## Models of Sharing Graphs: A Categorical Semantics of let and letrec (1997)

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@TECHREPORT{Hasegawa97modelsof,

author = {Masahito Hasegawa},

title = {Models of Sharing Graphs: A Categorical Semantics of let and letrec},

institution = {},

year = {1997}

}

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### Abstract

To my parents A general abstract theory for computation involving shared resources is presented. We develop the models of sharing graphs, also known as term graphs, in terms of both syntax and semantics. According to the complexity of the permitted form of sharing, we consider four situations of sharing graphs. The simplest is first-order acyclic sharing graphs represented by let-syntax, and others are extensions with higher-order constructs (lambda calculi) and/or cyclic sharing (recursive letrec binding). For each of four settings, we provide the equational theory for representing the sharing graphs, and identify the class of categorical models which are shown to be sound and complete for the theory. The emphasis is put on the algebraic nature of sharing graphs, which leads us to the semantic account of them. We describe the models in terms of the notions of symmetric monoidal categories and functors, additionally with symmetric monoidal adjunctions and traced