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EPISODE · May 4, 2024 · 9 MIN

Arithmetic operations in simply typed lambda calculus

from Iowa Type Theory Commute · host Aaron Stump

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.

Episode metadata supplied by the publisher feed · Published May 4, 2024

What this episode covers

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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This episode was published on May 4, 2024.

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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...

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