The **simply typed lambda calculus**, a form of type theory, is a typed interpretation of the lambda calculus with only one type constructor: that builds function types. It is the canonical and simplest example of a typed lambda 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.

The term *simple type* is also used to refer to extensions of the simply typed lambda calculus such as products, coproducts or natural numbers (System T) or even full recursion (like PCF). In contrast, systems which introduce polymorphic types (like System F) or dependent types (like the Logical Framework) are not considered *simply typed*. The former are still considered *simple* because the Church encodings of such structures can be done using only and suitable type variables, while polymorphism and dependency cannot.

Read more about Simply Typed Lambda Calculus: Syntax, Typing Rules, Alternative Syntaxes, General Observations, Important Results

### Other articles related to "simply typed lambda calculus, lambda":

**Simply Typed Lambda Calculus**- Important Results

... the elements of a model which are definable by

**lambda**terms ... with varying arity) exactly characterizes

**lambda**definability ... is decidable whether a given element of a model generated from finite sets is definable by a

**lambda**term (Plotkin-Statman-conjecture) ...

### Famous quotes containing the words calculus and/or simply:

“I try to make a rough music, a dance of the mind, a *calculus* of the emotions, a driving beat of praise out of the pain and mystery that surround me and become me. My poems are meant to make your mind get up and shout.”

—Judith Johnson Sherwin (b. 1936)

“There are very many people who read *simply* to prevent themselves from thinking.”

—G.C. (Georg Christoph)