We present a method for the automatic generation of test cases for HOL formulae containing primitive recursive predicates. These test cases can be used for the animation of specifications as well as for black-box test...
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Regarding effectivity of functions on the reals, there have been several proposed models of analog, continuous-time computation, as opposed to the digital, discrete nature of the type-2 computability. We study one of ...
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We present an extension to the mathlib library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects o...
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We describe a technique for inducing recursive functional programs over algebraic datatypes from few non-recursive and only positive ground example-equations. Induction is data-driven and based on structural regularit...
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We describe a technique for inducing recursive functional programs over algebraic datatypes from few non-recursive and only positive ground example-equations. Induction is data-driven and based on structural regularities between example terms. In our approach, functional programs are represented as constructor term rewriting systems containing recursive rewrite rules. In addition to the examples for the target functions, background knowledge functions that may be called by the induced functions can be given in form of ground equations. Our algorithm induces several dependent recursive target functions over arbitrary user-defined algebraic datatypes in one step and automatically introduces auxiliary subfunctions if needed. We have implemented a prototype of the described method and applied it to a number of problems.
A formal language - the EP database is defined in this article. We prove that it is semantically equivalent to a class of total recursive functions. The conclusion serves as the theoretical foundation of Froglingo tha...
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ISBN:
(纸本)9781617820717
A formal language - the EP database is defined in this article. We prove that it is semantically equivalent to a class of total recursive functions. The conclusion serves as the theoretical foundation of Froglingo that consolidates the multi-component system architecture of the traditional software technologies into a single component. It also suggests how one might assess easy-of-use more objectively.
One usually defines the notion of a computable real number by using recursive functions. However, there is a simple way due to A. Mostowski to characterize the computable real numbers by using only primitive recursive...
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During the execution of functional logic programs, E-unification problems have to be solved quite frequently, where the underlying equational theory is induced by recursive functions. But, what about the decidability ...
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Whilst widely recognised as an excellent means for solving problems and for designing software, functional programming languages have suffered from their inefficient implementations on conventional computers. A route ...
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Algorithms defined as recursive functions, such as in "pure" LISP, are shown to have structure sufficient to dis- tinguish between processes which must be executed in sequence and processes which may be exec...
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Algorithms defined as recursive functions, such as in "pure" LISP, are shown to have structure sufficient to dis- tinguish between processes which must be executed in sequence and processes which may be executed in parallel. An interpreter program is presented for executing LISP programs and simultaneously computing the number of processors needed at each step of program execution in order to achieve optimum parallel processing. Sample program runs are presented to show speed-up ratios between strictly sequential and optimally parallel executions. A possible hardware organization for a parallel processing system derived from the interpreter program is presented.
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