Jean-Claude Reynaud

Analysis of whole‐cell currents by patch clamp of guinea‐pig myenteric neurones in intact ganglia

Whole‐cell patch‐clamp recordings taken from guinea‐pig duodenal myenteric neurones within intact ganglia were used to determine the properties of S and AH neurones. Major currents that determine the states of AH neurones were identified and quantified. S neurones had resting potentials of −47 ± 6 mV and input resistances (Rin) of 713 ± 49 MΩ at voltages ranging from −90 to −40 mV. At more negative levels, activation of a time‐independent, caesium‐sensitive, inward‐rectifier current (IKir) decreased Rin to 103 ± 10 MΩ. AH neurones had resting potentials of −57 ± 4 mV and Rin was 502 ± 27 MΩ. Rin fell to 194 ± 16 MΩ upon hyperpolarization. This decrease was attributable mainly to the activation of a cationic h current, Ih, and to IKir. Resting potential and Rin exhibited a low sensitivity to changes in [K+]o in both AH and S neurones. This indicates that both cells have a low background K+ permeability. The cationic current, Ih, contributed about 20 % to the resting conductance of AH neurones. It had a half‐activation voltage of −72 ± 2 mV, and a voltage sensitivity of 8.2 ± 0.7 mV per e‐fold change. Ih has relatively fast, voltage‐dependent kinetics, with on and off time constants in the range of 50–350 ms. AH neurones had a previously undescribed, low threshold, slowly inactivating, sodium‐dependent current that was poorly sensitive to TTX. In AH neurones, the post‐action‐potential slow hyperpolarizing current, IAHP, displayed large variation from cell to cell. IAHP appeared to be highly Ca2+ sensitive, since its activation with either membrane depolarization or caffeine (1 mm) was not prevented by perfusing the cell with 10 mm BAPTA. We determined the identity of the Ca2+ channels linked to IAHP. Action potentials of AH neurones that were elongated by TEA (10 mm) were similarly shortened and IAHP was suppressed with each of the three Ω‐conotoxins GVIA, MVIIA and MVIIC (0.3–0.5 μm), but not with Ω‐agatoxin IVA (0.2 μm). There was no additivity between the effects of the three conotoxins, which indicates the presence of N‐ but not of P/Q‐type Ca2+ channels. A residual Ca2+ current, resistant to all toxins, but blocked by 0.5 mm Cd2+, could not generate IAHP. This patch‐clamp study, performed on intact ganglia, demonstrates that the AH neurones of the guinea‐pig duodenum are under the control of four major currents, IAHP, Ih, an N‐type Ca2+ current and a slowly inactivating Na+ current.

Cartesian effect categories are Freyd-categories

Most often, in a categorical semantics for a programming language, the substitution of terms is expressed by composition and finite products. However this does not deal with the order of evaluation of arguments, which may have major consequences when there are side-effects. In this paper Cartesian effect categories are introduced for solving this issue, and they are compared with strong monads, Freyd-categories and Haskells Arrows. It is proved that a Cartesian effect category is a Freyd-category where the premonoidal structure is provided by a kind of binary product, called the sequential product. The universal property of the sequential product provides Cartesian effect categories with a powerful tool for constructions and proofs. To our knowledge, both effect categories and sequential products are new notions.

Sketches and computation – II: dynamic evaluation and applications

In the first part of this paper (Duval and Reynaud 1994), we defined a categorical framework, based on the notion of sketch , for specification and evaluation in the senses of algebraic specifications and algebraic programming. Static evaluation in quasi-projective sketches was defined in Part I; in this paper, dynamic evaluation is introduced. It deals with more general structures, which may have no initial model. Until now, this process has not been used in algebraic specification systems, but computer algebra systems are beginning to use it as a basic tool. Finally, we give some applications of dynamic evaluation to computation in field extensions.

A duality between exceptions and states

Computational effects may often be interpreted in the Kleisli category of a monad or in the coKleisli category of a comonad. The duality between monads and comonads corresponds, in general, to a symmetry between construction and observation, for instance between raising an exception and looking up a state. Thanks to the properties of adjunction one may go one step further: the coKleisli-on-Kleisli category of a monad provides a kind of observation with respect to a given construction, while dually the Kleisli-on-coKleisli category of a comonad provides a kind of construction with respect to a given observation. In the previous examples this gives rise to catching an exception and updating a state. However, the interpretation of computational effects is usually based on a category which is not self-dual, like the category of sets. This leads to a breaking of the monad-comonad duality. For instance, in a distributive category the state effect has much better properties than the exception effect. This remark provides a novel point of view on the usual mechanism for handling exceptions. The aim of this paper is to build an equational semantics for handling exceptions based on the coKleisli-on-Kleisli category of the monad of exceptions. We focus on n-ary functions and conditionals. We propose a programmer’s language for exceptions and we prove that it has the required behaviour with respect to n-ary functions and conditionals.In this short note we study the semantics of two basic computational effects, exceptions and states, from a new point of view. In the handling of exceptions we dissociate the control from the elementary operation that recovers from the exception. In this way it becomes apparent that there is a duality, in the categorical sense, between exceptions and states.

Putting Algebraic Components Together: A Dependent Type Approach

We define a framework based on dependent types for putting algebraic components together. It is defined with freely generated categories. In order to preserve initial, loose and constrained semantics of components, we introduce the notion of SPEC-categories which look like specific finitely co-complete categories. A constructive approach which includes parametrization techniques is used to define new components from basic predefined ones. The problem of the internal coding of external signature symbols is introduced.

Sketches and computations over fields

The goal of this short paper is to describe one possible use of sketches in computer algebra. We show that sketches are a powerful tool for the description of mathematical structures and for the description of computations.

Relative Hilbert-Post Completeness for Exceptions

A theory is complete if it does not contain a contradiction, while all of its proper extensions do. In this paper, first we introduce a relative notion of syntactic completeness; then we prove that adding exceptions to a programming language can be done in such a way that the completeness of the language is not made worse. These proofs are formalized in a logical system which is close to the usual syntax for exceptions, and they have been checked with the proof assistant Coq.