Intuitionistic proof transformations and their application to constructive program synthesis
We present a translation of intuitionistic sequent proofs from a multi-succedent calculus LTmc into a single-succedent calculus LT. The former gives a basis for automated proof search whereas the latter is better suited for proof presentation and program construction from proofs in a system for constructive program synthesis. Well-known translations from the literature have a severe drawback; they use cuts in order to establish the transformation with the undesired consequence that the resulting program term is not intuitive. We establish a transformation based on permutation of inferences and discuss the relevant properties with respect to proof complexity and program terms.
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