CMSI 3802: Languages and Automata II: Homework #1 Answers

let [x, y] = [0, 0];
console.log(93.8 * 2 ** x + y);

import x from "x"
console.log(93.8 * {x} << x.r[z])

```
const x = x / {[x]: `${x}`}[x]("y")
```

class C {
  f({a, b: c}) {return ([a, f]) => C}
}

To make the expression -2**2...

...evaluate to 4, we make negation have higher precedence than exponentiation:

Exp     = Exp "+" Term | Term
Term    = Term "*" Factor | Factor
Factor  = Primary "**" Factor | Primary
Primary = "-" Primary | num | id | "(" Exp ")"

...evaluate to -4, we make negation have lower precedence than exponentiation. You can put the negation at the beginning of wither the Exp or the Term rule:
```
Exp     = "-"? (Exp "+" Term | Term)
Term    = Term "*" Factor | Factor
Factor  = Primary "**" Factor | Primary
Primary = num | id | "(" Exp ")"
```

...be a syntax error, we put negation and exponentiation in the same rule:

Exp     = Exp "+" Term | Term
Term    = Term "*" Factor | Factor
Factor  = Primary "**" Factor | "-"? Primary
Primary = num | id | "(" Exp ")"

Here is a grammar for Astro++ that enforces the appearance of break statements only within while loops. (In practice, most people don't actually capture this in the grammar, but it's a good exercise to actually do it!)

Astro {
  Program       = StmtNoBreak+
  StmtNoBreak   = Assignment
                | PrintStmt
                | IfStmtNoBreak
                | WhileStmt
  Stmt          = Assignment
                | PrintStmt
                | IfStmt
                | WhileStmt
                | BreakStmt
  Assignment    = id "=" Exp ";"
  PrintStmt     = print Exp ";"
  BreakStmt     = break ";"
  WhileStmt     = while Exp Block
  IfStmtNoBreak = if Exp BlockNoBreak (else (BlockNoBreak|IfStmtNoBreak))?
  IfStmt        = if Exp Block (else (Block|IfStmt))?
  BlockNoBreak  = "{" StmtNoBreak* "}"
  Block         = "{" Stmt* "}"
  Exp           = Exp1 ("<="|"<"|"=="|"!="|">="|">") Exp1  --relational
                | Exp1
  Exp1          = Exp1 ("+" | "-") Term                    --additive
                | Term
  Term          = Term ("*" | "/" | "%") Factor            --multiplicative
                | Factor
  Factor        = Primary "**" Factor                      --exponentiation
                | "-" Primary                              --negation
                | Primary  
  Primary       = id "(" ListOf<Exp, ","> ")"              --call
                | numeral                                  --num
                | id                                       --id
                | "(" Exp ")"                              --parens
  numeral       = digit+ ("." digit+)? (("E" | "e") ("+" | "-")? digit+)?
  print         = "print" ~idchar
  while         = "while" ~idchar
  if            = "if" ~idchar
  else          = "else" ~idchar
  break         = "break" ~idchar
  keyword       = print | while | if | else | break
  idchar        = letter | digit | "_"
  id            = ~keyword letter idchar*
  space        += "//" (~"\n" any)*                        --comment
}