• The curious case of exponentiation in simply typed lambda calculus

  • May 4 2024
  • Length: 7 mins
  • Podcast

The curious case of exponentiation in simply typed lambda calculus

Listen for free

View show details

  • Summary

  • Like addition and multiplication on Church-encoded numbers, exponentiation can be assigned a type in simply typed lambda calculus (STLC). But surprisingly, the type is non-uniform. If we abbreviate (A -> A) -> A -> A as Nat_A, then exponentiation, which is defined as \ x . \ y . y x, can be assigned type Nat_A -> Nat_(A -> A) -> Nat_A. The second argument needs to have type at strictly higher order than the first argument. This has the fascinating consequence that we cannot define self-exponentiation, \ x . exp x x. That term would reduce to \ x . x x, which is provably not typable in STLC.

    Show More Show Less
Mathematics Science
Show More Show Less
activate_Holiday_promo_in_buybox_DT_T2
activate_samplebutton_t1

What listeners say about The curious case of exponentiation in simply typed lambda calculus

Average customer ratings

Reviews - Please select the tabs below to change the source of reviews.

Audible.co.uk reviews

Amazon reviews
No Reviews are Available