Functional programming using caml light

Functional programming using caml light

[ciol]

Hello,
in this book ( http://caml.inria.fr/pub/docs/fpcl/index.html ), there is 
the following grammar (chapter 10.3, on streams etc...) :

Expr ::= Mult
        | Mult + Expr
        | Mult - Expr

[...]

after factoring common prefixes, the author obtains :

Expr ::= Mult RestExpr

RestExpr ::= + Mult RestExpr
             |- Mult RestEXpr
             |(* nothing *)

[...]

But I don't obtain the same result for RestExpr :

RestExpr ::= + Mult Expr
             |- Mult Expr
             | (* nothing *)

Am I wrong ? (and why ?)

----------------------------------

Another question (totally different) :
I've created the type :
type expr = Plus of expr * expr
           | Minus of expr * expr
           | Div of expr * expr
           | Sin of expr
           | Cos of expr
[etc... (not important)]

when I match an expression, I do for instance :
Plus (u, v) -> blablabla (u, v)
Minus (u, v) -> blablabla (u, v) (same result as above)
Div (u, v) -> a different result

Can I reduce the code in order to do such a thing :
Div (u, v) -> blabliblou
BinaryFunction (u, v) -> blablabla (u, v)

(BinaryFunction match for both Plus and Minus (all the others binary 
functions))

Thank you (maybe should I have written in french ?)

Re: Functional programming using caml light

[ciol]

ciol wrote:

> after factoring common prefixes, the author obtains :
> 
> Expr ::= Mult RestExpr
> 
> RestExpr ::= + Mult RestExpr
>             |- Mult RestEXpr
>             |(* nothing *)
> 
> [...]
> 
> But I don't obtain the same result for RestExpr :
> 
> RestExpr ::= + Mult Expr
>             |- Mult Expr
>             | (* nothing *)
> 

_Sorry_, it's an error, I obtain :
RestExpr ::= + Expr
            | - Expr
            | (* nothing *)

But I've just realized that the author's solution is in fact the same as 
mine (he replaced Expr in RestExpr by Mult RestExpr. But why ? Isn't it 
more complicated ? The result in caml will be identical  wont it be ?

Re: Functional programming using caml light

[ciol]

c'est bon j'ai trouvé, ma grammaire ne gère pas l'associativité à gauche  :
sur cet exemple "1 - 3 + 5", je vais l'analyser comme Moins (1, Plus (3, 
5)), alors que c'est évidemment Plus (Moins (1, 3), 5)

désolé.