Efficient execution in an automated reasoning environment

We describe a method that permits the user of a mechanized mathematical logic to write elegant logical definitions while allowing sound and efficient execution. In particular, the features supporting this method allow the user to install, in a logically sound way, alternative executable counterparts for logically defined functions. These alternatives are often much more efficient than the logically equivalent terms they replace. These features have been implemented in the ACL2 theorem prover, and we discuss several applications of the features in ACL2.Ministerio de Educación y Ciencia TIN2004–0388

Current transport versus continental inputs in the eastern Indian Ocean: Radiogenic isotope signatures of clay size sediments

Analyses of radiogenic neodymium (Nd), strontium (Sr), and lead (Pb) isotope compositions of clay-sized detrital sediments allow detailed tracing of source areas of sediment supply and present and past transport of particles by water masses in the eastern Indian Ocean. Isotope signatures in surface sediments range from −21.5 (ɛNd), 0.8299 (87Sr/86Sr), and 19.89 (206Pb/204Pb) off northwest Australia to +0.7 (ɛNd), 0.7069 (87Sr/86Sr), and 17.44 (206Pb/204Pb) southwest of Java. The radiogenic isotope signatures primarily reflect petrographic characteristics of the surrounding continental bedrocks but are also influenced by weathering-induced grain size effects of Pb and Sr isotope systems with superimposed features that are caused by current transport of clay-sized particles, as evidenced off Australia where a peculiar isotopic signature characterizes sediments underlying the southward flowing Leeuwin Current and the northward flowing West Australian Current (WAC). Gravity core FR10/95-GC17 off west Australia recorded a major isotopic change from Last Glacial Maximum values of −10 (ɛNd), 0.745 (87Sr/86Sr), and 18.8 (206Pb/204Pb) to Holocene values of −22 (ɛNd), 0.8 (87Sr/86Sr), and 19.3 (206Pb/204Pb), which documents major climatically driven changes of the WAC and in local riverine particle supply from Australia during the past 20 kyr. In contrast, gravity core FR10/95-GC5 located below the present-day pathway of the Indonesian throughflow (ITF) shows a much smaller isotopic variability, indicating a relatively stable ITF hydrography over most of the past 92 kyr. Only the surface sediments differ significantly in their isotopic composition, indicating substantial changes in erosional sources attributed to a change of the current regime during the past 5 kyr