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A Calculus for Constraint-Based Flow Typing

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Executive Summary

Flow typing offers an alternative to the traditional Hindley-Milner approach to type inference. A key distinction is that variables may have different types at different program points. Flow typing systems are typically formalised in the style of a dataflow analysis. Whilst a natural choice, this can hinder the formalisation and lead to difficult questions about termination. The authors present an alternative constraint-based formalisation of flow typing which leads to a simple proof of termination. Type inference is useful for simplifying and reasoning about statically typed languages. Scala, OCaml and, most recently, Java 7 all employ local type inference (in some form) to reduce syntactic overhead. Type inference can also be used to type existing untyped programs (e.g. in JavaScript or Python).

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