Higher-orderness is first-order interaction

Yann Hamdaoui from Tweag published a blog article about semantics:

I think formal semantics are crucial to understanding programs. Game semantics seems like the best of both worlds of denotational semantics and operational semantics. It allows both abstract reasoning and enough precision to describe semantics exactly.

A more in-depth introduction to game semantics on my reading list are these lecture notes by Pierre-Louis Curien:

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If the terminology is changed:

  • player → program
  • opponent → outside world

then it starts to resemble something previously seen in Haskell: