| 41. | In contrast in intensional type theory type checking is integer numbers, rational numbers, and real numbers.
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| 42. | The simplest way I can imagine having an expanding multiverse would be with a bubble universe type theory.
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| 43. | The type theory has a number of " type formers " and 4 kinds rules for each one.
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| 44. | They may also use formal logics that are stronger than first-order logic, such as type theory.
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| 45. | The common usage of " type theory " is when those types are used with a term rewrite system.
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| 46. | Multiple type theories are supported by Mizar is an example of a proof system that only supports set theory.
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| 47. | Induction-Recursion came out of investigations to the rules of Martin-L�f's intuitionistic type theory.
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| 48. | There is an element of U for every type in the type theory ( except U itself ! ).
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| 49. | Dependent types play a central role in intuitionistic type theory and in the design of functional programming languages like Epigram.
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| 50. | Type theory extends this identification to predicate logic by introducing dependent types, that is, types that contain values.
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