Full Abstraction for Reduced ML

Abstract

Abstract. We present the first effectively presentable fully abstract model for Stark's Reduced ML, the paradigmatic higher-order programming language combining call-by-value evaluation and integer-valued references. The model is constructed using techniques of nominal game semantics. Its distinctive feature is the presence of carefully restricted information about the store in plays, combined with conditions concerning the participants' ability to distinguish reference names. This leads to an explicit characterization of program equivalence.

Full abstraction for nominal general references

“…By constructing models for more nominal languages we better understand the essential features of nominal computation (e.g. name-availability [31]) and build stronger intuitions on nominal games. Another direction for further research is that of characterising the nominal effect -i.e.…”

“…higher-order store). Moreover, frugality alone is not enough for languages like Reduced ML or the ν-calculus: a name may have been used in a play but may still be inaccessible to some participant (that is, if it is outside his view [31]). On the other hand, our approach is advantageous in its simplicity and its applicability on a wide rage of nominal effects (see [48]), but suffers from the accuracy issues discussed above.…”

Algorithmic Games for Full Ground References

“…But, by frugality, the latter are reachable from the indices of available registers and therefore S 11 = S 21 , modulo permutation of fresh indices. Thus, ν 22 . By strong determinacy we get q 1 = q 2 and thuŝ…”

Isomorphisms of Types in the Presence of Higher-Order References

“…We chose to include bad variables in the language we consider for two reasons. Firstly, the games models that allow bad variables are notably simpler than those which do not [24], for which our methods do not directly apply. Secondly, the impact of allowing bad variables on our result will be reduced by the following proposition: To see how, we consider an extension L + of L + where we add a type constructor gvar for good variables, so that L + has both types var for bad variables and gvar for good variables.…”