Abstract: πCalculus is used to encode the semantics for the SKIcalculus which is a representative of combinator calculi. SKI calculus is Turing complete, and this work shows the expressiveness of πcalculus. Furthermore, this work provides a precondition for uniting and comparing combinator calculi, lambdacalculus as well as higherorder functions with other concurrent models under the theory of πcalculus.

Key words: πcalculus, Combinator calculi, SKIcalculus, semantics