typed lambda calculi造句

• There exist, however, typed lambda calculi that are not strongly normalizing.
• Product types can generally be considered " built-in " in typed lambda calculi via currying.
• Typed lambda calculi are foundational programming languages and are the base of typed functional programming languages such as imperative programming languages.
• The untyped lambda calculus is Turing-complete, but many typed lambda calculi, including System F, are not.
• System F can be seen as part of the lambda cube, together with even more expressive typed lambda calculi, including those with dependent types.
• Such typed lambda calculi derived from the Curry Howard paradigm led to software like Coq in which proofs seen as programs can be formalized, checked, and run.
• In proof theory, the relationship between classical mathematics and intuitionistic mathematics was clarified via tools such as the realizability method invented by Georg Kreisel and G鰀el's typed lambda calculi used in computer science.
• Typed lambda calculi are closely related to mathematical logic and proof theory via the Curry & ndash; Howard isomorphism and they can be considered as the internal language of classes of Cartesian closed categories ( CCCs ).
• Typed lambda calculi play an important role in the design of type systems for programming languages; here typability usually captures desirable properties of the program, e . g . the program will not cause a memory access violation.
• From a certain point of view, typed lambda calculi can be seen as 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 " a special case with only one type.