We describe a compositional approach to Craig interpolation based on the heuristic that simpler proofs of special cases are more likely to generalize. The method produces simple interpolants because it is able to summarize a large set of cases using one relatively simple fact. In particular, we present a method for finding such simple facts in the theory of linear rational arithmetic. This make...

Abstract Beautiful and expressive documents often require beautiful and expressive graphics. PGF and its front-end TikZ walk a thin line between power, portability and usability, giving a TEX-like approach to graphics. While PGF and TikZ are extensively documented, first-time users may prefer learning about these packages using a collection of graduated examples. The examples presented here cov...

Beautiful and expressive documents often require beautiful and expressive graphics. PGF and its front-end TikZ walk a fine line between power, portability and usability, giving a TEX-like approach to graphics. While PGF and TikZ are extensively documented, first-time users may prefer learning about these packages using a collection of graduated examples. The examples presented here cover a wide...

purpose: to estimate the magnitude and causes of visual impairment (vi) in subjects aged ≥ 50 years in varamin district in 2009 using the proposed method by the world health organization (who). method: this cross sectional population based survey was performed in varamin targeting people over the age of 50 years using the proportional probabilities to size and cluster compact segment sampling m...