head { cons p q }
=  lambda c {$c {lambda {x y} {$x}} } { cons p q }
by variable substitution and list reduction of the first element
-> cons p q {lambda {x y} {$x}}
by currying and lambda reduction and list reduction of the first element
=  lambda {a b f} {$f $a $b} p q {lambda {x y} {$x}}
by variable substitution and list reduction of the first element
-> lambda {b f } { $f p $b } q {lambda {x y} {$x}}
by currying
-> lambda f {$f p q} {lambda {x y} {$x}}
by currying
-> lambda {x y} {$x} p q        
by currying and lambda reduction and list reduction of the first element
-> lambda {y} {p} q
by currying
-> p
by currying and lambda reduction and list reduction of the first element