Definition:
An expression tree is a "tree structure that represents the phrase structure (meaning) of an algebraic / arithmetic expression." (ibid. p. 231)

• Graph Theory

• Two proofs of "eight plus three equals eleven"
  Note: the expression graph for this proof structure is not a tree.

• Two proofs of 1+1=2
  Expression trees of structure of these statements

  x+sy=s(x+y)
  1+sy=s(1+y)			x+0=x
  	1+s0=s(1+0)		1+0=1
  		1+s0=s1		s0=1
  			1+1=s1		s1=2
  				1+1=2