Type Inference for Parameterized Race-Free Java

Hindley and Milner's type system, in its purest form, allows what one might call full type inference. Even when a program contains no explicit type information, its very structure gives rise to a conjunction of type equations (or, more generally, to a constraint) whose resolution allows reconstructing the type of every variable and of every sub-expression. Actual programming languages based on this type system, such as Standard ML, Objective Caml, and Haskell, do allow users to provide explicit type information via optional type annotations. Yet, this extra information does not make type inference any easier: it simply gives rise to extra equations, leading to a more specific constraint.There are extensions of Hindley and Milner's type system where full type inference becomes undecidable or intractable. Then, it is common to require explicit type information, via mandatory type annotations. Polymorphic recursion is a simple and well-known instance of this phenomenon. This talk presents two more elaborate instances, commonly known as arbitrary-rank polymorphism and generalized algebraic data types.In both cases, type inference is made tractable thanks to mandatory type annotations. There is a twist, though: these required annotations are often numerous and redundant. So, it seems desirable to make them optional again, and to set up a distinct mechanism to guess some of the elided annotations. This mechanism, referred to as elaboration, can be heuristic. It must be predictable. In the two cases considered in this talk, it is a form of local type inference.This approach leads to a so-called stratified type inference system, where type information is propagated first in a local, ad hoc manner during elaboration, then in a possibly nonlocal, but well-specified manner during constraint solving. This appears to be one of the less displeasing ways of describing type inference systems that are able to exploit optional type annotations to infer better (or different) types.

Article Free Access Share on Refinement types for ML Authors: Tim Freeman School of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania School of Computer Science, Carnegie Mellon University, Pittsburgh, PennsylvaniaView Profile , Frank Pfenning School of Computer Science, Carnegie Mellon University, Pittsburgh, Pennsylvania School of Computer Science, Carnegie Mellon University, Pittsburgh, PennsylvaniaView Profile Authors Info & Claims PLDI '91: Proceedings of the ACM SIGPLAN 1991 conference on Programming language design and implementationMay 1991 Pages 268–277https://doi.org/10.1145/113445.113468Online:01 May 1991Publication History 293citation1,256DownloadsMetricsTotal Citations293Total Downloads1,256Last 12 Months93Last 6 weeks10 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

We investigate finite-rank intersection type systems, analyzing the complexity of their type inference problems and their relation to the problem of recognizing semantically equivalent terms. Intersection types allow something of type τ 1 Λ τ 2 to be used in some places at type τ 1 and in other places at type τ 2 . A finite-rank intersection type system bounds how deeply the Λ can appear in type expressions. Such type systems enjoy strong normalization, subject reduction, and computable type inference, and they support a pragmatics for implementing parametric polymorphism. As a consequence, they provide a conceptually simple and tractable alternative to the impredicative polymorphism of System F and its extensions, while typing many more programs than the Hindley-Milner type system found in ML and Haskell.While type inference is computable at every rank, we show that its complexity grows exponentially as rank increases. Let K (0, n ) = n and K ( t + 1, n ) = 2 K ( t,n ) ; we prove that recognizing the pure λ-terms of size n that are typable at rank k is complete for DTIME [ K ( k −1, n )]. We then consider the problem of deciding whether two λ-terms typable at rank k have the same normal form, generalizing a well-known result of Statman from simple types to finite-rank intersection types. We show that the equivalence problem is DTIME [ K ( K ( k − 1, n ), 2)]-complete. This relationship between the complexity of typability and expressiveness is identical in wellknown decidable type systems such as simple types and Hindley-Milner types, but seems to fail for System F and its generalizations. The correspondence gives rise to a conjecture that if Τ is a predicative type system where typability has complexity t ( n ) and expressiveness has complexity e ( n ), then t ( n ) = Ω(log* e ( n )).

For many compiled languages, source-level types are erased very early in the compilation process. As a result, further compiler passes may convert type-safe source into type-unsafe machine code. Type-unsafe idioms in the original source and type-unsafe optimizations mean that type information in a stripped binary is essentially nonexistent. The problem of recovering high-level types by performing type inference over stripped machine code is called type reconstruction, and offers a useful capability in support of reverse engineering and decompilation. In this paper, we motivate and develop a novel type system and algorithm for machine-code type inference. The features of this type system were developed by surveying a wide collection of common source- and machine-code idioms, building a catalog of challenging cases for type reconstruction. We found that these idioms place a sophisticated set of requirements on the type system, inducing features such as recursively-constrained polymorphic types. Many of the features we identify are often seen only in expressive and powerful type systems used by high-level functional languages. Using these type-system features as a guideline, we have developed Retypd: a novel static type-inference algorithm for machine code that supports recursive types, polymorphism, and subtyping. Retypd yields more accurate inferred types than existing algorithms, while also enabling new capabilities such as reconstruction of pointer const annotations with 98% recall. Retypd can operate on weaker program representations than the current state of the art, removing the need for high-quality points-to information that may be impractical to compute.

For many compiled languages, source-level types are erased very early in the compilation process. As a result, further compiler passes may convert type-safe source into type-unsafe machine code. Type-unsafe idioms in the original source and type-unsafe optimizations mean that type information in a stripped binary is essentially nonexistent. The problem of recovering high-level types by performing type inference over stripped machine code is called type reconstruction, and offers a useful capability in support of reverse engineering and decompilation. In this paper, we motivate and develop a novel type system and algorithm for machine-code type inference. The features of this type system were developed by surveying a wide collection of common source- and machine-code idioms, building a catalog of challenging cases for type reconstruction. We found that these idioms place a sophisticated set of requirements on the type system, inducing features such as recursively-constrained polymorphic types. Many of the features we identify are often seen only in expressive and powerful type systems used by high-level functional languages. Using these type-system features as a guideline, we have developed Retypd: a novel static type-inference algorithm for machine code that supports recursive types, polymorphism, and subtyping. Retypd yields more accurate inferred types than existing algorithms, while also enabling new capabilities such as reconstruction of pointer const annotations with 98% recall. Retypd can operate on weaker program representations than the current state of the art, removing the need for high-quality points-to information that may be impractical to compute.

Types are a good starting point for various software reengineering tasks. Unfortunately, programs requiring reengineering most desperately are written in languages without an adequate type system (such as COBOL). To solve this problem, we propose a method of automated type inference for these languages. The main ingredients are that if variables are compared using some relational operator their types must be the same; likewise if an expression is assigned to a variable, the type of the expression must be a subtype of that of the variable. We present the formal type system and inference rules for this approach, show their effect on various real life COBOL fragments, describe the implementation of our ideas in a prototype type inference tool for COBOL, and discuss a number of applications.

Atomicity is a fundamental correctness property in multithreaded programs. A method is atomic if, for every execution, there is an equivalent serial execution in which the actions of the method are not interleaved with actions of other threads. Atomic methods are amenable to sequential reasoning, which significantly facilitates subsequent analysis and verification. This article presents a type system for specifying and verifying the atomicity of methods in multithreaded Java programs using a synthesis of Lipton's theory of reduction and type systems for race detection. The type system supports guarded, write-guarded, and unguarded fields, as well as thread-local data, parameterized classes and methods, and protected locks. We also present an algorithm for verifying atomicity via type inference. We have applied our type checker and type inference tools to a number of commonly used Java library classes and programs. These tools were able to verify the vast majority of methods in these benchmarks as atomic, indicating that atomicity is a widespread methodology for multithreaded programming. In addition, reported atomicity violations revealed some subtle errors in the synchronization disciplines of these programs.

A mixin module is a programming abstraction that simultaneously generalizes λ-abstractions, records, and mutually recursive definitions. Although various mixin module type systems have been developed, no one has investigated principal typings or developed type inference for first-class mixin modules, nor has anyone added Milner's let-polymorphism to such a system.This paper proves that typability is NP-complete for the naive approach followed by previous mixin module type systems. Because a λ-calculus extended with record concatenation is a simple restriction of our mixin module calculus, we also prove the folk belief that typability is NP-complete for the naive early type systems for record concatenation.To allow feasible type inference, we present Martini, a new system of simple types for mixin modules with principal typings . Martini is conceptually simple, with no subtyping and a clean and balanced separation between unification-based type inference with type and row variables and constraint solving for safety of linking and field extraction. We have implemented a type inference algorithm and we prove its complexity to be O ( n 2 ), or O ( n ) given a fixed bound on the number of field labels. To prove the complexity, we need to present an algorithm for row unification that may have been implemented by others, but which we could not find written down anywhere. Because Martini has principal typings, we successfully extend it with Milner's let-polymorphism.

With the introduction of parametric types in Java, the type system becomes more complex to handle. The Java generics requires more programming efforts to instantiate appropriate types. In such a situation, a sound type inference algorithm may reduce programming load and ensure safety. Java type inference algorithm has eased programming efforts by reducing explicit instantiation of types. The Java type inference algorithm is being expanded. Still, the impact of inference in mainstream programming is limited. Moreover, the unsound approach for inference causes unpredictable behavior in program code. The limitations and unsoundness of Java type inference need to be discussed to avoid the failure of codes. In this paper, we discuss limitations and issues of type inference algorithm, such as the incapability to infer wildcards as return type in generic methods, and limitations of local variable type inference. Further, we discuss how the machine learning approaches can help to develop a safe type inference algorithm.

A system of constructor classes

With the success of programming models such as Khronos' OpenCL, heterogeneous computing is going mainstream. However, these models are low-level, even when considering them as systems programming models. For example, OpenCL is effectively an extended subset of C99, limited to the type unsafe procedural abstraction that C has provided for more than 30 years. Computer systems programming has for more than two decades been able to do a lot better. One successful case in point is the systems programming language C++, known for its strong(er) type system, templates, and object-oriented abstraction features.

In approximate computing, programs gain efficiency by allowing occasional errors. Controlling the probabilistic effects of this approximation remains a key challenge. We propose a new approach where programmers use a type system to communicate high-level constraints on the degree of approximation. A combination of type inference, code specialization, and optional dynamic tracking makes the system expressive and convenient. The core type system captures the probability that each operation exhibits an error and bounds the probability that each expression deviates from its correct value. Solver-aided type inference lets the programmer specify the correctness probability on only some variables—program outputs, for example—and automatically fills in other types to meet these specifications. An optional dynamic type helps cope with complex run-time behavior where static approaches are insufficient. Together, these features interact to yield a high degree of programmer control while offering a strong soundness guarantee. We use existing approximate-computing benchmarks to show how our language, DECAF, maintains a low annotation burden. Our constraint-based approach can encode hardware details, such as finite degrees of reliability, so we also use DECAF to examine implications for approximate hardware design. We find that multi-level architectures can offer advantages over simpler two-level machines and that solver-aided optimization improves efficiency.

MLF is a type system that seamlessly merges ML-style type inference with System-F polymorphism. We propose a system of graphic (type) constraints that can be used to perform type inference in both ML or MLF. We show that this constraint system is a small extension of the formalism of graphic types, originally introduced to represent MLF types. We give a few semantic preserving transformations on constraints and propose a strategy for applying them to solve constraints. We show that the resulting algorithm has optimal complexity for MLF type inference, and argue that, as for ML, this complexity is linear under reasonable assumptions.

Recent research has demonstrated the effectiveness of extending the Hindley-Milner (HM) type system with Boolean kinds to support type inference for a wide variety of features. However, the means to support classic type system provisions such as local let generalization and polymorphic recursion is either limited or unknown for such extensions. This paper contributes procedures for equational generalization and semiunification in arbitrary Boolean rings, enabling let generalization and polymorphic recursion in Boolean-kinded type inference. Additionally, methods to minimize the number of bound Boolean type variables are developed to keep types small in these systems. Boolean-kinded HM extensions are exemplified with nullable reference types , and how to use the developed procedures to support let generalization and polymorphic recursion is outlined.

This thesis proposes a novel way of performing type checking, whose results are incremental, depending on the provided local information. This new way of type checking is called co-contextual, where all context information of expressions, methods, classes, etc., is removed. Instead, we introduce corresponding structures using requirements. Standard type systems are translated to the co-contextual ones systematically using dualism as technique. Type systems play an important role to prevent execution errors from occurring during runtime. They are used to check programs statically for potential errors. Programs are type checked against a given set of rules. Depending on these rules programs are well-typed or not. The set of these rules is called typing rules. Each type rule associates types to the constructs of a program given a certain context. There can be different forms of contexts, depending on the features of the typed programming language. Functional languages use a typing context of variables and their types; object-oriented (OO) languages use additional class tables. Class tables are used for example to ensure that method and class declarations are well-typed. Type checking is performed top-down. While traversing the syntax tree of a program, typing contexts are extended with information on the expressions and their types. In case of OO, class tables are extended with clauses from class declarations, including the class members, i.e., fields, methods, or constructors. Contexts are passed through the nodes of the syntax tree in order to coordinate type checking between them. Therefore, while traversing the syntax tree top-down, the type checker creates dependencies between otherwise independent subexpressions. This way, it inhibits incrementalization and parallelization of type checking. That is, a change to a node of the syntax tree would require to redo the type check of the whole syntax tree. In this thesis a novel formulation of type systems is proposed, in order to remove dependencies between subexpressions. We propose a co-contextual formulation of typing rules that depends only on the local program constructs, e.g., expressions, methods, classes. The co-contextual typing rules have as conclusion a type and sets of requirements. That is, contexts and class tables are replaced by the dual concept of context and class table requirements. In addition, operations on contexts and class tables are replaced by new dual operations on requirements. The co-contextual type checker traverses a syntax tree bottom-up and merges context requirements of independently checked subexpressions. We describe a method for systematically constructing a co-contextual formulation of type rules from a regular context-based formulation and we show how co-contextual type rules give rise to incremental type checking. We derive co-contextual type checkers for functional and OO languages. As a representative of functional languages we consider PCF and extensions of it: records, parametric polymorphism, structural subtyping and let-polymorphism. Also, we investigate featherweight java (FJ) as the basis of OO languages and extensions of it: method overloading and generics. We build a1 co-contextual type checker for FJ enabling key features of OO languages: subtype polymorphism, nominal typing and implementation inheritance. The dualism between the co-contextual and contextual type systems preserves the correctness of the contextual calculus. That is, we prove the correctness of the co-contextual calculus via the equivalence between contextual type rules and their co-contextual formulations. We implemented an incremental type checker for PCF along with a performance evaluation showing that co-contextual type checking has performance comparable to standard context-based type checking, and incrementalization can improve performance significantly. Regarding FJ, we implemented a co-contextual type checker with incrementalization and compared its performance against javac on a number of realistic programs. Our performance evaluation shows significant speedups for the co-contextual type checker with incrementalization in comparison to javac.