Dependent type theory is rich enough to express that a program satisfies an input/output relational specification, but it could be hard to construct the proof term. On the other hand, squiggolists know very well how to show that one relation is included in another by algebraic reasoning. We demonstrate how to encode functional and relational derivations in a dependently typed programming language. A program is coupled with an algebraic derivation from a specification, whose correctness is guaranteed by the type system. Code accompanying the paper has been developed into an Agda library AoPA.
Despite its powerful module system, ML has not yet evolved for the modern world of dynamic and open modular programming, to which more primitive languages have adapted better so far. We present the design and semantics of a simple yet expressive first-class component system for ML. It provides dynamic linking in a type-safe and type-flexible manner, and allows selective execution in sandboxes. The system is defined solely by reduction to higher-order modules plus an extension with simple module-level dynamics, which we call packages. To represent components outside processes we employ generic pickling. We give a module calculus formalising the semantics of packages and pickling.
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we develop an approach for reconciling open programming -- the development of programs that support dynamic exchange of higher-order values with strong static typing. conventional functional language extended with a set of orthogonal features like higher-order modules, dynamic type checking, higher-order serialisation, and concurrency. On top of these a flexible system of dynamic components and a simple but expressive notion of distribution is realised. The central concept in this design is the packag}, a first-class value embedding a module along with its interface type. formal model for abstract types that is not invalidated by the presence of primitives for dynamic type inspection, as is the case for the standard model based on existential quantification. For that we present an idealised language in form of an extended lambda-calculus, which can express dynamic generation of types.
ML modules provide hierarchical namespace management, as well as fine-grained control over the propagation of type information, but they do not allow modules to be broken up into separately compilable, mutually recursive components. Mixin modules facilitate recursive linking of separately compiled components, but they are not hierarchically composable and typically do not support type abstraction. We synthesize the complementary advantages of these two mechanisms in MixML. A MixML module is like an ML structure with some components specified but not defined unifing the ML structure and signature languages into one. MixML seamlessly integrates hierarchical composition, translucent MLstyle data abstraction, and mixin-style recursive linking.Tthe design of MixML is minimalist emphasizing how all the interesting features of the ML module system can be understood simply as stylized uses of a small set of orthogonal underlying constructs, with mixin composition playing a central role.
An introduction to 2-categories is given by illustrating how the structure of typed lambda calculus may naturally be viewed as a 2-category. In this vein. the structure of computations or conversions gives rise to notions of lax 2':"adjointness.
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