scholarly journals Theory Exploration Powered by Deductive Synthesis

Author(s):  
Eytan Singher ◽  
Shachar Itzhaky

AbstractThis paper presents a symbolic method for automatic theorem generation based on deductive inference. Many software verification and reasoning tasks require proving complex logical properties; coping with this complexity is generally done by declaring and proving relevant sub-properties. This gives rise to the challenge of discovering useful sub-properties that can assist the automated proof process. This is known as the theory exploration problem, and so far, predominant solutions that emerged rely on evaluation using concrete values. This limits the applicability of these theory exploration techniques to complex programs and properties.In this work, we introduce a new symbolic technique for theory exploration, capable of (offline) generation of a library of lemmas from a base set of inductive data types and recursive definitions. Our approach introduces a new method for using abstraction to overcome the above limitations, combining it with deductive synthesis to reason about abstract values. Our implementation has shown to find more lemmas than prior art, avoiding redundant lemmas (in terms of provability), while being faster in most cases. This new abstraction-based theory exploration method is a step toward applying theory exploration to software verification and synthesis.

1994 ◽  
Vol 4 (3) ◽  
pp. 371-394 ◽  
Author(s):  
Gérard Huet

AbstractWe present the complete development, in Gallina, of the residual theory of β-reduction in pure λ-calculus. The main result is the Prism Theorem, and its corollary Lévy's Cube Lemma, a strong form of the parallel-moves lemma, itself a key step towards the confluence theorem and its usual corollaries (Church-Rosser, uniqueness of normal forms). Gallina is the specification language of the Coq Proof Assistant (Dowek et al., 1991; Huet 1992b). It is a specific concrete syntax for its abstract framework, the Calculus of Inductive Constructions (Paulin-Mohring, 1993). It may be thought of as a smooth mixture of higher-order predicate calculus with recursive definitions, inductively defined data types and inductive predicate definitions reminiscent of logic programming. The development presented here was fully checked in the current distribution version Coq V5.8. We just state the lemmas in the order in which they are proved, omitting the proof justifications. The full transcript is available as a standard library in the distribution of Coq.


2018 ◽  
Author(s):  
Lea F. Buchweitz ◽  
James T. Yurkovich ◽  
Christoph M. Blessing ◽  
Veronika Kohler ◽  
Fabian Schwarzkopf ◽  
...  

ABSTRACTNew technologies have given rise to an abundance of -omics data, particularly metabolomics data. The scale of these data introduces new challenges for the interpretation and extraction of knowledge, requiring the development of new computational visualization methodologies. Here, we present a new method for the visualization of time-course metabolomics data within the context of metabolic network maps. We demonstrate the utility of this method by examining previously published data for two cellular systems—the human platelet and erythrocyte under cold storage for use in transfusion medicine.The results comprise two animated videos that allow for new insights into the metabolic state of both cell types. In the case study of the platelet metabolome during storage, the new visualization technique elucidates a nicotinamide accumulation which mirrors that of hypoxanthine and might, therefore, reflect similar pathway usage. This visual analysis provides a possible explanation for why the salvage reactions in purine metabolism exhibit lower activity during the first few days of the storage period. The second case study displays drastic changes in specific erythrocyte metabolite pools at different times during storage at different temperatures.In conclusion, this new visualization technique introduced in this article constitutes a well-suitable approach for large-scale network exploration and advances hypothesis generation. This method can be applied to any system with data and a metabolic map to promote visualization and understand physiology at the network level. More broadly, we hope that our approach will provide the blueprints for new visualizations of other longitudinal -omics data types.AUTHOR SUMMARYProfiling the dynamic state of a metabolic network through the use of time-course metabolomics technologies allows insights into cellular biochemistry. Interpreting these data together at the systems level provides challenges that can be addressed through the development of new visualization approaches. Here, we present a new method for the visualization of time-course metabolomics data that integrates data into an existing metabolic network map. In brief, the metabolomics data are visualized directly on a network map with dynamic elements (nodes that either change size, fill level, or color corresponding with the concentration) while the user controls the time series (i.e., which time point is being displayed) through a graphical interface. We provide short videos that illustrate the utility of this method through its application to existing data sets for the human platelet and erythrocyte. The results presented here give blueprints for the development of visualization methods for other time-course -omics data types that attempt to understand systems-level physiology.


Author(s):  
C. C. Clawson ◽  
L. W. Anderson ◽  
R. A. Good

Investigations which require electron microscope examination of a few specific areas of non-homogeneous tissues make random sampling of small blocks an inefficient and unrewarding procedure. Therefore, several investigators have devised methods which allow obtaining sample blocks for electron microscopy from region of tissue previously identified by light microscopy of present here techniques which make possible: 1) sampling tissue for electron microscopy from selected areas previously identified by light microscopy of relatively large pieces of tissue; 2) dehydration and embedding large numbers of individually identified blocks while keeping each one separate; 3) a new method of maintaining specific orientation of blocks during embedding; 4) special light microscopic staining or fluorescent procedures and electron microscopy on immediately adjacent small areas of tissue.


1960 ◽  
Vol 23 ◽  
pp. 227-232 ◽  
Author(s):  
P WEST ◽  
G LYLES
Keyword(s):  

Sign in / Sign up

Export Citation Format

Share Document