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

By Benjamin C. Pierce

The research 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 allotted platforms. This booklet deals obtainable introductions to key principles within the box, with contributions by means of specialists on every one topic.

The subject matters coated contain designated sort analyses, which expand uncomplicated sort platforms to provide them a greater grip at the run time habit of platforms; sort platforms for low-level languages; purposes of sorts to reasoning approximately computing device courses; style thought as a framework for the layout of subtle module structures; and complicated thoughts in ML-style kind inference.

Advanced themes in kinds and Programming Languages builds on Benjamin Pierce's Types and Programming Languages (MIT Press, 2002); lots of the chapters could be obtainable to readers accustomed to simple notations and methods of operational semantics and kind systems—the fabric lined within the first 1/2 the sooner book.

Advanced issues in varieties and Programming Languages can be utilized within the lecture room and as a source for pros. such a lot chapters comprise workouts, ranging in trouble from quickly comprehension exams to difficult extensions, many with suggestions.

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The second relation, (S;t) →β (S ;t ), does all the real work. In order to avoid creation of two sets of operational rules, one for linear data, which is deallocated when used, and one for unrestricted data, which is never q deallocated, we define an auxiliary function, S ∼ x, to manage the differences. (S1 ,x un S∼x lin v,S2 ) ∼ x = = S1 ,S2 S Aside from these details, the operational semantics is standard. Preservation and Progress In order to prove the standard safety properties for our language, we need to be able to show that programs are well-formed after each step in evaluation.

P t ::= ... t t [q] P ::= ... lin (p2 a * (lin,p2 ,a) list)→(lin,p2 ,a) list = Λ a,p2 . λcell : lin (p2 a * (lin,p2 ,a) list). 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.

We also adapt the syntax for iterators as follows. iter (stop ⇒ t1 | hd with tl and r ⇒ t2 ) Inside the second clause of the iterator, we are only granted a single resource (r) with which to allocate data. Consequently, we can allocate at most one cons cell in t2 . This provides us with the power to rebuild a list of the same size, but we cannot write a function such as double that doubles the length of the list or exp that causes an exponential increase in size. 5 Further Applications 39 a single resource from an outer scope does not percolate inside the iterator and get reused on each iteration of the loop, we require that iterators be closed, mirroring the containment rules for recursive functions defined in earlier sections of this chapter.

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