Citation Context

..., meaning that it is based on possibly infinitely supported nominal sets with co-infinite support. In [GP01] a nominal semantics based on finite and co-infinite support was used. • Unlike [UPG04] and =-=[DGM10]-=- we use nominal abstract syntax to build our nominal terms. That is, in this paper nominal terms atoms-abstraction is directly equal to Gabbay-Pitts atoms-abstraction. Thus, nominal terms here are an ...

Citation Context

...plexity. As for the related topics, we would like to mention nominal anti-unification. There has been several papers exploring relationship between nominal terms and higher-order patterns (see, e.g., =-=[10, 12, 19, 20]-=- among others), proposing trans-lations between them in the context of solving unification problems. However, it is not immediately clear how to reuse those translations for anti-unification, in part...

Citation Context

...ose some list of atoms to abstract—if our language did not admit non-equivariant constants, as was the case for the original Urban-Pitts-Gabbay syntax from [UPG04] or its permissive variant from e.g. =-=[DGM10]-=-, then we could just write [L]H . In the case of tuples, we know we can write every element in the form [l]xi for 1 ≤ i ≤ n for some xi, by Lemma 4.9. 12 Proposition 4.17. [m]H from Definition 4.15 is...

Citation Context

...as been investigated by several authors, who designed and analyzed algorithms for nominal unification [3, 4, 15, 26], nominal matching [5], equivariant unification [6], permissive nominal unification =-=[8]-=-. However, in contrast to unification, its dual problem, anti-unification, has not been studied for nominal terms previously. In [18], it is referred to as “the as-of-yet undiscovered nominal anti-uni...

Citation Context

...ffer syntax to declare freshness of names if freshness is needed (as in [49, 7, 14]). An alternative approach to deal with freshness assumptions consists of using global declarations, as described in =-=[17]-=-. 3210 Conclusions and future work We have extended nominal syntax to include types that depend on terms, with a primitive notion of substitution for atoms. We have shown that freshness and α-equival...

Citation Context

...semantics for existential variables. That is, we will extend STLC syntax with ‘holes’. The technique used is essentially the same as the nominal terms of [40] (a permissive variant thereof, following =-=[6, 7]-=-) but taking semantics in nominal models of STLC instead of in datatypes of abstract syntax with binding. Because λ -abstraction maps to atoms-abstraction, the denotation of functions does not involve...

Citation Context

... [UPG04] and to informal freshness conditions of the form ‘x not free in t’ in informal practice. To see this intuition made formal see a translation from nominal terms to permissive-nominal terms in =-=[DGM10]-=-. There is no requirement to axiomatise α-equivalence because this is done automatically by the PNL system. Sugar (λa.r)r′ to r[a 7→r′]. Then axioms for β-equivalence are: ∀Y. a[a7→Y ] = Y ∀Z,X. Z[a 7...

Citation Context

...ose some list of atoms to abstract—if our language did not admit non-equivariant constants, as was the case for the original Urban-Pitts-Gabbay syntax from [UPG04] or its permissive variant from e.g. =-=[DGM10]-=-, then we could just write [L]H . In the case of tuples, we know we can write every element in the form [l]xi for 1 ≤ i ≤ n for some xi, by Lemma 4.9. 12 Proposition 4.17. [m]H from Definition 4.15 is...