A Language of Patterns for Subterm Selection

This paper describes the language of patterns that equips the SSReflect proof shell extension for the Coq system. Patterns are used to focus proof commands on subexpressions of the conjecture under analysis in a declarative manner. They are designed to ease the writing of proof scripts and to increase their readability and maintainability. A pattern can identify the subexpression of interest approximating the subexpression itself, or its enclosing context or both. The user is free to choose the most convenient option. Patterns are matched following an extremely precise and predictable discipline, that is carefully designed to admit an efficient implementation. In this paper we report on the language of patterns, its matching algorithm and its usage in the formal library developed by the Mathematical Components team to support the verification of the Odd Order Theorem.