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Type rules associate types to expressions given a typing context. As the type checker traverses the expression tree topdown, it extends the typing context with additional context information that becomes available. This way, the typing context coordinates type checking in otherwise independent subexpressions, which inhibits parallelization and incrementalization of type checking. We propose a co-contextual formulation of type rules that only take an expression as input and produce a type and adoi:10.1145/2814270.2814277 dblp:conf/oopsla/ErdwegBKKM15 fatcat:o6yug7ceu5dxbfajjxwltdhdzm