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Basic Syntactic Mutation (BSM) is a mutation based unification algorithm for the theories that are saturated by paramodulation. The algorithm has been introduced by Christopher Lynch et al. in the paper Basic Syntactic Mutation.

Inspired by the above work, we developed a new and simplified mutation-based unification algorithm for solving a unification problem modulo the theories that are both convergent and forward closed. We call the algorithm as BSM'. The BSM' procedure consists of inference rules such as Coalesce, Split, Imit, MutConflict, and ImitCycle. The inference procedure prioritize the rules in the following order: Coalesce, Split, and then applies the rules Imit, MuConflict, and ImitCycle in a non-deterministic way. We have implemented the procedure in Maude, a high performance reflective language.

For more details about the BSM' procedure, please see the following paper.

• Ajay K. Eeralla, Serdar Erbatur, Andrew M. Marshall, Christophe Ringeissen. Unification in Non-Disjoint Combinations with Forward-Closed Theories (extended version).

To run the algorithm you will need to have installed Maude.

Download and install Maude from here.

Download .maude file(s) to a directory. Then navigate to the directory and run the following commands.

1. Load the file using the following command

> load filename.maude 

2. Testing

> red in myBSMPrime : bsmUnify ( UnPr , RWS, BAL, N, SUB ) 

where UnPr is an unification problem, RWS is a rewrite system, BAL is a data structure that keeps tracking the box-status of the terms (Empty at the begining), N is a new-variable-counter (0 initially), and SUB is the substitution or solution. Of course, SUB is none at the begining.

• Ajay K. Eeralla, Serdar Erbatur, Andrew M. Marshall, Christophe Ringeissen. Rule-Based Unification in Combined Theories and the Finite Variant Property in Language and Automata Theory and Applications - 13th International Conference, LATA 2019, St. Petersburg, Russia, March 26-29, 2019, Proceedings.