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Subject reduction : ウィキペディア英語版
Subject reduction
In type theory, a type system has the property of subject reduction (also subject evaluation, type preservation or simply preservation) if evaluation of expressions does not cause their type to change. Formally, if Γ ⊢ ''e''1 : ''τ'' and ''e''1 → ''e''2 then Γ ⊢ ''e''2 : ''τ''.
Together with progress, it is an important meta-theoretical property for establishing type soundness of a type system.
The opposite property, if Γ ⊢ ''e''2 : ''τ'' and ''e''1 → ''e''2 then Γ ⊢ ''e''1 : ''τ'', is called subject expansion. It often does not hold as evaluation can erase ill-typed sub-terms of an expression, resulting in a well-typed one.
== References ==

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抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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