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

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

moves call Return value Write value Acknowledge

[[ 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]]

[[ Γ | – skip : com]]

[[ Γ | – skip : com]]

[[ Γ | – skip : com]]

[[ Γ | – 16 : nat]]

[[ Γ | – 16 : nat]]

[[ Γ | – 16 : nat]]

– b : bool]] [[ Γ, b : bool |

– b : bool]] [[ Γ, b : bool |

– b : bool]] [[ Γ, b : bool |

– b : bool]] [[ Γ, b : bool |

– b : bool]] [[ Γ, b : bool |

– b : bool]] [[ Γ, b : bool |

– b : bool]] [[ Γ, b : bool |

[[ Γ | – while : bool→com →com]]

[[ Γ | – while : bool→com →com]]

[[ Γ | – while : bool→com →com]]

[[ Γ | – while : bool→com →com]]

[[ Γ | – while : bool→com →com]]

[[ Γ | – while : bool→com →com]]

[[ Γ | – while : bool→com →com]]

[[ Γ | – while : bool→com →com]]

[[ Γ | – while : bool→com →com]]

@ composition

Interaction model

[[ Γ, i:nat| – while i<16 : com→com]]