CS 3540: Programming Languages and Paradigms

Task 1. Define a complete set of syntax procedures for Huey

For each type of expression in the BNF description, define:

• a type predicate,
• a constructor, and
• one or more access procedures that retrieve the relevant parts of the expression.

The names you choose for your constructor and type predicate should be the same except for the type predicate's trailing "?". The names your choose for your accessors may be short, but they should be descriptive.

Finally, create a general type predicate named (color? arg) that returns true if and only if arg is a legal expression in the language: an RGB value, a unary expression, a 2-color binary expression, or a 1-colorbinary expression.

The type predicate and constructor for RGB values should ensure that the components of the resulting value all lie in the range 0 ≤ n ≤ 255.

Task 2. Define a function named (preprocess sugared-exp)

sugared-exp is a Huey expression from the full syntax, which includes the operators darker and mix.

preprocess returns an expression in the core Huey language, with the syntactic abstractions translated into equivalent expressions, and all other expressions preserved. For example:

> (preprocess '(invert (rgb 150 99 42)))
'(invert (rgb 150 99 42))

> (preprocess '(darker (rgb 150 99 42)))
'((rgb 150 99 42) * 0.5)

> (preprocess '((rgb 4 4 4)
                +
                ((rgb 150 99 42) mix (rgb 50 108 21))))
'((rgb 4 4 4)
  +
  (((rgb 150 99 42) * 0.5) + ((rgb 50 108 21) * 0.5)))

Task 3. Define a function named (eval-exp exp)

exp is a Huey expression from the full syntax of the language. If exp is not a legal Huey expression, eval-exp signals an error. For example:

> (eval-exp '((rgb 0 0 0) + 3))
huey: illegal expression -- ((rgb 0 0 0) + 3)

eval-exp returns the value of exp as its result, according to the language's semantics. Note that exp can contain sugar, so eval-exp must pre-process its argument before evaluating it! You may want to make eval-exp an interface procedure that ensures its argument is a legal expression, preprocesses it, and calls a helper to evaluate the resulting core expression.

What Racket will display as a result of eval-exp depends on how you represent RGB values internally. If you use lists of size three, for example, it might display values such as these:

> (eval-exp '(invert (rgb 150 99 42)))
'(105 156 213)

> (eval-exp '((rgb 150 99 42) + (rgb 50 18 241)))
'(200 117 255)

> (eval-exp '((rgb 255 0 255) mix ((rgb 0 255 0) + (rgb 4 4 4))))
'(129 127 129)

If you implement RGB values differently, Racket will display different outputs, but the components of the colors will be the same.

The language description provides some sample expressions for testing. You can also find other simple test expressions in the description of Huey's semantics. Be sure to test other expressions, including some that are more complex.