Term Graph Representations for Cyclic Lambda-Terms
نویسندگان
چکیده
We study various representations for cyclic λ -terms as higher-order or as first-order term graphs. We focus on the relation between ‘λ -higher-order term graphs’ (λ -ho-term-graphs), which are firstorder term graphs endowed with a well-behaved scope function, and their representations as ‘λ -termgraphs’, which are plain first-order term graphs with scope-delimiter vertices that meet certain scoping requirements. Specifically we tackle the question: Which class of first-order term graphs admits a faithful embedding of λ -ho-term-graphs in the sense that (i) the homomorphism-based sharing-order on λ -ho-term-graphs is preserved and reflected, and (ii) the image of the embedding corresponds closely to a natural class (of λ -term-graphs) that is closed under homomorphism? We systematically examine whether a number of classes of λ -term-graphs have this property, and we find a particular class of λ -term-graphs that satisfies this criterion. Term graphs of this class are built from application, abstraction, variable, and scope-delimiter vertices, and have the characteristic feature that the latter two kinds of vertices have back-links to the corresponding abstraction. This result puts a handle on the concept of subterm sharing for higher-order term graphs, both theoretically and algorithmically: We obtain an easily implementable method for obtaining the maximally shared form of λ -ho-term-graphs. Furthermore, we open up the possibility to pull back properties from first-order term graphs to λ -ho-term-graphs, properties such as the complete lattice structure of bisimulation equivalence classes with respect to the sharing order.
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