Re: Function[x...] and #& not equivalent
- To: mathgroup at smc.vnet.net
- Subject: [mg74448] Re: Function[x...] and #& not equivalent
- From: "Szabolcs" <szhorvat at gmail.com>
- Date: Wed, 21 Mar 2007 02:57:43 -0500 (EST)
- References: <etof3e$i3d$1@smc.vnet.net>
wooks =EDrta:
> In[19]:=
> Clear[Eternity,x];
> Eternity[x_]:=Eternity[x];
>
> In[21]:=
> Clear[EmptyQ];
> EmptyQ[{}]:=True;
> EmptyQ[x_List]:=False;
> EmptyQ[x_]:=Print["Argument to EmptyQ must be a list."];
>
> This below works for the empty list it gives 0.
> In[25]:=
> Clear[length,list]
> Function[length,
> Function[list,If[EmptyQ[list],
> 0,
> 1 +
> length[Rest[list]]]]][
> Eternity][{}]
> Out[26]=
> 0
>
> What I am trying to do here is pass the function above as the
> definition of the parameter MkLength and then run the exactly the same
> thing by MkLength[Eternity].
> It doesn't work.
> In[27]:=
> Function[MkLength,MkLength[Eternity][Function[length,
> Function[list,If[EmptyQ[list],0,1 +
> length[Rest[list]]]]]]][{}]
>
> Out[27]=
> {}[Eternity][
> Function[length,Function[list,If[EmptyQ[list],
> 0,1+length[Rest[list]]]]]]
>
> But look what happens when I use the function abbreviation instead of
> Function[MkLength........
> In[29]:=
> #[Eternity]&[Function[length,
> Function[list,If[EmptyQ[list],0,1 + length[Rest[list]]]]]]
> [{}]
> Out[29]=
> 0
The abbreviated notation is equivalent with the first version only if
you put the ampersand at the end.
#[Eternity][Function[length,
Function[list,If[EmptyQ[list],0,1 + length[Rest[list]]]]]]
[{}] &
What you have written there can be expressed with the Function
notation as follows:
Function[MkLength, MkLength[Eternity]] [Function[length,
Function[list,If[EmptyQ[list],0,1 + length[Rest[list]]]]]]
[{}]