R. J. Back and J. von Wright. Structured derivations: A method for doing high-school mathematics carefully. Technical Report 246, Turku Centre for Computer Science, 1999. Home/Search Document Details and Download
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Isabelle/Isar - a versatile environment for human-readable formal .. - Wenzel (2002) (2 citations) (Correct)
....or inequalities, underline subexpressions to be replaced etc. then it is very likely that they are actually doing calculational reasoning. In fact, calculational reasoning has been occasionally proposed as simple means to rephrase mathematical proof into a slightly more formal setting (e.g. [Back and von Wright, 1999] [Back et al. 1997] although this does not necessarily include machine checking of proofs. Observing that logical equivalence and implication may be just as well used in calculations, some have even set out to do away with traditional natural deduction reasoning altogether (e.g. Dijkstra 145 ....
....reasoning o#ers a relatively simple conceptual basis to build tools for logical manipulations. For example, the popular Math pad tool supports transformations of algebraic expressions in a systematic way. Math pad has also acquired means for formal proof checking recently [Verhoeven and Backhouse, 1999], using PVS [Owre et al. 1996] as the backend. Presently, we cover quite general concepts of calculational reasoning within the Isar framework. We shall see how calculational reasoning may be expressed on top of existing Isar concepts in a very natural manner, and how it may be used in common ....
R. J. Back and J. von Wright. Structured derivations: A method for doing high-school mathematics carefully. Technical Report 246, Turku Centre for Computer Science, 1999.
Calculational Reasoning Revisited - An Isabelle/Isar experience - Bauer, Wenzel (2001) (1 citation) (Correct)
....of mixed equalities or inequalities, underline subexpressions to be replaced etc. then it is likely that they are doing calculational reasoning. In fact, calculational reasoning has been occasionally proposed as simple means to rephrase mathematical proof into a slightly more formal setting (e.g. [2, 1]) which does not necessarily include machine checking of proofs, of course. Observing that logical equivalence and implication may be just as well used in calculations, some have even set out to do away with traditional natural deduction style reasoning altogether [5] although that discipline ....
R. J. Back and J. von Wright. Structured derivations: A method for doing highschool mathematics carefully. Technical report, Turku Centre for C.S., 1999.
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