15-317 Constructive Logic
Lecture 24: Lax Logic

In this lecture we consider the problems that arise when trying to extend the Curry-Howard isomorphism between intuitionistic proofs and functional programs to include effects, such as input/output, mutable store, or exceptions. While it is difficult to describe these logically, at least we can isolate the effects so that statements we made previously about the connections between pure functions and intuitionistic reasoning continue to hold. Lax Logic provides a modality to achieve precisely this.

• Reading:
  • A Judgmental Reconstruction of Modal Logic, Sec 7-8
    Frank Pfenning and Rowan Davies, MSCS 11:511-540, 2001.
• Previous lecture: Linear Logic
• Next lecture: Authorization Logic
• Key concepts:
  • Computational effects
  • Pure computation
  • Potentially effect computation
  • Lax truth
  • Lax substitution principle

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Frank Pfenning