# Changes between Version 97 and Version 98 of TypeFunctionsSolving

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Timestamp:
Sep 30, 2008 5:09:45 AM (9 years ago)
Comment:

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• ## TypeFunctionsSolving

 v97 1.  '''Substitution:''' For any variable equality of the form `co :: x ~ t` (both local and wanted), we apply the substitution `[t/x]` to the '''left-hand side''' of all equalities.  We also perform the same substitution on all class constraints. 2. '''Instantiation:''' For any variable equality of the form `co :: alpha ~ t` or `co :: a ~ alpha`, where `co` is wanted, we instantiate `alpha` with `t` or `a`, respectively, and set `co := id`.  Moreover, we have to do the same for equalities of the form `co :: F t1..tn ~ alpha` unless we are in inference mode and `alpha` appears in the environment or any other wanteds. (We never instantiate any flexibles introduced by flattening locals.) The substitution step can lead to recursive equalities; i.e., we need to apply an occurs check after each substitution.  We need to instantiate all flexibles that arose during flattening of wanteds ''before'' we instantiate any other flexibles.  Consider `F delta ~ alpha, F alpha ~ delta`, where `alpha` is a skolem and `delta` a free flexible.  We need to produce `F (F delta) ~ delta` (and not `F (F alpha) ~ alpha`).  Otherwise, we may wrongly claim to having performed an improvement, which can lead to non-termination of the combined class-family solver. The substitution step can lead to recursive equalities; i.e., we need to apply an occurs check after each substitution.  We need to instantiate all flexibles that arose as skolems during flattening of wanteds ''before'' we instantiate any other flexibles.  Consider `F delta ~ alpha, F alpha ~ delta`, where `alpha` is a skolem and `delta` a free flexible.  We need to produce `F (F delta) ~ delta` (and not `F (F alpha) ~ alpha`).  Otherwise, we may wrongly claim to having performed an improvement, which can lead to non-termination of the combined class-family solver. Note that it is an important property of propagation that we only need to substitute into right-hand sides during finalisation.  After finalisation and zonking all flattening of locals is undone (c.f., note below the flattening code above).