Free-Style Theorem Proving
We propose a new proof language based on well-known existing styles such as procedural and declarative styles but also using terms as proofs, a specific feature of theorem provers based on the Curry-Howard isomorphism. We show that these three styles are really appropriate for specific domains and how it can be worth combining them to benefit from their advantages in every kind of proof. Thus, we present, in the context of the Coq proof system, a language, called Lpdt, which is intended to make a fusion between these three styles and which allows the user to be much more free in the way of building his/her proofs. We provide also a formal semantics of Lpdt for the Calculus of Inductive Constructions, as well as an implementation with a prototype for Coq, which can already run some relevant examples.
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