Generating list of functions from list of expressions

Question

I know how to create a function from concrete expression like

Function[{x, y}, x^2 + y^2]

But what if I have a list of expressions list1 and I know the set of variables which can occur in this list. I want to map all expressions of list1 to curresponding functions from these variables. Like

{x^2 + y^2, z^2, x, y}

should be mapped to

{
  Function[{x,y,z}, x^2 + y^2], 
  Function[{x,y,z}, z^2], 
  Function[{x,y,z}, x], 
  Function[{x,y,z}, y]
}

I've tried

Function[{x,y,z}, #] &/@ list1

but this doesn't work. Can someone help me with solution?

Answer 1

One way to do it is:

exprs = {x^2 + y^2, z^2, x, y};
Replace[Function[{x, y, z}, body], {Rule[body, #]} & /@ exprs, {-1}]

{
   Function[{x, y, z}, x^2 + y^2], 
   Function[{x, y, z}, z^2], 
   Function[{x, y, z}, x], 
   Function[{x, y, z}, y]
}