Download e-book for kindle: Advanced Topics in Types and Programming Languages by Benjamin C. Pierce

By Benjamin C. Pierce

ISBN-10: 0262162288

ISBN-13: 9780262162289

The examine of variety structures for programming languages now touches many parts of desktop technological know-how, from language layout and implementation to software program engineering, community defense, databases, and research of concurrent and disbursed structures. This publication deals obtainable introductions to key rules within the box, with contributions by way of specialists on every one topic.

The themes coated comprise designated sort analyses, which expand easy style structures to offer them a greater grip at the run time habit of platforms; kind platforms for low-level languages; purposes of sorts to reasoning approximately desktop courses; kind concept as a framework for the layout of refined module platforms; and complicated innovations in ML-style style inference.

Advanced issues in varieties and Programming Languages builds on Benjamin Pierce's Types and Programming Languages (MIT Press, 2002); lots of the chapters may be available to readers accustomed to easy notations and strategies of operational semantics and kind systems—the fabric coated within the first 1/2 the sooner book.

Advanced themes in kinds and Programming Languages can be utilized within the lecture room and as a source for pros. so much chapters contain workouts, ranging in trouble from quickly comprehension exams to not easy extensions, many with options.

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Extra resources for Advanced Topics in Types and Programming Languages

Example text

When applied to two types S and T, this yields the type Pair S T whose elements are pairs (s, t) of elements s from S and t from T (see TAPL, Chapter 29). However, the terminology “dependent types” is usually used to indicate a particular class of type-valued functions: those functions which send terms to types. In this chapter we study this kind of dependency. 1 Motivations We begin the chapter by looking at a few representative examples of where type-term dependency occurs naturally. 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.

This sequencing construct gives programmers explicit control over the order of evaluation of terms, which is crucial now that we are introducing data that must be used in a particular order. Terms that normally can contain multiple nested subexpressions such as pair introduction and function application are syntactically restricted so that their primary subterms are variables and the order of evaluation is clear. The other main addition is a new qualifier ord that marks data allocated on the stack.

Roll (lin inr (lin cell)) Now our most polymorphic map function may be written as follows. val map = Λ a,b. Λ pa ,pb . fun aux(f:(pa a → pb b), xs:(lin,pa ,a) list)) : (lin,pb ,b) list = case unroll xs ( inl _ ⇒ nil [b,pb ] () | inr xs ⇒ split xs as hd,tl in cons [b,pb ] (pb )>)) In order to ensure that our type system remains sound in the presence of pretype polymorphism, we add the obvious typing rules, but change very little else. However, adding qualifier polymorphism, as we have done, is a little more involved.

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

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