Theorem provers are tools that help users to write machine readable proofs. Some of this tools are also interactive. The need of such softwares is increasing since they provide proofs that are more certified than the hand written ones. Agda is based on type theory and on the propositions-as-types correspondence and has a Haskell-like syntax. This means that a proof of a statement is turned into a function. Inference systems are a way of defining inductive and coinductive predicates and induction and coinduction principles are provided to help proving their correctness with respect to a given specification in terms of soundness and completeness. Generalized inference systems deal with predicates whose inductive and coinductive interpretations do not provide the expected set of judgments. In this case inference systems are enriched by corules that are rules that can be applied at infinite depth in a proof tree. Induction and coinduction principles cannot be used in case of generalized inference systems and the bounded coinduction one has been proposed. We first present how Agda supports inductive and coinductive types highlighting the fact that data structures and predicates are defined using the same constructs. Then we move to the main topic of this thesis, which is investigating how generalized inference systems can be implemented and how their correctness can be proved.

中文翻译：

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Agda 中的灵活联合

定理证明器是帮助用户编写机器可读证明的工具。其中一些工具也是交互式的。对此类软件的需求正在增加，因为它们提供的证明比手写的证明更可靠。Agda 基于类型理论和命题作为类型的对应关系，并具有类似 Haskell 的语法。这意味着一个陈述的证明变成了一个函数。推理系统是定义归纳和合归纳谓词的一种方式，提供归纳和合归纳原则以帮助证明它们在合理性和完整性方面相对于给定规范的正确性。广义推理系统处理的谓词的归纳和合归纳解释不提供预期的判断集。在这种情况下，推理系统通过可在证明树中无限深度应用的规则来丰富。在广义推理系统的情况下不能使用归纳和联合归纳原理，并且已经提出了有界联合归纳。我们首先介绍 Agda 如何支持归纳和合归纳类型，强调数据结构和谓词使用相同的构造定义的事实。然后我们转到本论文的主要主题，即研究如何实现广义推理系统以及如何证明其正确性。我们首先介绍 Agda 如何支持归纳和合归纳类型，强调数据结构和谓词使用相同的构造定义的事实。然后我们转到本论文的主要主题，即研究如何实现广义推理系统以及如何证明其正确性。我们首先介绍 Agda 如何支持归纳和合归纳类型，强调数据结构和谓词使用相同的构造定义的事实。然后我们转到本论文的主要主题，即研究如何实现广义推理系统以及如何证明其正确性。