computations can be intuitive. For example, it is easy to understand roles of AND, OR, NOT gates and design a system without any intermediate, compilable layer. The gates can be directly used as they conform to human's thinking.

I have read a paper where it was stated that it is obviously correct way to code irreversibly, and compile to reversible form (can't find the paper now).

I am wondering if there exists a reversible model, that is as easy to understand as AND, OR, NOT model. The model should be therefore "direct" use of reversibility. So no compilation. But also: no models of form: $f(a) \rightarrow (a,f(a))$ (ie. models created by taking irreversible function $f$ and making it reversible by keeping copy of its input).
The paper you mention is probably one of Paul Vitányi's, possibly Time, Space, and Energy in Reversible Computing.

However, not everyone takes the viewpoint that simulation of irreversible computations is the main point. There is some research into what reversible computing can do in addition to such simulations, the beginnings of which is in Bennett's seminal paper Logical Reversibility of Computation on reversible Turing machines. See this paper for an elaboration of these ideas.

In terms of reversible logic circuits, there has been significant effort from the quantum computing community to build non-trivial circuits for arithmetic, e.g. Quantum networks for elementary arithmetic operations, some of which are purely classical, i.e., reversible. These implement a reversible variant of, say, addition, where one of the operands is conserved, but they do not rely on "irreversible thinking", do not use a history, and display a significant amount of ingenuity in their design.