Abstract: We present a system called Smyth for program sketching in a typed functional language whereby the concrete evaluation of ordinary assertions gives rise to input-output examples, which are then used to guide the search to complete the holes. The key innovation, called live bidirectional evaluation, propagates examples "backward" through partially evaluated sketches. Live bidirectional evaluation enables Smyth to (a) synthesize recursive functions without trace-complete sets of examples and (b) specify and solve interdependent synthesis goals. Eliminating the trace-completeness requirement resolves a significant limitation faced by prior synthesis techniques when given partial specifications in the form of input-output examples. To assess the practical implications of our techniques, we ran several experiments on benchmarks used to evaluate Myth, a state-of-the-art example-based synthesis tool. First, given expert examples (and no partial implementations), we find that Smyth requires on average 66