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dcterms:title
Data-flow analyses as effects and graded monads
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2020-06-28
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n4:ext-ca89c045a79d54af9529ef393835363c n4:ext-856a948953268faf12609599d9b3b562 n4:ext-d.a.orchard@kent.ac.uk
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bibo:abstract
In static analysis, two frameworks have been studied extensively: monotone data-flow analysis and type-and-effect systems. Whilst both are seen as general analysis frameworks, their relationship has remained unclear. Here we show that monotone data-flow analyses can be encoded as effect systems in a uniform way, via algebras of transfer functions. This helps to answer questions about the most appropriate structure for general effect algebras, especially with regards capturing control-flow precisely. Via the perspective of capturing data-flow analyses, we show the recent suggestion of using effect quantales is not general enough as it excludes non-distributive analyses e.g., constant propagation. By rephrasing the McCarthy transformation, we then model monotone data-flow effects via graded monads. This provides a model of data-flow analyses that can be used to reason about analysis correctness at the semantic level, and to embed data-flow analyses into type systems.
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167