Relational and Allegorical Semantics for Constraint Logic Programming

El cálculo de relaciones binarias fue creado por De Morgan en 1860 para ser posteriormente desarrollado en gran medida por Peirce y Schröder. Tarski, Givant, Freyd y Scedrov demostraron que las álgebras relacionales son capaces de formalizar la lógica de primer orden, la lógica de orden superior así como la teoría de conjuntos. A partir de los resultados matemáticos de Tarski y Freyd, esta tesis desarrolla semánticas denotacionales y operacionales para la programación lógica con restricciones usando el álgebra relacional como base. La idea principal es la utilización del concepto de semántica ejecutable, semánticas cuya característica principal es el que la ejecución es posible utilizando el razonamiento estándar del universo semántico, este caso, razonamiento ecuacional. En el caso de este trabajo, se muestra que las álgebras relacionales distributivas con un operador de punto fijo capturan toda la teoría y metateoría estándar de la programación lógica con restricciones incluyendo los árboles utilizados en la búsqueda de demostraciones. La mayor parte de técnicas de optimización de programas, evaluación parcial e interpretación abstracta pueden ser llevadas a cabo utilizando las semánticas aquí presentadas. La demostración de la corrección de la implementación resulta extremadamente sencilla. En la primera parte de la tesis, un programa lógico con restricciones es traducido a un conjunto de términos relacionales. La interpretación estándar en la teoría de conjuntos de dichas relaciones coincide con la semántica estándar para CLP. Las consultas contra el programa traducido son llevadas a cabo mediante la reescritura de relaciones. Para concluir la primera parte, se demuestra la corrección y equivalencia operacional de esta nueva semántica, así como se define un algoritmo de unificación mediante la reescritura de relaciones. La segunda parte de la tesis desarrolla una semántica para la programación lógica con restricciones usando la teoría de alegorías—versión categórica del álgebra de relaciones—de Freyd. Para ello, se definen dos nuevos conceptos de Categoría Regular de Lawvere y _-Alegoría, en las cuales es posible interpretar un programa lógico. La ventaja fundamental que el enfoque categórico aporta es la definición de una máquina categórica que mejora e sistema de reescritura presentado en la primera parte. Gracias al uso de relaciones tabulares, la máquina modela la ejecución eficiente sin salir de un marco estrictamente formal. Utilizando la reescritura de diagramas, se define un algoritmo para el cálculo de pullbacks en Categorías Regulares de Lawvere. Los dominios de las tabulaciones aportan información sobre la utilización de memoria y variable libres, mientras que el estado compartido queda capturado por los diagramas. La especificación de la máquina induce la derivación formal de un juego de instrucciones eficiente. El marco categórico aporta otras importantes ventajas, como la posibilidad de incorporar tipos de datos algebraicos, funciones y otras extensiones a Prolog, a la vez que se conserva el carácter 100% declarativo de nuestra semántica. ABSTRACT The calculus of binary relations was introduced by De Morgan in 1860, to be greatly developed by Peirce and Schröder, as well as many others in the twentieth century. Using different formulations of relational structures, Tarski, Givant, Freyd, and Scedrov have shown how relation algebras can provide a variable-free way of formalizing first order logic, higher order logic and set theory, among other formal systems. Building on those mathematical results, we develop denotational and operational semantics for Constraint Logic Programming using relation algebra. The idea of executable semantics plays a fundamental role in this work, both as a philosophical and technical foundation. We call a semantics executable when program execution can be carried out using the regular theory and tools that define the semantic universe. Throughout this work, the use of pure algebraic reasoning is the basis of denotational and operational results, eliminating all the classical non-equational meta-theory associated to traditional semantics for Logic Programming. All algebraic reasoning, including execution, is performed in an algebraic way, to the point we could state that the denotational semantics of a CLP program is directly executable. Techniques like optimization, partial evaluation and abstract interpretation find a natural place in our algebraic models. Other properties, like correctness of the implementation or program transformation are easy to check, as they are carried out using instances of the general equational theory. In the first part of the work, we translate Constraint Logic Programs to binary relations in a modified version of the distributive relation algebras used by Tarski. Execution is carried out by a rewriting system. We prove adequacy and operational equivalence of the semantics. In the second part of the work, the relation algebraic approach is improved by using allegory theory, a categorical version of the algebra of relations developed by Freyd and Scedrov. The use of allegories lifts the semantics to typed relations, which capture the number of logical variables used by a predicate or program state in a declarative way. A logic program is interpreted in a _-allegory, which is in turn generated from a new notion of Regular Lawvere Category. As in the untyped case, program translation coincides with program interpretation. Thus, we develop a categorical machine directly from the semantics. The machine is based on relation composition, with a pullback calculation algorithm at its core. The algorithm is defined with the help of a notion of diagram rewriting. In this operational interpretation, types represent information about memory allocation and the execution mechanism is more efficient, thanks to the faithful representation of shared state by categorical projections. We finish the work by illustrating how the categorical semantics allows the incorporation into Prolog of constructs typical of Functional Programming, like abstract data types, and strict and lazy functions.

A “REVOLTA” DE JEÚ E A ESTELA DE DÃ: Um Estudo Em 2 Reis 10,28-36

A pesquisa tem por objetivo trabalhar o evento da Revolta de Jeú, em conjunto com a Estela de Dã, tendo como ponto de partida para tal, a exegese da perícope de 2 Reis 10-28,36. A história Deuteronomista apresenta o ato da Revolta de Jeú como sendo um feito demasiadamente importante, na restauração do culto a Javé em Israel, a partir de um contexto onde o culto a outras divindades, em Israel Norte, estava em pleno curso. No entanto, a partir da análise conjunta da Estela de Dã, que tem como provável autor o rei Hazael de Damasco, somos desafiados a ler esta história pelas entrelinhas não contempladas pelo texto, que apontam para uma participação ativa de Hazael, nos desfechos referentes a Revolta de Jeú, como sendo o responsável direto que proporcionou a subida de Jeú ao trono em Israel, clarificando desta forma este importante período na história Bíblica. Para tal análise, observar-se-á três distintos tópicos, ligados diretamente ao tema proposto: (1) A Revolta de Jeú e a Redação Deuteronomista, a partir do estudo exegético da perícope de 2 Reis 10,28-36, onde estão descritas informações pontuais sobre período em que Jeú reinou em Israel; (2) Jeú e a Estela de Dã, a partir da apresentação e análise do conteúdo da Estela de Dã, tratando diretamente dos desdobramentos da guerra em Ramote de Gileade, de onde se dá o ponto de partida à Revolta de Jeú; e por fim (3) O Império da Síria, onde a partir da continuidade da análise do conteúdo da Estela de Dã, demonstraremos a significância deste reino, além de apontamentos diretamente ligados ao reinado de Hazael, personagem mui relevante no evento da Revolta de Jeú.

Abnormal photoresponses and light-induced apoptosis in rods lacking rhodopsin kinase

Phosphorylation is thought to be an essential first step in the prompt deactivation of photoexcited rhodopsin. In vitro, the phosphorylation can be catalyzed either by rhodopsin kinase (RK) or by protein kinase C (PKC). To investigate the specific role of RK, we inactivated both alleles of the RK gene in mice. This eliminated the light-dependent phosphorylation of rhodopsin and caused the single-photon response to become larger and longer lasting than normal. These results demonstrate that RK is required for normal rhodopsin deactivation. When the photon responses of RK−/− rods did finally turn off, they did so abruptly and stochastically, revealing a first-order backup mechanism for rhodopsin deactivation. The rod outer segments of RK−/− mice raised in 12-hr cyclic illumination were 50% shorter than those of normal (RK+/+) rods or rods from RK−/− mice raised in constant darkness. One day of constant light caused the rods in the RK−/− mouse retina to undergo apoptotic degeneration. Mice lacking RK provide a valuable model for the study of Oguchi disease, a human RK deficiency that causes congenital stationary night blindness.

The diversity and evolutionary relationships of the pregnancy-associated glycoproteins, an aspartic proteinase subfamily consisting of many trophoblast-expressed genes

The pregnancy-associated glycoproteins (PAGs) are structurally related to the pepsins, thought to be restricted to the hooved (ungulate) mammals and characterized by being expressed specifically in the outer epithelial cell layer (chorion/trophectoderm) of the placenta. At least some PAGs are catalytically inactive as proteinases, although each appears to possess a cleft capable of binding peptides. By cloning expressed genes from ovine and bovine placental cDNA libraries, by Southern genomic blotting, by screening genomic libraries, and by using PCR to amplify portions of PAG genes from genomic DNA, we estimate that cattle, sheep, and most probably all ruminant Artiodactyla possess many, possibly 100 or more, PAG genes, many of which are placentally expressed. The PAGs are highly diverse in sequence, with regions of hypervariability confined largely to surface-exposed loops. Nonsynonymous (replacement) mutations in the regions of the genes coding for these hypervariable loop segments have accumulated at a higher rate than synonymous (silent) mutations. Construction of distance phylograms, based on comparisons of PAG and related aspartic proteinase amino acid sequences, suggests that much diversification of the PAG genes occurred after the divergence of the Artiodactyla and Perissodactyla, but that at least one gene is represented outside the hooved species. The results also suggest that positive selection of duplicated genes has acted to provide considerable functional diversity among the PAGs, whose presence at the interface between the placenta and endometrium and in the maternal circulation indicates involvement in fetal–maternal interactions.