This is the manual of Cyan, a prototype-based object-oriented language. Cyan supports gradual typing (both static and dynamic typing), single inheritance, anonymous functions, generic prototypes with concepts, non-nullable types, partially safe object initialization, an object-oriented exception handling system, and a powerful Metaobject Protocol for metaprogramming at compile-time (this is described elsewhere).
NOOP is a mathematical model of nominally-typed OOP that proves the identification of inheritance and subtyping in mainstream nominally-typed OO programming languages and the validity of this identification. This report gives an overview of the main notions in OOP relevant to constructing a mathematical model of OOP such as NOOP. The emphasis in this report is on defining nominality, nominal typing and nominal subtyping of mainstream nominally-typed OO languages, and on contrasting the three notions with their counterparts in structurally-typed OO languages, i.e., with structurality, structura…
We revisit occurrence typing, a technique to refine the type of variables occurring in type-cases and, thus, capturesome programming patterns used in untyped languages. Although occurrence typing was tied from its inceptionto set-theoretic types-union types, in particular-it never fully exploited the capabilities of these types. Here weshow how, by using set-theoretic types, it is possible to develop a general typing framework that encompasses andgeneralizes several aspects of current occurrence typing proposals and that can be applied to tackle other problemssuch as the reconstruction of inte…
A key challenge when statically typing so-called dynamic languages is the ubiquity of value-based overloading, where a given function can dynamically reflect upon and behave according to the types of its arguments. Thus, to establish basic types, the analysis must reason precisely about values, but in the presence of higher-order functions and polymorphism, this reasoning itself can require basic types. In this paper we address this chicken-and-egg problem by introducing the framework of two-phased typing. The first "trust" phase performs classical, i.e. flow-, path- and value-insensitive type…
Dynamic languages are praised for their flexibility and expressiveness, but static analysis often yields many false positives and verification is cumbersome for lack of structure. Hence, unit testing is the prevalent incomplete method for validating programs in such languages. Falsification is an alternative approach that uncovers definite errors in programs. A falsifier computes a set of inputs that definitely crash a program. Success typing is a type-based approach to document programs in dynamic languages. We demonstrate that success typing is, in fact, an instance of falsification by mappi…
The statements `inheritance is not subtyping' and `mainstream OO languages unnecessarily place restrictions over inheritance' have rippled as mantras through the PL research community for years. Many mainstream OO developers and OO language designers however do not accept these statements. In \emph{nominally-typed} OO languages that these developers and language designers are dearly familiar with, inheritance simply is subtyping; and they believe OO type inheritance is an inherently nominal notion not a structural one. Nominally-typed OO languages are among the most used programming languages …
Gradual typing combines static and dynamic typing in the same program. One would hope that the performance in a gradually typed language would range between that of a dynamically typed language and a statically typed language. Existing implementations of gradually typed languages have not achieved this goal due to overheads associated with runtime casts. Takikawa et al. (2016) report up to 100$\times$ slowdowns for partially typed programs. In this paper we present a compiler, named Grift, for evaluating implementation techniques for gradual typing. We take a straightforward but surprisingly u…
Regular path query languages for data graphs are essentially \emph{untyped}. The lack of type information greatly limits the optimization opportunities for query engines and makes application development more complex. In this paper we discuss a simple, yet expressive, schema language for edge-labelled data graphs. This schema language is, then, used to define a query type inference approach with good precision properties.
This work studies gradual typing for row types and row polymorphism. Key ingredients in this work are the dynamic row type, which represents a statically unknown part of a row, and consistency for row types, which allows injecting static row types into the dynamic row type and, conversely, projecting the dynamic row type to any static row type. While consistency captures the behavior of the dynamic row type statically, it makes the semantics of a gradually typed language incoherent when combined with row equivalence which identifies row types up to field reordering. To solve this problem, we d…
In this paper, we describe our experience incorporating gradual types in a statically typed functional language with Hindley-Milner style type inference. Where most gradually typed systems aim to improve static checking in a dynamically typed language, we approach it from the opposite perspective and promote dynamic checking in a statically typed language. Our approach provides a glimpse into how languages like SML and OCaml might handle gradual typing. We discuss our implementation and challenges faced -- specifically how gradual typing rules apply to our representation of composite and recur…
Abstracting Gradual Typing (AGT) is a systematic approach to designing gradually-typed languages. Languages developed using AGT automatically satisfy the formal semantic criteria for gradual languages identified by Siek et al. [2015]. Nonetheless, vanilla AGT semantics can still have important shortcomings. First, a gradual language's runtime checks should preserve the space-efficiency guarantees inherent to the underlying static and dynamic languages. To the contrary, the default operational semantics of AGT break proper tail calls. Second, a gradual language's runtime checks should enforce b…
Modern languages are equipped with static type checking/inference that helps programmers to keep a clean programming style and to reduce errors. However, the ever-growing size of programs and their continuous evolution require building fast and efficient analysers. A promising solution is incrementality, so one only re-types those parts of the program that are new, rather than the entire codebase. We propose an algorithmic schema driving the definition of an incremental typing algorithm that exploits the existing, standard ones with no changes. Ours is a grey-box approach, meaning that just th…
Pattern-matching programming is an example of a rule-based programming style developed in functional languages. This programming style is intensively used in dialects of ML but is restricted to algebraic data-types. This restriction limits the field of application. However, as shown by Giavitto and Michel at RULE'02, case-based function definitions can be extended to more general data structures called topological collections. We show in this paper that this extension retains the benefits of the typed discipline of the functional languages. More precisely, we show that topological collections …
We describe an alternative approach to handling mutable references (aka. pointers) within a gradually typed language that has different efficiency characteristics than the prior approach of Herman et al. [2010]. In particular, we reduce the costs of reading and writing through references in statically typed regions of code. We reduce the costs to be the same as they would in a statically typed language, that is, simply the cost of a load or store instruction (for primitive data types). This reduction in cost is especially important for programmers who would like to use gradual typing to facili…
This paper addresses compositional and incremental type checking for object-oriented programming languages. Recent work achieved incremental type checking for structurally typed functional languages through co-contextual typing rules, a constraint-based formulation that removes any context dependency for expression typings. However, that work does not cover key features of object-oriented languages: Subtype polymorphism, nominal typing, and implementation inheritance. Type checkers encode these features in the form of class tables, an additional form of typing context inhibiting incrementaliza…
Type inference is an application domain that is a natural fit for logic programming (LP). LP systems natively support unification, which serves as a basic building block of typical type inference algorithms. In particular, polymorphic type inference in the Hindley--Milner type system (HM) can be succinctly specified and executed in Prolog. In our previous work, we have demonstrated that more advanced features of parametric polymorphism beyond HM, such as type-constructor polymorphism and kind polymorphism, can be similarly specified in Prolog. Here, we demonstrate a specification for records, …
In the realm of quantum computing, circuit description languages represent a valid alternative to traditional QRAM-style languages. They indeed allow for finer control over the output circuit, without sacrificing flexibility nor modularity. We introduce a generalization of the paradigmatic lambda-calculus Proto-Quipper-M, itself modeling the core features of the quantum circuit description language Quipper. The extension, called Proto-Quipper-K, is meant to capture a very general form of dynamic lifting. This is made possible by the introduction of a rich type and effect system in which not on…
A long-standing shortcoming of statically typed functional languages is that type checking does not rule out pattern-matching failures (run-time match exceptions). Refinement types distinguish different values of datatypes; if a program annotated with refinements passes type checking, pattern-matching failures become impossible. Unfortunately, refinement is a monolithic property of a type, exacerbating the difficulty of adding refinement types to nontrivial programs. Gradual typing has explored how to incrementally move between static typing and dynamic typing. We develop a type system of grad…
Session types are a rich type discipline, based on linear types, that lifts the sort of safety claims that come with type systems to communications. However, web-based applications and microservices are often written in a mix of languages, with type disciplines in a spectrum between static and dynamic typing. Gradual session types address this mixed setting by providing a framework which grants seamless transition between statically typed handling of sessions and any required degree of dynamic typing. We propose Gradual GV as a gradually typed extension of the functional session type system GV…
Abstracting Gradual Typing (AGT) is an approach to systematically deriving gradual counterparts to static type disciplines. The approach consists of defining the semantics of gradual types by interpreting them as sets of static types, and then defining an optimal abstraction back to gradual types. These operations are used to lift the static discipline to the gradual setting. The runtime semantics of the gradual language then arises as reductions on gradual typing derivations. To demonstrate the flexibility of AGT, we gradualize $λ_\text{SEC}$, the prototypical security-typed language, with re…
Bringing the benefits of gradual typing to a language with parametric polymorphism like System F, while preserving relational parametricity, has proven extremely challenging: first attempts were formulated a decade ago, and several designs have been recently proposed, with varying syntax, behavior, and properties. Starting from a detailed review of the challenges and tensions that affect the design of gradual parametric languages, this work presents an extensive account of the semantics and metatheory of GSF, a gradual counterpart of System F. In doing so, we also report on the extent to which…
Error detection facilities for dynamic languages are often based on unit testing. Thus, the advantage of rapid prototyping and flexibility must be weighed against cumbersome and time consuming test suite development. Lindahl and Sagonas' success typings provide a means of static must-fail detection in Erlang. Due to the constraint-based nature of the approach, some errors involving nested tuples and recursion cannot be detected. We propose an approach that uses an extension of model checking for pattern-matching recursion schemes with context-aware ranked tree automata to provide improved succ…
Context Oriented Programming (COP) concerns the ability of programs to adapt to changes in their running environment. A number of programming languages endowed with COP constructs and features have been developed. However, some foundational issues remain unclear. This paper proposes adopting static analysis techniques to reason on and predict how programs adapt their behaviour. We introduce a core functional language, ContextML, equipped with COP primitives for manipulating contexts and for programming behavioural variations. In particular, we specify the dispatching mechanism, used to select …
Recently, dynamically typed languages, such as Python, have gained unprecedented popularity. Although these languages alleviate the need for mandatory type annotations, types still play a critical role in program understanding and preventing runtime errors. An attractive option is to infer types automatically to get static guarantees without writing types. Existing inference techniques rely mostly on static typing tools such as PyType for direct type inference; more recently, neural type inference has been proposed. However, neural type inference is data hungry, and depends on collecting label…
We present a linear functional calculus with both the safety guarantees expressible with linear types and the rich language of combinators and composition provided by functional programming. Unlike previous combinations of linear typing and functional programming, we compromise neither the linear side (for example, our linear values are first-class citizens of the language) nor the functional side (for example, we do not require duplicate definitions of compositions for linear and unrestricted functions). To do so, we must generalize abstraction and application to encompass both linear and unr…
Expressive static typing disciplines are a powerful way to achieve high-quality software. However, the adoption cost of such techniques should not be under-estimated. Just like gradual typing allows for a smooth transition from dynamically-typed to statically-typed programs, it seems desirable to support a gradual path to certified programming. We explore gradual certified programming in Coq, providing the possibility to postpone the proofs of selected properties, and to check "at runtime" whether the properties actually hold. Casts can be integrated with the implicit coercion mechanism of Coq…
We present a calculus for processing semistructured data that spans differences of application area among several novel query languages, broadly categorized as "NoSQL". This calculus lets users define their own operators, capturing a wider range of data processing capabilities, whilst providing a typing precision so far typical only of primitive hard-coded operators. The type inference algorithm is based on semantic type checking, resulting in type information that is both precise, and flexible enough to handle structured and semistructured data. We illustrate the use of this calculus by encod…
Many object-oriented dynamic languages allow programmers to _extract methods_ from objects and treat them as functions. This allows for flexible programming patterns, but presents challenges for type systems. In particular, a simple treatment of method extraction would require methods to be contravariant in the receiver type, making overriding all-but-impossible. We present a detailed investigation of this problem, as well as an implemented and evaluated solution. Method extraction is a feature of many dynamically-typed and gradually-typed languages, ranging from Python and PHP to Flow and Typ…
Transient gradual typing imposes run-time type tests that typically cause a linear slowdown in programs' performance. This performance impact discourages the use of type annotations because adding types to a program makes the program slower. A virtual machine can employ standard just-in-time optimizations to reduce the overhead of transient checks to near zero. These optimizations can give gradually-typed languages performance comparable to state-of-the-art dynamic languages, so programmers can add types to their code without affecting their programs' performance.
Elixir is a functional programming language with dynamic typing. We propose a gradual type system that makes it possible to perform type-checking on a significant fragment of the language. An important feature of the type system is that it does not require any syntactic change to Elixir. Type information is provided by means of function signatures which are declared in terms of Elixir typespec directives. The proposed type system is based on subtyping and is backward compatible, as it allows the presence of untyped code fragments. We have implemented a prototype of the type-checker in Elixir i…
The lambda calculus, subject to typing restrictions, provides a syntax for the internal language of cartesian closed categories. This paper establishes a parallel result: staging annotations, subject to named level restrictions, provide a syntax for the internal language of Freyd categories, which are known to be in bijective correspondence with Arrows. The connection is made by interpreting multi-stage type systems as indexed functors from polynomial categories to their reindexings. This result applies only to multi-stage languages which are (1) homogeneous, (2) allow cross-stage persistence …
