  Search is an important technique in program synthesis that allows for
adaptive strategies such as focusing on particular search directions based on
execution results. Several prior works have demonstrated that neural models are
effective at guiding program synthesis searches. However, a common drawback of
those approaches is the inability to handle iterative loops, higher-order
functions, or lambda functions, thus limiting prior neural searches from
synthesizing longer and more general programs. We address this gap by designing
a search algorithm called LambdaBeam that can construct arbitrary lambda
functions that compose operations within a given DSL. We create semantic vector
representations of the execution behavior of the lambda functions and train a
neural policy network to choose which lambdas to construct during search, and
pass them as arguments to higher-order functions to perform looping
computations. Our experiments show that LambdaBeam outperforms neural,
symbolic, and LLM-based techniques in an integer list manipulation domain.
