#+TITLE: lispy.el demo 2: the substitution model for procedure application
#+LANGUAGE: en
#+OPTIONS: H:3 num:nil toc:nil
#+HTML_HEAD:
| [[https://github.com/abo-abo/lispy][Back to github]] | [[https://raw.githubusercontent.com/abo-abo/lispy/gh-pages/demo-2.org][This file in org-mode]] | [[http://abo-abo.github.io/lispy/][Function reference]] |
* Setup :noexport:
#+begin_src emacs-lisp :exports results :results silent
(defun make-html-cursor--replace (x)
(if (string= "||\n" x)
" \n"
(if (string= "||[" x)
"["
(format "%s"
(regexp-quote
(substring x 2))))))
(defun make-html-cursor (str x y)
(replace-regexp-in-string
"||\\(.\\|\n\\)"
#'make-html-cursor--replace
str))
(setq org-export-filter-src-block-functions '(make-html-cursor))
(setq org-html-validation-link nil)
(setq org-html-postamble nil)
(setq org-html-preamble "")
(setq org-html-text-markup-alist
'((bold . "%s")
(code . "%s")
(italic . "%s")
(strike-through . "%s")
(underline . "%s")
(verbatim . "%s")))
(setq org-html-style-default nil)
(setq org-html-head-include-scripts nil)
#+end_src
* Intro
Comes from [[http://emacs.stackexchange.com/questions/3203/how-to-understand-this-recursion-code][this emacs.stackexchange question]].
* Task summary
Understand how this code works:
#+begin_src emacs-lisp
(defun triangle-using-cond (number)
(cond ((<= number 0) 0)
((= number 1) 1)
((> number 1)
(+ number (triangle-using-cond (1- number))))))
#+end_src
I'll use [[http://mitpress.mit.edu/sicp/full-text/book/book-Z-H-10.html#%25_sec_1.1.5][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:
#+begin_src emacs-lisp
||(defun triangle-using-cond (number)
(cond ((<= number 0) 0)
((= number 1) 1)
((> number 1)
(+ number (triangle-using-cond (1- number))))))
(triangle-using-cond 4)
#+end_src
Eval the defun with ~e~. Then do ~je~ to eval the next expression to
get =10=.
** step 2
Press ~xfM~ to get:
#+begin_src emacs-lisp
||(cond ((<= 4 0)
0)
((= 4 1)
1)
((> 4 1)
(+ 4 (triangle-using-cond (1- 4)))))
#+end_src
With ~e~ check that the result is still =10=.
** step 3
Evaluate the =cond= branches in your mind and simplify with ~qhrr~.
#+begin_src emacs-lisp
||(+ 4 (triangle-using-cond (1- 4)))
#+end_src
Then ~ffxr~.
#+begin_src emacs-lisp
(+ 4 ||(triangle-using-cond 3))
#+end_src
** step 4
Press ~xfM~ again:
#+begin_src emacs-lisp
(+ 4 ||(cond ((<= 3 0)
0)
((= 3 1)
1)
((> 3 1)
(+ 3 (triangle-using-cond (1- 3))))))
#+end_src
Evaluate the =cond= branches in your mind and simplify with ~qirr~.
#+begin_src emacs-lisp
(+ 4 ||(+ 3 (triangle-using-cond (1- 3))))
#+end_src
Simplify further with ~ffxr~.
#+begin_src emacs-lisp
(+ 4 (+ 3 ||(triangle-using-cond 2)))
#+end_src
** step 5
Press ~xfM~ again:
#+begin_src emacs-lisp
(+ 4 (+ 3 ||(cond ((<= 2 0)
0)
((= 2 1)
1)
((> 2 1)
(+ 2 (triangle-using-cond (1- 2)))))))
#+end_src
Evaluate the =cond= branches in your mind and simplify with ~qjrr~.
#+begin_src emacs-lisp
(+ 4 (+ 3 ||(+ 2 (triangle-using-cond (1- 2)))))
#+end_src
Simplify further with ~ffxr~.
#+begin_src emacs-lisp
(+ 4 (+ 3 (+ 2 ||(triangle-using-cond 1))))
#+end_src
** step 6
Press ~xfM~ again:
#+begin_src emacs-lisp
(+ 4 (+ 3 (+ 2 ||(cond ((<= 1 0)
0)
((= 1 1)
1)
((> 1 1)
(+ 1 (triangle-using-cond (1- 1))))))))
#+end_src
Evaluate the =cond= branches in your mind and simplify with ~akrr~.
#+begin_src emacs-lisp
(+ 4 (+ 3 (+ 2 ||1)))
#+end_src
~C-e~ ~e~ to check that the result is still =10=. That's it.
#+BEGIN_HTML
#+END_HTML