Elaboration in Dependent Type Theory

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary mathematical text, and resolving ambiguities in mathematical expressions. We refer to the process of passing from a quasi-formal and partially-specified expression to a completely precise formal one as elaboration. We describe an elaboration algorithm for dependent type theory that has been implemented in the Lean theorem prover. Lean's elaborator supports higher-order unification, type class inference, ad hoc overloading, insertion of coercions, the use of tactics, and the computational reduction of terms. The interactions between these components are subtle and complex, and the elaboration algorithm has been carefully designed to balance efficiency and usability. We describe the central design goals, and the means by which they are achieved

Elaborating Inductive Definitions

We present an elaboration of inductive definitions down to a universe of datatypes. The universe of datatypes is an internal presentation of strictly positive families within type theory. By elaborating an inductive definition -- a syntactic artifact -- to its code -- its semantics -- we obtain an internalized account of inductives inside the type theory itself: we claim that reasoning about inductive definitions could be carried in the type theory, not in the meta-theory as it is usually the case. Besides, we give a formal specification of that elaboration process. It is therefore amenable to formal reasoning too. We prove the soundness of our translation and hint at its correctness with respect to Coq's Inductive definitions. The practical benefits of this approach are numerous. For the type theorist, this is a small step toward bootstrapping, ie. implementing the inductive fragment in the type theory itself. For the programmer, this means better support for generic programming: we shall present a lightweight deriving mechanism, entirely definable by the programmer and therefore not requiring any extension to the type theory.Comment: 32 pages, technical repor

Dependent Types for Pragmatics

This paper proposes the use of dependent types for pragmatic phenomena such as pronoun binding and presupposition resolution as a type-theoretic alternative to formalisms such as Discourse Representation Theory and Dynamic Semantics.Comment: This version updates the paper for publication in LEU

Imaginary relish and exquisite torture: The elaborated intrusion theory of desire

The authors argue that human desire involves conscious cognition that has strong affective connotation and is potentially involved in the determination of appetitive behavior rather than being epiphenomenal to it. Intrusive thoughts about appetitive targets are triggered automatically by external or physiological cues and by cognitive associates. When intrusions elicit significant pleasure or relief, cognitive elaboration usually ensues. Elaboration competes with concurrent cognitive tasks through retrieval of target-related information and its retention in working memory. Sensory images are especially important products of intrusion and elaboration because they simulate the sensory and emotional qualities of target acquisition. Desire images are momentarily rewarding but amplify awareness of somatic and emotional deficits. Effects of desires on behavior are moderated by competing incentives, target availability, and skills. The theory provides a coherent account of existing data and suggests new directions for research and treatment

Conversion and verification procedure for goal-based control programs

Fault tolerance and safety verification of control systems are essential for the success of autonomous robotic systems. A control architecture called Mission Data System, developed at the Jet Propulsion Laboratory, takes a goal-based control approach. In this paper, a method for converting goal network control programs into linear hybrid systems is developed. The linear hybrid system can then be verified for safety in the presence of failures using existing symbolic model checkers. An example task is developed and successfully verified using HyTech, a symbolic model checking software for linear hybrid systems

The effectiveness of "Learning by doing" as a strategy that uses the elaboration of didactic material done by the learners

Tesis (Pedagogía en Inglés)Nowadays, the instruction of vocabulary on the acquisition and learning of English as a second language is important and it has been recognized as a relevant aspect by academics and theoreticians of the area. The aim of this study is to prove, through a concrete and an experimental form, the effectiveness of the constructivist strategy that uses the elaboration of didactic material as an improvement manner for the acquisition and learning of explicit vocabulary that, at the same time, may be meaningful to the pupils. The “Learning by Doing” strategy has been built under the perspective of the theory of constructivism, which has been adapted to be applied on two different educational establishments; both subsidized. The first school is located in El Belloto and the second school institution located in Villa Alemana. Accordingly, the thesis study was carried out on 5 different courses with a final average of 132 students. This inquiry has a quantitative nature with a quasi – experimental design that has as a sample a paired – dependent kind, which took into account the control subunits and the experimental subunits from each EFL (English as a Foreign Language) classroom where the strategy previously mentioned was conducted. As described on the previous paragraph, the results were analyzed using a mathematical – statistical type of measurement denominated “T – Test” table. These demonstrated that the constructivist strategy namely “Learning by Doing” improve the learning of explicit vocabulary on those grades belonging to the primary education. Nowadays, the instruction of vocabulary on the acquisition and learning of English as a second language is important and it has been recognized as a relevant aspect by academics and theoreticians of the area. The aim of this study is to prove, through a concrete and an experimental form, the effectiveness of the constructivist strategy that uses the elaboration of didactic material as an improvement manner for the acquisition and learning of explicit vocabulary that, at the same time, may be meaningful to the pupils. The “Learning by Doing” strategy has been built under the perspective of the theory of constructivism, which has been adapted to be applied on two different educational establishments; both subsidized. The first school is located in El Belloto and the second school institution located in Villa Alemana. Accordingly, the thesis study was carried out on 5 different courses with a final average of 132 students. This inquiry has a quantitative nature with a quasi – experimental design that has as a sample a paired – dependent kind, which took into account the control subunits and the experimental subunits from each EFL (English as a Foreign Language) classroom where the strategy previously mentioned was conducted. As described on the previous paragraph, the results were analyzed using a mathematical – statistical type of measurement denominated “T – Test” table. These demonstrated that the constructivist strategy namely “Learning by Doing” improve the learning of explicit vocabulary on those grades belonging to the primary education.En la actualidad, la instrucción del vocabulario es importante para la adquisición y aprendizaje del inglés como segunda lengua. Esto ha sido reconocido como un aspecto relevante por académicos y teóricos del área. El objetivo de esta investigación es probar a través de una forma concreta y experimental la efectividad de una estrategia que usa la elaboración de material didáctico como manera de mejorar la adquisición y el aprendizaje del vocabulario explícito, y que éste a su vez sea significativo para el alumno. La estrategia “Learning by Doing” ha sido construida bajo la perspectiva de la teoría del constructivismo, la cual ha sido adaptada para ser aplicada en dos establecimientos educacionales diferentes, ambos subvencionados. El primero situado en El Belloto y el segundo ubicado en Villa Alemana. Por consiguiente, esta investigación se realizó en 5 cursos diferentes con un promedio final de 132 alumnos. Esta investigación tiene una naturaleza cuantitativa con un diseño cuasi – experimental y tiene como muestra un tipo dependiente y pareado, la cual tomó en consideración las subunidades controles y las subunidades experimentales de cada clase “EFL” en donde la estrategia previamente mencionada fue llevada a cabo. Según lo descrito en el párrafo anterior, los resultados fueron analizados usando un tipo de medición matemático – estadística denominada tabla “T – Test”. Éstos demostraron que la estrategia constructivista nombrada “Learning by Doing” mejoró el aprendizaje de vocabulario explícito en aquellos cursos pertenecientes a la educación general básica. Sin embargo, el curso perteneciente a la enseñanza media no mostró ninguna señal de mejoramiento cuando la estrategia que usa la elaboración de material didáctico llegó a su fin