In this paper, we first describe the isothermal constrained loop extension DNA amplification (ICLEDA), which is a variant of amplification combining the advantages of rolling circle amplification (RCA) and of strand displacement amplification (SDA). Then, we formalize this process in terms of the theory of formal languages, which yields two new operations of sticking and displacement on normal and circular strings. The obtained formalism is quite expressive and we show how to implement the computation of any boolean function on DNA strands using ICLEDA. We also discuss variants of the model that could eventually bring more computational power.