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

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By Benjamin C. Pierce

The examine of kind platforms for programming languages now touches many components of laptop technological know-how, from language layout and implementation to software program engineering, community safety, databases, and research of concurrent and allotted structures. This e-book deals obtainable introductions to key principles within the box, with contributions by way of specialists on every one topic.

The subject matters coated contain exact style analyses, which expand basic sort platforms to provide them a greater grip at the run time habit of structures; sort structures for low-level languages; functions of varieties to reasoning approximately desktop courses; kind idea as a framework for the layout of refined module platforms; and complex ideas in ML-style variety inference.

Advanced subject matters 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 easy notations and methods of operational semantics and sort systems—the fabric lined within the first 1/2 the sooner book.

Advanced themes in forms and Programming Languages can be utilized within the lecture room and as a source for execs. such a lot chapters comprise routines, ranging in trouble from fast comprehension exams to not easy extensions, many with strategies.

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But this is not the only problem. Higher-order functions make it even easier to construct exponential-time algorithms: val compose = λ(fg:(T list→T list) * (T list→T list)). λ(x:T list). compose l) Fortunately, a substructural type system can be used to eliminate both problems by allowing us to define a class of non-size-increasing functions and by preventing the construction of troublesome higher-order functions, such as exp2 . The first step is to demand that all user-defined objects have affine type.

The idea of formulating the system with a generic context splitting operator was taken from Cervesato and Pfenning’s presentation of Linear LF (2002). The algorithmic type system described in section 1-5 solves what is commonly known in the linear logic programming and theorem proving literature, as the resource management problem. Many of the ideas for the current presentation came from work by Cervesato, Hodas, and Pfenning (2000), who solve the more general problem that arises when linear logic’s additive connectives are considered.

The typing rules use the qualifier relation q1 q2 , which specifies that ord lin un, to ensure such problems do not arise. The typing rules for the ordered lambda calculus appear in Figure 1-21. For the most part, the containment rules and context splitting rules encapsulate 34 1 Substructural Type Systems Γ =1 Γ1 ◦ Γ2 Γ = Γ1 ◦ Γ2 Context Split Γ =2 Γ1 ◦ Γ2 Γ = Γ1 ◦ Γ2 ∅ =1 ∅ ◦ ∅ Γ =1 Γ1 ◦ Γ2 Γ , x:ord P =1 (Γ1 , x:ord P) ◦ Γ2 Γ =2 Γ1 ◦ Γ2 Γ , x:ord P =2 Γ1 ◦ (Γ2 , x:ord P) Γ =2 Γ1 ◦ Γ2 (M-Top) (M-Empty) (M-Ord1) (M-Ord2) Γ =1,2 Γ1 ◦ Γ2 Γ , x:lin P =1,2 (Γ1 , x:lin P) ◦ Γ2 Γ =1,2 Γ1 ◦ Γ2 Γ , x:lin P =1,2 Γ1 ◦ (Γ2 , x:lin P) (M-1to2) (M-LinA) (M-LinB) Γ =1,2 Γ1 ◦ Γ2 Γ , x:un P =1,2 (Γ1 , x:un P) ◦ (Γ2 , x:un P) (M-Un) Figure 1-20: Ordered lambda calculus: Context splitting the tricky elements of the type system.

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