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Nested General Recursion and Partiality in Type Theory
 Theorem Proving in Higher Order Logics: 14th International Conference, TPHOLs 2001, volume 2152 of Lecture Notes in Computer Science
, 2000
"... We extend Bove's technique for formalising simple general recursive algorithms in constructive type theory to nested recursive algorithms. The method consists in defining an inductive specialpurpose accessibility predicate, that characterises the inputs on which the algorithm terminates. As a resul ..."
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Cited by 24 (10 self)
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We extend Bove's technique for formalising simple general recursive algorithms in constructive type theory to nested recursive algorithms. The method consists in defining an inductive specialpurpose accessibility predicate, that characterises the inputs on which the algorithm terminates. As a result, the typetheoretic version of the algorithm can be defined by structural recursion on the proof that the input values satisfy this predicate. This technique results in definitions in which the computational and logical parts are clearly separated; hence, the typetheoretic version of the algorithm is given by its purely functional content, similarly to the corresponding program in a functional programming language. In the case of nested recursion, the special predicate and the typetheoretic algorithm must be defined simultaneously, because they depend on each other. This kind of definitions is not allowed in ordinary type theory, but it is provided in type theories extended wit...
Hidden Verification for Computational Mathematics
"... We present hidden verification as a means to make the power of computational logic available to users of computer algebra systems while shielding them fi'om its complexity. We have implemented in PVS a library of facts about elementary and transcendental functions, and automatic procedures to at ..."
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Cited by 1 (1 self)
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We present hidden verification as a means to make the power of computational logic available to users of computer algebra systems while shielding them fi'om its complexity. We have implemented in PVS a library of facts about elementary and transcendental functions, and automatic procedures to attempt proofs of continuity, convergence and differentiability for functions in this class. These are called directly from Maple by a simple pipelined interface. Hence we are able to support the analysis of differential equations in Maple by direct calls to PVS for: result refinement and verification, discharge of verification conditions, harnesses to ensure more reliable differential equation solvers, and verifiable lookup tables.
Digital Look Up Tables and Real Number Theorem Proving
, 2001
"... We consider the utility of digital look up tables, as adjuncts/helpers to computer algebra systems. The requirements for dealing with logical side conditions raised by such tables are considered and proposals for using theorem proving technology as black box aids are considered. In addition, the ..."
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Cited by 1 (0 self)
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We consider the utility of digital look up tables, as adjuncts/helpers to computer algebra systems. The requirements for dealing with logical side conditions raised by such tables are considered and proposals for using theorem proving technology as black box aids are considered. In addition, the use of real number theorem proving libraries to support validation of table entries is also presented.