lispy.el demo 2: the substitution model for procedure application

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Intro

Comes from this emacs.stackexchange question.

Task summary

Understand how this code works: 

(defun triangle-using-cond (number)
  (cond ((<= number 0) 0)
        ((= number 1) 1)
        ((> number 1)
         (+ number (triangle-using-cond (1- number))))))

I'll use The Substitution Model for Procedure Application from SICP.

Screencast

The screencast for this demo is here: https://www.youtube.com/watch?v=D7mK2q3yve4

Step-by-step expansion

step 1

Start with this code: 

(defun triangle-using-cond (number)
  (cond ((<= number 0) 0)
        ((= number 1) 1)
        ((> number 1)
         (+ number (triangle-using-cond (1- number))))))
(triangle-using-cond 4)

Eval the defun with e. Then do je to eval the next expression to get 10.

step 2

Press xfM to get: 

(cond ((<= 4 0)
       0)
      ((= 4 1)
       1)
      ((> 4 1)
       (+ 4 (triangle-using-cond (1- 4)))))

With e check that the result is still 10.

step 3

Evaluate the cond branches in your mind and simplify with qhrr. 

(+ 4 (triangle-using-cond (1- 4)))

Then ffxr. 

(+ 4 (triangle-using-cond 3))

step 4

Press xfM again: 

(+ 4 (cond ((<= 3 0)
              0)
             ((= 3 1)
              1)
             ((> 3 1)
              (+ 3 (triangle-using-cond (1- 3))))))

Evaluate the cond branches in your mind and simplify with qirr. 

(+ 4 (+ 3 (triangle-using-cond (1- 3))))

Simplify further with ffxr. 

(+ 4 (+ 3 (triangle-using-cond 2)))

step 5

Press xfM again: 

(+ 4 (+ 3 (cond ((<= 2 0)
                   0)
                  ((= 2 1)
                   1)
                  ((> 2 1)
                   (+ 2 (triangle-using-cond (1- 2)))))))

Evaluate the cond branches in your mind and simplify with qjrr. 

(+ 4 (+ 3 (+ 2 (triangle-using-cond (1- 2)))))

Simplify further with ffxr. 

(+ 4 (+ 3 (+ 2 (triangle-using-cond 1))))

step 6

Press xfM again: 

(+ 4 (+ 3 (+ 2 (cond ((<= 1 0)
                        0)
                       ((= 1 1)
                        1)
                       ((> 1 1)
                        (+ 1 (triangle-using-cond (1- 1))))))))

Evaluate the cond branches in your mind and simplify with akrr. 

(+ 4 (+ 3 (+ 2 1)))

C-e e to check that the result is still 10. That's it.