Editing Typing rule (section)

{{short description|How a type system assigns a type to a syntactic construction}}

In [[type theory]], a '''typing rule''' is an [[inference rule]] that describes how a [[type system]] assigns a type to a [[Syntax (programming languages)|syntactic]] construction.<ref name="TAPL">{{cite book |last1=Pierce |first1=Benjamin C. |title=Types and Programming Languages |date=2002 |publisher=MIT Press |location=Cambridge, Mass. |isbn=0262162091 |edition=1st}}</ref>{{rp|94}} These rules may be applied by the type system to determine if a [[Computer program|program]] is well-typed and what type [[Expression (computer science)|expression]]s have.  A [[prototypical]] example of the use of typing rules is in defining [[type inference]] in the [[simply typed lambda calculus]], which is the [[internal language]] of [[Cartesian closed categories]].<ref>{{cite web |last1=Baez |first1=John |title=The n-Category Café |url=https://golem.ph.utexas.edu/category/2006/08/cartesian_closed_categories_an_1.html |website=golem.ph.utexas.edu |access-date=30 September 2022 |language=en}}</ref>