Permissive nominal terms and their unification Gilles

We introduce permissive nominal terms. Nominal terms are one way to extend first-order terms with binding. They lack some properties of firstand higher-order terms: Terms must be reasoned on in a context of ‘freshness assumptions’; it is not always possible to ‘choose a fresh variable symbol’ for a nominal term; and it is not always possible to ‘alpha-convert a bound variable symbol’. Permissive nominal terms resemble nominal terms but recover these ‘always fresh’ and ‘always alpha-rename’ properties, familiar from firstand higher-order syntax. Freshness contexts are elided and the notion of unifier is based on substitution alone rather than on nominal terms’ notion of substitution plus freshness conditions. Expressivity is not lost moving to the permissive case.