By abstracting over well-known properties of De Bruijn's representation with nameless dummies, we design a new theory of syntax with variable binding and capture-avoiding substitution. We propose it as a simpler alternative to Fiore, Plotkin, and Turi's approach, with which we establish a strong formal link. We also show that our theory easily incorporates simple types and equations between terms.

翻译：通过抽象德布鲁因表示法中无名占位符的已知性质，我们设计了一种新的语法理论，该理论支持变量绑定和避免捕获的替换。我们提出将其作为Fiore、Plotkin和Turi方法的更简单替代方案，并与之建立了严密的形式化联系。我们还证明，该理论能轻松融入简单类型及项之间的等式关系。