1 files changed, 21 insertions, 20 deletions
diff --git a/chapter-interprocedural-sccp/README.md b/chapter-interprocedural-sccp/README.md
index 7310de80..d17f937c 100644
--- a/chapter-interprocedural-sccp/README.md
+++ b/chapter-interprocedural-sccp/README.md
@@ -3,11 +3,11 @@
 English | [日本語](README.ja.md)
 
 [Previous: SCCP Within a Function](../chapter-sccp/README.md) |
-[Next: SSA Before Types Are Known](../chapter-incomplete-types/README.md) |
+[Next: SSA Before Types Are Known](../chapter-incomplete-types/README.md)
 
-The previous chapter runs SCCP with each function, and assumes very
+The previous chapter runs SCCP within each function, and assumes very
 conservative typing across calls.  This chapter lets the same worklist
-discover call edges and propagate values between functions.  
+discover call edges and propagate values between functions.
 
 ## Discovering calls while solving types
 
@@ -20,21 +20,21 @@ Such edges make up a [Call Graph](https://en.wikipedia.org/wiki/Call_graph).
 We extend the normal SCCP algorithm to observe when a `Call`s function pointer
 input changes - when it picks up new function targets.  There are only a finite
 number so we represent them exactly with *function indices*, or *fidx*
-internally, as described earlier chapters.  (Separate compilation adds a
-special index for the infinite unknown functions that are called outside this
-compilation unit).
+internally, as described in earlier chapters. Unknown targets still require
+conservative summaries. Later, separate compilation must also preserve function
+identities across object files.
 
 Once we observe a new *fidx* at a `Call`, we *link* the `Call` with the `Fun`,
 and the `Return` with the `CallEnd`.  Such linkage acts exactly as-if we added
-a CFG edge from the `Call` to the `Fun`, and the `Call`s arguments to the
-`Fun`s `ParmNodes`.  `FunNodes` extend `RegionNodes` (and `ParmNodes` extend
+a CFG edge from the `Call` to the `Fun`, and data edges from the `Call`s arguments
+to the `Fun`s `ParmNodes`.  `FunNodes` extend `RegionNodes` (and `ParmNodes` extend
 `PhiNodes`), so this linkage uses the same semantics.  `Fun`s become reachable
 when called; `Parm`s merge (*meet*) all calling arguments, and so on.
 Similarly, `CallEnd`s merge results from all called functions, computing the
 *meet* over all the `Return`s.
 
 This *link* step adds a few checks to our algorithm's inner loop, and also
-builds a precise Call Graph which allows our SCCP to run interprocedurally.
+builds a conservative Call Graph from the targets found by type propagation.
 Other than discovering a few new edges as the algorithm proceeds, the core
 algorithm is unchanged.  We are guaranteed to terminate with a fixed point
 solution, and may discover e.g. certain call parameters are constants (or
@@ -42,25 +42,26 @@ e.g. not-null) on all calling paths.
 
 ## Recursion is a loop in disguise
 
-We use the notion of *widening* integer ranges at loop heads, see Chapter XXX.
+We use *widening* of integer ranges at loop heads, as described in the
+[previous chapter](../chapter-sccp/README.md#convergence-and-calls).
 This allows us to have a sharper notion of integers over `BOTTOM` without also
-allowing the lattice to fall 2^32 times.  The same issue arises during
+allowing the range to grow one integer at a time. The same issue arises during
 recursive calls: an argument can flow from a Parm through arithmetic into a
 recursive call, then back to the same Parm.
 
 ```simple
-val fact = { int x -> x ? 0 : f(x-1)+1; };
+val f = { int x -> x == 0 ? 0 : f(x-1)+1; };
 ```
 
-Here if we pass in `f(999)` , parameter `x` will have the integer range
-`[999]`.  We'll then track the recursive call to `f(998)` via normal SCCP 
-and realize the parameter `x` has a range `[999-998]`.  Lather, rinse, repeat 
-and we're at `[999-997]`.  We need to *widen* integer parameters at `Parms`
-not just loop-head `Phis`.  
+If the only outside call is `f(999)`, parameter `x` starts with the range
+`[999,999]`. We'll then track the recursive call to `f(998)` via normal SCCP
+and discover that `x` has range `[998,999]`. Lather, rinse, repeat,
+and we're at `[997,999]`. We need to *widen* integer parameters at `Parms`,
+not just loop-head `Phis`.
 
 The same issue arises during the recursive return: the first return will be
-with `0` when `x` is zero, then we return `0+1` or the range `[0-1]` then range
-`[0-2]`, etc.  `CallEnds` also need to widen.
+with `0` when `x` is zero, then we return `0+1` or the range `[0,1]`, then range
+`[0,2]`, etc. `CallEnds` also need to widen.
 
 Loop Phis, Parms, and CallEnds get widening points, and since this same issue
 hits in 3 unrelated places, their comments all cross-reference each other.
@@ -72,7 +73,7 @@ A `FunPtrNode` (function address) that survives outside a direct call may be
 called by code we cannot see.  We have to assume the address escapes into
 unknown code, which later calls it.  We preserve its unknown-caller input,
 since we cannot tell what that unknown caller will pass.  Precise escape
-analysis is introduced later exactly to inmprove this.
+analysis is introduced later to improve this.
 
 ## Building and checking