Run the automata chapter's Racket examples at render time

chapters/_subfiles/automata/_racket-numeral_exm.qmd

@@ -1,10 +1,11 @@
 ::: {#exm-racket-numeral}
 #### Checking numerals in Racket
 
 In the form of @exr-racket-step, the DFA of @sol-decimal-numeral is the table below,
 with the symbol `'digit` for the input $\mathtt{d}$ and the symbol `'point` for the input $\mathtt{.}$:
 
-```racket
+```{racket}
+#| code-fold: false
 (define numeral-table
   '((n0 (digit n1) (point n4))
     (n1 (digit n1) (point n2))
@@ -16,7 +17,8 @@
 To check real text, `classify` turns each character into an input,
 and `numeral?` runs the DFA with `accepts?` from @exm-racket-run:
 
-```racket
+```{racket}
+#| code-fold: false
 (define (classify c)
   (cond [(char<=? #\0 c #\9) 'digit]
         [(char=? c #\.) 'point]
@@ -35,13 +37,13 @@
 
 A character that is neither a digit nor a point is classified `'other`, which is not an input of the DFA,
 so `numeral?` returns `#f` for any text that contains one, without running the DFA.
-Then
+Applied to eight strings, `numeral?` returns:
 
-```racket
+```{racket}
+#| code-fold: false
 (map numeral? '("3.14" "2026" "7." ".5" "1.2.3" "d.d" "-3" "\u00BD"))
 ```
 
-returns `'(#t #t #f #f #f #f #f #f)`:
 `"3.14"` and `"2026"` are numerals, and the others are not.
 The letter d in `"d.d"` is classified `'other`, not `'digit`,
 and so is the one character of `"\u00BD"`, the fraction one half,

chapters/_subfiles/automata/_racket-run_exm.qmd

@@ -1,11 +1,12 @@
 ::: {#exm-racket-run}
 #### Running a DFA in Racket
 
 With `step` as in @exr-racket-step,
 `run` returns the run (@def-run) from a state `s` on a list `xs` of inputs,
 and `accepts?` says whether a DFA accepts (@def-accept) the string whose inputs are the list `xs`:
 
-```racket
+```{racket}
+#| code-fold: false
 (define (run table s xs)
   (if (empty? xs)
       (list s)
@@ -21,11 +22,23 @@
 - `(member x L)` is `#f` if `x` is not in the list `L`, and a list that is not `#f` if it is.
 - `(string->list w)` is the list of the characters of the string `w`.
 
-`(run pairs-table 'q0 (string->list "abab"))` returns `'(q0 q1 q0 q1 q0)`,
-and `(run pairs-table 'q0 (string->list "aab"))` returns `'(q0 q1 q2 q2)`, the runs of @exm-pairs-accept.
-`(accepts? pairs-table 'q0 '(q0) (string->list "abab"))` returns `#t`,
-`(accepts? pairs-table 'q0 '(q0) (string->list "ba"))` returns `#f`,
-and `(accepts? pairs-table 'q0 '(q0) (string->list ""))` returns `#t`, since $A$ accepts $\lambda$.
+`run` returns the runs of @exm-pairs-accept on `"abab"` and `"aab"`:
+
+```{racket}
+#| code-fold: false
+(run pairs-table 'q0 (string->list "abab"))
+(run pairs-table 'q0 (string->list "aab"))
+```
+
+$A$ accepts `"abab"` and the empty string $\lambda$, but not `"ba"`:
+
+```{racket}
+#| code-fold: false
+(accepts? pairs-table 'q0 '(q0) (string->list "abab"))
+(accepts? pairs-table 'q0 '(q0) (string->list ""))
+(accepts? pairs-table 'q0 '(q0) (string->list "ba"))
+```
+
 Let $w$ be the string whose symbols are the elements of `xs`, in order.
 `run` reads the first symbol of $w$ first, as @def-run does, so by @thm-run-last the last state of `(run table s xs)` is $\delta^*(s, w)$.
 

chapters/_subfiles/automata/_racket-step_exr.qmd

@@ -4,7 +4,8 @@
 In Racket, the table of the DFA $A$ (@exm-pairs-table) can be stored as a list with one list for each state,
 which starts with the state and goes on with a list `(x t)` for each input `x`, where `t` is the state that `x` leads to:
 
-```racket
+```{racket}
+#| code-fold: false
 (define pairs-table
   '((q0 (#\a q1) (#\b q0))
     (q1 (#\a q2) (#\b q0))

chapters/_subfiles/automata/_racket-step_sol.qmd

@@ -5,4 +5,13 @@ and its rest is `'((#\a q2) (#\b q0))`.
 `(assoc #\b ...)` finds `'(#\b q0)` in that list, and its second element is `'q0`.
 So `(step pairs-table 'q1 #\b)` returns `'q0`, which is $\delta(q_1, \mathtt{b})$ (@exm-pairs-dfa).
 
+Racket returns the same values:
+
+```{racket}
+#| code-fold: false
+(assoc 'q1 pairs-table)
+(rest (assoc 'q1 pairs-table))
+(step pairs-table 'q1 #\b)
+```
+
 :::

chapters/automata.qmd

@@ -13,6 +13,8 @@ format:
 
 {{< include ../latex-macros/macros.qmd >}}
 
+{{< include _subfiles/_racket-setup.qmd >}}
+
 ::: {.callout-note appearance='simple' collapse=true}
 ## Source