D.B.MacQueen, G.D.Plotkin, R.Sethi: An ideal model for recursive polymorphic types, Information and Control 71, pp. 95-130, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....= E X A D ; E D , x:A=a = E x a D . E[E ] indicates that E is a given subexpression of expression E. Then E[E ] denotes the substitution of (a particular occurrence of) E by E in E. Here E, E and E are expressions of any sort. A type C is contractive in a (free) type variable X [MacQueen Plotkin Sethi 86] written CSX, if and only if C is either: a type variable different from X, a function or tuple type, an operator application whose reduced form is contractive in X, or a recursive type whose body is contractive in X. The body of a legal recursive type must also be contractive in the recursion ....

D.B.MacQueen, G.D.Plotkin, R.Sethi: An ideal model for recursive polymorphic types, Information and Control 71, pp. 95-130, 1986.

....= E XYA D ; E D , x:A=a = E xYa D . E[E ] indicates that E is a given subexpression of expression E. Then E[E ] denotes the substitution of (a particular occurrence of) E by E in E. Here E, E and E are expressions of any sort. A type C is contractive in a (free) type variable X [MacQueen Plotkin Sethi 86] written C X , if and only if C is either: a type variable different from X, a function or tuple type, an operator application whose reduced form is contractive in X, or a recursive type whose body is contractive in X. The body of a legal recursive type must also be contractive in the recursion ....

D.B.MacQueen, G.D.Plotkin, R.Sethi: An ideal model for recursive polymorphic types, Information and Control 71, pp. 95-130, 1986.

....about run time errors, we procede in the following sections by interpreting e is semantically well typed to mean E[ e ]h wrong , and finally we give an algorithm which statically checks well typing. 10. Semantics of type expressions The semantics of types is given in the weak ideal model [MacQueen 86] V) the set of nonempty left closed subset of V which are closed under least upper bounds of increasing sequences and do not contain wrong) V) is a lattice of domains, where the ordering is set inclusion. V) is closed under intersections and finite unions, as well as the usual domain ....

....new semantic problems. The interactions of inheritance and parametric polymorphism in typechecking are addressed in [Cardelli 85] There are now several competing (although not totally independent) styles of parametric polymorphism, noticeably in [Milner 78] Reynolds 74, McCracken 84] and [MacQueen 86] Inheritance is orthogonal to all of these, so it seems better to study it independently, at least initially. However, the final goal is to achieve full integration of parametric polymorphism and multiple inheritance, merging functional programming with object oriented programming at the ....

D.B.MacQueen, G.D.Plotkin, R.Sethi: An ideal model for recursive polymorphic types, Information and Control 71, pp. 95-130, 1986.

....X: K=A = E XA D ; E D , x:A=a = E xa D . E[E ] indicates that E is a given subexpression of expression E. Then E[E ] denotes the substitution of (a particular occurrence of) E by E in E. Here E, E and E are expressions of any sort. A type C is contractive in a (free) type variable X [MacQueen Plotkin Sethi 86] written CX , if and only if C is either: a type variable different from X, a function or tuple type, an operator application whose reduced form is contractive in X, or a recursive type whose body is contractive in X. The body of a legal recursive type must also be contractive in the recursion ....

D.B.MacQueen, G.D.Plotkin, R.Sethi: An ideal model for recursive polymorphic types, Information and Control 71, pp. 95-130, 1986.

....to characterize the type system at an intuitive level, and can be easily formalized as a type inference system. The rules are sound and can stand on their own, but have been discovered and justified by studying a particular semantics of types, developed in [Hindley 69] Milner 78] Damas 82] MacQueen 84a] and [Mitchell 84] Although we do not need to discuss that semantic theory of types in detail, it may be useful to explain the basic intuitions behind it. These intuitions can in turn be useful in understanding the typing rules, particularly regarding the concept of subtypes which will be ....

D.B.MacQueen, G.D.Plotkin, R.Sethi: An ideal model for recursive polymorphic types, Proc. Popl 1984. Also to appear in Information and Control.

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D.B.MacQueen, G.D.Plotkin, R.Sethi: An ideal model for recursive polymorphic types, Information and Control 71, pp. 95-130, 1986.

No context found.

D.B.MacQueen, G.D.Plotkin, R.Sethi: An ideal model for recursive polymorphic types, Proc. Popl 1984. Also to appear in Information and Control.

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