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Sometimes it it useful to be able to define a truly \emph{new} type
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Sometimes it it useful to be able to define a truly \emph{new} type
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that the typechecker will recognize as distinct from all other types.
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that the typechecker will recognize as distinct from all other types.
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For example, one might wish to define a type with internal invariants,
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For example, one might wish to define a type with internal invariants,
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or use a collection of data in a way is semantically different from
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or use a collection of data in a way that is semantically different from
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the default implementations of arithmetic or comparison. For
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the default implementations of arithmetic or comparison. For
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situations like this, where the programmer desires a lightweight
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situations like this, where the programmer desires a lightweight
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abstraction barrier, a \texttt{newtype} declaration allows the
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abstraction barrier, a \texttt{newtype} declaration allows the
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