Commit 43a5970a authored by Simon Peyton Jones's avatar Simon Peyton Jones
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parent 67565a72
...@@ -662,8 +662,8 @@ Definition [Can-rewrite relation] ...@@ -662,8 +662,8 @@ Definition [Can-rewrite relation]
A "can-rewrite" relation between flavours, written f1 >= f2, is a A "can-rewrite" relation between flavours, written f1 >= f2, is a
binary relation with the following properties binary relation with the following properties
R1. >= is transitive (R1) >= is transitive
R2. If f1 >= f, and f2 >= f, (R2) If f1 >= f, and f2 >= f,
then either f1 >= f2 or f2 >= f1 then either f1 >= f2 or f2 >= f1
Lemma. If f1 >= f then f1 >= f1 Lemma. If f1 >= f then f1 >= f1
...@@ -690,7 +690,7 @@ See Note [Flavours with roles]. ...@@ -690,7 +690,7 @@ See Note [Flavours with roles].
Theorem: S(f,a) is well defined as a function. Theorem: S(f,a) is well defined as a function.
Proof: Suppose (a -f1-> t1) and (a -f2-> t2) are both in S, Proof: Suppose (a -f1-> t1) and (a -f2-> t2) are both in S,
and f1 >= f and f2 >= f and f1 >= f and f2 >= f
Then by (R2) f1 >= f2 or f2 >= f1, which contradicts (WF) Then by (R2) f1 >= f2 or f2 >= f1, which contradicts (WF1)
Notation: repeated application. Notation: repeated application.
S^0(f,t) = t S^0(f,t) = t
...@@ -702,9 +702,6 @@ A generalised substitution S is "inert" iff ...@@ -702,9 +702,6 @@ A generalised substitution S is "inert" iff
(IG1) there is an n such that (IG1) there is an n such that
for every f,t, S^n(f,t) = S^(n+1)(f,t) for every f,t, S^n(f,t) = S^(n+1)(f,t)
(IG2) if (b -f-> t) in S, and f >= f, then S(f,t) = t
that is, each individual binding is "self-stable"
By (IG1) we define S*(f,t) to be the result of exahaustively By (IG1) we define S*(f,t) to be the result of exahaustively
applying S(f,_) to t. applying S(f,_) to t.
...@@ -719,8 +716,8 @@ guarantee that this recursive use will terminate. ...@@ -719,8 +716,8 @@ guarantee that this recursive use will terminate.
Note [Extending the inert equalities] Note [Extending the inert equalities]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This is the main theorem! Theorem [Stability under extension]
This is the main theorem!
Suppose we have a "work item" Suppose we have a "work item"
a -fw-> t a -fw-> t
and an inert generalised substitution S, and an inert generalised substitution S,
......
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