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Dependent type: Quiz

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Question 1: If arbitrary values are allowed in dependent types, then deciding type equality may involve deciding whether two arbitrary programs produce the same result; hence ________ becomes undecidable.
Primitive data typeC (programming language)Type systemProgramming language

Question 2: The ________ implies that types can be constructed that express arbitrarily complex mathematical properties.
Type theoryCurry–Howard correspondenceFunctional programmingIntuitionistic logic

Question 3: The eight corners of the resulting cube-shaped diagram each correspond to a type system, with ________ in the least expressive corner, and calculus of constructions in the most expressive.
Simply typed lambda calculusAlonzo ChurchCurry–Howard correspondenceFixed point combinator

Question 4: Dependent types play a central role in intuitionistic type theory and in the design of experimental ________ like Dependent ML and Epigram.
Functional programmingImperative programmingDeclarative programmingProgramming paradigm

Question 5: Some recent research (Setzer 2007) has been directed at combining dependent type theory with ________.
Programming paradigmObject (computer science)Object-oriented programmingUnified Modeling Language

Question 6: The system λP of pure first order dependent types, corresponding to the logical framework LF, is obtained by generalising the function space type of the ________ to the dependent product type.
Fixed point combinatorSimply typed lambda calculusAlonzo ChurchCurry–Howard correspondence

Question 7: In ________ and logic, a dependent type is a type that depends on a value.
Computer scienceProgramming paradigmComputer programmingSoftware engineering







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