Changes between Version 107 and Version 108 of TypeFunctionsSolving
 Timestamp:
 Apr 24, 2009 7:15:48 AM (7 years ago)
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TypeFunctionsSolving
v107 v108 255 255 * '''Step A:''' For any (local or wanted) variable equality of the form `co :: x ~ t`, we apply the substitution `[t/x]` to the '''righthand side''' of all equalities (wanteds only to wanteds). We also perform the same substitution on class constraints (again, wanteds only to wanteds). 256 256 * '''Step B:''' We have two cases: 257 * ''In checking mode,'' for any wanted family equality of the form `co :: F t1..tn ~ alpha`, w e apply the substitution `[F t1..tn/alpha]` to the righthand side of all wanted variable equalities and to both sides of all wanted family equalities with the exception that, if `alpha` is a local flexible (introduced during flattening of wanteds), we do '''not''' substitute into family equalities of the form `co' :: G s1..sm ~ delta`, where `delta` is a nonlocal flexible.257 * ''In checking mode,'' for any wanted family equality of the form `co :: F t1..tn ~ alpha`, where `alpha` is a skolem flexible, we apply the substitution `[F t1..tn/alpha]` to the righthand side of all wanted variable equalities and to both sides of all wanted family equalities. 258 258 * ''In inference mode,'' we proceed as in checking mode, but we do not substitute into variable equalities. 259 * '''Step C:''' Same as Step B, but `alpha` is not a skolem flexible. 259 260 At this point all variables bound in the next step have disappeared from the constraint set; it is as if the variables have been locally instantiated. 260 261 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 is a local skolem flexible that is propagated into the environment by another binding. … … 263 264 * The substitution step can lead to recursive equalities; i.e., we need to apply an occurs check after each substitution. 264 265 * We perform substitutions in two steps due to situations as ` F s ~ alpha, alpha ~ t`. Here, we want to substitute `alpha ~ t` first as `alpha` may occur in class dictionaries where a rigid type may help to select a class instance. 265 * We need to substitute all flexibles that arose as skolems during flattening of wanteds ''before'' we substitute 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 nontermination of the combined classfamily solver .266 * We need to substitute all flexibles that arose as skolems during flattening of wanteds ''before'' we substitute 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 nontermination of the combined classfamily solver — this is the reason for separating Step B and Step C. 266 267 * We need to substitute family equalities into both sides of family equalities; consider, `F t1..tn ~ alpha, G s1..sm ~ alpha`. 267 268 * We must not substitute family equalities into righthand sides of variable equalities. (If the variable equality directly or indirectly instantiates a flexible that is free in the environment, we would instantiate it with a family application, which we set out to avoid.)