Changes between Version 100 and Version 101 of TypeFunctionsSolving

Timestamp:

04/14/09 00:48:12 (4 years ago)

Author:

chak

Comment:

--

TypeFunctionsSolving

@@ -250 +250 @@
  1.  '''Substitution:''' 
   * '''Pass A:''' For any variable equality of the form `co :: x ~ t` (both local and wanted), we apply the substitution `[t/x]` to the '''right-hand side''' of all equalities.  We also perform the same substitution on class constraints.
-  * '''Pass B:''' For any family equality of the form `co :: F t1..tn ~ alpha`, we apply the substitution `[F t1..tn/alpha]` to the '''both sides''' of all family equalities.
+  * '''Pass B:''' Unless we are in inference mode, for any wanted family equality of the form `co :: F t1..tn ~ alpha`, we apply the substitution `[F t1..tn/alpha]` to '''both sides''' of all family equalities.  We need to substitute all flexibles that arose as skolems during flattening of wanteds ''before'' we substitute any other flexibles.
  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 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.
+
+Important points are the following:
+ * The substitution step can lead to recursive equalities; i.e., we need to apply an occurs check after each substitution.  
+ * 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 non-termination of the combined class-family solver.
+ * We need to substitute family equalities into both sides of family equalities; consider, `F t1..tn ~ alpha, G s1..sm ~ alpha`.
 
 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).