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 (+ 21 )))
C-e e to check that the result is still 10
. That's it.