• Arithmetic operations in simply typed lambda calculus

  • May 4 2024
  • Length: 10 mins
  • Podcast

Arithmetic operations in simply typed lambda calculus

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  • Summary

  • It is maybe not so well known that arithmetic operations -- at least some of them -- can be implemented in simply typed lambda calculus (STLC). Church-encoded numbers can be given the simple type (A -> A) -> A -> A, for any simple type A. If we abbreviate that type as Nat_A, then addition and multiplication can both be typed in STLC, at type Nat_A -> Nat_A -> Nat_A. Interestingly, things change with exponentiation, which we will consider in the next episode.
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