Advanced Topics in Types and Programming Languages by Benjamin C. Pierce

By Benjamin C. Pierce

The research of style structures for programming languages now touches many parts of computing device technology, from language layout and implementation to software program engineering, community protection, databases, and research of concurrent and disbursed structures. This booklet bargains available introductions to key rules within the box, with contributions through specialists on each one topic.

The subject matters lined contain exact variety analyses, which expand basic kind structures to offer them a greater grip at the run time habit of structures; variety platforms for low-level languages; purposes of varieties to reasoning approximately laptop courses; variety concept as a framework for the layout of subtle module platforms; and complex thoughts in ML-style variety inference.

Advanced issues in kinds and Programming Languages builds on Benjamin Pierce's Types and Programming Languages (MIT Press, 2002); many of the chapters might be obtainable to readers conversant in simple notations and strategies of operational semantics and sort systems—the fabric lined within the first 1/2 the sooner book.

Advanced subject matters in varieties and Programming Languages can be utilized within the school room and as a source for execs. so much chapters contain routines, ranging in hassle from fast comprehension exams to demanding extensions, many with strategies.

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It was also inspired by the ordered lambda calculus of Petersen, Harper, Crary, and Pfenning (2003), though there are some technical differences. Ahmed and Walker (2003) and Ahmed, Jia, and Walker (2003) use an ordered, modal logic to specify memory invariants and have integrated the logical specifications into a low-level typed language. Igarashi and Kobayashi (2002) have used ordered types to explore the more general problem of resource usage analysis. In addition, they have developed effective type inference algorithms for their type systems.

Programming with Vectors and Format Strings The prototypical example of programming with dependent types is introduced by the type family of vectors (one-dimensional arrays): Vector :: Nat → ∗ This kinding assertion states that Vector maps a natural number k:Nat to a type. The idea is that the type Vector k contains vectors of length k of elements of some fixed type, say data. To use vectors, we need a way of introducing them. A useful initialization function takes a length n, a value t of type data, and returns a vector with n The system studied in this chapter is the dependently typed lambda-calculus, λLF (Figures 2-1, 2-2), extended with Σ-types (Figure 2-5) and the Calculus of Constructions (Figure 2-7).

Consequently, all parts of ∆ are propagated from the conclusion of any rule to all premises. We also need the occasional side condition to check that whenever a programmer writes down a type, its free variables are contained in the current type context ∆. For instance the rules for function abstraction and application will now be written as follows. t2 : q T1 →T2 ∆; Γ1 t1 : q T1 →T2 ∆; Γ1 ◦ Γ2 ∆; Γ2 t2 : T1 (T-App) t1 t2 : T2 The most important way to test our system for faults is to prove the type substitution lemma.

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Advanced Topics in Types and Programming Languages by Benjamin C. Pierce
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