Top-down synthesis of divide-and-conquer algorithms
Artificial Intelligence
Principles of artificial intelligence
Principles of artificial intelligence
Derived Preconditions and Their Use in Program Synthesis
Proceedings of the 6th Conference on Automated Deduction
On automating the construction of programs.
On automating the construction of programs.
A strong restriction of the inductive completion procedure
Journal of Symbolic Computation
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Reasoning by cases, a natural feature of human reasoning, has been difficult to formulate so that it can be performed naturally when needed. Several difficulties arise: (1) how to motivate the use of reasoning by cases when and only when needed, (2) how to determine an appropriate analysis of the goal into cases, and (3) how to carry out the deduction in each case and combine the results. In this paper we focus on how reasoning by cases can be naturally accomplished in the framework of derived antecedents (Smith 1982). Our main technical contributions are (1) a set of strategies that draw on the context of a deduction to provide an appropriate case analysis for a goal, and (2) inference rules for carrying out reasoning by cases and forming conditional terms for the existentially quantified variables in the initial goal.