Resource-guided program synthesis

Abstract

This article presents resource-guided synthesis, a technique for synthesizing recursive programs that satisfy both a functional specification and a symbolic resource bound. The technique is type-directed and rests upon a novel type system that combines polymorphic refinement types with potential annotations of automatic amortized resource analysis. The type system enables efficient constraint-based type checking and can express precise refinement-based resource bounds. The proof of type soundness shows that synthesized programs are correct by construction. By tightly integrating program exploration and type checking, the synthesizer can leverage the user-provided resource bound to guide the search, eagerly rejecting incomplete programs that consume too many resources. An implementation in the resource-guided synthesizer ReSyn is used to evaluate the technique on a range of recursive data structure manipulations. The experiments show that ReSyn synthesizes programs that are asymptotically more efficient than those generated by a resource-agnostic synthesizer. Moreover, synthesis with ReSyn is faster than a naive combination of synthesis and resource analysis. ReSyn is also able to generate implementations that have a constant resource consumption for fixed input sizes, which can be used to mitigate side-channel attacks.

Raising expectations: automating expected cost analysis with types

“…Beyond AARA, there have been many other approaches to formal resource analysis of deterministic programs. Some approaches, similarly to AARA, do so via a type system, including sized types [Vasconcelos 2008] refinement types [Çiçek et al 2017, 2015Knoth et al 2019;Radicek et al 2018;Wang et al 2017;Xi 2002], linear dependent types [Dal Lago and Gaboardi 2011;Dal Lago and Petit 2013], and annotated type systems [Crary and Weirich 2000;Danielsson 2008]. Such a type-based approach usually involves constraint solving, some notion of linearity, and high composability, like AARA.…”

Liquid resource types

“…Potential Annotations. ReSyn [Knoth et al 2019] extends liquid types with the ability to reason about the resource consumption of programs in addition to their functional properties. To this end, a type can also be annotated with a numeric logic expression called potential, as well as a logical refinement.…”

“…Refinements. We follow the approach of liquid types [Knoth et al 2019;Polikarpova et al 2016;Rondon et al 2012] and develop a refinement language that is distinct from the term language. Fig.…”

“…Types. We adapt the methodology of Re 2 [Knoth et al 2019] and classify types into four categories. Base types B are natural numbers, Booleans, nullary and binary products, inductive datatypes, and type variables.…”

“…Liquid Types and Resources. Recent work on ReSyn [Knoth et al 2019] takes a first step in this direction by extending a liquid type system with resource analysis. Liquid types [Rondon et al 2008] support automatic verification of nontrivial functional properties with an SMT solver.…”