Fred:An Approach to Generating Real, Correct, Reusable Programs from Proofs

In this paper we describe our system for automatically extracting "correct" programs from proofs using a development of the Curry-Howard process. Although program extraction has been developed by many authors (see, for example, [HN88], [Con97] and [HKPM97]), our system has a number of novel features designed to make it very easy to use and as close as possible to ordinary mathematical terminology and practice. These features include 1. the use of Henkin's technique [Hen50] to reduce higher-order logic to many-sorted (first-order) logic; 2. the free use of new rules for induction subject to certain conditions; 3. the extensive use of previously programmed (total, recursive) functions; 4. the use of templates to make the reasoning much closer to normal mathematical proofs and 5. a conceptual distinction between the computational type theory (for representing programs) and the logical type theory (for reasoning about programs). As an example of our system we give a constructive proof of the well known theorem that every graph of even parity, which is non-trivial in the sense that it does not consist of isolated vertices, has a cycle. Given such a graph as input, the extracted program produces a cycle as promised

Kajian Lebar Retak Balok Beton Akibat Penggunaan Tulangan Aluminium Paduan

The use of concrete structures in a corrosive environment requires a minimum concrete cover thickness of 50 mm.Tthick concrete cover is certainly very risky occurrence of spalling which result in reduced capacity of the cross section of the structure. For this study utilizes the aluminum alloy material as additional reinforcement bars that fill a third of thick concrete cover, where the aluminum has properties that are resistant to corrosion. The purpose of this study to obtain the contribution of aluminum alloy in the capacity of the concrete beam section and a wide crack that occurs without using reinforcement rebars. This study uses five pieces of beam specimen dimensions of 300 mm x 150 mm and a span length of 1600 mm. The beam using materials mortar, concrete and 13 mm diameters of aluminum alloy that were tested for bending strength. As for each of the aluminum ratio of 0% (B0); 0.34% (B1); 0.68% (B2); 1.02% (B3) and 1.36% (B4). Testing method requiring a single point of loading. The results showed that the load capacity of the test specimen when the first crack in the beam but not significantly increased with increasing amount of aluminum, which is equal to 1 times, 1,002 times, 1.01 times, 1.03 times and 1.07 times the beam ratio aluminum 0%. The maximum load capacity has increased along with increasing the number of aluminum, which is equal to 1 times, 1.64 times, 2.95 times, 4.00 times and 5.17 times its maximum capacity aluminum beam ratio of 0%. Rated maximum bending stress concrete (FCR) are eligible crack width 0.4 mm when conditions permit loading is an aluminum beam with a ratio of 0.68%; 1.02%; 1.36% 3.81 MPa; 3.89 MPa; 4.02 MPa

Lifetime Lamb and Wool Production of Targhee or Finn-Dorset-Targhee Ewes Managed as a Farm or Range Flock

Improving the reproductive rate of the ewe flock offers one of the greatest single opportunities for increasing the efficiency of lamb production. Combining ewe breeds that have specific strengths should result in a more productive ewe. Crossing Finnsheep, known for high prolificacy, with the Dorset, known for milking ability and meat conformation, and the Targhee, known for hardiness and wool production, should result in a highly productive ewe. This study was designed to compare the lifetime lamb and wool production of 1/4 Finn 1/4 Dorset-Yl Targhee (FDT) ewes to straightbred Targhee (T) ewes under a farm or range production system

Effect of Gliricidia sepium leaves and molases inclusion on aerobic stability, value and digestibility of Napier grass silage

Most tropical roughage feeds are generally deficient in nitrogen, energy or some minerals and vitamins. A study was conducted to evaluate the effect of adding Gliricidia (Gliricidia sepium) leaves and molasses to Napier grass (Pennisetum purpureum) silage. Silage were prepared from Napier grass and mixed with Gliricidia and molasses. There were four treatments involved which were NG, containing Napier grass only which was the experiment control, GS containing Napier grass mixed with 5% Gliricidia leaves, ML containing the Napier grass mixed with 5% molasses, and MG containing Napier grass mixed with 5% molasses and 5% Gliricidia leaves. The treatments were analyzed for aerobic stability, dry matter (DM), crude protein (CP), neutral detergent fibre (NDF), acid detergent fibre (ADF), acid detergent lignin (ADL), and digestibility. There were no significant differences in aerobic stability of silage between treatments, and the treatments with Gliricidia were higher in crude protein (p<0.05) and had better digestibility (p<0.05) when compared to the control. In conclusion, Gliricidia leaves as additives to Napier grass silage can improve its nutritive value and quality