Hindley-Milner type inference with ergonomic blame assignment.

blame is a type-error blame assignment algorithm for languages with Hindley-Milner type inference, but without generalization of intermediate terms. This means that it is not suitable for languages with let-generalization. Let is an example of a term that is not suitable for this algorithm.

With the contemporary knowledge that "Let Should Not Be Generalised", as argued by luminaries such as Simon Peyton Jones, optimistically this limitation shouldn't apply to new programming languages. This blame assignment algorithm can also be used in a limited sense for existing languages, which do have let-generalization, to provide better type errors in specific definitions which don't happen to use generalizing terms.

The algorithm is pretty simple:

• Invoke all the inferBody calls as infer normally would, but with one important difference: where inferBody would normally get the actual inference results of its child nodes, placeholders are generated in their place
• Globally sort all of the tree nodes according to a given node prioritization (this prioritization would be custom for each language)
• According to the order of prioritization, attempt to unify each infer-result with its placeholder using inferOfUnify. If a unification fails, roll back its state changes. The nodes whose unification failed are the ones assigned with type errors.

Lamdu uses this algorithm for its "insist type" feature, which moves around the blame for type mismatches.

Note: If a similar algorithm already existed somewhere, I would very much like to know!