How to use InterpolatingFunction generated by Mathematica 5.2 in version 8.0.1?

Question

Let us interpolate the same data using Mathematica 5.2, 7.0.1 and 8.0.1:

Interpolation[{{0, 0}, {1, 1}, {2, 3}, {3, 4}, {4, 3}, {5, 0}}] // InputForm

The outputs are:

Mathematica 5.2:

InterpolatingFunction[{{0, 5}}, 
 {2, 0, True, False, {3}, {0}}, {{0, 1, 2, 3, 4, 5}}, 
 {{0}, {1}, {3}, {4}, {3}, {0}}, {Automatic}]

Mathematica 7.0.1:

InterpolatingFunction[{{0, 5}}, {3, 1, 0, {6}, {4}, 0, 0, 0, 0}, 
 {{0, 1, 2, 3, 4, 5}}, {{0}, {1}, {3}, {4}, {3}, {0}}, {Automatic}]

Mathematica 8.0.1:

InterpolatingFunction[{{0, 5}}, {4, 3, 0, {6}, {4}, 0, 0, 0, 0, Automatic}, 
 {{0, 1, 2, 3, 4, 5}}, {{0}, {1}, {3}, {4}, {3}, {0}}, {Automatic}]

The output of Mathematica 5.2 still works when used as input in version 7.0.1 but not in version 8.0.1. It seems that support of the old-style InterpolatingFunction was dropped in version 8. Is it possible to reuse InterpolatingFunction data generated by Mathematica 5.2 in version 8.0.1?

Fiddlededee

Is there any reason you don't want to extract the points from older version's InterpolatingFunction and then construct another InterpolatingFunction object in a newer version with those points? – Gazo

@Leonid Not, this may be a solution. But I have no idea how to correctly extract the points from InterpolatingFunction in version 5.2 in a general way (the InterpolatingFunction may be returned by NDSolve). – Fiddlededee

@Alexey, look for the built-in package: "DifferentialEquationsInterpolatingFunctionAnatomy", it contains functions that can extract range, data points, etc. from the InterpolatingFunction structure. – Fraternity

@István I am looking for version-independent solution. In this way I need to convert InterpolatingFunction into data set inside of version 5.2 because it is not guaranteed (and I have not checked whether it even works in v.8) that in newer versions of Mathematica DifferentialEquations`InterpolatingFunctionAnatomy` will support the old-style InterpolatingFunction from v.5.2. – Fiddlededee

@Alexey I don't remember exact details now and don't have version 5 currently installed, but I recall that this is a matter of extracting some Part(s) of InterpolatingFunction object. You can try some example to figure out which parts are responsible for the points. – Gazo

I removed my posting after I realized (with Mr.Wizard's help) that I had misunderstood your question. – Maldives

DifferentialEquationsInterpolatingFunctionAnatomy should be version-independent, and is the best way to extract information from interpolating functions (since as you've noticed the InputForm representation is undocumented and subject to change.) – Tarbox

@István @Brett Thank you. I just realized that Mathematica 5.2 contains its own package DifferentialEquations`InterpolatingFunctionAnatomy`. – Fiddlededee