Type Directed Partial Evaluation for Level-1 Shift and Reset

We present an implementation in the Coq proof assistant of type directed partial evaluation (TDPE) algorithms for call-by-name and call-by-value versions of shift and reset delimited control operators, and in presence of strong sum types. We prove that the algorithm transforms well-typed programs to ones in normal form. These normal forms can not always be arrived at using the so far known equational theories. The typing system does not allow answer-type modification for function types and allows delimiters to be set on at most one atomic type. The semantic domain for evaluation is expressed in Constructive Type Theory as a dependently typed monadic structure combining Kripke models and continuation passing style translations.