# How to find a lambda term to complete a function?

I tried to complete this exercise but i stopped… Defining a $$\lambda$$-term M such that: $$() \: \simeq_{\beta} \: $$

I chose $$M=\lambda m \lambda a \lambda b \lambda p \,((p)m)b \:$$ then i have to find a representation T of a function using M that value true if the sequence is empty and false if it’s not. A sequence is defined as: $$[]=\lambda x_0\lambda x_1 \lambda z z \ [b]=\lambda x_0 \lambda x_1 \lambda z (z) x_b\ [b_1 b_2]=\lambda x_0 \lambda x_1 \lambda z ((z)x_{b_1})x_{b_2} \ .\. \ . \ [b_1 .. b_n]= \lambda x_0 \lambda x_1 \lambda z (…((z) x_{b_1})x_{b_2}…)x_{b_n}$$ so the sequence of exercise is : $$[01101]= \lambda x_0 \lambda x_1 \lambda z (((((z)x_0)x_1)x_1)x_0)x_1$$ For example T need to be: $$(T)[01101] \simeq_{\beta}$$ false while $$(T) []\simeq_{\beta}$$ true. I really find that difficult. How i can do that?