Dependent Types
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In computer science and logic, a dependent type is a Type system|type that depends on a value. Dependent types play a central role in intuitionistic type theory and in the design of functional programming languages like ATS (programming language)|ATS, Agda (theorem prover)|Agda and Epigram (programming language)|Epigram. An example is the type of n-tuples of real numbers. This is a dependent type because the type depends on the value n. Deciding equality of dependent types in a program may require computations. If arbitrary values are allowed in dependent types, then deciding type equality may involve deciding whether two arbitrary programs produce the same result; hence type checking may become Undecidable problem|undecidable. The Curry–Howard correspondence implies that types can be constructed that express arbitrarily complex mathematical properties. If the user can supply a constructive proof that a type is inhabited (i.e., that a value of that type exists) then a compiler can c...
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Type System    
Higher Order    
Polymorphism    
Indexation    
First Order    
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