Abstract
We consider unifaction modulo some equational theory E: Given are terms s, t ε Τ (E) built from the signature ε(E) of E and from variables x in V. A substitution unifies s,t if σ(s) ≡E σ(t), i.e. σ(s), σ(t) are equivalent modulo theory E.
In particular we give a unification algorithm for theories E = E 1 ∪ ⋯ ∪ E n which are combinations of theories with disjoint signatures, ε(E i ) ∩ ε(E j ) = Φ for i ≠ j. Our method works if for each theory E i there exists a restricted unification algorithm: Given a set of equations P = {s 1
t 1, ..., s m
t m }, a linear ordering < of the variables in P, a set L of locked variables, the algorithm returns solutions σ with the following properties: • σ(s j ) ≡ Ei(t j ) • x does not occur in σ(y) if y < x • σ(x) = x if x ε L. No other restrictions are needed for the theories E i .
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References
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© 1993 Springer-Verlag Berlin Heidelberg
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Auer, P. (1993). Unification in the combination of disjoint theories. In: Abdulrab, H., Pécuchet, JP. (eds) Word Equations and Related Topics. IWWERT 1991. Lecture Notes in Computer Science, vol 677. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56730-5_37
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DOI: https://doi.org/10.1007/3-540-56730-5_37
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Online ISBN: 978-3-540-47636-8
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