3. Full abstraction * abstract-machine Compositional * black-box Game semantics

4. players ‘p’ makes Program moves ‘o’ makes Context moves ‘O’ goes first

5. moves call Return value Write value Acknowledge

6. [[ Γ | all plays: all sequences of alternating observable moves that caN be made between M (played by ‘P’) and any legal context (played by ‘O’) –M: τ]]

7. [[ Γ | – skip : com]]

8. [[ Γ | – skip : com]]

9. [[ Γ | – skip : com]]

10. [[ Γ | – 16 : nat]]

11. [[ Γ | – 16 : nat]]

12. [[ Γ | – 16 : nat]]

13. – b : bool]] [[ Γ, b : bool |

14. – b : bool]] [[ Γ, b : bool |

15. – b : bool]] [[ Γ, b : bool |

16. – b : bool]] [[ Γ, b : bool |

17. – b : bool]] [[ Γ, b : bool |

18. – b : bool]] [[ Γ, b : bool |

19. – b : bool]] [[ Γ, b : bool |

20. [[ Γ | – while : bool→com →com]]

21. [[ Γ | – while : bool→com →com]]

22. [[ Γ | – while : bool→com →com]]

23. [[ Γ | – while : bool→com →com]]

24. [[ Γ | – while : bool→com →com]]

25. [[ Γ | – while : bool→com →com]]

26. [[ Γ | – while : bool→com →com]]

27. [[ Γ | – while : bool→com →com]]

28. [[ Γ | – while : bool→com →com]]

29. @ composition

30. Interaction model

31. [[ Γ, i:nat| – while i<16 : com→com]]