Abstract. This paper proposes and analyses a monadic translation of an intuitionistic sequent calculus. The source of the translation is a typed λ-calculus previously introduced by the authors, corresponding to the intuitionistic fragment of the call-by-name variant of λµμ of Curien and Herbelin, and the target is a variant of Moggi's monadic meta-language, where the rewrite relation includes extra permutation rules that may be seen as variations of the "associativity" of bind (the Kleisli extension operation of the monad). The main result is that the monadic translation simulates reduction strictly, so that strong normalisation (which is enjoyed at the target, as we show) can be lifted from the target to the source. A variant translation, obtained by adding an extra monad application in the translation of types, still enjoys strict simulation, while requiring one fewer extra permutation rule from the target. Finally we instantiate, for the cases of the identity monad and the continuations monad, the meta-language into the simply-typed λ-calculus. By this means, we give a generic account of translations of sequent calculus into natural deduction, which encompasses the traditional mapping studied by Zucker and Pottinger, and CPS translations of intuitionistic sequent calculus.
In REF ) the intuitionistic fragment of cbn λµμ is the domain of a monadic translation into an intuitionistic monadic meta-language (resulting from the enrichment of Moggi's monadic meta-language with some permutative reduction rules); and that monadic translation is afterwards composed with an instantiation to the identity monad.
Monadic translation of intuitionistic sequent calculus
Types for Proofs and Programs
Types for Proofs and Programs
Computer Science