Space-Efficient Manifest Contracts

Abstract

The standard algorithm for higher-order contract checking can lead to unbounded space consumption and can destroy tail recursion, altering a program's asymptotic space complexity. While space efficiency for gradual types-contracts mediating untyped and typed code-is well studied, sound space efficiency for manifest contractscontracts that check stronger properties than simple types, e.g., "is a natural" instead of "is an integer"-remains an open problem.We show how to achieve sound space efficiency for manifest contracts with strong predicate contracts. The essential trick is breaking the contract checking down into coercions: structured, blame-annotated lists of checks. By carefully preventing duplicate coercions from appearing, we can restore space efficiency while keeping the same observable behavior.Along the way, we define a framework for space efficiency, traversing the design space with three different space-efficient manifest calculi. We examine the diverse correctness criteria for contract semantics; we conclude with a coercion-based language whose contracts enjoy (galactically) bounded, sound space consumption-they are observationally equivalent to the standard, space-inefficient semantics.This is an extended version of Greenberg [2015], with a great deal of material that does not appear in the conference paper: an exploration of the design space with two other space-efficient calculi and complete proofs.

Space-Efficient Manifest Contracts

“…We have highlighted in yellow the four syntactic forms relevant to contract checking. This paper paper discusses two modes of λH: classic λH, mode C,and eidetic λH, mode E. Each of these languages uses the syntax of Figure 1, while the typing rules In an extended version of this work, we develop two additional modes with slightly different properties from eidetic λH, filling out a "framework" for spaceefficient manifest contracts [10]. We omit the other two modes here to save space for eidetic λH, which is the only mode that is sound with respect to classic λH.…”

Space-Efficient Latent Contracts

“…Space efficiency for gradual types [24] (a/k/a contracts constrained to type tests) is well studied [14,15,25,9,23]; Greenberg [11] developed a space-efficient semantics for general, non-dependent contracts. He used a manifest calculus, conflating contracts and types; however, contracts are typically implemented in latent calculi, where contracts are distinct from whatever types may exist.…”

“…The rest of this paper discusses a formulation of contracts that enjoys sound space efficiency; that is, where we slightly change the implementation of contracts so that (a) programs are observationally equivalent to the standard semantics, but (b) contracts consume a bounded amount of space. In this paper, we've omitted some of the more detailed examples and motivation-we refer curious readers to Greenberg [11], though we intend the paper to be self-contained.…”

“…Join-free reductions ( EFix) We give this case explicitly, as the original proof in Greenberg [11] doesn't talk about fixpoints. We must show mon(c, µ(x :T ).…”

“…Space-efficient contract monitoring for contracts enforcing simple type disciplines (a/k/a gradual typing) is well studied. Prior work establishes a space-efficient semantics for manifest contracts without dependency [11]; we adapt that work to a latent calculus with dependency. We guarantee space efficiency when no dependency is used; we cannot generally guarantee space efficiency when dependency is used, but instead offer a framework for making such programs space efficient on a case-by-case basis.…”