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This paper contains an interpretation of de Bruijn's name-free expression in $ mathrm{C} &-monoid. We show that certain construction of $ mathrm{C} $-monoid (Kleisli C-monoid) corresponds with the exp...ression of $ lambda $-calculus by de Bruijn's name-free expression. In particular, the procedure of substitution in de Bruijn's name-free expression, which is more accurate than that in calculus, is systematically characterized in $ mathrm{C} $-monoid.show more
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