Unrolling a recursive function involves explicitly laying out some or all of the recursive steps, rather than relying on recursion via a fixed-point combinator. In UPLC, the typical pfix implementation uses a Y-combinator under the hood. Each recursive step incurs additional evaluation costs (CPU and memory) due to the execution of the Y-combinator. By eliminating these costs in each recursive step, unrolled functions reduce execution overhead. However, since each recursive step is explicitly laid out, unrolled functions consume more script size.

There are various unrolling strategies available. It is important to carefully study the implications of each strategy, as they may impose different requirements, such as hard limit on recursion depth.

Generally for all strategies, calling the "recursion step"--that is r in fix $ r a b ... -> ...--multiple times will result in exponential increase of the script size in each step of unrolling. This is because everytime the recursion step is called, it generates UPLC code for that specific branch(and all the subsequent branches down the unrolling!). To prevent this, it is possible to have plet r $ r' -> can be used multiple times...

Also, due to some of the other optimization performed; specifically pmatch's branch detection which requires hashing terms of all subsequent deconstruction branches, only tail-call recursion would perform fast enough to be used for large unrolling.