![](/assets/artwork/1x1-42817eea7ade52607a760cbee00d1495.gif)
7 min
![](/assets/artwork/1x1-42817eea7ade52607a760cbee00d1495.gif)
The curious case of exponentiation in simply typed lambda calculus Iowa Type Theory Commute
-
- Teknologi
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 con...
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 con...
7 min