F. Parisi-Presicce and S. Veglioni. Heterogeneous unified algebras. In Proceedings of MFCS'93, 18th International Symposium on Mathematical Foundations of Computer Science, pages 618--628. Springer LNCS 711, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... is supported by the fact, discussed in detail in the paper, that besides the formalisms already mentioned other well known total equational approaches to types such as many sorted equational logic, equational type logic [21] unified algebras [28] and heterogeneous unified algebras [30] can be faithfully embedded in it. Similarly, a wide range of partial equational specification formalisms, including essentially algebraic theories [11, 1] hierarchical equational partial logic [32] left exact sketches [2] limit theories [10] conditional) many sorted partial equational logic ....

....: and a partial order predicate in addition to the equality predicate, and satisfying suitable axioms that characterize the latticetheoretic and typing properties of unified algebras. Similarly, the heterogeneous version of unified algebras (HUnifEqtl) proposed by Parisi Presicce and Veglioni [30] has an embedding into into many sorted Horn logic with equality HUnifEqtl , MSHorn = provided that the signature morphisms are restricted to be injective (see [30, Props. 18 21] Of course, the well known case of (conditional) many sorted equational logic (MSEqtl) is also a sublogic of ....

F. Parisi-Presicce and S. Veglioni. Heterogeneous unified algebras. In Proceedings of MFCS'93, 18th International Symposium on Mathematical Foundations of Computer Science, pages 618--628. Springer LNCS 711, 1993.

....syntax, can be specified (see e.g. 698] Moreover, considerable conciseness is obtained by the use the Kleene star and other standard operations on types. Adopting ideas from [692, 693] a compromise between unified algebras, which are one sorted, and many sorted algebras has been proposed in [759] where each element of a given set of sorts is viewed as a maximal element in a coalesced sum of disjoint unified algebras, each representing the constructible subsets of the appropriate sort. In [11] a novel axiomatization and rewriting theory for the unified algebra of regular events are ....

F. Parisi-Presicce and S. Veglioni. Heterogeneous Unified Algebras. In A. M. Bozyszkowski and S. Sokolowski, editors, Mathematical Foundations of Computer Science 1993. 18th International Symposium, MFCS '93, Gda'ansk, Poland, August/September 1993, pages 618--628. Springer LNCS 711, 1993. \Phi.

....controversial aspects. We have concentrated our effort to the analysis of the following structures: Many Sorted Algebra [27, 2, 24, 22, 10] universal Order Sorted Algebra [11, 42, 47] overloaded Order Sorted Algebra [15, 23, 18] Unified Algebra [37, 36, 38] and Heterogeneous Unified Algebra [41], a novel framework holding, in a sense, both a syntactic and a semantic notion of sort. We found that all issues concerning classifications raised by other models, including partial ones, are covered by the structures considered. For example, Equational Type Logic [30] Type Horn Logic [44] and ....

.... fact the fascinating theory of modularization developed by Mosses [38] based on initial semantics does not match some semantic requirements like, for example, that the semantics of an imported module be preserved (in order to allow the importation of meaning instead of a mere importation of code) [41, 50]. However, these criticisms must not be extended to all universal structures, in fact Equational Type Logic and Type Horn Logic are examples of liberal institutions, thanks to a great effort made in order to define a more suitable forgetful functor, but paying a price in terms of clarity and ....

[Article contains additional citation context not shown here]

Francesco Parisi-Presicce and Simone Veglioni. Heterogeneous unified algebras. In Proceedings, Mathematical Foundations of Computer Science `93. Springer, 1993. Lecture Notes in Computer Science, Volume 711.

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