Solving Equations

Simple equations can be solved by search, using rules of algebra to transform equations into equivalent forms until an equation for the desired variable is produced.

We will think of the same data structure in several ways:

• Equation: y = m · x + b
• List structure: (= Y (+ (* M X) B))
  or ( op lhs rhs ) recursively

• Tree:

  (3,3) (0.2,0.2) (0,0)M (1.0,1.0) (0,0)* (1.8,0.2) (0,0)X (2.6,1.0) (0,0)B (1.8,1.8) (0,0)+ (1.0,2.6) (0,0)= (0.2,1.8) (0,0)Y (4.8,1.8) (0,0) rhs (4.0,2.6) (0,0) op (3.2,1.8) (0,0) lhs (4.1,2.5) (1,-1)0.6 (3.3,1.9) (1,1)0.6 (0.3,0.3) (1,1)0.6 (1.1,1.1) (1,1)0.6 (0.3,1.9) (1,1)0.6 (1.1,2.5) (1,-1)0.6 (1.9,1.7) (1,-1)0.6 (1.1,0.9) (1,-1)0.6

• Executable code: eval can evaluate an expression using a set of variable bindings.