An Expr describes a simple structure for algebraic expressions. Generally,
a type Expr[A] indicates that A has some structure that mirrors Expr.
To get at this symmetry, you must use the type class Coexpr[A]. This let's
us switch between types A and Expr[A], giving us the ability to extract
structure from a type A, traverse, and construct the expression tree of
A, without having to deal with A as a concrete type.
Using Coexpr let's us provide further general constructors and pattern
matchers. These are defined as the same name as the case class, but without
the Expr appended. So, we can, for example, pattern match on an instance
a of the generic type A. Suppose we wanted to map patterns like ab + ac
to a(b + c), then we could do the following:
a match {
case Add(Mul(a, b), Mul(c, d)) if a == c => Mul(a, Add(b, d))
case _ => a
}
An
Exprdescribes a simple structure for algebraic expressions. Generally, a typeExpr[A]indicates thatAhas some structure that mirrorsExpr. To get at this symmetry, you must use the type classCoexpr[A]. This let's us switch between typesAandExpr[A], giving us the ability to extract structure from a typeA, traverse, and construct the expression tree ofA, without having to deal withAas a concrete type.Using
Coexprlet's us provide further general constructors and pattern matchers. These are defined as the same name as the case class, but without theExprappended. So, we can, for example, pattern match on an instanceaof the generic typeA. Suppose we wanted to map patterns like ab + ac to a(b + c), then we could do the following:a match { case Add(Mul(a, b), Mul(c, d)) if a == c => Mul(a, Add(b, d)) case _ => a }