On Mon, Dec 25, 2023 at 01:10:50PM +0100, Waldek Hebisch wrote:
> On Sun, Dec 24, 2023 at 09:48:07PM -0800, 'Nasser M. Abbasi' via FriCAS -
> computer algebra system wrote:
> > I am learning little Fricas. But confused about this
> >
> >
> > (21) -> g2(x: Integer): Integer == x^2
> > Function declaration g2 : Integer -> Integer has been added to
> > workspace.
> >
> > Is the above function supposed to accept only Integer type as input and
> > return Integer? Then why does this call work:
> >
> > 22) -> g2(7.0)
> > Compiling function g2 with type Integer -> Integer
> > (22) 49
> > Type:
> > PositiveInteger
> >
> > It seems to have casted 7.0 to 7? And should not the type returned be
> > Integer and not PositiveInteger?
> >
> > 23) -> typeOf(7.0)
> > (23) Float
> >
> > Fricas does however catch the error when passing string:
> >
> > 24) -> g2("hello")
> > Conversion failed in the compiled user function g2 .
> > Cannot convert the value from type String to Integer .
> >
> > Compare to Maple
> > -------------------------------------------------
> > g2:=proc(x::integer)::integer;
> > x^2;
> > end proc;
> >
> > g2(7.0);
> > Error, invalid input: g2 expects its 1st argument, x, to be of type
> > integer, but received 7.0
> > -----------------------------------------------
> >
> > And that is what I was expecting, given that Fricas is very strongly typed.
> >
> > Did I do something wrong or do I need to turn some setting on or something?
>
> FriCAS has notion of "coercion", "retraction" and "convertion". There
> is a difference between them, but basically FriCAS "knows" that some
> functions can be used to change types. In particular, FriCAS has
> 'retract' function that can change Float to Integer: it will work only
> when Float happens to have integer value, otherwise will fail. In
> interactive use, when types do not match FriCAS automatically tries
> to inserts convertion functions to ensure type agreement. In effect,
> FriCAS treats your 'g(7.0)' as 'g(retract(7.0))'. In similar spirit,
> FriCAS tries to show result in narrowest possible type, that is why it
> prints 'PositiveInteger'.
>
> Note: On command line FriCAS tries very hard to change types so
> that expression can be evaluated. In user defined functions
> FriCAS is doing less work, but still inserts convertion like
> above. In Spad language FriCAS is insterting only small number
> of "obvious" coercions.
>
> This may look not very consistent, but simply having to insert
> coercions and convertions everywhere is too inconvenient for
> most users, so convenience wins. In Spad you are programming
> and for readability supposed to be more explicit. Function
> definitions in "interpreter" are an intermediate thing.
>
> Concering user settings: this can not be changed by normal
> settings.
A few more remaks. In your previous example:
concat([1, 2, 3], ["e", "f", "g"])
FriCAS was too shy to invent List(Any). OTOH in
(5) -> [1, 2, 3, "e", "f", "g"]
(5) [1, 2, 3, "e", "f", "g"]
Type: List(Any)
it introduced List(Any).
in
concat([1, 2, 3]::List(Any), ["e", "f", "g"])
FriCAS saw List(Any) as type of first argument and decided to
coerce second argument to match.
in
concat([1, 2, 3], ["e", "f", "g"])$List(Any)
FriCAS saw that it needs arguments of type List(Any) and coerced
both arguments to match.
--
Waldek Hebisch
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