Brian T. Howard. Inductive, coinductive, and pointed types. In Proc. 1 st int. conf. on Functional programming. ACM Press, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....be implemented equally well in an eager language or lazy language. We demonstrate this by presenting implementations of cycamores in both SML and Haskell. 1. 3 Related Work There is a vast literature on programming with fold and unfold operators on a variety of data structures; references include [14, 16, 8, 2, 7, 11]. Terminology di#ers widely in this literature. In the terminology of [16] fold and unfold are only given the informal names of bananas and lenses for the symbols used to write them, the results of fold(#) and unfold(#) are called, respectively, catamorphisms and anamorphisms, and the terms ....

....of [16] fold and unfold are only given the informal names of bananas and lenses for the symbols used to write them, the results of fold(#) and unfold(#) are called, respectively, catamorphisms and anamorphisms, and the terms in and out are used for what we call make and make 1 . Howard s [8] it (iteration) and gen (coiteration) loosely correspond to our fold and unfold, but Howard (like many other authors in type theory) uses the names fold and unfold for type level operations that have the same role as make and make 1 do here. It is especially important to avoid confusion with the ....

B. T. Howard. Inductive, coinductive, and pointed types. In Proc.

....typing system by changing translation of types. The present paper reports how we can integrate affinity and linearity to reach a uniform, single structure, and what applications it would have for the study of types for programming languages. The endeavour is similar to pointed types by Howard [26, 35], but carried out using a different tool set. Secure Information Flow. We choose type based analysis of secure information flow [2, 14, 38, 43, 44, 47] as an application domain of the integrated type structure. In this analysis, we use a typing system to ensure that information flow is always ....

....we can embed in the secure version of the calculus. Grey box shows a property satisfied by the corresponding calculus. Related Work. Literature lists a few prominent examples of integrated type disciplines based on function types, which often use monads. Two basic examples are pointed types [26, 35] (mentioned above) and incorporation of imperative constructs in Haskell [27] Dependency core calculus (DCC) 2] is a powerful functional metalanguage for secrecy, using pointed types. The semantics is given by a denotational universe based on logical relations. The calculus is effective for ....

[Article contains additional citation context not shown here]

Howard, B. T., Inductive, coinductive, and pointed types, ICFP'96, 102--109, ACM, 1996.

....Phil Wadler suggested that something like the system in this paper might work. We have benefited from discussions with Erik Meijer, and the paper has been improved by feedback from Tim Sheard, Andrew Tolmack and Andrew Moran. After writing this paper, we became aware of the work of Brian Howard [4], who uses an equivalent treatment of lifting and pointed types to describe a language in which initial, final and retractive types co exist. ....

Brian T. Howard. Inductive, projective, and pointed types. In ACM Int. Conf. on Functional Programming, Philadelphia, May 1996.

.... the details of the encoding here; those details appear in the companion technical report [4] 6 Related Work and Conclusions The properties and applications of languages with inductive types similar to the constructor level of LX have been well studied by Mendler [18, 17] Werner [31] Howard [13, 14], and Gordon [11] among others. Most of those studies include coinductive and polymorphic types as well as inductive types. It appears as though extending LX with coinductive and polymorphic kinds would not be problematic. We have omitted such extensions at present in order to simplify the ....

Brian T. Howard. Inductive, coinductive, and pointed types. In Proceedings of the 1996 ACM SIGPLAN International Conference on Functional Programming, pages 102--109, 1996.

....g (C g) Here, g is small and non recursive, so when processing g (C g) g will be inlined. But the inlined call very soon rewrites to g (C g) which is just the expression we started with. The problem here is that the data type T is recursive, and it appears contravariantly in its own definition [How96]. Of these two forms of divergence, the former is an immediate and pressing problem, since almost any interesting Haskell program involves recursion. The rest of this section focuses entirely on recursive definitions. In contrast, the latter situation is rather rare, and (embarrassingly) GHC can ....

BT Howard. Inductive, co-inductive, and pointed types. In ICFP96 [ICF96].

....types, induces a subset of types called the pointed types: ffl s is a pointed type; ffl if s and t are pointed types, then (s Theta t) and T (s) are pointed types; and ffl if t is a pointed type, then (s t) is a pointed type. For a recent account of pointed types, see the paper by Howard [14] or Mitchell s text [18] Similarly, the T operation on types induces a subset of types called the types protected at level : Table 1: Typing Rules for DCC. Var] G;x : s; G 0 x : s [Unit] G ( unit [Lam] G;x : s 1 e : s 2 G (lx : s 1 : e) s 1 s 2 ) App] G e : s 1 s ....

B. T. Howard. Inductive, coinductive, and pointed types. In Proceedings of the 1996 ACM SIGPLAN International Conference on Functional Programming, pages 102--109. ACM, 1996.

.... the details of the encoding here; those details appear in the companion technical report [4] 6 Related Work and Conclusions The properties and applications of languages with inductive types similar to the constructor level of LX have been well studied by Mendler [18, 17] Werner [31] Howard [13, 14], and Gordon [11] among others. Most of those studies include coinductive and polymorphic types as well as inductive types. It appears as though extending LX with coinductive and polymorphic kinds would not be problematic. We have omitted such extensions at present in order to simplify the ....

Brian T. Howard. Inductive, coinductive, and pointed types. In Proceedings of the 1996 ACM SIGPLAN International Conference on Functional Programming, pages 102--109, 1996.

No context found.

Brian T. Howard. Inductive, coinductive, and pointed types. In Proc. 1 st int. conf. on Functional programming. ACM Press, 1996.

No context found.

Brian T. Howard. Inductive, coinductive, and pointed types. In Proc. 1 st int. conf. on Functional programming. ACM Press, 1996.

No context found.

B. T. Howard. Inductive, coinductive, and pointed types. In Proc. 1996.

No context found.

Howard, B. T., Inductive, coinductive, and pointed types, ICFP'96, 102-109, ACM, 1996.

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