We present an interpretation of protocol narrations by means of translation into the spi-calculus. Our translation allows participants to play multiple roles in parallel, leading to a more general interpretation that considers a wider range of attacks than previous work. We test the validity of our translation by introducing correspondence assertions [Woo and Lam, S&P 1993] to both the protocol narrations and the spi-calculus, and verifying a number of examples by using SpiCA2 [Dahl, Kobayashi, Sun, and Hu"ttel, ATVA 2011], a sound and automatic type-based verifier of correspondence assertions.