Computation as Simulation

It is useful to view computation as simulation, cf.: isomorphism of semigroups.[Preparata, F. P. and Yeh, R. T., Introduction to Discrete Structures, Addison-Wesley, 1973, p. 129.]

Given two semigroups G₁ = [S, °] and G₂ = [T, * ] , an invertible function φ : S → T is said to be an isomorphism between G₁ and G₂ if, for every a and b in S ,          φ (a ° b) = φ (a) * φ (b)

from which:          a ° b = φ ^-1 ( φ (a) * φ (b) )

(defun string+ (x y)
  (princ-to-string             ; phi inverse
    (+                         ; + in model space
       (read-from-string x)    ; phi 
       (read-from-string y)))) ; phi 

>(string+ "2" "3")
"5"