Internal models of system F for decompilation

This paper considers Girard’s internal coding of each term of System F by some term of a code type. This coding is the type-erasing coding definable already in the simply typed lambda-calculus using only abstraction on term variables. It is shown that there does not exist any decompiler for System F in System F, where the decompiler maps a term of System F to its code. An internal model of F is given by interpreting each type of F by some type equipped with maps between the type and the code type. This paper gives a decompiler–normalizer for this internal model in F, where the decompiler–normalizer maps any term of the internal model to the code of its normal form. It is also shown that for any model of F the composition of this internal model and the model produces another model of F whose equational theory is below untyped beta–eta-equality.