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.