[plt-scheme] typed scheme vs. PLAI types
Hi all,
I have a (naive and hopefully not too stupid :-;) question about defining algebraic data types in typed scheme.
I would like to define type aliases and algebraic data types for a relational algebra. I don't know too much of Haskell, but I find algebraic data types helpful to think about data representation, so in order to find an "example" I could then follow in typed scheme,
I started out with the following (just as a first approximation):
type Relation = (Attlist, [Tuple])
type Attlist = [Attribute]
type Attribute = (String, String)
type Tuple = [String]
data Expr = Prop | RelExpr
data RelExpr = Project Relation Attlist
| Restrict Relation Prop
| Join [Relation]
data Prop = Const Bool
| Is Expr Expr
| And Prop Prop
| Or Prop Prop
When I try to do a similar thing in typed scheme, it looks fine for the type aliases, but regarding the algebraic types, it seems to me I have to define structures and then a type alias which defines a union of them:
(define-type-alias Relation (Pair Attlist (Listof Tuple)))
(define-type-alias Attlist (Listof Attribute))
(define-type-alias Attribute (Pair String String))
(define-type-alias Tuple (Listof String))
(define-struct: Project ((rel : Relation) (attl : Attlist)))
(define-struct: Restrict ((rel : Relation) (prop : Prop)))
(define-struct: Join ((rels : (Listof Relation))))
(define-type-alias RelExpr (U Project Restrict Join))
(define-type-alias Expr (U Prop RelExpr))
(define-struct: Is ((expr1 : Expr) (expr2 : Expr)))
(define-struct: And ((expr1 : Expr) (expr2 : Expr)))
(define-struct: Or ((expr1 : Expr) (expr2 : Expr)))
(define-type-alias Prop (U Boolean Is And Or))
This looks rather ugly, especially having structs for the Is, And and Or expressions... I guess this should be done completely differently, but I don't see how. (So my first question would be, how can I do this better in typed scheme?)
What I would in fact like is a define-type like in PLAI, where it would look like this ( I'm leaving out the aliases, as I don't know how to define them in PLAI):
(define-type Prop
(CONST (b boolean?))
(IS (e1 Expr?) (e2 Expr?))
(AND (p1 Prop?) (p2 Prop?))
(OR (p1 Prop?) (p2 Prop?)))
(define-type RelExpr
(Project (r Relation?) (a Attlist?))
(Restrict (r Relation?) (p Prop?))
(Join (r1 Relation?) (r2 Relation?)))
My second question is, why does typed scheme not have such a define-type? (I find it very appealing because it makes the algebraic type definition very concise.)
Many thanks in advance,
Sigrid