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Component-based synthesis seeks to build programs using the APIs provided by a set of libraries. Oftentimes, these APIs have effects, which make it challenging to reason about the correctness of potential synthesis candidates. This is because changes to global state made by effectful library procedures affect how they may be composed together, yielding an intractably large search space that can confound typical enumerative synthesis techniques. If the nature of these effects are exposed as part of their specification, however, deductive synthesis approaches can be used to help guide the search for components. In this paper, we present a new specification-guided synthesis procedure that uses Hoare-style pre- and post-conditions to express fine-grained effects of potential library component candidates to drive a bi-directional synthesis search strategy. The procedure alternates between a forward search process that seeks to build larger terms given an existing context but which is otherwise unaware of the actual goal, alongside a backward search mechanism that seeks terms consistent with the desired goal but which is otherwise unaware of the context from which these terms must be synthesized. To further improve efficiency and scalability, we integrate a conflict-driven learning procedure into the synthesis algorithm that provides a semantic characterization of previously encountered unsuccessful search paths that is used to prune the space of possible candidates as synthesis proceeds. We have implemented our ideas in a tool called Cobalt and demonstrate its effectiveness on a number of challenging synthesis problems defined over OCaml libraries equipped with effectful specifications.