# fixed point

Harris, Andrew Andrew.Harris at jhuapl.edu
Fri Oct 31 11:15:40 EST 2003

```Hi -

I am trying to work out how the following function using "fix" is
evaluated.  I am hoping someone could look at my step-by-step breakdown of
how I think evaluation works and see if I'm correct.  My main question is
how the order of operation (fixity?) is understood in going from step [3] to
[4], if this is indeed how the evaluation would take place.

Any help is appreciated,
-andrew

Here's the Haskell function:

---
fix f = f (fix f)

wierdFunc2 x y z = if y - z > z then x (y-z) z
else y - z

myRemainder = fix wierdFunc2
---

Here's my "evaluation":

myRemainder 12 5		-- [1]
=
fix wierdFunc2 12 5	-- [2] by substitution
=
wierdFunc2 fix wierdFunc2 12 5	-- [3] apply "fix"
=
wierdFunc2 myRemainder 12 5		-- [4] by substitution (?)
=
myRemainder 7 5				-- [5] apply "wierdFunc2"
=
fix wierdFunc2 7 5	-- [6] by substitution
=
wierdFunc2 fix wierdFunc2 7 5	-- [7] apply "fix"
=
wierdFunc2 myRemainder 7 5		-- [8] by substitution (?)
=
2	-- [9] apply "wierdFunc2"
```

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