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- Wolfgang Gehrke
- RTA
- 1995

We present a canonical system for comonads which can be extended to the notion of a computational comonad BG92] where the crucial point is to nd an appropriate representation. These canonical systems are checked with the help of the Larch Prover GG91] exploiting a method by G. Huet Hue90a] to represent typing within an untyped rewriting system. The… (More)

- Wolfgang Gehrke
- 1994

In this paper we give a detailed catalogue for several canonical rewrite systems which have been compiled by Hullot in 1980. All the deenitions are given precisely and a trace of a completion system (RRL) for those equational theories is also included. In some examples the canonical system generated by RRL diiers from the system presented by Hullot since… (More)

- Wolfgang Gehrke, Jochen Pfalzgraf
- J. Autom. Reasoning
- 2001

- Wolfgang Gehrke, Carla Limongelli
- DISCO
- 1996

This paper shows the expressive power of the functional programming language Standard ML (SML) in the context of computer algebra. It is focused on a special application of the p-adic lifting technique, the Hensel algorithm, that is utilized in a symbolic but also numeric context. This experiment demonstrates that SML provides a suitable frame for the… (More)

- Wolfgang Gehrke
- 1994

In this report canonical rewriting systems for the most basic categorical notions are presented. These are categories themselves, functors, and natural transformations. The appendix explains the methods used to prove termination and connuence of the discussed systems. Finally traces of tests with the Larch Prover and a program in Elf illustrating a more… (More)

- Wolfgang Gehrke
- 1997

sponsored by the project MURST 40% \Calcolo Algebrico e Simbolico" ABSTRACT We investigate the utilization of parametric code to perform algebraic computation on the one hand and to allow for related deduction on the other hand. This method is illustrated by the implementation of several number systems and the study of their main properties. The examples… (More)

- Wolfgang Gehrke
- 2007

This article explores the expressiveness of the SML module system in the context of linear algebra. The selected examples range from rings with a doubling construction over vector spaces with related abstract operations to the notion of an algebra. The functional and in particular the functorial approach is argued to be appropriate for problems in linear… (More)

- Wolfgang Gehrke
- 1994

We present a full proof of a canonical system for adjunctions as already suggested in Cur93]. Termination can be shown in a similar style to HL86]. Connuence is shown by checking all critical pairs. This is done rstly in the Larch Prover GG91] and secondly more correctly in the programming language Elf Pfe89]. Exploiting theorems from category theory BW85]… (More)

- Wolfgang Gehrke
- 1997

supported by the Italian project MURST ex 40% \Rappresentazione della conoscenza e meccanismi di ragionamento" ABSTRACT We report on an extension of the SML implementation o f t he logic programming l a n guage Elf Pfe94] to support the c heck o f c o n vergence for higher-order critical pairs. Since Elf is based on the Edinburgh Logical Framework HHP93] it… (More)

This paper shows how explicit parallel function calls can be deened and implemented on top of Concurrent ML hiding the details about creation and communication of diierent threads. The provided parallel schemes are mainly inspired by the And/Or-parallelism known from logic programming and pipelining which together provide an outline how other schemes can be… (More)