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- W3022927208 abstract "Publisher SummaryThis chapter explains the use of function definitions. As a function definition is just an equation, there is in principle no difference between using function definitions and using other equality theorems. The chapter discusses non-recursive functions, computing values, and recursive and non-recursive expansions. If there is a function call of f and f is non-recursive, it is clear that expanding its definition is safe in the sense that it will not lead to infinite loops. The function f is called an explicit value preserving if and only if, f is TRUE, FALSE, IF, EQUAL, one of the functions introduced by the shell principle, or f was defined under the principle of definition and the body of f calls only f or explicit value-preserving functions. Making intelligent decisions about whether to use a definition is crucial to proving theorems in a theory with a definition principle (be it a recursive one or not). Unnecessary expansion of definitions will swamp a theorem-prover (mechanical or otherwise) with irrelevant detail. Failure to expand a definition can prevent a proof from being found at all. This chapter highlights three heuristics that are useful to know while considering whether to expand a recursive definition. The heuristics are non-recursive functions, computing values, and diving in to see." @default.
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- W3022927208 date "1979-01-01" @default.
- W3022927208 modified "2023-09-28" @default.
- W3022927208 title "Using Definitions" @default.
- W3022927208 doi "https://doi.org/10.1016/b978-0-12-122950-4.50012-7" @default.
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