• The curious case of exponentiation in simply typed lambda calculus

  • May 4 2024
  • Duración: 7 m
  • Podcast

The curious case of exponentiation in simply typed lambda calculus

Escúchala gratis

Ver detalles del espectáculo

  • Resumen

  • 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.

    Más Menos
Matemáticas Ciencia
Más Menos

Lo que los oyentes dicen sobre The curious case of exponentiation in simply typed lambda calculus

Calificaciones medias de los clientes

Reseñas - Selecciona las pestañas a continuación para cambiar el origen de las reseñas.

Reseñas de Audible.com

Opiniones de Amazon
No hay comentarios disponibles