This sucks.

04-typed-racket/main.rkt

@@ -12,8 +12,7 @@
     [(and (even? a) (even? b)) (* 2 (gcd2 (floor (/ a 2)) (floor (/ b 2))))]
     [(even? b) (gcd2 a (floor (/ b 2)))]
     [(even? a) (gcd2 (floor (/ a 2)) b)]
-    [else
+    [else (if (<= a b)
-     (if (<= a b)
               (gcd2 a (- b a))
               (gcd2 b (- a b)))]))
 

05-parsing/main.rkt

@@ -1,5 +1,32 @@
 #lang pl
 
+#|
+
+"{{{2 + 5}} * {5 * {{3 + 6}}}}"
+The parenthesis    ^here & ^here are necessary because otherwise it would be an AE, not a Prod as R3 requires. It requires this to maintain order of operations.
+
+"{{{2 + 5}} * {5 * {{3 * 6}}}}"
+The parenthesis are no longer needed, as {3 * 6} is itself a prod satisfying R3.
+
+If you have a grammar language with easy precedence, it's nice. Otherwise, it's cursed.
+
+In Yacc:
+%left ADD SUB
+%left MUL DIV
+%precedence NEG
+
+exp:
+    ...
+    | NUM {...}
+    | GROUPSTART exp GROUPEND { ... }
+    | SUB exp {...}
+    | exp SUM exp {...}
+    | exp SUB exp {...}
+    | exp MUL exp {...}
+    | exp DIV exp {...}
+
+|#
+
 (define-type AE
   [R1 Prod AE]
   [R2 Prod])
@@ -12,30 +39,46 @@
   [R5 Number]
   [R6 AE])
 
+#|
+<AE> ::= <PROD> + <AE> (1)
+       | <PROD> (2)
+<PROD> ::= <ATOM> * <PROD> (3)
+         | <ATOM> (4)
+<ATOM> ::= <num> (5)
+         | { <AE> } (6)
+|#
+
 ; Symbols:
 ; 'sum
 ; 'mul
 ; 'groups
 ; 'groupe
 
-; parse-ae: s: Sexpr → AE
+(: parseae : (Sexpr -> AE))
-(: parse-ae : (Sexpr -> AE))
+(define (parseae s)
-; Parse a Sexpr.
-(define (parse-ae s)
-  ; parseae: s: Sexpr, a: Sexpr → AE
-  (: parseae : (Sexpr Sexpr -> AE))
-  ; Parse a Sexpr and while accumulating in a.
-  (define (parseae s a)
   (match s
-      [(list prod ae) (parseae/group (rest s) '())]
+    [(list prod '+ ae) (R1 (parseprod prod) (parseae ae))]
-      [(cons (number: n) r) (R2 (R4 (R5 n)))]))
+    [prod (R2 (parseprod prod))]))
 
-  (parseae s '()))
+(: parseprod : (Sexpr -> Prod))
+(define (parseprod s)
+  (match s
+    [(list atom '* prod) (R3 (parseatom atom) (parseprod prod))]
+    [ atom (R4 (parseatom atom))]))
 
+(: parseatom : (Sexpr -> Atom))
+(define (parseatom s)
+  (match s
+    [ (number: n) (R5 n)]
+    [(list ae) (R6 (parseae ae))]))
 
-(test (parse-ae '(3)) => (R2 (R4 (R5 3))))
+(: parse : (String -> AE))
-(test (parse-ae '(groups 3 groupe)) => (R2 (R4 (R6 (R2 (R4 (R5 3)))))))
+(define (parse s) (parseae (string->sexpr s)))
-(test (parse-ae '(1 plus 1)) => (R1 (R4 (R5 1)) (R2 (R4 (R5 1)))))
+
+(test (parse "5") => (R2 (R4 (R5 5))))
+(test (parse "{2 + 5}") => (R1 (R4 (R5 2)) (R2 (R4 (R5 5)))))
+(test (parse "{{{2 + 5}} * {5 * {{3 + 6}}}}") => (R2 (R3 (R6 (R1 (R4 (R5 2)) (R2 (R4 (R5 5))))) (R3 (R5 5) (R4 (R6 (R1 (R4 (R5 3)) (R2 (R4 (R5 6)))))))))
+      )
 
 ; parse-ae/h: s: Sexpr, ae: AE → AE
 
@@ -49,6 +92,8 @@
 <ATOM> ::= <num> (5)
            | { <AE> } (6)
 
+These are not wrapped in the few rules at the top level to convert them to AEs
+
 "5"
 <atom> (5)
  <num> 5