Convergence of program transformers in the metric space of trees

AbstractIn recent years increasing consensus has emerged that program transformers, e.g. partial evaluation and unfold/fold transformations, should terminate; a compiler should stop even if it performs fancy optimizations! A number of techniques to ensure termination of program transformers have been invented, but their correctness proofs are sometimes long and involved. We present a framework for proving termination of program transformers, cast in the metric space of trees. We first introduce the notion of an abstract program transformer; a number of well-known program transformers can be viewed as instances of this notion. We then formalize what it means that an abstract program transformer terminates and give a general sufficient condition for an abstract program transformer to terminate. We also consider some specific techniques for satisfying the condition. As applications we show that termination of some well-known program transformers either follows directly from the specific techniques or is easy to establish using the general condition. Our framework facilitates simple termination proofs for program transformers. Also, since our framework is independent of the language being transformed, a single correctness proof can be given in our framework for program transformers that use essentially the same technique in the context of different languages. Moreover, it is easy to extend termination proofs for program transformers to accommodate changes to these transformers. Finally, the framework may prove useful for designing new termination techniques for program transformers

An Experiment in Ping-Pong Protocol Verification by Nondeterministic Pushdown Automata

An experiment is described that confirms the security of a well-studied class of cryptographic protocols (Dolev-Yao intruder model) can be verified by two-way nondeterministic pushdown automata (2NPDA). A nondeterministic pushdown program checks whether the intersection of a regular language (the protocol to verify) and a given Dyck language containing all canceling words is empty. If it is not, an intruder can reveal secret messages sent between trusted users. The verification is guaranteed to terminate in cubic time at most on a 2NPDA-simulator. The interpretive approach used in this experiment simplifies the verification, by separating the nondeterministic pushdown logic and program control, and makes it more predictable. We describe the interpretive approach and the known transformational solutions, and show they share interesting features. Also noteworthy is how abstract results from automata theory can solve practical problems by programming language means.Comment: In Proceedings MARS/VPT 2018, arXiv:1803.0866

The next 700 program transformers

In this paper, we describe a hierarchy of program transformers, capable of performing fusion to eliminate intermediate data structures, in which the transformer at each level of the hierarchy builds on top of those at lower levels. The program transformer at level 1 of the hierarchy corresponds to positive supercompilation, and that at level 2 corresponds to distillation. We give a number of examples of the application of our transformers at different levels in the hierarchy and look at the speedups that are obtained. We determine the maximum speedups that can be obtained at each level, and prove that the transformers at each level terminate

Homeomorphic Embedding for Online Termination of Symbolic Methods

Well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of techniques for program analysis, specialisation, transformation, and verification. In this paper we survey and discuss this use of homeomorphic embedding and clarify the advantages of such an approach over one using well-founded orders. We also discuss various extensions of the homeomorphic embedding relation. We conclude with a study of homeomorphic embedding in the context of metaprogramming, presenting some new (positive and negative) results and open problems

Stream Fusion, to Completeness

Stream processing is mainstream (again): Widely-used stream libraries are now available for virtually all modern OO and functional languages, from Java to C# to Scala to OCaml to Haskell. Yet expressivity and performance are still lacking. For instance, the popular, well-optimized Java 8 streams do not support the zip operator and are still an order of magnitude slower than hand-written loops. We present the first approach that represents the full generality of stream processing and eliminates overheads, via the use of staging. It is based on an unusually rich semantic model of stream interaction. We support any combination of zipping, nesting (or flat-mapping), sub-ranging, filtering, mapping-of finite or infinite streams. Our model captures idiosyncrasies that a programmer uses in optimizing stream pipelines, such as rate differences and the choice of a "for" vs. "while" loops. Our approach delivers hand-written-like code, but automatically. It explicitly avoids the reliance on black-box optimizers and sufficiently-smart compilers, offering highest, guaranteed and portable performance. Our approach relies on high-level concepts that are then readily mapped into an implementation. Accordingly, we have two distinct implementations: an OCaml stream library, staged via MetaOCaml, and a Scala library for the JVM, staged via LMS. In both cases, we derive libraries richer and simultaneously many tens of times faster than past work. We greatly exceed in performance the standard stream libraries available in Java, Scala and OCaml, including the well-optimized Java 8 streams

An Experiment Combining Specialization with Abstract Interpretation

It was previously shown that control-flow refinement can be achieved by a program specializer incorporating property-based abstraction, to improve termination and complexity analysis tools. We now show that this purpose-built specializer can be reconstructed in a more modular way, and that the previous results can be achieved using an off-the-shelf partial evaluation tool, applied to an abstract interpreter. The key feature of the abstract interpreter is the abstract domain, which is the product of the property-based abstract domain with the concrete domain. This language-independent framework provides a practical approach to implementing a variety of powerful specializers, and contributes to a stream of research on using interpreters and specialization to achieve program transformations.Comment: In Proceedings VPT/HCVS 2020, arXiv:2008.0248

An Automatic Program Generator for Multi-Level Specialization

Program specialization can divide a computation into several computation stages. This paper investigates the theoretical limitations and practical problems of standard specialization tools, presents multi-level specialization, and demonstrates that, in combination with the cogen approach, it is far more practical than previously supposed. The program generator which we designed and implemented for a higher-order functional language converts programs into very compact multi-level generating extensions that guarantee fast successive specialization. Experimental results show a remarkable reduction of generation time and generator size compared to previous attempts of multi-level specialization by self-application. Our approach to multi-level specialization seems well-suited for applications where generation time and program size are critical

Cheap deforestation for non-strict functional languages

In functional languages intermediate data structures are often used as glue to connect separate parts of a program together. Deforestation is the process of automatically removing intermediate data structures. In this thesis we present and analyse a new approach to deforestation. This new approach is both practical and general. We analyse in detail the problem of list removal rather than the more general problem of arbitrary data structure removal. This more limited scope allows a complete evaluation of the pragmatic aspects of using our deforestation technology. We have implemented our list deforestation algorithm in the Glasgow Haskell compiler. Our implementation has allowed practical feedback. One important conclusion is that a new analysis is required to infer function arities and the linearity of lambda abstractions. This analysis renders the basic deforestation algorithm far more effective. We give a detailed assessment of our implementation of deforestation. We measure the effectiveness of our deforestation on a suite of real application programs. We also observe the costs of our deforestation algorithm

Lightweight Modular Staging and Embedded Compilers:Abstraction without Regret for High-Level High-Performance Programming

Programs expressed in a high-level programming language need to be translated to a low-level machine dialect for execution. This translation is usually accomplished by a compiler, which is able to translate any legal program to equivalent low-level code. But for individual source programs, automatic translation does not always deliver good results: Software engineering practice demands generalization and abstraction, whereas high performance demands specialization and concretization. These goals are at odds, and compilers can only rarely translate expressive high-level programs tomodern hardware platforms in a way that makes best use of the available resources. Explicit program generation is a promising alternative to fully automatic translation. Instead of writing down the program and relying on a compiler for translation, developers write a program generator, which produces a specialized, efficient, low-level program as its output. However, developing high-quality program generators requires a very large effort that is often hard to amortize. In this thesis, we propose a hybrid design: Integrate compilers into programs so that programs can take control of the translation process, but rely on libraries of common compiler functionality for help. We present Lightweight Modular Staging (LMS), a generative programming approach that lowers the development effort significantly. LMS combines program generator logic with the generated code in a single program, using only types to distinguish the two stages of execution. Through extensive use of component technology, LMS makes a reusable and extensible compiler framework available at the library level, allowing programmers to tightly integrate domain-specific abstractions and optimizations into the generation process, with common generic optimizations provided by the framework. Compared to previous work on programgeneration, a key aspect of our design is the use of staging not only as a front-end, but also as a way to implement internal compiler passes and optimizations, many of which can be combined into powerful joint simplification passes. LMS is well suited to develop embedded domain specific languages (DSLs) and has been used to develop powerful performance-oriented DSLs for demanding domains such as machine learning, with code generation for heterogeneous platforms including GPUs. LMS has also been used to generate SQL for embedded database queries and JavaScript for web applications