Guarded algebraic data types, which subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, and phantom types, and are closely related to inductive types, have the distinguishing feature that, when typechecking a function defined by cases, every branch must be checked under di#erent typing assumptions. This mechanism allows exploiting the presence of dynamic tests in the code to produce extra static type information. We propose an extension of the constraint-based type system HM(X) with pattern matching, guarded algebraic data types, and polymorphic recursion. After establishing a type safety theorem, we show that, up to a few mandatory type annotations, type inference may be reduced to constraint solving. We devote particular attention to keeping the amount of user-supplied type information to a minimum and to ensuring that the generated constraints are e#ciently tractable. To the best of our knowledge, this is the first generic and comprehensive account of type inference in the presence of guarded algebraic data types.
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