The paper presents a parser implementing Marek Świdziński's formal grammar of the Polish language. The grammar was written by a linguist, without a computational implementation in mind, unlike most formal grammars. The aim of the work reported here is to examine what the exact set of sentences accepted by the grammar is and what structures are assigned to them. For that reason, it was crucial to remain as close to the original grammar as possible. The resulting program, named Świgra, goes far beyond a toy parser due to the use of a morphological analyser and a broad range of linguistic phenomena covered by Świdziński's grammar. In this article preliminary results of the parser evaluation are also provided.