Variability permeates software development to satisfy ever-changing requirements and mass-customization needs. A prime example is the Linux kernel, which employs the C preprocessor to specify a set of related but distinct kernel variants. To study, analyze, and verify variational software, several formal languages have been proposed. For example, the choice calculus has been successfully applied for type checking and symbolic execution of configurable software, while other formalisms have been used for variational model checking, change impact analysis, among other use cases. Yet, these languages have not been formally compared, hence, little is known about their relationships. Crucially, it is unclear to what extent one language subsumes another, how research results from one language can be applied to other languages, and which language is suitable for which purpose or domain. In this paper, we propose a formal framework to compare the expressive power of languages for static (i.e. compile-time) variability. By establishing a common semantic domain to capture a widely used intuition of explicit variability, we can formulate the basic, yet to date neglected, properties of soundness, completeness, and expressiveness for variability languages. We then prove the (un)soundness and (in)completeness of a range of existing languages, and relate their ability to express the same variational systems. We implement our framework as an extensible open source Agda library in which proofs act as correct compilers between languages or differencing algorithms. We find different levels of expressiveness as well as complete and incomplete languages w.r.t. our unified semantic domain, with the choice calculus being among the most expressive languages.

Abstract Incremental satisfiability (SAT) solving is an extension of classic SAT solving that enables solving a set of related SAT problems by identifying and exploiting shared terms. However, using incremental solvers effectively is hard since performance is sensitive to the input order of subterms and results must be tracked manually. For analyses that generate sets of related SAT problems, such as those in software product lines, incremental solvers are either not used or their use is not clearly described in the literature. This paper translates the ordering problem to an encoding problem and automates the use of incremental solving. We introduce variational SAT solving, which differs from incremental solving by accepting all related problems as a single variational input and returning all results as a single variational output. Variational solving syntactically encodes differences in related SAT problems as local points of variation. With this syntax, our approach automates the interaction with the incremental solver and enables a method to automatically optimize sharing in the input. To evaluate these ideas, we formalize a variational SAT algorithm, construct a prototype variational solver, and perform an empirical analysis on two real-world datasets that applied incremental solvers to software evolution scenarios. We show, assuming a variational input, that the prototype solver scales better for these problems than four off-the-shelf incremental solvers while also automatically tracking individual results.

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.

Many problems require working with data that varies in its structure and content. Current approaches, such as schema evolution or data integration tools, are highly tailored to specific kinds of variation in databases. While these approaches work well in their roles, they do not address all kinds of variation and do address the interaction of different kinds of variation in databases. In this paper, we define a framework for capturing variation as a generic and orthogonal con- cern in relational databases. We define variational schemas, variational databases, and variational queries for capturing variation in the structure, content, and information needs of relational databases, respectively. We define a type system that ensures variational queries are consistent with respect to a variational schema. Finally, we design and implement a variational database management system as an abstraction layer over a traditional relational database management system. Using previously developed use cases, we show the feasibility of our framework and demonstrate the performance of different approaches used in our system

Graphical user interfaces (GUIs) are ubiquitous in real-world software and a notorious source of bugs that are difficult to catch through software testing. Model checking has been used to prove the absence of certain kinds of bugs, but model checking works on an abstract model of the GUI application, which might be inconsistent with its implementation. We present a library for developing directly verified, state-dependent GUI applications in the dependently typed programming language Agda. In the library, the type of a GUI's controller depends on a specification of the GUI itself, statically enforcing consistency between them. Arbitrary properties can be defined and proved in terms of user interactions and state transitions. Our library connects to a custom-built Haskell back-end for declarative vector-based GUI elements. Compared to an earlier version of our library built on an existing imperative GUI framework, the more declarative back-end supports simpler definitions and proofs.

Explanations of data structures and algorithms are complex interactions of several notations, including natural language, mathematics, pseudocode, and diagrams. Currently, such explanations are created ad hoc using a variety of tools and the resulting artifacts are static, reducing explanatory value. We envision a domain-specific language for developing rich, interactive explanations of data structures and algorithms. In this paper, we analyze this domain to sketch requirements for our language. We perform a grounded theory analysis to generate a qualitative coding system for explanation artifacts collected online. This coding system implies a common structure among explanations of algorithms and data structures. We believe this structure can be reused as the semantic basis of a domain-specific language for creating interactive explanation artifacts. This work is part of our effort to develop the paradigm of explanation-oriented programming, which shifts the focus of programming from computing results to producing rich explanations of how those results were computed.

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.

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.

Highly configurable software often uses preprocessor annotations to handle variability. However, understanding, maintaining, and evolving code with such annotations is difficult, mainly because a developer has to work with all variants at a time. Dedicated methods and tools that allow working on a subset of all variants could ease the engineering of highly configurable software. We investigate the potential of one kind of such tools: projection-based variation control systems. For such systems we aim to understand: (i) what end-user operations they need to support, and (ii) whether they can realize the actual evolution of real-world, highly configurable software. We conduct an experiment that investigates variability-related evolution patterns and that evaluates the feasibility of a projection-based variation control system by replaying parts of the history of a highly configurable real-world 3D printer firmware project. Among others, we show that the prototype variation control system does indeed support the evolution of a highly configurable system and that in general, it does not degrade the code.

Humans play an active role in the execution of certain kinds of programs, such as spreadsheets, workflows and interactive notebooks. Interacting closely with execution is especially useful when end-users are learning from examples while doing their work. In order to better understand the language features needed to support this kind of use, we investigated a particularly rigid and formalized category of “program” people write for each other: lab protocols. These protocols present a linear, idealized process despite the complex contingencies of the lab work they describe. However, they employ a variety of techniques for limiting or expanding the semantic interpretation of individual steps and for integrating outside protocols. We use these observations to derive implications for the design of interactive and mixed-initiative programming languages.

Editing the source code of variational software is complicated by the presence of variation annotations, such as #ifdef statements, and by code that is only included in some configurations. When editing some configurations and not others, it would be easier to edit a simplified version of the source code that includes only the configurations we currently care about. In this paper, we present a projectional editing model for variational software. Using our approach, a programmer can partially configure a variational program, edit this simplified view of the code, and then automatically update the original, fully variational source code. The model is based on an isolation principle where edits affect only the variants that are visible in the view. We show that this principle has several nice properties that are suggested by related work on bidirectional transformations.

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.

We present a formal calculus for modeling and implementing variation in software. It unifies the compositional and annotative approaches to feature implementation and supports the development of abstractions that can be used to directly relate feature models to their implementation. Since the compositional and annotative approaches are complementary, the calculus enables implementers to use the best combination of tools for the job and focus on inherent feature interactions, rather than those introduced by biases in the representation. The calculus also supports the abstraction of recurring variational patterns and provides a metaprogramming platform for organizing variation in artifacts.

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.

Maintaining variation in software is a difficult problem that poses serious challenges for the understanding and editing of software artifacts. Although the C preprocessor (CPP) is often the default tool used to introduce variability to software, because of its simplicity and flexibility, it is infamous for its obtrusive syntax and has been blamed for reducing the comprehensibility and maintainability of software. In this paper, we address this problem by developing a prototype for managing software variation at the source code level. We evaluate the difference between our prototype and CPP with a user study, which indicates that the prototype helps users reason about variational code faster and more accurately than CPP. Our results also support the research of others, providing evidence for the effectiveness of related tools, such as CIDE and FeatureCommander.

Many areas of computer science are concerned with some form of variation in software---from managing changes to software over time to supporting families of related artifacts. We present the choice calculus, a fundamental representation for software variation that can serve as a common language of discourse for variation research, filling a role similar to the lambda calculus in programming language research. We also develop an associated theory of software variation, including sound transformations of variation artifacts, the definition of strategic normal forms, and a design theory for variation structures, which will support the development of better algorithms and tools.

The principle of causation is fundamental to science and society and has remained an active topic of discourse in philosophy for over two millennia. Modern philosophers often rely on ``neuron diagrams'', a domain-specific visual language for discussing and reasoning about causal relationships and the concept of causation itself. In this paper we formalize the syntax and semantics of neuron diagrams. We discuss existing algorithms for identifying causes in neuron diagrams, show how these approaches are flawed, and propose solutions to these problems. We separate the standard representation of a dynamic execution of a neuron diagram from its static definition and define two separate, but related semantics, one for the causal effects of neuron diagrams and one for the identification of causes themselves. Most significantly, we propose a simple language extension that supports a clear, consistent, and comprehensive algorithm for automatic causal inference.

This work considers the intersection of explanation-oriented language design and software variation management, two seemingly disparate research areas that turn out to be quite complementary. Successful explanations are often highly variable to adapt to the needs of a particular user, but this also makes them complex and unwieldy unless supported by a sound theory of variation.

Continuing our research in explanation-oriented language design, we present a domain-specific visual language for explaining probabilistic reasoning. Programs in this language, called explanation objects, can be manipulated according to a set of laws to automatically generate many equivalent explanation instances. We argue that this increases the explanatory power of our language by allowing a user to view a problem from many different perspectives.

Abstract Experimental game theory is increasingly important for research in many fields. Unfortunately, it is poorly supported by computer tools. We have created Hagl, a domain-specific language embedded in Haskell, to reduce the development time of game-theoretic experiments and make the definition and exploration of games and strategies simple and fun.

We present a visual language for strategies in game theory, which has potential applications in economics, social sciences, and in general science education. This language facilitates explanations of strategies by visually representing the interaction of playerspsila strategies with game execution. We have utilized the cognitive dimensions framework in the design phase and recognized the need for a new cognitive dimension of ldquotraceabilityrdquo that considers how well a language can represent the execution of a program. We consider how traceability interacts with other cognitive dimensions and demonstrate its use in analyzing existing languages. We conclude that the design of a visual representation for execution traces should be an integral part of the design of visual languages because understanding a program is often tightly coupled to its execution.

We are developing a new paradigm of explanation-oriented languages whose objective is not only to describe the computation of values, but also to provide explanations of how and why those values are obtained. We have begun exploring this approach in the design of a visual notation for strategies in game theory. We plan to apply these ideas to other domains of public interest to both benefit those domains and to expand and solidify the theory behind explanation-oriented design.