  Accattoli, Dal Lago, and Vanoni have recently proved that the space used by
the Space KAM, a variant of the Krivine abstract machine, is a reasonable space
cost model for the lambda-calculus accounting for logarithmic space, solving a
longstanding open problem. In this paper, we provide a new system of multi
types (a variant of intersection types) and extract from multi type derivations
the space used by the Space KAM, capturing into a type system the space
complexity of the abstract machine. Additionally, we show how to capture also
the time of the Space KAM, which is a reasonable time cost model, via minor
changes to the type system.
