We present a simple programming language based on G\"odel numbering and prime factorization, enhanced with explicit, scoped loops, allowing for easy program composition. Further, we will present a theorem prover that allows expressing and working with formal systems. The theorem prover is simple as it relies merely on a substitution rule and set equality to derive theorems. Finally, we will represent the programming language in the theorem prover. We will show the syntax and semantics of both, and then provide a few example programs and their evaluation.

翻译：我们展示了一种基于 G\“ odel 编号” 的简单编程语言, 并提供了一种基于 G\ “ odel 序号” 和 质因子化的简单编程语言, 用清晰的、 范围极广的环圈加以强化, 使得程序组成容易。 此外, 我们将展示一个允许表达和与正规系统合作的理论证明。 理论证明很简单, 因为它仅仅依赖替代规则, 并且设定了获得定理的平等 。 最后, 我们将在定理验证中代表编程语言 。 我们将展示两者的语法和语义, 然后提供几个示例程序及其评价 。