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pvs:libraries [2016/08/24 22:14] jonathan [Example Theory] |
pvs:libraries [2016/09/13 18:06] (current) jonathan |
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| ====== Reals ====== | ====== Reals ====== | ||
| - | Hypatheon is useful for browsing libraries. In the Prelude, we have real_axioms, reals and real_props. For example, in real_props we have the Lemma "both_sides_div_pos_neg_ge1" which allows us to divide both sides of an inequality ''x >= y'' by the same value ''n0z: VAR nonzero_real'': | + | Hypatheon is useful for browsing libraries. In the Prelude, we have |
| + | * real_axioms, | ||
| + | * reals | ||
| + | * real_props | ||
| + | * extra_real_props. | ||
| + | |||
| + | For example, in real_props we have the Lemma "both_sides_div_pos_neg_ge1" which allows us to divide both sides of an inequality ''x >= y'' by the same value ''n0z: VAR nonzero_real'': | ||
| <code> | <code> | ||
| Line 14: | Line 20: | ||
| There are also libraries of decision procedures such as | There are also libraries of decision procedures such as | ||
| - | * [[http://shemesh.larc.nasa.gov/people/cam/Sturm/|sturm]]: Sturm's Theorem is a well-known result in real algebraic geometry that provides a function that computes the number of roots of a univariate polynomial in a semi-open interval, and is included in the NASA PVS libraries. | + | * [[http://shemesh.larc.nasa.gov/people/cam/Sturm/|sturm]]: Sturm's Theorem is a well-known result in real algebraic geometry that provides a function that computes the number of roots of a univariate polynomial in a semi-open interval, and is included in the NASA PVS libraries. Strategy ''mono-poly'' automatically discharges monotinicity properties of polynomials on a real interval. |
| * [[http://shemesh.larc.nasa.gov/people/cam/Tarski/|tarski]].Tarski's Theorem is a generalization of Sturm's theorem that provides a linear relationship between functions known as Tarski queries and cardinalities of certain sets. It's also in the NASA library. | * [[http://shemesh.larc.nasa.gov/people/cam/Tarski/|tarski]].Tarski's Theorem is a generalization of Sturm's theorem that provides a linear relationship between functions known as Tarski queries and cardinalities of certain sets. It's also in the NASA library. | ||
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| IMPORTING Sturm@strategies | IMPORTING Sturm@strategies | ||
| IMPORTING Tarski@strategies | IMPORTING Tarski@strategies | ||
| - | (Tarski is heavy so wait for it to load and finish). | + | (Tarski is heavy so wait for it to load and finish). Note that the ''(eval-formula)'' from PVSio can also be used to prove the D2 example. |
| ===== Example Theory ===== | ===== Example Theory ===== | ||
| - | <file text logic.text> | + | <file text real.pvs> |
| - | logic : THEORY | + | real : THEORY |
| BEGIN | BEGIN | ||
| %(sturm) and (mono-poly) incorporate some nice decision procedures | %(sturm) and (mono-poly) incorporate some nice decision procedures | ||
| Line 77: | Line 83: | ||
| - | END logic | + | END real |
| - | </code> | + | </file> |
| <code> | <code> | ||
| - | Proof summary for theory logic | + | Proof summary for theory real |
| conja1................................proved - complete [shostak](0.06 s) | conja1................................proved - complete [shostak](0.06 s) | ||
| conja2................................proved - complete [shostak](0.39 s) | conja2................................proved - complete [shostak](0.39 s) | ||
| Line 96: | Line 102: | ||
| Grand Totals: 10 proofs, 10 attempted, 9 succeeded (1.81 s) | Grand Totals: 10 proofs, 10 attempted, 9 succeeded (1.81 s) | ||
| </code> | </code> | ||
| - | |||
pvs/libraries.1472076864.txt.gz · Last modified: 2016/08/24 22:14 by jonathan
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