generalized Algebraic Dynamic Programming A selection of (sequence) alignment algorithms. Both terminal, and syntactic variables, as well as the index type is not fixed here. This makes it possible to select the correct structure of the grammar here, but bind the required data type for alignment in user code. That being said, these algorithms are mostly aimed towards sequence alignment problems. List of grammars for sequences: global alignment linear scoring: Needleman-Wunsch style affine scoring: Gotoh semiglobal alignment overhang alignment List of grammar for trees: global alignment linear scoring affine scoring simplified affine scoring global editing linear scoring We now provide tree alignment and editing algorithms as well. We do not depend on ADPfusionForest to achieve this because grammar rules are completely disconnected from the underlying ADPfusion machinery.