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the untyped lambda calculus, which is the primary subject of this article, in the sense that typed lambda calculi can express less than the untyped calculus.

The simply typed lambda calculus was originally introduced by Alonzo Church in 1940 as an attempt to avoid paradoxical uses of the untyped lambda calculus, and it exhibits many desirable and interesting properties.

One alternative is to remove type annotations entirely (so that the syntax is identical to the untyped lambda calculus), while ensuring that terms are well-typed via Hindley–Milner type inference.

In contrast, an untyped language, such as most assembly languages, allows any operation to be performed.

Racket project with the goal of allowing developers to migrate code from an untyped programming language to the same syntax enriched with a sound type system.

computational system that may be perceived as a reduced version of the untyped lambda calculus.

The pure untyped lambda calculus does not satisfy the strong normalization property, and.

refinements of the untyped lambda calculus, but from another point of view, they can also be considered the more fundamental theory and untyped lambda calculus.

In the untyped lambda calculus, all functions are higher-order; in a typed lambda calculus.

If no schema is in use, the node will be untyped, and the type of the resulting atomic value will be untypedAtomic.

Compare this to the syntax of untyped lambda calculus:e :: x \mid \lambda x.