ACL2s: “The ACL2 Sedan”

AbstractACL2 is the latest inception of the Boyer-Moore theorem prover, the 2005 recipient of the ACM Software System Award. In the hands of experts it feels like a finely tuned race car, and it has been used to prove some of the most complex theorems ever proved about commercially designed systems. Unfortunately, ACL2 has a steep learning curve. Thus, novices tend have a very different experience: they crash and burn. As part of a project to make ACL2 and formal reasoning safe for the masses, we have developed ACL2s, the ACL2 sedan. ACL2s includes many features for streamlining the learning process that are not found in ACL2. In general, the goal is to develop a tool that is “self-teaching,” i.e., it should be possible for an undergraduate to sit down and play with it and learn how to program in ACL2 and how to reason about the programs she writes

Sr isotopes in arcs revisited: tracking slab dehydration using δ88/86Sr and 87Sr/86Sr systematics of arc lavas

Dehydration of the subducting slab is a crucial process in the generation of hydrous convergent margin magmas, yet the exact processes of how and where the slab dehydrates and how these fluids are transported to the mantle wedge remain obscure. Strontium is a “fluid-mobile” element and as such well suited to investigate the source of slab-derived fluids. We employ mass-dependent Sr isotope systematics (δ88/86Sr; the deviation in 88Sr/86Sr of a sample relative to NIST SRM 987) of primitive arc lavas, in tandem with conventional radiogenic 87Sr/86Sr measurements, as a novel tracer of slab dehydration. To characterise the δ88/86Sr composition of subduction zone inputs, we present new δ88/86Sr data for subducting sediments, altered oceanic crust and MORB. Calcareous sediments are isotopically lighter and carbonate-free sediments are isotopically heavier than mid-ocean ridge basalts (MORB). Samples of the altered oceanic crust display elevated 87Sr/86Sr but only the most intensely altered sample has significantly higher δ88/86Sr than pristine MORB. Mafic arc lavas from the Aegean and Mariana arc invariably have a mass-dependent Sr isotope composition that is indistinguishable from MORB and lower 87Sr/86Sr than upper altered oceanic crust. This δ88/86Sr-87Sr/86Sr signature of the arc lavas, in combination with their high but variable Sr/Nd, can only be explained if it is provided by a fluid that acquired its Sr isotope signature in the deeper, less altered part of the subducted oceanic crust. We propose a model where the breakdown of serpentinite in the slab mantle releases a pulse of fluid at sub-arc depths. These fluids travel through and equilibrate with the overlying oceanic crust and induce wet partial melting of the upper altered crust and sediments. This hydrous melt is then delivered to the mantle source of arc magmas as a single metasomatic component. From mass balance it follows that the slab-derived fluid contributes >70% of the Sr budget of both Mariana and Aegean arc lavas. Whereas this fluid-dominated character is unsurprising for the sediment-poor Mariana arc, the Aegean arc sees the subduction of 3–6 km of calcareous sediments that were found to exert very little control on the Sr budget of the arc magmas and are overwhelmed by the fluid contribution

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

Management of penetrating injuries of the upper extremities

Background: Routine surgical exploration after penetrating upper extremity trauma (PUET) to exclude arterial injury leads to a large number of negative explorations and iatrogenic injuries. Selective non-operative mana

Can we quantify sediment recycling in Italy's post-collisional subduction system?

Recycling of Earth's crustal components through subduction contributes to the observed geochemical heterogeneity in worldwide lavas, yet quantifying the in- and output fluxes is difficult because of the unknown compositions of subducted components and sediment transfer processes in subduction zones. Italian post-collisional magmatism is often mafic but potassiumrich, suggesting a significant contribution of subducted sediments in this complex geodynamic setting. Isotopic and elemental variability in the volcanic products across Italy likely reflects sediment recycling with variable composition and quantity from north to south. Here we report the geochemical compositions of sediments that accreted to the Apennine accretionary prism whose lateral counterparts have potentially subducted and contributed to the Italian melt source. The aim is to use the major-, trace- and Sr- Nd-Pb isotope compositions of the sediments and Italy's volcanic products to quantify subduction recycling through melt modelling. Sediments were collected from the northern-, central- and southern Apennines (Liguria, Emilia-Romagna, Umbria and Calabria) with a focus on exhumed units from below the various decollement levels. These included Triassic to Jurassic deep sea sediments in ophiolitic sequences deposited in the Ligurian- Piemonte Oceanic Basin, and Triassic to Neogene distal units of the Adria continental margin. End-member compositions are defined by deep sea clays and metapelites rich in K2O, SiO2, LILE, HFSE, REE with high 87Sr/86Sr (0.7458) and 206Pb/204Pb (19.4), and marls poor in K2O, SiO2, LILE, HFSE, REE, but rich in CaO and Sr, with low 87Sr/86Sr (0.7083) and 206Pb/204Pb (18.7). The geochemical compositions of the most primitive volcanics and olivine-hosted melt inclusions will be used to reconstruct subduction recycling processes by melt modelling of a sediment metasomatized mantle wedge. Sediment transport mechanisms, sediment/vein mineralogy, melting behavior, and melt extraction processes will be evaluated

Isotopic evolution of prehistoric magma sources of Mt. Etna, Sicily: Insights from the Valle Del Bove

Mount Etna in NE Sicily occupies an unusual tectonic position in the convergence zone between the African and Eurasian plates, near the Quaternary subduction-related Aeolian arc and above the down-going Ionian oceanic slab. Magmatic evolution broadly involves a transition from an early tholeiitic phase (~ 500 ka) to the current alkaline phase. Most geochemical investigations have focussed on either historic (> 130-years old) or recent (< 130-years old) eruptions of Mt. Etna or on the ancient basal lavas (ca. 500 ka). In this study, we have analysed and modelled the petrogenesis of alkalic lavas from the southern wall of the Valle del Bove, which represent a time span of Mt. Etna’s prehistoric magmatic activity from ~ 85 to ~ 4 ka. They exhibit geochemical variations that distinguish them as six separate lithostratigraphic and volcanic units. Isotopic data (143Nd/144Nd = 0.51283–0.51291; 87Sr/86Sr = 0.70332–0.70363; 176Hf/177Hf = 0.28288–0.28298; 206Pb/204Pb = 19.76–20.03) indicate changes in the magma source during the ~ 80 kyr of activity that do not follow the previously observed temporal trend. The oldest analysed Valle del Bove unit (Salifizio-1) erupted basaltic trachyandesites with variations in 143Nd/144Nd and 87Sr/86Sr ratios indicating a magma source remarkably similar to that of recent Etna eruptions, while four of the five subsequent units have isotopic compositions resembling those of historic Etna magmas. All five magma batches are considered to be derived from melting of a mixture of spinel lherzolite and pyroxenite (± garnet). In contrast, the sixth unit, the main Piano Provenzana formation (~ 42–30 ka), includes the most evolved trachyandesitic lavas (58–62 wt% SiO2) and exhibits notably lower 176Hf/177Hf, 143Nd/144Nd, and 206Pb/204Pb ratios than the other prehistoric Valle del Bove units. This isotopic signature has not yet been observed in any other samples from Mt. Etna and we suggest that the parental melts of the trachyandesites were derived predominantly from ancient pyroxenite in the mantle source of Etna