On Thu, Oct 9, 2008 at 8:55 AM, Francois Maltey wrote:
>
> Your example shows that axiom allows to "currify" 2 variables with
> this syntax, but how do you create a 3-variable function ?
>
> fct := x +-> (y +-> (z +-> gcd (x,y,z)))
>
> fct 4 is a 2-variable function.
> fct 4 6 is a 1-variable function
> fct 4 6 8 = 2
>
Perhaps it looks like it, but there are no Curry operations shown
above. Each of these is a function of only one variable. The
expression 'fct 4 6 8' is interpreted as ((fct(4))(6))(8).
Curry applies if I am given a function with several inputs, e.g.
(1) -> fct(x:Integer,y:Integer,z:Integer):Integer == gcd( [x,y,z] )
Type: Void
and create new higher-order function with fewer inputs which only
"partially evaluates" the original function, returning a function as
output.
(2) -> fct''(x:Integer,y:Integer):(Integer->Integer) == z +-> fct(x,y,z)
Function declaration fct'' : (Integer,Integer) -> (Integer ->
Integer) has been added to workspace.
Type: Void
In other words the value of the function fct''(2,4) is itself a
function of one argument.
(3) -> fct''(2,4)
Compiling function fct with type (Integer,Integer,Integer) ->
Integer
Compiling function fct'' with type (Integer,Integer) -> (Integer ->
Integer)
(3) theMap(#<COMPILED-FUNCTION *2;fct'';1;frame1-1>,679)
Type: (Integer -> Integer)
Evaluating this function
(4) -> fct''(2,4)(8)
(4) 2
Type: PositiveInteger
Is exactly equivalent to fct(2,4,8).
Similarly if we wish to partially evaluate on only one input:
(5) -> fct'(x:Integer):((Integer,Integer)->Integer) == (y,z) +-> fct(x,y,z)
Function declaration fct' : Integer -> ((Integer,Integer) -> Integer
) has been added to workspace.
Type: Void
(6) -> fct'(2)
Compiling function fct' with type Integer -> ((Integer,Integer) ->
Integer)
(6) theMap(#<COMPILED-FUNCTION *1;fct';1;frame1-1>,678)
Type: ((Integer,Integer) -> Integer)
(7) -> fct'(2)(4,8)
(7) 2
Type: PositiveInteger
Axiom has some higher-order Curry operations in MappingPackage2 and
MappingPackage3 but these are not quite as flexible as the notation
above.
Regards,
Bill Page.
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