Gradual typing has emerged as a promising typing discipline for reconciling static and dynamic typing, which have respective strengths and shortcomings. Thanks to its promises, gradual typing has gained tremendous momentum in both industry and academia. A main challenge in gradual typing is that, however, the performance of its programs can often be unpredictable, and adding or removing the type of a a single parameter may lead to wild performance swings. Many approaches have been proposed to optimize gradual typing performance, but little work has been done to aid the understanding of the performance landscape of gradual typing and navigating the migration process (which adds type annotations to make programs more static) to avert performance slowdowns. Motivated by this situation, this work develops a machine-learning-based approach to predict the performance of each possible way of adding type annotations to a program. On top of that, many supports for program migrations could be developed, such as finding the most performant neighbor of any given configuration. Our approach gauges runtime overheads of dynamic type checks inserted by gradual typing and uses that information to train a machine learning model, which is used to predict the running time of gradual programs. We have evaluated our approach on 12 Python benchmarks for both guarded and transient semantics. For guarded semantics, our evaluation results indicate that with only 40 training instances generated from each benchmark, the predicted times for all other instances differ on average by 4% from the measured times. For transient semantics, the time difference ratio is higher but the time difference is often within 0.1 seconds.

Gradual typing has emerged as a popular design point in programming languages, attracting significant interests from both academia and industry. Programmers in gradually typed languages are free to utilize static and dynamic typing as needed. To make such languages sound, runtime checks mediate the boundary of typed and untyped code. Unfortunately, such checks can incur significant runtime overhead on programs that heavily mix static and dynamic typing. To combat this overhead without necessitating changes to the underlying implementations of languages, we present discriminative typing . Discriminative typing works by optimistically inferring types for functions and implementing an optimized version of the function based on this type. To preserve safety it also implements an un-optimized version of the function based purely on the provided annotations. With two versions of each function in hand, discriminative typing translates programs so that the optimized functions are called as frequently as possible while also preserving program behaviors. We have implemented discriminative typing in Reticulated Python and have evaluated its performance compared to guarded Reticulated Python. Our results show that discriminative typing improves the performance across 95% of tested programs, when compared to Reticulated, and achieves more than 4× speedup in more than 56% of these programs. We also compare its performance against a previous optimization approach and find that discriminative typing improved performance across 93% of tested programs, with 30% of these programs receiving speedups between 4 to 25 times. Finally, our evaluation shows that discriminative typing remarkably reduces the overhead of gradual typing on many mixed type configurations of programs. In addition, we have implemented discriminative typing in Grift and evaluated its performance. Our evaluation demonstrations that DT significantly improves performance of Grift.

Abstract Gradual typing allows programs to enjoy the benefits of both static typing and dynamic typing. While it is often desirable to migrate a program from more dynamically typed to more statically typed or vice versa, gradual typing itself does not provide a way to facilitate this migration. This places the burden on programmers who have to manually add or remove type annotations. Besides the general challenge of adding type annotations to dynamically typed code, there are subtle interactions between these annotations in gradually typed code that exacerbate the situation. For example, to migrate a program to be as static as possible, in general, all possible combinations of adding or removing type annotations from parameters must be tried out and compared. In this paper, we address this problem by developing migrational typing , which efficiently types all possible ways of replacing dynamic types with fully static types for a gradually typed program. The typing result supports automatically migrating a program to be as static as possible or introducing the least number of dynamic types necessary to remove a type error. The approach can be extended to support user-defined criteria about which annotations to modify. We have implemented migrational typing and evaluated it on large programs. The results show that migrational typing scales linearly with the size of the program and takes only 2–4 times longer than plain gradual typing.

This paper explores a new online learning problem where the input sequence lives in an over-time varying feature space and the ground-truth label of any input point is given only occasionally, making online learners less restrictive and more applicable. The crux in this setting lies in how to exploit the very limited labels to efficiently update the online learners. Plausible ideas such as propagating labels from labeled points to their neighbors through uncovering the point-wise geometric relations face two challenges: (1) distance measurement fails to work as different points may be described by disparate sets of features and (2) storing the geometric shape, which is formed by all arrived points, is unrealistic in an online setting. To address these challenges, we first construct a universal feature space that accumulates all observed features, making distance measurement feasible. Then, we use manifolds to represent the geometric shapes and approximate them in a sparse means, making manifolds computational and memory tractable in online learning. We frame these two building blocks into a regularized risk minimization algorithm. Theoretical analysis and empirical evidence substantiate the viability and effectiveness of our proposal.

Lifelong machine learning (LML) has driven the development of extensive web applications, enabling the learning systems deployed on web servers to deal with a sequence of tasks in an incremental fashion. Such systems can retain knowledge from learned tasks in a knowledge base and seamlessly apply it to improve the future learning. Unfortunately, most existing LML methods require labels in every task, whereas providing persistent human labeling for all future tasks is costly, onerous, error-prone, and hence impractical. Motivated by this situation, we propose a new paradigm named unsupervised lifelong learning with curricula (ULLC), where only one task needs to be labeled for initialization and the system then performs lifelong learning for subsequent tasks in an unsupervised fashion. A main challenge of realizing this paradigm lies in the occurrence of negative knowledge transfer, where partial old knowledge becomes detrimental for learning a given task yet cannot be filtered out by the learner without the help of labels. To overcome this challenge, we draw insights from the learning behaviors of humans. Specifically, when faced with a difficult task that cannot be well tackled by our current knowledge, we usually postpone it and work on some easier tasks first, which allows us to grow our knowledge. Thereafter, once we go back to the postponed task, we are more likely to tackle it well as we are more knowledgeable now. The key idea of ULLC is similar – at any time, a pool of candidate tasks are organized in a curriculum by their distances to the knowledge base. The learner then starts from the closer tasks, accumulates knowledge from learning them, and moves to learn the faraway tasks with a gradually augmented knowledge base. The viability and effectiveness of our proposal are substantiated through extensive empirical studies on both synthetic and real datasets.

Learning with streaming data has received extensive attention during the past few years. Existing approaches assume that the feature space is fixed or changes by following explicit regularities, limiting their applicability in real-time applications. For example, in a smart healthcare platform, the feature space of the patient data varies when different medical service providers use nonidentical feature sets to describe the patients' symptoms. To fill the gap, we in this article propose a novel learning paradigm, namely, Generative Learning With Streaming Capricious (GLSC) data, which does not make any assumption on the feature space dynamics. In other words, GLSC handles the data streams with a varying feature space, where each arriving data instance can arbitrarily carry new features and/or stop carrying partial old features. Specifically, GLSC trains a learner on a universal feature space that establishes relationships between old and new features, so that the patterns learned in the old feature space can be used in the new feature space. The universal feature space is constructed by leveraging the relatednesses among features. We propose a generative graphical model to model the construction process, and show that learning from the universal feature space can effectively improve the performance with theoretical guarantees. The experimental results demonstrate that GLSC achieves conspicuous performance on both synthetic and real data sets.

Mining vertex-wise interactions in graphs helps reveal useful information in real-world applications, such as bioinformatics networks BioGRID and DrugBank and academic networks DBLP and Arxiv. A main challenge in developing a general learning method for this setting is that each vertex may be associated with features from heterogeneous feature spaces, representing very disparate information. Moreover, features could be raw and low-level, leading to sparse representations. Some solutions in this area treat all feature spaces as equally important and concatenate features from heterogeneous feature spaces into a single feature vector. Others harmonize different feature spaces by respecting their relative significance in mining vertex-wise interactions but requiring construct specialized harmonizing function and/or handcrafting expressive features, both of which entail expert knowledge. Motivated by this observation, we propose a new learning paradigm named Deep Matrix Tri-Factorization (DM3F), which draws insights from deep models: (i) DM3F replaces the linear combination with a neural architecture that can learn an arbitrary harmonizing function from data; and (ii) DM3F allows raw feature inputs and automatically extracts high-level feature representations via a layer-by-layer learning mechanism. These two characteristics of DM3F make it accessible for users without expert knowledge. DM3F includes two orthogonal and complementary models, allowing an ensemble mechanism to optimize its performance during both training and predicting. A theoretical analysis of DM3F reveals that it possesses several desirable properties, including that it strictly generalizes matrix factorization models. We demonstrate the performance of DM3F on two real-world datasets.

Gradual typing provides a methodology to integrate static and dynamic typing, harmonizing their often conflicting advantages in a single language. When a user wants to enjoy the advantages of static typing, most gradual languages require that they add type annotations. Many nontrivial tasks must be undertaken while adding type annotations, including understanding program behaviors and invariants. Unfortunately, if this is done incorrectly then the added type annotations can be wrong–leading to inconsistencies between the program and the type annotations. Gradual typing implementations detect such inconsistencies at runtime, raise cast errors, and generate messages. However, solely relying on such error messages for understanding and fixing inconsistencies and their resulting cast errors is often insufficient for multiple reasons. One reason is that while such messages cover inconsistencies in one execution path, fixing them often requires reconciling information from multiple paths. Another is that users may add many wrong type annotations that they later find difficult to identify and fix, when considering all added annotations. Recent studies provide evidence that type annotations added during program migration are often wrong and that many programmers prefer compile-time warnings about wrong annotations. Motivated by these results, we develop exploratory typing to help with the static detection, understanding, and fixing of inconsistencies. The key idea of exploratory typing is that it systematically removes dynamic types and explores alternative types for static type annotations that can remedy inconsistencies. To demonstrate the feasibility of exploratory typing, we have implemented it in PyHound, which targets programs written in Reticulated Python, a gradual variant of Python. We have evaluated PyHound on a set of Python programs, and the evaluation results demonstrate that our idea can effectively detect inconsistencies in 98% of the tested programs and fix 93% of inconsistencies, significantly outperforming pytype, a widely used Python tool for enforcing type annotations.

Learning with streaming data has received extensive attention during the past few years. Existing approaches assume the feature space is fixed or changes by following explicit regularities, limiting their applicability in dynamic environments where the data streams are described by an arbitrarily varying feature space. To handle such capricious data streams, we in this paper develop a novel algorithm, named OCDS (Online learning from Capricious Data Streams), which does not make any assumption on feature space dynamics. OCDS trains a learner on a universal feature space that establishes relationships between old and new features, so that the patterns learned in the old feature space can be used in the new feature space. Specifically, the universal feature space is constructed by leveraging the relatednesses among features. We propose a generative graphical model to model the construction process, and show that learning from the universal feature space can effectively improve performance with theoretical analysis. The experimental results demonstrate that OCDS achieves conspicuous performance on synthetic and real datasets.

Type inference is an important part of functional programming languages and has been increasingly adopted to imperative programming. However, providing effective error messages in response to type inference failures (due to type errors in programs) continues to be a challenge. Type error messages generated by compilers and existing error debugging approaches often point to bogus error locations or lack sufficient information for removing the type error, making error debugging ineffective. Counter-factual typing (CFT) addressed this problem by generating comprehensive error messages with each message includes a rich set of information. However, CFT has a large response time, making it too slow for interactive use. In particular, our recent study shows that programmers usually have to go through multiple iterations of updating and recompiling programs to remove a type error. Interestingly, our study also reveals that program updates are minor in each iteration during type error debugging. We exploit this fact and develop eCFT, an efficient version of CFT, which doesn't recompute all error fixes from scratch for each updated program but only recomputes error fixes that are changed in response to the update. Our key observation is that minor program changes lead to minor error suggestion changes. eCFT is based on principal typing, a typing scheme more amenable to reuse previous typing results. We have evaluated our approach and found it is about 12.4× faster than CFT in updating error fixes.

In C programs, error specifications, which specify the value range that each function returns to indicate failures, are widely used to check and propagate errors for the sake of reliability and security. Various kinds of C analyzers employ error specifications for different purposes, e.g., to detect error handling bugs, yet a general approach for generating precise specifications is still missing. This limits the applicability of those tools. In this paper, we solve this problem by developing a machine learning-based approach named MLPEx. It generates error specifications by analyzing only the source code, and is thus general. We propose a novel machine learning paradigm based on transfer learning, enabling MLPEx to require only one-time minimal data labeling from us (as the tool developers) and zero manual labeling efforts from users. To improve the accuracy of generated error specifications, MLPEx extracts and exploits project-specific information. We evaluate MLPEx on 10 projects, including 6 libraries and 4 applications. An investigation of 3,443 functions and 17,750 paths reveals that MLPEx generates error specifications with a precision of 91% and a recall of 94%, significantly higher than those of state-of-the-art approaches. To further demonstrate the usefulness of the generated error specifications, we use them to detect 57 bugs in 5 tested projects.

Abstract When type inference fails, it is often difficult to pinpoint the cause of the type error among many potential candidates. Generating informative messages to remove the type error is another difficult task due to the limited availability of type information. Over the last three decades many approaches have been developed to help debug type errors. However, most of these methods suffer from one or more of the following problems: (1) Being incomplete, they miss the real cause. (2) They cover many potential causes without distinguishing them. (3) They provide little or no information for how to remove the type error. Any one of this problems can turn the type-error debugging process into a tedious and ineffective endeavor. To address this issue, we have developed a method named counter-factual typing , which (1) finds a comprehensive set of error causes in AST leaves, (2) computes an informative message on how to get rid of the type error for each error cause, and (3) ranks all messages and iteratively presents the message for the most likely error cause. The biggest technical challenge is the efficient generation of all error messages, which seems to be exponential in the size of the expression. We address this challenge by employing the idea of variational typing that systematically reuses computations for shared parts and generates all messages by typing the whole ill-typed expression only once. We have evaluated our approach over a large set of examples collected from previous publications in the literature. The evaluation result shows that our approach outperforms previous approaches and is computationally feasible.

Gradual typing allows programs to enjoy the benefits of both static typing and dynamic typing. While it is often desirable to migrate a program from more dynamically-typed to more statically-typed or vice versa, gradual typing itself does not provide a way to facilitate this migration. This places the burden on programmers who have to manually add or remove type annotations. Besides the general challenge of adding type annotations to dynamically typed code, there are subtle interactions between these annotations in gradually typed code that exacerbate the situation. For example, to migrate a program to be as static as possible, in general, all possible combinations of adding or removing type annotations from parameters must be tried out and compared. In this paper, we address this problem by developing migrational typing, which efficiently types all possible ways of adding or removing type annotations from a gradually typed program. The typing result supports automatically migrating a program to be as static as possible, or introducing the least number of dynamic types necessary to remove a type error. The approach can be extended to support user-defined criteria about which annotations to modify. We have implemented migrational typing and evaluated it on large programs. The results show that migrational typing scales linearly with the size of the program and takes only 2–4 times longer than plain gradual typing.

Gradual typing allows programmers to use both static and dynamic typing in a single program. However, a well-known problem with sound gradual typing is that the interactions between static and dynamic code can cause significant performance degradation. These performance pitfalls are hard to predict and resolve, and discourage users from using gradual typing features. For example, when migrating to a more statically typed program, often adding a type annotation will trigger a slowdown that can be resolved by adding more annotations elsewhere, but since it is not clear where the additional annotations must be added, the easier solution is to simply remove the annotation. To address these problems, we develop: (1) a static cost semantics that accurately predicts the overhead of static-dynamic interactions in a gradually typed program, (2) a technique for efficiently inferring such costs for all combinations of inferrable type assignments in a program, and (3) a method for translating the results of this analysis into specific recommendations and explanations that can help programmers understand, debug, and optimize the performance of gradually typed programs. We have implemented our approach in Herder, a tool for statically analyzing the performance of different typing configurations for Reticulated Python programs. An evaluation on 15 Python programs shows that Herder can use this analysis to accurately and efficiently recommend type assignments that optimize the performance of these programs without sacrificing the safety guarantees provided by static typing.

Providing better supports for debugging type errors has been an active research area in the last three decades. Numerous approaches from different perspectives have been developed. Most approaches work well under certain conditions only, for example, when type errors are caused by single leaves and when type annotations are correct. However, the research community is still unaware of which conditions hold in practice and what the real debugging situations look like. We address this problem with a study of 3 program data sets, which were written in different years, using different compilers, and were of diverse sizes. They include more than 55,000 programs, among which more than 2,700 are ill typed. We investigated all the ill-typed programs, and our results indicate that current error debugging support is far from sufficient in practice since only about 35% of all type errors were caused by single leaves. In addition, type annotations cannot always be trusted in error debuggers since about 30% of the time type errors were caused by wrong type annotations. Our study also provides many insights about the debugging behaviors of students in functional programming, which could be exploited for developing more effective error debuggers.

Type inference is convenient by allowing programmers to elide type annotations, but this comes at the cost of often generating very confusing and opaque type error messages that are of little help to fix type errors. Though there have been many successful attempts at making type error messages better in the past thirty years, many classes of errors are still difficult to fix. In particular, current approaches still generate imprecise and uninformative error messages for type errors arising from errors in grouping constructs like parentheses and brackets. Worse, a recent study shows that these errors usually take more than 10 steps to fix and occur quite frequently (around 45% to 60% of all type errors) in programs written by students learning functional programming. We call this class of errors, nonstructural errors . We solve this problem by developing Learnskell, a type error debugger that uses machine learning to help diagnose and deliver high quality error messages, for programs that contain nonstructural errors. While previous approaches usually report type errors on typing constraints or on the type level, Learnskell generates suggestions on the expression level. We have performed an evaluation on more than 1,500 type errors, and the result shows that Learnskell is quite precise. It can correctly capture 86% of all nonstructural errors and locate the error cause with a precision of 63%/87% with the first 1/3 messages, respectively. This is several times more than the precision of state-of-the-art compilers and debuggers. We have also studied the performance of Learnskell and found out that it scales to large programs.

Variation is ubiquitous in software. Many applications can benefit from making this variation explicit, then manipulating and computing with it directly---a technique we call "variational programming". This idea has been independently discovered in several application domains, such as efficiently analyzing and verifying software product lines, combining bounded and symbolic model-checking, and computing with alternative privacy profiles. Although these domains share similar core problems, and there are also many similarities in the solutions, there is no dedicated programming language support for variational programming. This makes the various implementations tedious, prone to errors, hard to maintain and reuse, and difficult to compare. In this paper we present a calculus that forms the basis of a programming language with explicit support for representing, manipulating, and computing with variation in programs and data. We illustrate how such a language can simplify the implementation of variational programming tasks. We present the syntax and semantics of the core calculus, a sound type system, and a type inference algorithm that produces principal types.

We present a new method for GADT type inference that improves the precision of previous approaches. In particular, our approach accepts more type-correct programs than previous approaches when they do not employ type annotations. A side benefit of our approach is that it can detect a wide range of runtime errors that are missed by previous approaches. Our method is based on the idea to represent type refinements in pattern-matching branches by choice types, which facilitate a separation of the typing and reconciliation phases and thus support case expressions. This idea is formalized in a type system, which is both sound and a conservative extension of the classical Hindley-Milner system. We present the results of an empirical evaluation that compares our algorithm with previous approaches.

Previous research on static analysis for program families has focused on lifting analyses for single, plain programs to program families by employing idiosyncratic representations. The lifting effort typically involves a significant amount of work for proving the correctness of the lifted algorithm and demonstrating its scalability. In this paper, we propose a parameterized static analysis framework for program families that can automatically lift a class of type-based static analyses for plain programs to program families. The framework consists of a parametric logical specification and a parametric variational constraint solver. We prove that a lifted algorithm is correct provided that the underlying analysis algorithm is correct. An evaluation of our framework has revealed an error in a previous manually lifted analysis. Moreover, performance tests indicate that the overhead incurred by the general framework is bounded by a factor of 2.

Current C++ implementations typecheck templates in two phases: Before instantiation, those parts of the template are checked that do not depend on template parameters, while the checking of the remaining parts is delayed until template instantiation time when the template arguments become available. This approach is problematic because it causes two major usability problems. First, it prevents library developers to provide guarantees about the type correctness for modules involving templates. Second, it can lead, through the incorrect use of template functions, to inscrutable error messages. Moreover, errors are often reported far away from the source of the program fault.

Changing a program in response to a type error plays an important part in modern software development. However, the generation of good type error messages remains a problem for highly expressive type systems. Existing approaches often suffer from a lack of precision in locating errors and proposing remedies. Specifically, they either fail to locate the source of the type error consistently, or they report too many potential error locations. Moreover, the change suggestions offered are often incorrect. This makes the debugging process tedious and ineffective.

Producing precise and helpful type error messages has been a challenge for the implementations of functional programming languages for over 3 decades now. Many different approaches and methods have been tried to solve this thorny problem, but current type-error reporting tools still suffer from a lack of precision in many cases. Based on the rather obvious observation that different approaches work well in different situations, we have studied the question of whether a combination of tools that exploits their diversity can lead to improved accuracy. Specifically, we have studied Helium, a Haskell implementation particularly aimed at producing good type error messages, and Lazy Typing, an approach developed previously by us to address the premature-error-commitment problem in type checkers. By analyzing the respective strengths and weaknesses of the two approaches we were able to identify a strategy to combine both tools that could markedly improve the accuracy of reported errors. Specifically, we report an evaluation of 1069 unique ill-typed programs out of a total of 11256 Haskell programs that reveals that this combination strategy enjoys a correctness rate of 79%, which is an improvement of 22%/17% compared to using Lazy Typing/Helium alone. In addition to describing this particular case study, we will also report insights we gained into the combination of error-reporting tools in general.

Through the use of conditional compilation and related tools, many software projects can be used to generate a huge number of related programs. The problem of typing such variational software is difficult. The brute-force strategy of generating all variants and typing each one individually is: (1) usually infeasible for efficiency reasons and (2) produces results that do not map well to the underlying variational program. Recent research has focused mainly on efficiency and addressed only the problem of type checking. In this work we tackle the more general problem of variational type inference and introduce variational types to represent the result of typing a variational program. We introduce the variational lambda calculus (VLC) as a formal foundation for research on typing variational programs. We define a type system for VLC in which VLC expressions are mapped to correspondingly variational types. We show that the type system is correct by proving that the typing of expressions is preserved over the process of variation elimination, which eventually results in a plain lambda calculus expression and its corresponding type. We identify a set of equivalence rules for variational types and prove that the type unification problem modulo these equivalence rules is unitary and decidable; we also present a sound and complete unification algorithm. Based on the unification algorithm, the variational type inference algorithm is an extension of algorithm W . We show that it is sound and complete and computes principal types. We also consider the extension of VLC with sum types, a necessary feature for supporting variational data types, and demonstrate that the previous theoretical results also hold under this extension. Finally, we characterize the complexity of variational type inference and demonstrate the efficiency gains over the brute-force strategy.

Conditional compilation and software product line technologies make it possible to generate a huge number of different programs from a single software project. Typing each of these programs individually is usually impossible due to the sheer number of possible variants. Our previous work has addressed this problem with a type system for variational lambda calculus (VLC), an extension of lambda calculus with basic constructs for introducing and organizing variation. Although our type inference algorithm is more efficient than the brute-force strategy of inferring the types of each variant individually, it is less robust since type inference will fail for the entire variational expression if any one variant contains a type error. In this work, we extend our type system to operate on VLC expressions containing type errors. This extension directly supports locating ill-typed variants and the incremental development of variational programs. It also has many subtle implications for the unification of variational types. We show that our extended type system possesses a principal typing property and that the underlying unification problem is unitary. Our unification algorithm computes partial unifiers that lead to result types that (1) contain errors in as few variants as possible and (2) are most general. Finally, we perform an empirical evaluation to determine the overhead of this extension compared to our previous work, to demonstrate the improvements over the brute-force approach, and to explore the effects of various error distributions on the inference process.

Feature modeling is widely used in software product-line engineering to capture the commonalities and variabilities within an application domain. As feature models evolve, they can become very complex with respect to the number of features and the dependencies among them, which can cause the product derivation based on feature selection to become quite time consuming and error prone. We address this problem by presenting techniques to find good feature selection sequences that are based on the number of products that contain a particular feature and the impact of a selected feature on the selection of other features. Specifically, we identify a feature selection strategy, which brings up highly selective features early for selection. By prioritizing feature selection based on the selectivity of features our technique makes the feature selection process more efficient. Moreover, our approach helps with the problem of unexpected side effects of feature selection in later stages of the selection process, which is commonly considered a difficult problem. We have run our algorithm on the e-Shop and Berkeley DB feature models and also on some automatically generated feature models. The evaluation results demonstrate that our techniques can shorten the product derivation processes significantly.