Finding The Lazy Programmer's Bugs

Traditionally developers and testers created huge numbers of explicit tests, enumerating interesting cases, perhaps biased by what they believe to be the current boundary conditions of the function being tested. Or at least, they were supposed to. A major step forward was the development of property testing. Property testing requires the user to write a few functional properties that are used to generate tests, and requires an external library or tool to create test data for the tests. As such many thousands of tests can be created for a single property. For the purely functional programming language Haskell there are several such libraries; for example QuickCheck [CH00], SmallCheck and Lazy SmallCheck [RNL08]. Unfortunately, property testing still requires the user to write explicit tests. Fortunately, we note there are already many implicit tests present in programs. Developers may throw assertion errors, or the compiler may silently insert runtime exceptions for incomplete pattern matches. We attempt to automate the testing process using these implicit tests. Our contributions are in four main areas: (1) We have developed algorithms to automatically infer appropriate constructors and functions needed to generate test data without requiring additional programmer work or annotations. (2) To combine the constructors and functions into test expressions we take advantage of Haskell's lazy evaluation semantics by applying the techniques of needed narrowing and lazy instantiation to guide generation. (3) We keep the type of test data at its most general, in order to prevent committing too early to monomorphic types that cause needless wasted tests. (4) We have developed novel ways of creating Haskell case expressions to inspect elements inside returned data structures, in order to discover exceptions that may be hidden by laziness, and to make our test data generation algorithm more expressive. In order to validate our claims, we have implemented these techniques in Irulan, a fully automatic tool for generating systematic black-box unit tests for Haskell library code. We have designed Irulan to generate high coverage test suites and detect common programming errors in the process

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

A parallel functional language compiler for message-passing multicomputers

The research presented in this thesis is about the design and implementation of Naira, a parallel, parallelising compiler for a rich, purely functional programming language. The source language of the compiler is a subset of Haskell 1.2. The front end of Naira is written entirely in the Haskell subset being compiled. Naira has been successfully parallelised and it is the largest successfully parallelised Haskell program having achieved good absolute speedups on a network of SUN workstations. Having the same basic structure as other production compilers of functional languages, Naira's parallelisation technology should carry forward to other functional language compilers. The back end of Naira is written in C and generates parallel code in the C language which is envisioned to be run on distributed-memory machines. The code generator is based on a novel compilation scheme specified using a restricted form of Milner's 7r-calculus which achieves asynchronous communication. We present the first working implementation of this scheme on distributed-memory message-passing multicomputers with split-phase transactions. Simulated assessment of the generated parallel code indicates good parallel behaviour. Parallelism is introduced using explicit, advisory user annotations in the source' program and there are two major aspects of the use of annotations in the compiler. First, the front end of the compiler is parallelised so as to improve its efficiency at compilation time when it is compiling input programs. Secondly, the input programs to the compiler can themselves contain annotations based on which the compiler generates the multi-threaded parallel code. These, therefore, make Naira, unusually and uniquely, both a parallel and a parallelising compiler. We adopt a medium-grained approach to granularity where function applications form the unit of parallelism and load distribution. We have experimented with two different task distribution strategies, deterministic and random, and have also experimented with thread-based and quantum- based scheduling policies. Our experiments show that there is little efficiency difference for regular programs but the quantum-based scheduler is the best in programs with irregular parallelism. The compiler has been successfully built, parallelised and assessed using both idealised and realistic measurement tools: we obtained significant compilation speed-ups on a variety of simulated parallel architectures. The simulated results are supported by the best results obtained on real hardware for such a large program: we measured an absolute speedup of 2.5 on a network of 5 SUN workstations. The compiler has also been shown to have good parallelising potential, based on popular test programs. Results of assessing Naira's generated unoptimised parallel code are comparable to those produced by other successful parallel implementation projects

Catamorphism-based program transformations for non-strict functional languages

In functional languages intermediate data structures are often used as glue to connect separate parts of a program together. These intermediate data structures are useful because they allow modularity, but they are also a cause of inefficiency: each element need to be allocated, to be examined, and to be deallocated. Warm fusion is a program transformation technique which aims to eliminate intermediate data structures. Functions in a program are first transformed into the so called build-cata form, then fused via a one-step rewrite rule, the cata-build rule. In the process of the transformation to build-cata form we attempt to replace explicit recursion with a fixed pattern of recursion (catamorphism). We analyse in detail the problem of removing - possibly mutually recursive sets of - polynomial datatypes. Wehave implemented the warm fusion method in the Glasgow Haskell Compiler, which has allowed practical feedback. One important conclusion is that catamorphisms and fusion in general deserve a more prominent role in the compilation process. We give a detailed measurement of our implementation on a suite of real application programs

Improving Implicit Parallelism

We propose a new technique for exploiting the inherent parallelism in lazy functional programs. Known as implicit parallelism, the goal of writing a sequential program and having the compiler improve its performance by determining what can be executed in parallel has been studied for many years. Our technique abandons the idea that a compiler should accomplish this feat in ‘one shot’ with static analysis and instead allow the compiler to improve upon the static analysis using iterative feedback. We demonstrate that iterative feedback can be relatively simple when the source language is a lazy purely functional programming language. We present three main contributions to the field: the auto- matic derivation of parallel strategies from a demand on a structure, and two new methods of feedback-directed auto-parallelisation. The first method treats the runtime of the program as a black box and uses the ‘wall-clock’ time as a fitness function to guide a heuristic search on bitstrings representing the parallel setting of the program. The second feedback approach is profile directed. This allows the compiler to use profile data that is gathered by the runtime system as the pro- gram executes. This allows the compiler to determine which threads are not worth the overhead of creating them. Our results show that the use of feedback-directed compilation can be a good source of refinement for the static analysis techniques that struggle to account for the cost of a computation. This lifts the burden of ‘is this parallelism worthwhile?’ away from the static phase of compilation and to the runtime, which is better equipped to answer the question

Hybrid eager and lazy evaluation for efficient compilation of Haskell

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Includes bibliographical references (p. 208-220).This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.The advantage of a non-strict, purely functional language such as Haskell lies in its clean equational semantics. However, lazy implementations of Haskell fall short: they cannot express tail recursion gracefully without annotation. We describe resource-bounded hybrid evaluation, a mixture of strict and lazy evaluation, and its realization in Eager Haskell. From the programmer's perspective, Eager Haskell is simply another implementation of Haskell with the same clean equational semantics. Iteration can be expressed using tail recursion, without the need to resort to program annotations. Under hybrid evaluation, computations are ordinarily executed in program order just as in a strict functional language. When particular stack, heap, or time bounds are exceeded, suspensions are generated for all outstanding computations. These suspensions are re-started in a demand-driven fashion from the root. The Eager Haskell compiler translates Ac, the compiler's intermediate representation, to efficient C code. We use an equational semantics for Ac to develop simple correctness proofs for program transformations, and connect actions in the run-time system to steps in the hybrid evaluation strategy.(cont.) The focus of compilation is efficiency in the common case of straight-line execution; the handling of non-strictness and suspension are left to the run-time system. Several additional contributions have resulted from the implementation of hybrid evaluation. Eager Haskell is the first eager compiler to use a call stack. Our generational garbage collector uses this stack as an additional predictor of object lifetime. Objects above a stack watermark are assumed to be likely to die; we avoid promoting them. Those below are likely to remain untouched and therefore are good candidates for promotion. To avoid eagerly evaluating error checks, they are compiled into special bottom thunks, which are treated specially by the run-time system. The compiler identifies error handling code using a mixture of strictness and type information. This information is also used to avoid inlining error handlers, and to enable aggressive program transformation in the presence of error handling.by Jan-Willem Maessen.Ph.D

Granularity in Large-Scale Parallel Functional Programming

This thesis demonstrates how to reduce the runtime of large non-strict functional programs using parallel evaluation. The parallelisation of several programs shows the importance of granularity, i.e. the computation costs of program expressions. The aspect of granularity is studied both on a practical level, by presenting and measuring runtime granularity improvement mechanisms, and at a more formal level, by devising a static granularity analysis. By parallelising several large functional programs this thesis demonstrates for the first time the advantages of combining lazy and parallel evaluation on a large scale: laziness aids modularity, while parallelism reduces runtime. One of the parallel programs is the Lolita system which, with more than 47,000 lines of code, is the largest existing parallel non-strict functional program. A new mechanism for parallel programming, evaluation strategies, to which this thesis contributes, is shown to be useful in this parallelisation. Evaluation strategies simplify parallel programming by separating algorithmic code from code specifying dynamic behaviour. For large programs the abstraction provided by functions is maintained by using a data-oriented style of parallelism, which defines parallelism over intermediate data structures rather than inside the functions. A highly parameterised simulator, GRANSIM, has been constructed collaboratively and is discussed in detail in this thesis. GRANSIM is a tool for architecture-independent parallelisation and a testbed for implementing runtime-system features of the parallel graph reduction model. By providing an idealised as well as an accurate model of the underlying parallel machine, GRANSIM has proven to be an essential part of an integrated parallel software engineering environment. Several parallel runtime- system features, such as granularity improvement mechanisms, have been tested via GRANSIM. It is publicly available and in active use at several universities worldwide. In order to provide granularity information this thesis presents an inference-based static granularity analysis. This analysis combines two existing analyses, one for cost and one for size information. It determines an upper bound for the computation costs of evaluating an expression in a simple strict higher-order language. By exposing recurrences during cost reconstruction and using a library of recurrences and their closed forms, it is possible to infer the costs for some recursive functions. The possible performance improvements are assessed by measuring the parallel performance of a hand-analysed and annotated program

Static analysis of Martin-Löf's intuitionistic type theory

Martin-Löf's intuitionistic type theory has been under investigation in recent years as a potential source for future functional programming languages. This is due to its properties which greatly aid the derivation of provably correct programs. These include the Curry-Howard correspondence (whereby logical formulas may be seen as specifications and proofs of logical formulas as programs) and strong normalisation (i.e. evaluation of every proof/program must terminate). Unfortunately, a corollary of these properties is that the programs may contain computationally irrelevant proof objects: proofs which are not to be printed as part of the result of a program. We show how a series of static analyses may be used to improve the efficiency of type theory as a lazy functional programming language. In particular we show how variants of abstract interpretation may be used to eliminate unnecessary computations in the object code that results from a type theoretic program. After an informal treatment of the application of abstract interpretation to type theory (where we discuss the features of type theory which make it particularly amenable to such an approach), we give formal proofs of correctness of our abstract interpretation techniques, with regard to the semantics of type theory. We subsequently describe how we have implemented abstract interpretation techniques within the Ferdinand functional language compiler. Ferdinand was developed as a lazy functional programming system by Andrew Douglas at the University of Kent at Canterbury. Finally, we show how other static analysis techniques may be applied to type theory. Some of these techniques use the abstract interpretation mechanisms previously discussed

Static analysis of functional languages

Static analysis is the name given to a number of compile time analysis techniques used to automatically generate information which can lead to improvements in the execution performance of function languages. This thesis provides an introduction to these techniques and their implementation. The abstract interpretation framework is an example of a technique used to extract information from a program by providing the program with an alternate semantics and evaluating this program over a non-standard domain. The elements of this domain represent certain properties of interest. This framework is examined in detail, as well as various extensions and variants of it. The use of binary logical relations and program logics as alternative formulations of the framework , and partial equivalence relations as an extension to it, are also looked at. The projection analysis framework determines how much of a sub-expression can be evaluated by examining the context in which the expression is to be evaluated, and provides an elegant method for finding particular types of information from data structures. This is also examined. The most costly operation in implementing an analysis is the computation of fixed points. Methods developed to make this process more efficient are looked at. This leads to the final chapter which highlights the dependencies and relationships between the different frameworks and their mathematical disciplines.KMBT_22

Prototyping parallel functional intermediate languages

Non-strict higher-order functional programming languages are elegant, concise, mathematically sound and contain few environment-specific features, making them obvious candidates for harnessing high-performance architectures. The validity of this approach has been established by a number of experimental compilers. However, while there have been a number of important theoretical developments in the field of parallel functional programming, implementations have been slow to materialise. The myriad design choices and demands of specific architectures lead to protracted development times. Furthermore, the resulting systems tend to be monolithic entities, and are difficult to extend and test, ultimatly discouraging experimentation. The traditional solution to this problem is the use of a rapid prototyping framework. However, as each existing systems tends to prefer one specific platform and a particular way of expressing parallelism (including implicit specification) it is difficult to envisage a general purpose framework. Fortunately, most of these systems have at least one point of commonality: the use of an intermediate form. Typically, these abstract representations explicitly identify all parallel components but without the background noise of syntactic and (potentially arbitrary) implementation details. To this end, this thesis outlines a framework for rapidly prototyping such intermediate languages. Based on the traditional three-phase compiler model, the design process is driven by the development of various semantic descriptions of the language. Executable versions of the specifications help to both debug and informally validate these models. A number of case studies, covering the spectrum of modern implementations, demonstrate the utility of the framework