In this work we study relations between sequence and context unification.
These problems represent two generalizations of word equations. Sequence
unification is decidable, while decidability of context unification is still an open
problem. We use "currying" transformation to encode sequence unification
into a fragment of context unification whose solutions are restricted to have a
special shape, called left-hole contexts. Extending this restriction to the entire
context unification problem, we obtain a new decidable variant of context
unification that we call left-hole context unification. Inverse "currying"
transforms left-hole context unification into a new decidable extension of
sequence unification. Besides, we obtain a new decidability proof of sequence
unification.

This is a joint work with Jordi Levy and Mateu Villaret.