
Generalizing inference systems by coaxioms
After surveying classical results, we introduce a generalized notion of ...
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Generating induction principles and subterm relations for inductive types using MetaCoq
We implement three Coq plugins regarding inductive types in MetaCoq. The...
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Memoryless Determinacy of Infinite Parity Games: Another Simple Proof
The memoryless determinacy of infinite parity games was proven independe...
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Transforming Proof Tableaux of Hoare Logic into Inference Sequences of Rewriting Induction
A proof tableau of Hoare logic is an annotated program with pre and pos...
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Coaxioms: flexible coinductive definitions by inference systems
We introduce a generalized notion of inference system to support more fl...
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A Simple Functional Presentation and an Inductive Correctness Proof of the Horn Algorithm
We present a recursive formulation of the Horn algorithm for deciding th...
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Removing Algebraic Data Types from Constrained Horn Clauses Using Difference Predicates
We address the problem of proving the satisfiability of Constrained Horn...
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Flexible Coinduction in Agda
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 propositionsastypes correspondence and has a Haskelllike 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.
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