Nominal syntax with atom substitutions
Nominal syntax is a generalisation of first-order syntax that includes names, a notion of name binding and an elegant axiomatisation of alpha-equivalence, based on nominal set theory. However, it does not take into account non-capturing atom substitution, which is not a primitive notion in nominal s...
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| Published in | Journal of computer and system sciences Vol. 119; pp. 34 - 59 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
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Elsevier Inc
01.08.2021
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| ISSN | 0022-0000 1090-2724 |
| DOI | 10.1016/j.jcss.2021.01.002 |
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| Abstract | Nominal syntax is a generalisation of first-order syntax that includes names, a notion of name binding and an elegant axiomatisation of alpha-equivalence, based on nominal set theory. However, it does not take into account non-capturing atom substitution, which is not a primitive notion in nominal syntax. We consider an extension of nominal syntax with non-capturing atom substitutions and show that matching is decidable and finitary but unification is undecidable in general. The proof of undecidability of unification is obtained by reducing Hilbert's tenth problem to unification of extended nominal terms. We provide a general matching algorithm and characterise a class of problems for which matching is unitary, giving rise to expressive and efficient rewriting systems. |
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| AbstractList | Nominal syntax is a generalisation of first-order syntax that includes names, a notion of name binding and an elegant axiomatisation of alpha-equivalence, based on nominal set theory. However, it does not take into account non-capturing atom substitution, which is not a primitive notion in nominal syntax. We consider an extension of nominal syntax with non-capturing atom substitutions and show that matching is decidable and finitary but unification is undecidable in general. The proof of undecidability of unification is obtained by reducing Hilbert's tenth problem to unification of extended nominal terms. We provide a general matching algorithm and characterise a class of problems for which matching is unitary, giving rise to expressive and efficient rewriting systems. |
| Author | Fernández, Maribel Domínguez, Jesús |
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| Cites_doi | 10.1145/944746.944729 10.1016/0168-0072(94)90083-3 10.1017/S0960129500003108 10.1093/logcom/exp033 10.1016/j.entcs.2007.01.017 10.1016/j.tcs.2004.06.016 10.1016/j.ic.2006.12.002 10.1016/j.entcs.2007.02.009 10.1007/s001650200016 10.1016/j.tcs.2008.05.012 10.1016/j.entcs.2005.11.039 10.1007/s00165-007-0056-1 10.1016/0304-3975(81)90040-2 10.1016/S0890-5401(03)00138-X 10.1006/inco.2000.2877 10.1145/2159531.2159532 10.1093/jigpal/jzq006 |
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| Keywords | Matching Non-capturing substitution Nominal syntax Rewriting Unification |
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| SubjectTerms | Matching Nominal syntax Non-capturing substitution Rewriting Unification |
| Title | Nominal syntax with atom substitutions |
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