branch: externals/org-mathsheet
commit 688e66613b22d5f27c689036d5854a1b8d0b7424
Author: Ian Martins <ia...@jhu.edu>
Commit: Ian Martins <ia...@jhu.edu>
Can produce problems from template
---
mathsheet.org | 280 +++++++++++++++++++++++++++++++++++++++++++++++++++++++---
1 file changed, 269 insertions(+), 11 deletions(-)
diff --git a/mathsheet.org b/mathsheet.org
index f290b37773..e3a13d57ae 100644
--- a/mathsheet.org
+++ b/mathsheet.org
@@ -1,25 +1,281 @@
* goal
the goal is to generate a math practice sheet.
+
+similar to https://www.math-aids.com
* script
** vars
-#+property: header-args+ :var student="Noble" problem-count=24
+-#+property: header-args+ :var student="Noble" problem-count=24
** problem sets
*** add and subtract
-TODO support "var c in [b 5]"
-#+name: first-set
+#+name: firstset
+| weight | order | problem | descr |
+|--------+-------+-------------------------------+------------------------|
+| 3 | 1 | [1..10] + [0..10] | simple |
+| 2 | 2 | [1..10] + [8..15] | second number bigger |
+| 1 | 3 | [1..10] + [1..7] + [1..5] | three numbers |
+| 1 | 4 | [a=3..10] - [0..$a] | subtraction |
+| 1 | 4 | [a=1..10] + [0..10] - [1..$a] | three with subtraction |
+| 0 | 0 | [$a*[1..5]] / [a=1..10] | division |
+
+** problem generation
+
+TODO create a package. if you C-c C-c on a table
+1. if you are on the header, generate a worksheet
+2. if you on on a row, generate a single example
+
+*** var-list
+need ~var-list~ to keep track of the variables between fields.
+
+#+name: var-list
+#+begin_src elisp
+(defvar ianxm/var-list '()
+"List of variables used in a problem")
+#+end_src
+*** scan field
+
+must call with point at the start of a field. moves the point to the
+end of the field. returns a list of fields, formatted as:
+
+#+begin_example
+'(var (deps) start-marker end-marker nil)
+#+end_example
+
+~var~ is a variable name if there is an assignment, or it is a
+placeholder like ~_0~, ~_1~, etc. the last entry is nil for "not
+visited." ~var~ must be interned and must be the first index since we
+use this as an alist.
+
+~start-marker~ and ~end-marker~ are markers in the (temp) buffer.
+
+for example:
+#+begin_example
+[$a + 2 + [a=1..5]] => '((nil (a) m1 m19 nil) (a nil m11 m18 nil))
+#+end_example
+
+~open-fields~ is a stack of fields with the current field on top. we
+push a new field to the stack when we start a new field.
+~closed-fields~ is a list of fields that have been completed. we push a
+new field to the list when we close the current field.
+
+#+name: scan-problem
+#+begin_src elisp
+ (defun ianxm/scan-problem ()
+ (interactive)
+ (let ((field-index 0)
+ open-fields ; stack (open close (vars) deps)
+ closed-fields) ; list (open close (vars) deps)
+
+ (with-peg-rules
+ ((stuff (* (or var letter digit symbol field space)))
+ (field open (opt assignment) stuff close)
+ (space (* [space]))
+ (open (region "[")
+ `(l r -- (progn
+ (setq
+ open-fields (push (list
+ (intern (concat "_"
(number-to-string field-index)))
+ nil (copy-marker l) nil nil)
+ open-fields)
+ field-index (1+ field-index))
+ ".")))
+ (assignment (region (substring letter)) "="
+ `(l v r -- (progn
+ (setcar
+ (car open-fields)
+ (intern v))
+ ".")))
+ (var "$" (substring letter)
+ `(v -- (progn
+ (setcar
+ (nthcdr 1 (car open-fields))
+ (push (intern v) (nth 1 (car open-fields))))
+ ".")))
+ (close (region "]")
+ `(l r -- (progn
+ (setcar (nthcdr 3 (car open-fields)) (copy-marker
l t))
+ (when (> (length open-fields) 1)
+ (setcar
+ (nthcdr 1 (nth 1 open-fields))
+ (push (caar open-fields) (nth 1 (nth 1
open-fields)))))
+ (setq
+ closed-fields
+ (push (pop open-fields) closed-fields))
+ ".")))
+ (letter [a-z])
+ (digit [0-9])
+ (symbol (or "." "+" "-" "*" "/" "(" ")")))
+
+ (peg-run (peg stuff)
+ (lambda (x) (message "failed %s" x))
+ (lambda (x)
+ (funcall x)
+ closed-fields)))))
+#+end_src
+
+*** reduce field
+
+must call with point at the start of a field. moves point to the end
+of the field. returns a list containing the value to which the field
+reduces.
+
+#+name: reduce-field
+#+begin_src elisp
+ (defun ianxm/reduce-field ()
+ (interactive)
+ (with-peg-rules
+ ((field "[" space (or range sequence assignment expression value)
space "]")
+ (expression (list value space operation space value (* space
operation space value))
+ `(vals -- (string-to-number
+ (calc-eval
+ (mapconcat
+ (lambda (x) (if (numberp x)
(number-to-string x) x))
+ vals
+ " ")))))
+ (operation (substring (or "+" "-" "*" "/")))
+ (assignment var-lhs space "=" space (or range sequence)
+ `(v r -- (progn
+ (setq var-list (push (cons (intern v) r)
var-list))
+ r)))
+ (range value ".." value
+ `(min max -- (+ (random (- max min)) min)))
+ (sequence (list value "," value (* "," value))
+ `(vals -- (seq-random-elt vals)))
+ (value (or (substring (opt "-") (+ digit)) var-rhs parenthetical)
+ `(v -- (if (stringp v) (string-to-number v) v)))
+ (parenthetical "(" expression ")"
+ (action (message "paren")))
+ (var-lhs (substring letter)) ; var for assignment
+ (var-rhs "$" (substring letter) ; var for use
+ `(v -- (let ((val (alist-get (intern v) var-list)))
+ (or val (error "var %s not set" v)))))
+ (space (* [space]))
+ (letter [a-z])
+ (digit [0-9]))
+
+ (peg-run (peg field)
+ (lambda (x) (message "failed %s" x))
+ (lambda (x) (funcall x)))))
+#+end_src
+
+#+begin_example
+ simple range
+ [10..11]
+
+ complex range
+ [-10..[10..20]]
+
+ complex with assignment
+ [a=1..[2..8]]
+
+ complex with inner assignment
+ [-10..[b=10..20]]
+
+ simple with variable
+ [0..[$a..$b]]
+#+end_example
+
+*** replace field
+
+replace a field with the value returned from processing it.
+
+#+name: replace-field
+#+begin_src elisp
+ (defun ianxm/replace-field (node)
+ (let ((start (nth 2 node))
+ (end (1+ (nth 3 node)))
+ val)
+ (goto-char start)
+ (when (looking-at "\\[")
+ (setq val (car (ianxm/reduce-field)))
+ (goto-char start)
+ (delete-char (- end start) t)
+ (insert (number-to-string val)))))
+#+end_src
+
+*** dfs visit
+
+check dependencies then visit the node
+
+#+name: dfs-visit
+#+begin_src elisp
+ (defun ianxm/dfs-visit (node fields)
+ (pcase (nth 4 node)
+ (1 (error "cycle detected")) ; cycle
+ (2) ; skip
+ (_ ; process
+ (setcar (nthcdr 4 node) 1) ; started
+ (let ((deps (nth 1 node)))
+ (dolist (dep deps)
+ (ianxm/dfs-visit
+ (assq dep fields)
+ fields)))
+ (ianxm/replace-field node) ; visit
+ (setcar (nthcdr 4 node) 2)))) ; mark done
+#+end_src
+*** fill fields in problem
+
+processes all fields in a problem.
+
#+begin_example
-var a in [1 10]
-var b in [0 10]
-var c in [1 5]
-var d in [0 15]
-problem weight 3 order 1 "a + b"
-problem weight 2 order 1 "a + d"
-problem weight 1 order 2 "a + b + c"
-problem weight 1 order 3 "a + c - b"
+(full-problem (buffer-substring (point-at-bol) (point-at-eol)))
#+end_example
+#+name: fill-problem
+#+begin_src elisp :var full-problem="[$a + 2 + [a=1..5]]"
+ (defun ianxm/fill-problem (full-problem)
+ (interactive)
+ (let (fields)
+ (with-temp-buffer
+ ;; stage problem in temp buffer
+ (insert full-problem)
+ (beginning-of-buffer)
+
+ ;; find fields, assignments, dependencies
+ (setq fields (ianxm/scan-problem))
+ (message "fields %s" fields)
+
+ ;; order fields according to dependencies
+ (dolist (node fields)
+ (ianxm/dfs-visit node fields))
+ (setq var-list '())
+ (buffer-string))))
+#+end_src
+
+test with this
+#+begin_src elisp :noweb yes
+ <<full>>
+
+ (ianxm/fill-problem "[1..12] + [1..10]")
+ ;;(ianxm/fill-problem "[1..[2..[10..100]]]")
+ ;;(ianxm/fill-problem "[$a*[1..10]] / [a=1..10]")
+ ;;(ianxm/fill-problem "[$a]/(3+[a=1..5])")
+
+#+end_src
+
+#+RESULTS:
+: 11 + 8
+
+*** full script
+tangles everything needed to convert a template to a problem
+
+#+name: full
+#+begin_src elisp :noweb yes :tangle mathsheet.el
+<<var-list>>
+
+<<scan-problem>>
+
+<<reduce-field>>
+
+<<catalog-fields>>
+
+<<replace-field>>
+
+<<dfs-visit>>
+
+<<fill-problem>>
+#+end_src
** generate problem set from template
#+name: problem-set
@@ -77,6 +333,8 @@ problem weight 1 order 3 "a + c - b"
#+RESULTS: one-problem
: (7 + 8 . 15)
+*** TODO dedup
+
** lay out problems and answers
this generates a problem set.
