Compare with a call-by-value xform:
- <x> => \k.kx
- <\aM> => \k.k(\a<M>)
- <MN> => \k.<M>(\m.<N>(\n.mnk))
+ {x} => \k.kx
+ {\aM} => \k.k(\a{M})
+ {MN} => \k.{M}(\m.{N}(\n.mnk))
This time the reduction unfolds in a different manner:
- <(\x.y)((\x.z)w)> I
- (\k.<\x.y>(\m.<(\x.z)w>(\n.mnk))) I
- <\x.y>(\m.<(\x.z)w>(\n.mnI))
- (\k.k(\x.<y>))(\m.<(\x.z)w>(\n.mnI))
- <(\x.z)w>(\n.(\x.<y>)nI)
- (\k.<\x.z>(\m.<w>(\n.mnk)))(\n.(\x.<y>)nI)
- <\x.z>(\m.<w>(\n.mn(\n.(\x.<y>)nI)))
- (\k.k(\x.<z>))(\m.<w>(\n.mn(\n.(\x.<y>)nI)))
- <w>(\n.(\x.<z>)n(\n.(\x.<y>)nI))
- (\k.kw)(\n.(\x.<z>)n(\n.(\x.<y>)nI))
- (\x.<z>)w(\n.(\x.<y>)nI)
- <z>(\n.(\x.<y>)nI)
- (\k.kz)(\n.(\x.<y>)nI)
- (\x.<y>)zI
- <y>I
+ {(\x.y)((\x.z)w)} I
+ (\k.{\x.y}(\m.{(\x.z)w}(\n.mnk))) I
+ {\x.y}(\m.{(\x.z)w}(\n.mnI))
+ (\k.k(\x.{y}))(\m.{(\x.z)w}(\n.mnI))
+ {(\x.z)w}(\n.(\x.{y})nI)
+ (\k.{\x.z}(\m.{w}(\n.mnk)))(\n.(\x.{y})nI)
+ {\x.z}(\m.{w}(\n.mn(\n.(\x.{y})nI)))
+ (\k.k(\x.{z}))(\m.{w}(\n.mn(\n.(\x.{y})nI)))
+ {w}(\n.(\x.{z})n(\n.(\x.{y})nI))
+ (\k.kw)(\n.(\x.{z})n(\n.(\x.{y})nI))
+ (\x.{z})w(\n.(\x.{y})nI)
+ {z}(\n.(\x.{y})nI)
+ (\k.kz)(\n.(\x.{y})nI)
+ (\x.{y})zI
+ {y}I
(\k.ky)I
I y
3. What happens (in terms of evaluation order) when the application
rule for CBN CPS is changed to `[MN] = \k.[N](\n.[M]nk)`? Likewise,
What happens when the application rule for CBV CPS is changed to
-`<MN> = \k.<N>(\n.<M>(\m.mnk))`?
+`{MN} = \k.{N}(\n.{M}(\m.mnk))`?
4. What happens when the application rules for the CPS xforms are changed to
<pre>
- [MN] = \k.<M>(\m.m<N>k)
- <MN> = \k.[M](\m.[N](\n.mnk))
+ [MN] = \k.{M}(\m.m{N}k)
+ {MN} = \k.[M](\m.[N](\n.mnk))
</pre>
Thinking through the types