Examples of using Type theory in English and their translations into Chinese
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Main article: Type theory.
Type theory, basis for the study of type systems.
Also, this personality type theory is interesting.
What type theory will replace quantum theory and relativity?
The intersection of logic and type theory is a vast and active research area.
The design and study of type systems is known as type theory.
Anyway, enough type theory, let's check out some generic code.
Some of the systems included in the cube were first defined in Automath.Homotopy type theory.
In type theory lingo, it's called the empty type, because it has no values.
Any complete type, like i32, bool,or char is of kind*(this notation comes from the field of type theory).
In the context of type theory, such structures are called product types.
What's more, the constructivist mathematics that descended from Brouwer'sideas proved vital in the subsequent development of type theory.
Type theory has a natural deduction presentation in terms of formation, introduction and elimination rules;
If every program can be reduced to a canonical form,then the type theory is said to be normalising(or weakly normalising).
Like logic, type theory has many extensions and variants, including first-order and higher-order versions.
When you're designing a language with a sophisticated type system,it really helps a lot if you actually know something about type theory.
The difference between logic and type theory is primarily a shift of focus from the types(propositions) to the programs(proofs).
Seen as a programming language, Coq implements a dependently typed functional programming language, while seen as a logical system,it implements a higher-order type theory.
An important result in computer science and type theory is that a type system corresponds to a particular logic system.
In type theory, the type of functions accepting values of type A and returning values of type B may be written as A→ B or BA.
In computer programming, especially functional programming and type theory, an algebraic data type is a kind of composite type, i.
Modern type theory was invented partly in response to Russell's paradox, and features prominently in Russell and Whitehead's Principia Mathematica.
Simply typed lambda calculus which is a higher-order logic; intuitionistic type theory; system F;LF is often used to define other type theories; calculus of constructions and its derivatives.
Dependent type theory in full generality is very powerful: it is able to express almost any conceivable property of programs directly in the types of the program.
In the 1980s, Per Martin-Löf developed intuitionistic type theory(also called constructive type theory), which associated functional programs with constructive proofs expressed as dependent types. .
Subtyping in type theory is characterized by the fact that any expression of type A may also be given type B if A<: B; the formal typing rule that codifies this is known as the subsumption rule.
In programming languages and type theory, polymorphism is the provision of a single interface to entities of different types. .
Martin-Löf's intuitionistic type theory developed the notion of dependent types and directly influenced the development of the calculus of constructions and the logical framework LF.
IF is often used to define other type theories;
Normalisability is a rare feature of most non-trivial type theories, which is a big departure from the logical world.