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• W2964123418 abstract "The primary goal of this paper is to provide a way to reason abstractly in ACL2, while being able to specialise later. This kind of reasoning is necessary in the development of large modular proofs. Our main contribution is a macro, called instance-of-defspec, providing a convenient way to manipulate abstract functions and their properties. In our approach, w e build generic theorems, and use our macro to apply them on more specific instances, that is: reuse proof s. For this to work, we reuse functions as well, by instantiating generic functions with more specific ones. While both function- and proof reuse are possible to some extent in ACL2, we provide a single macro to do both in a way that is more convenient than the existing solutions. Aside from the theoretical example presented in our paper, we briefly discuss the use of our solution in the development of a generic theory of communication networks, called GENOC (10). This effort is a large and modular proof development of about fifty thousands lines of ACL2 code. Our macro already provides a thousand lines reduction of our code base. This paper uses monoid-operations and fold operations as leading examples. A monoid is simply a closed and associative operation with an identity element, for which we will write ◦ and 0 respectively. A fold operation is an operation that changes a list (a0... ak) into a value (a0◦···◦ak). The leading example is not of particular importance on its own, but used to illust rate the macro instance-of-defspec. Using the encapsulate environment, ACL2 provides a way to hide function definition s, while preserving certain function properties. We can then prove a theorem about such functions, using only the function properties in the proof. If we would then write a new function that satisfies all the properties used in the proof, we know that the function will satisfy the theorem as well. However, even though we know that the function satisfies the theorem, the only way to a ctually use this knowledge in further proofs is by telling it to ACL2 in the form of a new theorem. Using an uninterpreted function in the definition of a concrete function raises similar issues. We provide a macro called instance-of-defspec, that will allow ACL2 users to instantiate abstract functions while being able to use higher order theorems and functions." @default.
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• W2964123418 date "2013-04-01" @default.
• W2964123418 modified "2023-09-24" @default.
• W2964123418 title "A macro for reusing abstract functions and theorems" @default.
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