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Fixing a few suspected typos #1

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14 changes: 7 additions & 7 deletions EATT/README.md
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Original file line number Diff line number Diff line change
Expand Up @@ -33,7 +33,7 @@ name ::=
(alphanumeric)

defs ::=
| name : term = term; term -- top-level definition
| name : term = term; defs -- top-level definition
| <eof> -- end of file

term ::=
Expand Down Expand Up @@ -155,7 +155,7 @@ ctx |- A : Type
---------------
stratified(A)

stratified(f) uses(x,f) <= 1 level(x,f) == 0
stratified(f) uses(x,f) <= 1 level(x,b) == 0
--------------------------------------------------
stratified(λx.f)

Expand Down Expand Up @@ -201,7 +201,7 @@ Let `profile(t, n)` be the number of applications and duplications at level `n`
of a term `t`. For example, the following term:

```
λt. ((t #λx.x) #(λy.y λz.z))
t := λf. ((f #λx.x) #(λy.y λz.z))
```

Has the following profile:
Expand All @@ -216,7 +216,7 @@ Because there are 2 applications on level 0 and 1 application on level 1.
The following term:

```
λf.
t := λf.
dup a = (λk.k #f)
dup b = #λx. (a (a x))
# λx. (b (b x))
Expand All @@ -232,8 +232,8 @@ profile(t, 1) == 4
Because there are 1 application and 2 duplications on level 0 and 4 applications
on level 1.

The key fact to note is that evaluating a redex on level `n` of a term `t`
always decreases `profile(t, n)` by at least 1, and leaves `profile(t, m)`
The key fact to note is that evaluating a redex on level `n` of a stratified term
`t` always decreases `profile(t, n)` by at least 1, and leaves `profile(t, m)`
untouched for any `m < n`. Let's consider the relevant reductions.

An application on level `n`:
Expand All @@ -244,7 +244,7 @@ An application on level `n`:

Evaluates to `f[x <- a]`. Since `x` can only occur at most once (because lambdas
are affine), then no new applications or duplications can be created by that
evaluation. Moreover, since the number of boxes surrounding
evaluation.

Since the number of boxes surrounding the occurrence of `x` in `f` must be `0`,
then `a` will stay on level `n` after reduction. Moreover, since `x` only
Expand Down