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We consider the application of Constraint Handling Rules (CHR) for thespecification of type inference systems, such as that used by Haskell.Confluence of CHR guarantees that the answer provided by type inference iscorrect and consistent. The standard method for establishing confluence relieson an assumption that the CHR program is terminating. However, many examples inpractice give rise to non-terminating CHR programs, rendering this methodinapplicable. Despite no guarantee of termination or confluence, the GlasgowHaskell Compiler (GHC) supports options that allow the user to proceed withtype inference anyway, e.g. via the use of the UndecidableInstances flag. Inthis paper we formally identify and verify a set of relaxed criteria, namelyrange-restrictedness, local confluence, and ground termination, that ensure theconsistency of CHR-based type inference that maps to potentiallynon-terminating CHR programs.

On Termination, Confluence and Consistent CHR-based Type Inference