Bottom-up synthesis of recursive functional programs using angelic execution

Abstract

We present a novel bottom-up method for the synthesis of functional recursive programs. While bottom-up synthesis techniques can work better than top-down methods in certain settings, there is no prior technique for synthesizing recursive programs from logical specifications in a purely bottom-up fashion. The main challenge is that effective bottom-up methods need to execute sub-expressions of the code being synthesized, but it is impossible to execute a recursive subexpression of a program that has not been fully constructed yet. In this paper, we address this challenge using the concept of angelic semantics. Specifically, our method finds a program that satisfies the specification under angelic semantics (we refer to this as angelic synthesis), analyzes the assumptions made during its angelic execution, uses this analysis to strengthen the specification, and finally reattempts synthesis with the strengthened specification. Our proposed angelic synthesis algorithm is based on version space learning and therefore deals effectively with many incremental synthesis calls made during the overall algorithm. We have implemented this approach in a prototype called Burst and evaluate it on synthesis problems from prior work. Our experiments show that Burst is able to synthesize a solution to 94% of the benchmarks in our benchmark suite, outperforming prior work.

Program Synthesis from Graded Types

“…Whilst we compared our approach (with graded + types + examples considered at the end) to Myth (with types + examples integrated) to show that grading reduces the number of examples, comparing with the assertion-based approach in Smyth is further work. Another recent work, Burst, also leverages the Myth benchmark, but using a 'bottom-up' technique [41] (in contrast to our top-down approach, Section 4.2). The bottom-up approach synthesises a sequence of complete programs which can be refined and tested under an 'angelic semantics'.…”

“…In standard terminology, our algorithm is 'top-down' (see, e.g., [17,47,23,53]), or goal-directed, in which we start with a type goal and an input context and progress by gradually building the syntax tree from the empty term following the focussing-ordered rules of our calculus. This contrasts with 'bottom-up' approaches [2,41,44] which maintain complete programs which can be executed (tested) and combined.…”

Languages with Decidable Learning: A Meta-theorem

“…Tree automata underlie many practical algorithms for synthesis based on compactly representing large spaces of programs and expressions [Gulwani 2011;Handa and Rinard 2020;Koppel et al 2022;Miltner et al 2022;Wang et al 2017aWang et al ,b, 2018. The main idea is to efficiently represent classes of expressions which are equivalent with respect to some examples.…”

“…The result was a potentially large transition system, not a compact program. The use of tree automata that work over syntax trees was advanced in [Madhusudan 2011] and has been used for practical algorithms in several program synthesis contexts [Handa and Rinard 2020;Koppel et al 2022;Miltner et al 2022;Wang et al 2017aWang et al ,b, 2018.…”

Metric Program Synthesis for Inverse CSG

“…Intuitively, FTAs are useful in synthesis because they can compactly encode a set of programs, represented in terms of their abstract syntax tree [Miltner et al 2022;Wang et al 2017Wang et al , 2018. In particular, when used in the context of synthesis, states of the FTA correspond to values (e.g., integers), and the alphabet corresponds to the set of DSL operators (e.g., +, ×).…”