Concerning classical computational models able to express all the Primitive Recursive Functions (PRF), there are interesting results regarding limits on their algorithmic expressiveness or, equivalently, efficiency, namely the ability to express algorithms with minimal computational cost. By introducing the reversible programming model Forest, at our knowledge, we provide a first study of analogous properties, adapted to the context of reversible computational models that can represent all the functions in PRF. Firstly, we show that Forest extends Matos' linear reversible computational model MSRL, the very extension being a guaranteed terminating iteration that can be halted by means of logical predicates. The consequence is that Forest is PRF complete, because MSRL is. Secondly, we show that Forest is strictly algorithmically more expressive than MSRL: it can encode a reversible algorithm for the minimum between two integers in optimal time, while MSRL cannot.

翻译：关于能够表达所有原始递归函数（PRF）的经典计算模型，已有研究揭示了它们在算法表达力（或等价地，计算效率）上的有趣极限结果，即能否以最小计算成本表达算法。通过引入可逆编程模型Forest，据我们所知，我们首次针对能够表示PRF中所有函数的可逆计算模型，研究了其相应的性质。首先，我们证明Forest扩展了Matos的线性可逆计算模型MSRL，这种扩展本质上是一种保证终止的迭代机制，可通过逻辑谓词实现中止。由于MSRL具有PRF完备性，因此Forest也具有PRF完备性。其次，我们证明Forest在算法表达力上严格优于MSRL：它能够以最优时间复杂度编码两个整数间最小值的可逆算法，而MSRL无法实现这一点。