true = λf.λx.f

false = λf.λx.x

not = λp.p false true

and = λp.λq.p q p

or = λp.λq.p p q

xor = λp.λq.p (not q) q

nand = λp.λq.(not (and p q))

nor = λp.λq.(not (or p q))

xnor = λp.λq.(not (xor p q))

mux = λp.λq.λs.(or (and p (not s)) (and q s))

impl = λp.λq.(or (not p) q)

if = λb.λt.λe.b t e

complement = λp.λb.(not (p b))

conjoin = λa.λb.λx.(and (a x) (b x))

disjoin = λa.λb.λx.(or (a x) (b x))

always = λx.true

never = λx.false