In this article we present a syntax-based translation system, called TABL (Translation using Alignment-Based Learning). It translates natural language sentences by mapping grammar rules of the source language to those of the target language. All grammar rules are induced using the Alignment-Based Learning grammatical inference framework. By parsing a sentence in the source language, the grammar rules that are used in the derivation are translated using the mapping and subsequently, a derivation in the target language is generated. Here, we illustrate that this is a valid machine translation approach, as the initial results are encouraging. We assess some remaining problems and current restrictions to this approach and propose possible solutions.