Dynamic Inference of Static Types for Ruby
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
First Class Overloading Via Insersection Type Parameters⋆
First Class Overloading via Insersection Type Parameters? Elton Cardoso2, Carlos Camar~ao1, and Lucilia Figueiredo2 1 Universidade Federal de Minas Gerais, [email protected] 2 Universidade Federal de Ouro Preto [email protected], [email protected] Abstract The Hindley-Milner type system imposes the restriction that function parameters must have monomorphic types. Lifting this restric- tion and providing system F “first class" polymorphism is clearly desir- able, but comes with the difficulty that inference of types for system F is undecidable. More practical type systems incorporating types of higher- rank have recently been proposed, that rely on system F but require type annotations for the definition of functions with polymorphic type parameters. However, these type annotations inevitably disallow some possible uses of higher-rank functions. To avoid this problem and to pro- mote code reuse, we explore using intersection types for specifying the types of function parameters that are used polymorphically inside the function body, allowing a flexible use of such functions, on applications to both polymorphic or overloaded arguments. 1 Introduction The Hindley-Milner type system [9] (HM) has been successfuly used as the basis for type systems of modern functional programming languages, such as Haskell [23] and ML [20]. This is due to its remarkable properties that a compiler can in- fer the principal type for any language expression, without any help from the programmer, and the type inference algorithm [5] is relatively simple. This is achieved, however, by imposing some restrictions, a major one being that func- tion parameters must have monomorphic types. For example, the following definition is not allowed in the HM type system: foo g = (g [True,False], g ['a','b','c']) Since parameter g is used with distinct types in the function's body (being applied to both a list of booleans and a list of characters), its type cannot be monomorphic, and this definition of foo cannot thus be typed in HM. -
Disjoint Polymorphism
Disjoint Polymorphism João Alpuim, Bruno C. d. S. Oliveira, and Zhiyuan Shi The University of Hong Kong {alpuim,bruno,zyshi}@cs.hku.hk Abstract. The combination of intersection types, a merge operator and parametric polymorphism enables important applications for program- ming. However, such combination makes it hard to achieve the desirable property of a coherent semantics: all valid reductions for the same expres- sion should have the same value. Recent work proposed disjoint inter- sections types as a means to ensure coherence in a simply typed setting. However, the addition of parametric polymorphism was not studied. This paper presents Fi: a calculus with disjoint intersection types, a vari- ant of parametric polymorphism and a merge operator. Fi is both type- safe and coherent. The key difficulty in adding polymorphism is that, when a type variable occurs in an intersection type, it is not statically known whether the instantiated type will be disjoint to other compo- nents of the intersection. To address this problem we propose disjoint polymorphism: a constrained form of parametric polymorphism, which allows disjointness constraints for type variables. With disjoint polymor- phism the calculus remains very flexible in terms of programs that can be written, while retaining coherence. 1 Introduction Intersection types [20,43] are a popular language feature for modern languages, such as Microsoft’s TypeScript [4], Redhat’s Ceylon [1], Facebook’s Flow [3] and Scala [37]. In those languages a typical use of intersection types, which has been known for a long time [19], is to model the subtyping aspects of OO-style multiple inheritance. -
Polymorphic Intersection Type Assignment for Rewrite Systems with Abstraction and -Rule Extended Abstract
Polymorphic Intersection Type Assignment for Rewrite Systems with Abstraction and -rule Extended Abstract Steffen van Bakel , Franco Barbanera , and Maribel Fernandez´ Department of Computing, Imperial College, 180 Queen’s Gate, London SW7 2BZ. [email protected] Dipartimento di Matematica, Universita` degli Studi di Catania, Viale A. Doria 6, 95125 Catania, Italia. [email protected] LIENS (CNRS URA 8548), Ecole Normale Superieure,´ 45, rue d’Ulm, 75005 Paris, France. [email protected] Abstract. We define two type assignment systems for first-order rewriting ex- tended with application, -abstraction, and -reduction (TRS ). The types used in these systems are a combination of ( -free) intersection and polymorphic types. The first system is the general one, for which we prove a subject reduction theorem and show that all typeable terms are strongly normalisable. The second is a decidable subsystem of the first, by restricting types to Rank 2. For this sys- tem we define, using an extended notion of unification, a notion of principal type, and show that type assignment is decidable. Introduction The combination of -calculus (LC) and term rewriting systems (TRS) has attracted attention not only from the area of programming language design, but also from the rapidly evolving field of theorem provers. It is well-known by now that type disciplines provide an environment in which rewrite rules and -reduction can be combined with- out loss of their useful properties. This is supported by a number of results for a broad range of type systems [11, 12, 20, 7, 8, 5]. In this paper we study the combination of LC and TRS as a basis for the design of a programming language. -
Dotty Phantom Types (Technical Report)
Dotty Phantom Types (Technical Report) Nicolas Stucki Aggelos Biboudis Martin Odersky École Polytechnique Fédérale de Lausanne Switzerland Abstract 2006] and even a lightweight form of dependent types [Kise- Phantom types are a well-known type-level, design pattern lyov and Shan 2007]. which is commonly used to express constraints encoded in There are two ways of using phantoms as a design pattern: types. We observe that in modern, multi-paradigm program- a) relying solely on type unication and b) relying on term- ming languages, these encodings are too restrictive or do level evidences. According to the rst way, phantoms are not provide the guarantees that phantom types try to en- encoded with type parameters which must be satised at the force. Furthermore, in some cases they introduce unwanted use-site. The declaration of turnOn expresses the following runtime overhead. constraint: if the state of the machine, S, is Off then T can be We propose a new design for phantom types as a language instantiated, otherwise the bounds of T are not satisable. feature that: (a) solves the aforementioned issues and (b) makes the rst step towards new programming paradigms type State; type On <: State; type Off <: State class Machine[S <: State] { such as proof-carrying code and static capabilities. This pa- def turnOn[T >: S <: Off] = new Machine[On] per presents the design of phantom types for Scala, as im- } new Machine[Off].turnOn plemented in the Dotty compiler. An alternative way to encode the same constraint is by 1 Introduction using an implicit evidence term of type =:=, which is globally Parametric polymorphism has been one of the most popu- available. -
Rank 2 Type Systems and Recursive De Nitions
Rank 2 typ e systems and recursive de nitions Technical Memorandum MIT/LCS/TM{531 Trevor Jim Lab oratory for Computer Science Massachusetts Institute of Technology August 1995; revised Novemb er 1995 Abstract We demonstrate an equivalence b etween the rank 2 fragments of the p olymorphic lamb da calculus System F and the intersection typ e dis- cipline: exactly the same terms are typable in each system. An imme- diate consequence is that typability in the rank 2 intersection system is DEXPTIME-complete. Weintro duce a rank 2 system combining intersections and p olymorphism, and prove that it typ es exactly the same terms as the other rank 2 systems. The combined system sug- gests a new rule for typing recursive de nitions. The result is a rank 2 typ e system with decidable typ e inference that can typ e some inter- esting examples of p olymorphic recursion. Finally,we discuss some applications of the typ e system in data representation optimizations suchasunboxing and overloading. Keywords: Rank 2 typ es, intersection typ es, p olymorphic recursion, boxing/unboxing, overloading. 1 Intro duction In the past decade, Milner's typ e inference algorithm for ML has b ecome phenomenally successful. As the basis of p opular programming languages like Standard ML and Haskell, Milner's algorithm is the preferred metho d of typ e inference among language implementors. And in the theoretical 545 Technology Square, Cambridge, MA 02139, [email protected]. Supp orted by NSF grants CCR{9113196 and CCR{9417382, and ONR Contract N00014{92{J{1310. -
A Facet-Oriented Modelling
A Facet-oriented modelling JUAN DE LARA, Universidad Autónoma de Madrid (Spain) ESTHER GUERRA, Universidad Autónoma de Madrid (Spain) JÖRG KIENZLE, McGill University (Canada) Models are the central assets in model-driven engineering (MDE), as they are actively used in all phases of software development. Models are built using metamodel-based languages, and so, objects in models are typed by a metamodel class. This typing is static, established at creation time, and cannot be changed later. Therefore, objects in MDE are closed and fixed with respect to the class they conform to, the fields they have, and the wellformedness constraints they must comply with. This hampers many MDE activities, like the reuse of model-related artefacts such as transformations, the opportunistic or dynamic combination of metamodels, or the dynamic reconfiguration of models. To alleviate this rigidity, we propose making model objects open so that they can acquire or drop so-called facets. These contribute with a type, fields and constraints to the objects holding them. Facets are defined by regular metamodels, hence being a lightweight extension of standard metamodelling. Facet metamodels may declare usage interfaces, as well as laws that govern the assignment of facets to objects (or classes). This paper describes our proposal, reporting on a theory, analysis techniques and an implementation. The benefits of the approach are validated on the basis of five case studies dealing with annotation models, transformation reuse, multi-view modelling, multi-level modelling and language product lines. Categories and Subject Descriptors: [Software and its engineering]: Model-driven software engineering; Domain specific languages; Design languages; Software design engineering Additional Key Words and Phrases: Metamodelling, Flexible Modelling, Role-Based Modelling, METADEPTH ACM Reference Format: Juan de Lara, Esther Guerra, Jörg Kienzle. -
Webassembly Specification
WebAssembly Specification Release 1.1 WebAssembly Community Group Andreas Rossberg (editor) Mar 11, 2021 Contents 1 Introduction 1 1.1 Introduction.............................................1 1.2 Overview...............................................3 2 Structure 5 2.1 Conventions.............................................5 2.2 Values................................................7 2.3 Types.................................................8 2.4 Instructions.............................................. 11 2.5 Modules............................................... 15 3 Validation 21 3.1 Conventions............................................. 21 3.2 Types................................................. 24 3.3 Instructions.............................................. 27 3.4 Modules............................................... 39 4 Execution 47 4.1 Conventions............................................. 47 4.2 Runtime Structure.......................................... 49 4.3 Numerics............................................... 56 4.4 Instructions.............................................. 76 4.5 Modules............................................... 98 5 Binary Format 109 5.1 Conventions............................................. 109 5.2 Values................................................ 111 5.3 Types................................................. 112 5.4 Instructions.............................................. 114 5.5 Modules............................................... 120 6 Text Format 127 6.1 Conventions............................................ -
Approximations, Fibrations and Intersection Type Systems
Approximations, Fibrations and Intersection Type Systems Damiano Mazza*, Luc Pellissier† & Pierre Vial‡ June 16, 2017 Introduction The discovery of linear logic [7] has introduced the notionof linearity in computer science and proof theory. A remarkable fact of linear logic lies in its approximation theorem, stating that an arbitrary proof (not necessarily linear, that is, using its premisses any number of times) can be approximated arbitrarily well by a linear proof. This notion of approximation has then been explored in different directions [4, 10,14]. Approximations are known to be related to relational models, which in turn are related to intersection types [2, 12, 13]. In this work, we investigate approximations in the “type-systems as functors” perspective pioneered by [11]. After recasting fundamental properties of type systems, such as subject reduction and expansion in this framework, we give an intersection type system framework for linear logic, whose derivations are simply-typed approximations. Any calculus that translates meaningfully to linear logic is then endowed by a intersection type system, computed by pulling back one of these intersection type systems for linear logic, and which inherit its properties. All standard intersection type systems (idempotent, such as in [6, 1] or not, such as in [3]) for call-by-name and call-by-value λ-calculus, characterizing weak, strong, and head normalization, fit in this picture, thus justifying the equation: Simply-typed approximations = intersection types derivations. We moreover obtain new type systems, by considering other translations and reductions. 1 What is a type system? The starting point of this research is the work of [11]. -
1 Intro to ML
1 Intro to ML 1.1 Basic types Need ; after expression - 42 = ; val it = 42: int -7+1; val it =8: int Can reference it - it+2; val it = 10: int - if it > 100 then "big" else "small"; val it = "small": string Different types for each branch. What will happen? if it > 100 then "big" else 0; The type checker will complain that the two branches have different types, one is string and the other is int If with then but no else. What will happen? if 100>1 then "big"; There is not if-then in ML; must use if-then-else instead. Mixing types. What will happen? What is this called? 10+ 2.5 In many programming languages, the int will be promoted to a float before the addition is performed, and the result is 12.5. In ML, this type coercion (or type promotion) does not happen. Instead, the type checker will reject this expression. div for integers, ‘/ for reals - 10 div2; val it =5: int - 10.0/ 2.0; val it = 5.0: real 1 1.1.1 Booleans 1=1; val it = true : bool 1=2; val it = false : bool Checking for equality on reals. What will happen? 1.0=1.0; Cannot check equality of reals in ML. Boolean connectives are a bit weird - false andalso 10>1; val it = false : bool - false orelse 10>1; val it = true : bool 1.1.2 Strings String concatenation "University "^ "of"^ " Oslo" 1.1.3 Unit or Singleton type • What does the type unit mean? • What is it used for? • What is its relation to the zero or bottom type? - (); val it = () : unit https://en.wikipedia.org/wiki/Unit_type https://en.wikipedia.org/wiki/Bottom_type The boolean type is inhabited by two values: true and false. -
Foundations of Path-Dependent Types
Foundations of Path-Dependent Types Nada Amin∗ Tiark Rompf †∗ Martin Odersky∗ ∗EPFL: {first.last}@epfl.ch yOracle Labs: {first.last}@oracle.com Abstract 1. Introduction A scalable programming language is one in which the same A scalable programming language is one in which the same concepts can describe small as well as large parts. Towards concepts can describe small as well as large parts. Towards this goal, Scala unifies concepts from object and module this goal, Scala unifies concepts from object and module systems. An essential ingredient of this unification is the systems. An essential ingredient of this unification is to concept of objects with type members, which can be ref- support objects that contain type members in addition to erenced through path-dependent types. Unfortunately, path- fields and methods. dependent types are not well-understood, and have been a To make any use of type members, programmers need a roadblock in grounding the Scala type system on firm the- way to refer to them. This means that types must be able ory. to refer to objects, i.e. contain terms that serve as static We study several calculi for path-dependent types. We approximation of a set of dynamic objects. In other words, present µDOT which captures the essence – DOT stands some level of dependent types is required; the usual notion for Dependent Object Types. We explore the design space is that of path-dependent types. bottom-up, teasing apart inherent from accidental complexi- Despite many attempts, Scala’s type system has never ties, while fully mechanizing our models at each step. -
Deconfined Intersection Types in Java
Deconfined Intersection Types in Java Dedicated to Maurizio Gabbrielli on the Occasion of His 60th Birthday Mariangiola Dezani-Ciancaglini Computer Science Department, University of Torino, Italy [email protected] Paola Giannini Department of Advanced Science and Technology, University of Eastern Piedmont, Alessandria, Italy [email protected] Betti Venneri Department of Statistics, Computer Science, Applications, University of Firenze, Italy betti.venneri@unifi.it Abstract We show how Java intersection types can be freed from their confinement in type casts, in such a way that the proposed Java extension is safe and fully compatible with the current language. To this aim, we exploit two calculi which formalise the simple Java core and the extended language, respectively. Namely, the second calculus extends the first one by allowing an intersection type to be used anywhere in place of a nominal type. We define a translation algorithm, compiling programs of the extended language into programs of the former calculus. The key point is the interaction between λ-expressions and intersection types, that adds safe expressiveness while being the crucial matter in the translation. We prove that the translation preserves typing and semantics. Thus, typed programs in the proposed extension are translated to typed Java programs. Moreover, semantics of translated programs coincides with the one of the source programs. 2012 ACM Subject Classification Theory of computation → Type structures; Theory of computation → Semantics and reasoning Keywords and phrases Intersection Types, Featherweight Java, Lambda Expressions Digital Object Identifier 10.4230/OASIcs.Gabbrielli.2020.3 Acknowledgements We are very pleased to dedicate this work to Maurizio, whose notable contri- butions to the theory of programming languages are well known and appreciated by the scientific community. -
Local Type Inference
Local Type Inference BENJAMIN C. PIERCE University of Pennsylvania and DAVID N. TURNER An Teallach, Ltd. We study two partial type inference methods for a language combining subtyping and impredica- tive polymorphism. Both methods are local in the sense that missing annotations are recovered using only information from adjacent nodes in the syntax tree, without long-distance constraints such as unification variables. One method infers type arguments in polymorphic applications using a local constraint solver. The other infers annotations on bound variables in function abstractions by propagating type constraints downward from enclosing application nodes. We motivate our design choices by a statistical analysis of the uses of type inference in a sizable body of existing ML code. Categories and Subject Descriptors: D.3.1 [Programming Languages]: Formal Definitions and Theory General Terms: Languages, Theory Additional Key Words and Phrases: Polymorphism, subtyping, type inference 1. INTRODUCTION Most statically typed programming languages offer some form of type inference, allowing programmers to omit type annotations that can be recovered from context. Such a facility can eliminate a great deal of needless verbosity, making programs easier both to read and to write. Unfortunately, type inference technology has not kept pace with developments in type systems. In particular, the combination of subtyping and parametric polymorphism has been intensively studied for more than a decade in calculi such as System F≤ [Cardelli and Wegner 1985; Curien and Ghelli 1992; Cardelli et al. 1994], but these features have not yet been satisfactorily This is a revised and extended version of a paper presented at the 25th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages (POPL), 1998.