9- Algebraization of realizability

In the €rst parts of this thesis, we introduced several calculi for which we gave a Krivine realizability interpretation. Namely, in addition to Krivine’s λc -calculus, we presented interpretations for the callby-name, call-by-value and call-by-need λμμ̃-calculi, for dLt̂p and for dLPAω . Amongst others, we could cite Munch-Maccagnoni’s interpretation for System L [126], Lepigre’s interpretation for his callby-value calculus with a semantical value restriction [108], or Jaber’s interpretation of SECD machine code [80]. Since classical realizability interpretations provide powerful tools for computational analysis of programs, it naturally raises the question of knowing what is, in a calculus, the structure necessary to the de€nition of a classical realizability interpretation.