Relational Programming in miniKanren: Techniques, Applications, and Implementations

Thesis (Ph.D.) - Indiana University, Computer Sciences, 2009The promise of logic programming is that programs can be written relationally, without distinguishing between input and output arguments. Relational programs are remarkably flexible—for example, a relational type-inferencer also performs type checking and type inhabitation, while a relational theorem prover generates theorems as well as proofs and can even be used as a simple proof assistant. Unfortunately, writing relational programs is difficult, and requires many interesting and unusual tools and techniques. For example, a relational interpreter for a subset of Scheme might use nominal unification to support variable binding and scope, Constraint Logic Programming over Finite Domains (CLP(FD)) to implement relational arithmetic, and tabling to improve termination behavior. In this dissertation I present miniKanren, a family of languages specifically designed for relational programming, and which supports a variety of relational idioms and techniques. I show how miniKanren can be used to write interesting relational programs, including an extremely flexible lean tableau theorem prover and a novel constraint-free binary arithmetic system with strong termination guarantees. I also present interesting and practical techniques used to implement miniKanren, including a nominal unifier that uses triangular rather than idempotent substitutions and a novel “walk”-based algorithm for variable lookup in triangular substitutions. The result of this research is a family of languages that supports a variety of relational idioms and techniques, making it feasible and useful to write interesting programs as relations

A type-theoretic framework for software component synthesis

A language-agnostic approach for type-based component-oriented software synthesis is developed from the fundamental principles of abstract algebra and Combinatory Logic. It relies on an enumerative type inhabitation algorithm for Finite Combinatory Logic with Intersection Types (FCL) and a universal algebraic construction to translate terms of Combinatory Logic into any given target language. New insights are gained on the combination of semantic domains of discourse with intersection types. Long standing gaps in the algorithmic understanding of the type inhabitation question of FCL are closed. A practical implementation is developed and its applications by the author and other researchers are discussed. They include, but are not limited to, vast improvements in the context of synthesis of software product line members. An interactive theorem prover, Coq, is used to formalize and check all the theoretical results. This makes them more reusable for other developments and enhances confidence in their correctness.Es wird ein sprachunabhängiger Ansatz für die typbasierte und komponentenorientierte Synthese von Software entwickelt. Hierzu werden grundlegende Erkenntnisse über abstrakte Algebra und kombinatorische Logik verwendet. Der Ansatz beruht auf dem enumerativen Typinhabitationsproblem der endlichen kombinatorischen Logik mit Intersektionstypen, sowie einer universellen algebraischen Konstruktion, um Ergebnisterme in jede beliebe Zielsprache übersetzen zu können. Es werden neue Einblicke gewonnen, wie verschiedene semantische Domänen des Diskurses über Softwareeigenschaften miteinander verbunden werden können. Offene Fragestellungen im Zusammenhand mit der Algorithmik des Typinhabitationsproblems für Intersektionstypen werden beantwortet. Eine praktische Implementierung des Ansatzes wird entwickelt und ihre bisherigen Anwendungen durch den Autor und andere Wissenschaftler werden diskutiert. Diese beinhalten starke Verbesserungen im Zusammenhang mit der Synthese von Ausprägungen von Software Produktlinien. Ein interaktiver Theorembeweiser wir genutzt, um alle Ergebnisse der Arbeit zu formalisieren und mechanisch zu überprüfen. Dies trägt zum einen zur Wiederverwendbarkeit der theoretischen Ergebnisse in anderen Kontexten bei, und erhöht zum andern das Vertrauen in ihre Korrektheit

A Functional, Comprehensive and Extensible Multi-Platform Querying and Transformation Approach

This thesis is about a new model querying and transformation approach called FunnyQT which is realized as a set of APIs and embedded domain-specific languages (DSLs) in the JVM-based functional Lisp-dialect Clojure. Founded on a powerful model management API, FunnyQT provides querying services such as comprehensions, quantified expressions, regular path expressions, logic-based, relational model querying, and pattern matching. On the transformation side, it supports the definition of unidirectional model-to-model transformations, of in-place transformations, it supports defining bidirectional transformations, and it supports a new kind of co-evolution transformations that allow for evolving a model together with its metamodel simultaneously. Several properties make FunnyQT unique. Foremost, it is just a Clojure library, thus, FunnyQT queries and transformations are Clojure programs. However, most higher-level services are provided as task-oriented embedded DSLs which use Clojure's powerful macro-system to support the user with tailor-made language constructs important for the task at hand. Since queries and transformations are just Clojure programs, they may use any Clojure or Java library for their own purpose, e.g., they may use some templating library for defining model-to-text transformations. Conversely, like every Clojure program, FunnyQT queries and transformations compile to normal JVM byte-code and can easily be called from other JVM languages. Furthermore, FunnyQT is platform-independent and designed with extensibility in mind. By default, it supports the Eclipse Modeling Framework and JGraLab, and support for other modeling frameworks can be added with minimal effort and without having to modify the respective framework's classes or FunnyQT itself. Lastly, because FunnyQT is embedded in a functional language, it has a functional emphasis itself. Every query and every transformation compiles to a function which can be passed around, given to higher-order functions, or be parametrized with other functions

Deconstructing Datalog

The deductive query language Datalog has found a wide array of uses, including static analy- sis (Smaragdakis and Bravenboer, 2010), business analytics (Aref et al., 2015), and distributed programming (Alvaro et al., 2010, 2011). Datalog is high-level and declarative, but simple and well-studied enough to admit efficient implementation strategies. For example, Whaley et al. found they could replace a hand-tuned C implementation of context-sensitive pointer analysis with a comparably-performing Datalog program that was 100x smaller (Whaley and Lam, 2004; Whaley et al., 2005). However, Datalog’s semantics are not stable under extensions. For instance, adding arithmetic operations breaks Datalog’s termination guarantee. Despite this, nearly all practical implementations extend Datalog beyond its theoretical core to add niceties such as arithmetic, datatypes, aggregations, and so on. Moreover, pure Datalog cannot abstract over repeated code: one may express a static analysis over a particular program, but to express the same analysis over multiple programs, one must duplicate the analysis code for each program analyzed. This thesis deconstructs Datalog from a categorical and type theoretic perspective to determine what makes it tick. Datalog’s semantic guarantees are provided by brute syntactic restrictions, such as stratification and the absence of function symbols. In place of these, we find compositional semantic properties such as monotonicity, which we capture using types. We show that this permits integrating Datalog’s features with those of typed functional languages, such as algebraic data types and higher order functions. In particular, this thesis makes the following contributions: 1. We define and expound the semantics and metatheory of Datafun, a pure and total higher-order typed functional language capturing the essence of Datalog. Where Data- log has predicates defined by a restricted class of Horn clauses, Datafun has finite sets and set comprehensions; Datalog’s bottom-up recursive queries become iterative fixed points; and Datalog’s stratification condition becomes a matter of tracking monotonicity with types. 2. We show how to generalize seminaïve evaluation to handle higher-order functions. Seminaïve evaluation is a technique from the Datalog literature which improves the performance of Datalog’s most distinctive feature: recursive queries. These are com- puted iteratively, and under a naïve evaluation strategy, each iteration recomputes all previous values. Seminaïve evaluation computes a safe approximation of the difference between iterations. This can asymptotically improve the performance of Datalog queries. Seminaïve evaluation is defined partly as a program transformation and partly as a modified iteration strategy, and takes advantage of the first-order nature of Datalog. We extend this transformation to handle higher-order programs written in Datafun. 3. In the process of generalizing seminaïve evaluation, we uncover a theory of incremental, monotone, higher-order computation, in which values change over time by growing larger, and programs respond incrementally to these increases