Beau­tiful Racket / racket school 2019

• 1 intro
• 2 algebra
• 3 precalc
• 4 boss battle
• 5 alpha
• 6 bravo
• 7 charlie
• 8 delta
• 9 echo
• 10 foxtrot
• 11 golf
• 12 grand finale
• 13 thank you

1. 

   We impose prece­dence among oper­a­tions by nesting them more deeply in the parse tree, which in turn causes them to be eval­u­ated first. For instance, this math expres­sion:

   

   1 + 2 * 3 + 4

   1	1 + 2 * 3 + 4

   
   

   Must be eval­u­ated as if it were written like so:

   

   ((1 + (2 * 3)) + 4)

   1	((1 + (2 * 3)) + 4)

   
   

   Or rearranged into S-expres­sions:

   

   (+ (+ 1 (* 2 3)) 4)

   1	(+ (+ 1 (* 2 3)) 4)

   
   

   Our grammar should natu­rally produce this parse tree.

2. 

   Left-to-right asso­cia­tivity (e.g., a+b+c means (a+b)+c, not a+(b+c)) is handled by recur­sive rules in the grammar (e.g., sum is defined in terms of sum).

   

   Which of these gram­mars is correct?
   And what’s wrong with the other two?

   

   #lang brag
   sum : sum "+" ("a" | "b" | "c")

   1 2	#lang brag sum : sum "+" ("a" | "b" | "c")

   
   

   #lang brag
   sum : ("a" | "b" | "c") ["+" sum]

   1 2	#lang brag sum : ("a" | "b" | "c") ["+" sum]

   
   

   #lang brag
   sum : [sum "+"] ("a" | "b" | "c")

   1 2	#lang brag sum : [sum "+"] ("a" | "b" | "c")

   
   

   (parse-to-datum "a+b+c")

   1	(parse-to-datum "a+b+c")

   
3. 

   Oper­ator prece­dence (e.g., c*a+b*c means (c*a)+(b*c), not ((c*a)+b)*c) is imple­mented by chaining produc­tion rules in the grammar (e.g., sum is defined in terms of product).

   

   Which of these gram­mars is correct?
   And what’s wrong with the other two?

   

   #lang brag
   product : [product "*"] sum
   sum : [sum "+"] ("a" | "b" | "c" )

   1 2 3

   #lang brag product : [product "*"] sum sum : [sum "+"] ("a" | "b" | "c" )

   
   

   #lang brag
   sum : [sum "+"] product
   product : [product "*"] ("a" | "b" | "c")

   1 2 3

   #lang brag sum : [sum "+"] product product : [product "*"] ("a" | "b" | "c")

   
   

   #lang brag
   sum : [product "+"] product
   product : [var "*"] var
   var : "a" | "b" | "c"

   1 2 3 4

   #lang brag sum : [product "+"] product product : [var "*"] var var : "a" | "b" | "c"

   
   

   (parse-to-datum "c*a+b*c")

   1	(parse-to-datum "c*a+b*c")

   
4. 

   Paren­the­sized oper­a­tions are just one more level of prece­dence.

5. 

   Keep doing this until you have your math tower.

• 

  Multi­line comments.

• 

  Nega­tive inte­gers.

• 

  Multi­pli­ca­tion, subtrac­tion, and divi­sion.

• 

  Paren­the­sized math expres­sions.

precalc/test.rkt



#lang precalc
fun f(x, y, z) = x + x + x * (y + y) + y * z - z - z

fun g(z) = f(z, z, z) # line comment
g(-10) # = 300

fun h() = g(10)
h() # = 300

fun k(x) = x / 10 / 10 / (x / x)
k(h()) # = 3
k(-10 * (15 + 3 * 5)) # = -3

/*
multiline comment
0 / 0 / 0
*/

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

#lang precalc fun f(x, y, z) = x + x + x * (y + y) + y * z - z - z fun g(z) = f(z, z, z) # line comment g(-10) # = 300 fun h() = g(10) h() # = 300 fun k(x) = x / 10 / 10 / (x / x) k(h()) # = 3 k(-10 * (15 + 3 * 5)) # = -3 /* multiline comment 0 / 0 / 0 */



300
300
3
-3

1 2 3 4

300 300 3 -3

• 1 intro
• 2 algebra
• 3 precalc
• 4 boss battle
• 5 alpha
• 6 bravo
• 7 charlie
• 8 delta
• 9 echo
• 10 foxtrot
• 11 golf
• 12 grand finale
• 13 thank you