B. C. Pierce. Bounded quantification with bottom. Technical Report 492, Computer Science Department, Indiana University, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... Boolg: ff] ff] represents the collection of all types [ such that there is a definition of function ( of type Bool. Due to space restrictions, we will not present rules of type systems with constrained polymorphic types. We encourage the reader to see [CF99a, FM96, Car96, Pie97] 19 Constrained types are adequate for expressing the types of overloaded symbols [CF99a] as illustrated by the following examples: f( ff ff Boolg: ff ff Bool ( f( ff ff ffg: ff ff ff sort : f( ff ff Boolg: ff] ff] Another form of constrained ....

....(in this case, the abstract type is transparent) In other parts 18 There exists a large number of articles on the subject in recent literature. Languages that include subtype bounded parameters include Eiffel, Trellis Owl, Sather, PolyTOIL, Rapide, Fun, Quest and Abel. See references in e.g. Pie97, Car96] 20 of the program, that use the defined abstract type, the abstract type is distinct from any other types (in this case, the case, the abstract type is opaque) In some programming languages, this distinction is obtained through the use of a special construct for the definition of ....

B. C. Pierce. Bounded quantification with bottom. Technical Report 492, Computer Science Department, Indiana University, 1997.

....of subtyping [15, 14] rather than the weaker rule from our earlier paper. Induced Equivalence Relations The equivalence relation induced by A B and B A may be stronger than the usual intensional equality associated with type theory, syntactic equivalence on normal forms. One such case is [31], where the types 8(X : Bot)X X and 8(X : Bot)Bot Bot are equivalent in the subtype relation 2 , even though they are not syntactically identical. A similar situation appears in intersection types disciplines, where = A and also A and A . A final example is extensible records ....

B. C. Pierce. Bounded quantification with bottom. Technical Report 492, Computer Science Department, Indiana University, 1997.

....to the empty set; an expression of the bottom type never reduces to an object instantiation new N(e) Any operation on the element of the empty set is vacuously allowed and the result also belongs to the empty set. Similar rules can be found in an extension of System F# with the bottom type [15]. As stupid casts, we signal stupid warning here as the GJ compiler actually rejects expressions of the bottom type: these rules are nevertheless needed to show type soundness through subject reduction. Reduction Rules Thanks to the auxiliary definitions, the computation rule for raw method ....

Benjamin C. Pierce. Bounded quantification with bottom. Technical Report 492, Computer Science Department, Indiana University, 1997.

....internal language the target for the type inference methods described in Section 3 we extend Cardelli and Wegner s Kernel Fun calculus [CW85] of subtyping and impredicative polymorphism. We only give definitions here; the meta theory of the system is developed in detail in a companion paper [Pie97]. 2.1 Syntax We extend the original Kernel Fun system [CW85] in a few significant ways. Firstly, we add a minimal type Bot. Our type inference algorithm keeps track of various type constraints by calculating the least upper bound and greatest lower bound of pairs of types. The Bot type plays a ....

....it we could not guarantee that least upper bounds and greatest lowerbounds always exist. The properties of Kernel Fun with Bot are similar to those of pure Kernel Fun, but there are a number of significant differences in details. The properties of the internal language are developed in detail in [Pie97]. Secondly, we extend abstraction and application so that several arguments (including both types and terms) may be passed at the same time. In other words, we favor a fully uncurried style of function definition and application (though currying is, of course, still available) This bias will ....

[Article contains additional citation context not shown here]

Benjamin C. Pierce. Bounded quantification with bottom. Technical Report 492, Computer Science Department, Indiana University, 1997.

.... continue to hold for the extended system (including the combination with the bidirectional propagation technique) but the algorithms involved in generating constraint sets become somewhat more subtle, due principally to some surprising interactions between bounded quantifiers and the Bot type [Pie97]. In particular, the intuitive property that a type variable has no subtypes except itself and Bot fails to hold; for example, if the context contains X :Bot, then we have X : Y for any variable Y. Moreover, we impose a slight restriction on the types of polymorphic functions for which ....

Benjamin C. Pierce. Bounded quantification with bottom. Technical Report 492, Computer Science Department, Indiana University, 1997.

No context found.

B. C. Pierce. Bounded quantification with bottom. Technical Report 492, Computer Science Department, Indiana University, 1997.

No context found.

Benjamin C. Pierce. Bounded quantification with bottom. CSCI Technical Report 492, Indiana University, November 1997.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC