practical type checking of functions defined on context-free languages

A type checking method for the functional language LFC is presented. A distinct feature of LFC is that it uses Context-Free (CF) languages as data types to represent compound data structures. This makes LFC a dynamically typed language. To improve efficiency, a practical type checking method is presented, which consists of both static and dynamic type checking. Although the inclusion relation of CF.languages is not decidable,a special subset of the relation is decidable, i.e., the sentential form relation, which can be statically checked.Moreover, most of the expressions in actual LFC programs appear to satisfy this relation according to the statistic data of experiments. So, despite that the static type checking is not complete, it undertakes most of the type checking task. Consequently the run-time efficiency is effectively improved. Another feature of the type checking is that it converts the expressions with implicit structures to structured representation. Structure reconstruction technique is presented.

Typability and Type Checking in the Second-Order Λ-Calculus Are Equivalent and Undecidable (Preliminary Draft)

We consider the problems of typability[1] and type checking[2] in the Girard/Reynolds second-order polymorphic typed λ-calculus, for which we use the short name "System F" and which we use in the "Curry style" where types are assigned to pure λ -terms. These problems have been considered and proven to be decidable or undecidable for various restrictions and extensions of System F and other related systems, and lower-bound complexity results for System F have been achieved, but they have remained "embarrassing open problems"[3] for System F itself. We first prove that type checking in System F is undecidable by a reduction from semi-unification. We then prove typability in System F is undecidable by a reduction from type checking. Since the reverse reduction is already known, this implies the two problems are equivalent. The second reduction uses a novel method of constructing λ-terms such that in all type derivations, specific bound variables must always be assigned a specific type. Using this technique, we can require that specific subterms must be typable using a specific, fixed type assignment in order for the entire term to be typable at all. Any desired type assignment may be simulated. We develop this method, which we call "constants for free", for both the λK and λI calculi.

Safe Compositional Specification of Networking Systems: TRAFFIC The Language and Its Type Checking

This paper formally defines the operational semantic for TRAFFIC, a specification language for flow composition applications proposed in BUCS-TR-2005-014, and presents a type system based on desired safety assurance. We provide proofs on reduction (weak-confluence, strong-normalization and unique normal form), on soundness and completeness of type system with respect to reduction, and on equivalence classes of flow specifications. Finally, we provide a pseudo-code listing of a syntax-directed type checking algorithm implementing rules of the type system capable of inferring the type of a closed flow specification.

Certificates for Incremental Type Checking

The central topic of this thesis is the study of algorithms for type checking, both from the programming language and from the proof-theoretic point of view. A type checking algorithm takes a program or a proof, represented as a syntactical object, and checks its validity with respect to a specification or a statement. It is a central piece of compilers and proof assistants. We postulate that since type checkers are at the interface between proof theory and program theory, their study can let these two fields mutually enrich each other. We argue by two main instances: first, starting from the problem of proof reuse, we develop an incremental type checker; secondly, starting from a type checking program, we evidence a novel correspondence between natural deduction and the sequent calculus.

Type extension and efficient AST manipulation

Oberon-2 is an object-oriented language with a class structure based on type extension. The runtime structure of Oberon-2 is described and the low-level mechanism for dynamic type checking explained. It is shown that the superior type-safety of the language, when used for programming styles based on heterogeneous, pointer-linked data structures, has an entirely negligible cost in runtime performance.

Hidden Type Variables and Conditional Extension for More Expressive Generic Programs

Generic object-oriented programming languages combine parametric polymorphism and nominal subtype polymorphism, thereby providing better data abstraction, greater code reuse, and fewer run-time errors. However, most generic object-oriented languages provide a straightforward combination of the two kinds of polymorphism, which prevents the expression of advanced type relationships. Furthermore, most generic object-oriented languages have a type-erasure semantics: instantiations of type parameters are not available at run time, and thus may not be used by type-dependent operations. This dissertation shows that two features, which allow the expression of many advanced type relationships, can be added to a generic object-oriented programming language without type erasure: 1. type variables that are not parameters of the class that declares them, and 2. extension that is dependent on the satisfiability of one or more constraints. We refer to the first feature as hidden type variables and the second feature as conditional extension. Hidden type variables allow: covariance and contravariance without variance annotations or special type arguments such as wildcards; a single type to extend, and inherit methods from, infinitely many instantiations of another type; a limited capacity to augment the set of superclasses after that class is defined; and the omission of redundant type arguments. Conditional extension allows the properties of a collection type to be dependent on the properties of its element type. This dissertation describes the semantics and implementation of hidden type variables and conditional extension. A sound type system is presented. In addition, a sound and terminating type checking algorithm is presented. Although designed for the Fortress programming language, hidden type variables and conditional extension can be incorporated into other generic object-oriented languages. Many of the same problems would arise, and solutions analogous to those we present would apply.

On the fly type specialization without type analysis

Les langages de programmation typés dynamiquement tels que JavaScript et Python repoussent la vérification de typage jusqu’au moment de l’exécution. Afin d’optimiser la performance de ces langages, les implémentations de machines virtuelles pour langages dynamiques doivent tenter d’éliminer les tests de typage dynamiques redondants. Cela se fait habituellement en utilisant une analyse d’inférence de types. Cependant, les analyses de ce genre sont souvent coûteuses et impliquent des compromis entre le temps de compilation et la précision des résultats obtenus. Ceci a conduit à la conception d’architectures de VM de plus en plus complexes. Nous proposons le versionnement paresseux de blocs de base, une technique de compilation à la volée simple qui élimine efficacement les tests de typage dynamiques redondants sur les chemins d’exécution critiques. Cette nouvelle approche génère paresseusement des versions spécialisées des blocs de base tout en propageant de l’information de typage contextualisée. Notre technique ne nécessite pas l’utilisation d’analyses de programme coûteuses, n’est pas contrainte par les limitations de précision des analyses d’inférence de types traditionnelles et évite la complexité des techniques d’optimisation spéculatives. Trois extensions sont apportées au versionnement de blocs de base afin de lui donner des capacités d’optimisation interprocédurale. Une première extension lui donne la possibilité de joindre des informations de typage aux propriétés des objets et aux variables globales. Puis, la spécialisation de points d’entrée lui permet de passer de l’information de typage des fonctions appellantes aux fonctions appellées. Finalement, la spécialisation des continuations d’appels permet de transmettre le type des valeurs de retour des fonctions appellées aux appellants sans coût dynamique. Nous démontrons empiriquement que ces extensions permettent au versionnement de blocs de base d’éliminer plus de tests de typage dynamiques que toute analyse d’inférence de typage statique.

On the fly type specialization without type analysis

Les langages de programmation typés dynamiquement tels que JavaScript et Python repoussent la vérification de typage jusqu’au moment de l’exécution. Afin d’optimiser la performance de ces langages, les implémentations de machines virtuelles pour langages dynamiques doivent tenter d’éliminer les tests de typage dynamiques redondants. Cela se fait habituellement en utilisant une analyse d’inférence de types. Cependant, les analyses de ce genre sont souvent coûteuses et impliquent des compromis entre le temps de compilation et la précision des résultats obtenus. Ceci a conduit à la conception d’architectures de VM de plus en plus complexes. Nous proposons le versionnement paresseux de blocs de base, une technique de compilation à la volée simple qui élimine efficacement les tests de typage dynamiques redondants sur les chemins d’exécution critiques. Cette nouvelle approche génère paresseusement des versions spécialisées des blocs de base tout en propageant de l’information de typage contextualisée. Notre technique ne nécessite pas l’utilisation d’analyses de programme coûteuses, n’est pas contrainte par les limitations de précision des analyses d’inférence de types traditionnelles et évite la complexité des techniques d’optimisation spéculatives. Trois extensions sont apportées au versionnement de blocs de base afin de lui donner des capacités d’optimisation interprocédurale. Une première extension lui donne la possibilité de joindre des informations de typage aux propriétés des objets et aux variables globales. Puis, la spécialisation de points d’entrée lui permet de passer de l’information de typage des fonctions appellantes aux fonctions appellées. Finalement, la spécialisation des continuations d’appels permet de transmettre le type des valeurs de retour des fonctions appellées aux appellants sans coût dynamique. Nous démontrons empiriquement que ces extensions permettent au versionnement de blocs de base d’éliminer plus de tests de typage dynamiques que toute analyse d’inférence de typage statique.

采用了剪枝优化的子类型关系判定算法

静态类型化XML处理语言为处理XML数据提供了新的途径,但现有的此类语言大多数效率较低.研究此类语言的一个重要问题——子类型关系的判定,并使用剪枝优化策略对XDuce的子类型关系判定算法进行优化.实验数据显示,优化后算法的执行效率平均提高20%.该策略具有普遍性,对所有使用类似算法的静态类型化XML处理语言都有效.

Message-Driven Processor Architecture: Verson 11

The Message-Driven Processor is a node of a large-scale multiprocessor being developed by the Concurrent VLSI Architecture Group. It is intended to support fine-grained, message passing, parallel computation. It contains several novel architectural features, such as a low-latency network interface, extensive type-checking hardware, and on-chip memory that can be used as an associative lookup table. This document is a programmer's guide to the MDP. It describes the processor's register architecture, instruction set, and the data types supported by the processor. It also details the MDP's message sending and exception handling facilities.

The Undecidability of Mitchell's Subtyping Relationship

Mitchell defined and axiomatized a subtyping relationship (also known as containment, coercibility, or subsumption) over the types of System F (with "→" and "∀"). This subtyping relationship is quite simple and does not involve bounded quantification. Tiuryn and Urzyczyn quite recently proved this subtyping relationship to be undecidable. This paper supplies a new undecidability proof for this subtyping relationship. First, a new syntax-directed axiomatization of the subtyping relationship is defined. Then, this axiomatization is used to prove a reduction from the undecidable problem of semi-unification to subtyping. The undecidability of subtyping implies the undecidability of type checking for System F extended with Mitchell's subtyping, also known as "F plus eta".

Typability is Undecidable for F+Eta

System F is the well-known polymorphically-typed λ-calculus with universal quantifiers ("∀"). F+η is System F extended with the eta rule, which says that if term M can be given type τ and M η-reduces to N, then N can also be given the type τ. Adding the eta rule to System F is equivalent to adding the subsumption rule using the subtyping ("containment") relation that Mitchell defined and axiomatized [Mit88]. The subsumption rule says that if M can be given type τ and τ is a subtype of type σ, then M can be given type σ. Mitchell's subtyping relation involves no extensions to the syntax of types, i.e., no bounded polymorphism and no supertype of all types, and is thus unrelated to the system F≤("F-sub"). Typability for F+η is the problem of determining for any term M whether there is any type τ that can be given to it using the type inference rules of F+η. Typability has been proven undecidable for System F [Wel94] (without the eta rule), but the decidability of typability has been an open problem for F+η. Mitchell's subtyping relation has recently been proven undecidable [TU95, Wel95b], implying the undecidability of "type checking" for F+η. This paper reduces the problem of subtyping to the problem of typability for F+η, thus proving the undecidability of typability. The proof methods are similar in outline to those used to prove the undecidability of typability for System F, but the fine details differ greatly.

What Are Polymorphically-Typed Ambients?

Abstract: The Ambient Calculus was developed by Cardelli and Gordon as a formal framework to study issues of mobility and migrant code. We consider an Ambient Calculus where ambients transport and exchange programs rather that just inert data. We propose different senses in which such a calculus can be said to be polymorphically typed, and design accordingly a polymorphic type system for it. Our type system assigns types to embedded programs and what we call behaviors to processes; a denotational semantics of behaviors is then proposed, here called trace semantics, underlying much of the remaining analysis. We state and prove a Subject Reduction property for our polymorphically typed calculus. Based on techniques borrowed from finite automata theory, type-checking of fully type-annotated processes is shown to be decidable; the time complexity of our decision procedure is exponential (this is a worst-case in theory, arguably not encountered in practice). Our polymorphically-typed calculus is a conservative extension of the typed Ambient Calculus originally proposed by Cardelli and Gordon.

Safe Compositional Specification of Networking Systems: A Compositional Analysis Approach

We present a type inference algorithm, in the style of compositional analysis, for the language TRAFFIC—a specification language for flow composition applications proposed in [2]—and prove that this algorithm is correct: the typings it infers are principal typings, and the typings agree with syntax-directed type checking on closed flow specifications. This algorithm is capable of verifying partial flow specifications, which is a significant improvement over syntax-directed type checking algorithm presented in [3]. We also show that this algorithm runs efficiently, i.e., in low-degree polynomial time.

Deadlock analysis of asynchronous sequential processes

In this thesis we present ad study an object-oriented language, characterized by two different types of objects, passive and active objects, of which we define the operational syntax and semantics. For this language we also define the type system, that will be used for the type checking and for the extraction of behavioral types, which are an abstract description of the behavior of the methods, used in deadlock analysis. Programs can manifest deadlock due to the errors of the programmer. To statically identify possible unintended behaviors we studied and implemented a technique for the analysis of deadlock based on behavioral types.