An example of how to define abstractions in Clojure

abstraction.clj

;; BinOp ::= [Symbol Operand Operand]
;; Operand ::= Number | BinaryOperation

(defprotocol Numerical
  "A thing which has a numerical value"
  (value [this]))

(defprotocol PrintableMathExpression
  "A mathematical expression which can be printed
  using infix or prefix notation"
  (prefix [this])
  (infix [this]))

(defrecord BinOp 
  [operator rand1 rand2]
  
  Numerical
  (value [this] ((eval (:operator this))
                 (value (:rand1 this))
                 (value (:rand2 this))))
  
  PrintableMathExpression
  (prefix [this]
          (list (:operator this)
                (prefix (:rand1 this))
                (prefix (:rand2 this))))
  
  (infix [this]
         (list (infix (:rand1 this))
               (:operator this)
               (infix (:rand2 this)))))

(defn binop 
  {:pre #(and (symbol? %1)
              (extends? Numerical %2)
              (extends? Numerical %3))}
  [rator rand1 rand2]
  (->BinOp rator rand1 rand2))

(extend-type Number
  Numerical    
  (value [this] this)
  
  PrintableMathExpression  
  (prefix [this] this)
  (infix [this] this))


;; Test what we have wrought!
(def expression (binop '+ 
                       (binop '* 7 8) 
                       (binop '/ 
                              100 
                              (binop '* 2 2))))

(prefix expression)
(infix expression)
(value expression)