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==Typed lambda calculus==
A useful way to write complex functions is the [[lambda calculus]]. For example, one can write the meaning of ''sleeps'' as the following lambda expression, which is a function from an individual ''x'' to the proposition that ''x sleeps''.
::<math>\lambda x. \mathrm{sleep}'(x)</math>
Such lambda terms are functions whose ___domain is what precedes the period, and whose range are the type of thing that follows the period. If ''x'' is a variable that ranges over elements of <math>D_e</math>, then the following lambda term denotes the [[identity function]] on individuals:
::<math>\lambda x.x</math>
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