FRed: Conditional Model Checking via Reducers and Folders

There are many hard verification problems that are currently only solvable by applying several verifiers that are based on complementing technologies. Conditional model checking (CMC) is a successful solution for cooperation between verification tools. In CMC, the first verifier outputs a condition describing the state space that it successfully verified. The second verifier uses the condition to focus its verification on the unverified state space. To use arbitrary second verifiers, we recently proposed a reducer-based approach. One can use the reducer-based approach to construct a conditional verifier from a reducer and a (non-conditional) verifier: the reducer translates the condition into a residual program that describes the unverified state space and the verifier can be any off-the-shelf verifier (that does not need to understand conditions). Until now, only one reducer was available. But for a systematic investigation of the reducer concept, we need several reducers. To fill this gap, we developed FRed, a Framework for exploring different REDucers. Given an existing reducer, FRed allows us to derive various new reducers, which differ in their trade-off between size and precision of the residual program. For our experiments, we derived seven different reducers. Our evaluation on the largest and most diverse public collection of verification problems shows that we need all seven reducers to solve hard verification tasks that were not solvable before with the considered verifiers.

A novel method for modeling age and length selectivity of sockeye salmon as applied to the Bristol Bay Port Moller test fishery

This paper presents a novel approach for assessing sources selectivity in test fisheries using the Port Moller test fishery (PMTF) as a case study. The PMTF intercepts sockeye salmon (Oncorhynchus nerka) migrating to Bristol Bay, Alaska, to estimate run strength and timing. In 2011, the mesh size of gillnets used in the test fishery was decreased for half of the net panels to generate more accurate run estimates by correcting for greater selectivity of larger 3-ocean fish (fish that have spent 3 years in the ocean) relative to smaller 2-ocean fish (fish that have spent 2 years in the ocean). Here, we quantify two sources of age selectivity in the PMTF program, length selectivity parameterized by mean fish length (which should be corrected by the net mesh change) and length-independent selectivity, which we refer to as residual program selectivity (which would not be impacted by the net mesh change), both before and after the net change. Model parameters of selectivity show strong support length selectivity was eliminated, but residual program selectivity still existed after the reduction in net mesh size. Our results demonstrate the necessity of considering both vulnerability and accessibility to fishing gear when assessing selectivity in test fisheries.

Integrating Herbicide Programs with Harvest Weed Seed Control and Other Fall Management Practices for the Control of Glyphosate-Resistant Palmer Amaranth (Amaranthus palmeri)

A large-plot field experiment was conducted at Keiser, AR, from fall of 2010 through fall of 2013 to understand to what extent soybean in-crop herbicide programs and postharvest fall management practices impact Palmer amaranth population density and seed production over three growing seasons. The effect of POST-only (glyphosate-only) or PRE followed by (fb) POST (glyphosate or glufosinate) + residual herbicide treatments were evaluated alone and in combination with postharvest management options of soybean residue spreading or soil incorporation, use of cover crops, windrowing with/without burning, and residue removal. Significant differences were observed between fall management practices on Palmer amaranth population density each fall. The use of cover crops and residue collection and removal fb the incorporation of crop residues into soil during the formation of beds were the most effective practices in reducing Palmer amaranth population. In contrast, the effects of fall management practices on Palmer amaranth seed production were inconsistent among years. The inclusion of a PRE herbicide application into the herbicide program significantly reduced Palmer amaranth population density and subsequent seed production each year when compared to the glyphosate-only program. Additionally, the glufosinate-containing residual program was superior to the glyphosate-containing residual program in reducing Palmer amaranth seed production. PRE fb POST herbicides resulted in significant decreases in the Palmer amaranth population density and seed production compared to POST application of glyphosate alone for all fall management practices, including the no-till practice. This study demonstrated that crop residue management such as chaff removal from the field, the use of cover crops, or seed incorporation during bed formation in combination with an effective PRE plus POST residual herbicide program is important for optimizing in-season management of Palmer amaranth and subsequently reducing the population density, which has a profound impact on lessening the risk for herbicide resistance and the consistency and effectiveness of future weed management efforts.

RS-2 Tagging, Encoding, and Jones Optimality

A partial evaluator is said to be Jones-optimal if the result of specializing a self-interpreter with respect to a source program is textually identical to the source program, modulo renaming. Jones optimality has already been obtained if the self-interpreter is untyped. If the self-interpreter is typed, however, residual programs are cluttered with type tags. To obtain the original source program, these tags must be removed.<br /> <br />A number of sophisticated solutions have already been proposed. We observe, however, that with a simple representation shift, ordinary partial evaluation is already Jones-optimal, modulo an encoding. The representation shift amounts to reading the type tags as constructors for higher-order abstract syntax. We substantiate our observation by considering a typed self-interpreter whose input syntax is higher-order. Specializing this interpreter with respect to a source program yields a residual program that is textually identical to the source program, modulo renaming.

A Simple Solution to Type Specialization

Partial evaluation specializes terms, but traditionally this<br />specialization does not apply to the type of these terms. As a result, specializing, e.g., an interpreter written in a typed language, which requires a "universal" type to encode expressible values, yields residual programs with type tags all over. Neil Jones has stated that getting rid of these type tags was an open problem, despite possible solutions such as Torben Mogensen's "constructor specialization." To solve this problem, John Hughes has proposed a new paradigm for partial evaluation, "Type Specialization," based on type inference instead of being based on symbolic interpretation. Type Specialization is very elegant in principle but it also appears non-trivial in practice. Stating the problem in terms of types instead of in terms of type encodings suggests a very simple type-directed solution, namely, to use a projection from the universal type to the specific type of the residual program. Standard partial evaluation then yields a residual program<br />without type tags, simply and efficiently.

Higher-Order Rewriting and Partial Evaluation

We demonstrate the usefulness of higher-order rewriting techniques for specializing programs, i.e., for partial evaluation. More precisely, we demonstrate how casting program specializers as combinatory reduction systems (CRSs) makes it possible to formalize the corresponding program transformations as meta-reductions, i.e., reductions in the internal "substitution calculus." For partial-evaluation problems, this means that instead of having to prove on a case-by-case basis that one's "two-level functions" operate properly, one can concisely formalize them as a combinatory reduction system and obtain as a corollary that static reduction does not go wrong and yields a well-formed residual program.<br />We have found that the CRS substitution calculus provides an adequate expressive power to formalize partial evaluation: it provides sufficient termination strength while avoiding the need for additional restrictions such as types that would complicate the description unnecessarily (for our purpose). We also review the benefits and penalties entailed by more expressive higher-order formalisms. In addition, partial evaluation provides a number of examples of higher-order rewriting where being higher order is a central (rather than an occasional or merely exotic) property. We illustrate this by demonstrating how standard but non-trivial partial-evaluation examples are<br />handled with higher-order rewriting.

Pragmatic Aspects of Type-Directed Partial Evaluation

Type-directed partial evaluation stems from the residualization of static values in dynamic contexts, given their type and the type of their free variables. Its algorithm coincides with the algorithm for coercing<br />a subtype value into a supertype value, which itself coincides with<br />Berger and Schwichtenberg's normalization algorithm for the simply typed lambda-calculus. Type-directed partial evaluation thus can be used to specialize a compiled, closed program, given its type.<br />Since Similix, let-insertion is a cornerstone of partial evaluators for call-by-value procedural languages with computational effects (such as divergence). It prevents the duplication of residual computations, and more generally maintains the order of dynamic side effects in the residual program. This article describes the extension of type-directed partial evaluation<br />to insert residual let expressions. This extension requires the<br />user to annotate arrow types with effect information. It is achieved by delimiting and abstracting control, comparably to continuation-based specialization in direct style. It enables type-directed partial evaluation of programs with effects (e.g., a definitional lambda-interpreter for an imperative language) that are in direct style. The residual programs<br />are in A-normal form. A simple corollary yields CPS (continuation-passing style) terms instead. We illustrate both transformations with two interpreters for Paulson's Tiny language, a classical example in partial evaluation.

A partial evaluator for the untyped lambda-calculus

This article describes theoretical and practical aspects of an implemented self-applicable partial evaluator for the untyped lambda-calculus with constants and a fixed point operator. To the best of our knowledge, it is the first partial evaluator that is simultaneously higher-order, non-trivial, and self-applicable.Partial evaluation produces aresidual programfrom a source program and some of its input data. When given the remaining input data the residual program yields the same result that the source program would when given all its input data. Our partial evaluator produces a residual lambda-expression given a source lambda-expression and the values of some of its free variables. By self-application, the partial evaluator can be used to compile and to generate stand-alone compilers from a denotational or interpretive specification of a programming language.An essential component in our self-applicable partial evaluator is the use of explicitbinding time information.We use this to annotate the source program, marking asresidualthe parts for which residual code is to be generated and marking aseliminablethe parts that can be evaluated using only the data that is known during partial evaluation. We give a simple criterion,well-annotatedness,that can be used to check that the partial evaluator can handle the annotated higher-order programs without committing errors.Our partial evaluator is simple, is implemented in a side-effect free subset of Scheme, and has been used to compile and to generate compilers and a compiler generator. In this article we examine two machine-generated compilers and find that their structures are surprisingly natural.