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Proof Logic : A logical framework for theorem proving
Proof Logic is a functional and equational logical framework for theorem proving based on Combinatory Logic and LambdaCalculus, whose expressions are both terms and proofs proving the equality between two terms.
Symbolic LambdaCalculus is a logical formalism based on lambdacalculus and combinatory logic, in which there is only one kind of objects, which can represent either terms or equalities. It uses de Bruijn's and lambdacalculus notations.