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Neural sequence models exhibit limited compositional generalization ability in semantic parsing tasks. Compositional generalization requires algebraic recombination, i.e., dynamically recombining structured expressions in a recursive manner. However, most previous studies mainly concentrate on recombining lexical units, which is an important but not sufficient part of algebraic recombination. In this paper, we propose LEAR, an end-toend neural model to learn algebraic recombination for compositional generalization. The key insight is to model the semantic parsing task as a homomorphism between a latent syntactic algebra and a semantic algebra, thus encouraging algebraic recombination. Specifically, we learn two modules jointly: a Composer for producing latent syntax, and an Interpreter for assigning semantic operations. Experiments on two realistic and comprehensive compositional generalization benchmarks demonstrate the effectiveness of our model. The source code is publicly available at https://github.com/microsoft/ContextualSP.