Revisiting Multi-Commitments

These include OP_CAT, OP_PAIRCOMMIT, OP_VECTORCOMMIT, OP_TWEAKADD, and OP_SHA256 related operations. Each of these opcodes presents unique advantages and disadvantages, particularly when considering their application in a scripting environment that either includes or excludes OP_CAT.

In scenarios where the script is restored to its Global State Replication (GSR) form, OP_CAT emerges as a naturally occurring opcode, thus rendering any concerns regarding introspection irrelevant. However, it's notable for its witness malleability issues, which often necessitate added inefficiencies in scripts leveraging this opcode. On the other hand, OP_TWEAKADD is highlighted for its utility, especially in state carrying and making the process more streamlined, albeit with worse witness malleability compared to OP_CAT. Furthermore, OP_SHA256STREAM is recognized for enhancing OP_CAT and OP_SHA256 heavy scripts by eliminating stack element size limitations and ensuring execution safety post-GSR.

The analysis then categorizes OP_PAIRCOMMIT and OP_VECTORCOMMIT as less suitable due to their reliance on a consensus around OP_CAT, which is challenged by its computational completeness with other opcodes, complicating second-order effect considerations. Conversely, in environments lacking OP_CAT, OP_PAIRCOMMIT falls short in enabling fine-grained introspection, state-carrying covenants, and new arithmetic capabilities, among others. Meanwhile, OP_VECTORCOMMIT is acknowledged for its optimization benefits over multiple calls to OP_PAIRCOMMIT, particularly for managing larger numbers of smaller pieces.

The exploration further extends to a world without OP_CAT but with access to MATT, where OP_TWEAKADD and OP_VECTORCOMMIT are essential for vector state carrying, despite potential witness malleability issues as outlined in the BIP. In this context, OP_PAIRCOMMIT is seen as potentially useful for more complex state scenarios envisioned by MATT, whereas OP_SHA256TAGGED serves as a reasonable yet mildly inefficient alternative.

Lastly, the discussion underscores the problematic nature of OP_SHA256STREAM in contexts devoid of OP_CAT, primarily due to its facilitation of transaction and parent transaction introspection, which could reintroduce complexities and vulnerabilities initially mitigated by excluding OP_CAT.

This summary encapsulates a nuanced examination of various opcode proposals within the Bitcoin scripting landscape, reflecting a collaborative effort to weigh their respective merits and limitations in pursuit of enhanced functionality and security.