Fix typos and add a missing Unicode symbol

This commit is contained in:
Alexander Skiba 2021-03-10 03:22:46 +07:00
parent a23fd711ac
commit 88763966a7
No known key found for this signature in database
GPG key ID: D223CF0753D9278E
4 changed files with 11 additions and 10 deletions

View file

@ -654,5 +654,5 @@ import Relation.Binary using (Decidable)
U+2228 LOGICAL OR (\or, \vee)
⊃ U+2283 SUPERSET OF (\sup)
ᵇ U+1D47 MODIFIER LETTER SMALL B (\^b)
⌊ U+230A LEFT FLOOR (\cll)
⌋ U+230B RIGHT FLOOR (\clr)
⌊ U+230A LEFT FLOOR (\clL)
⌋ U+230B RIGHT FLOOR (\clR)

View file

@ -520,15 +520,15 @@ it sparingly, but it is occasionally essential.
## Leibniz equality
The form of asserting equality that we have used is due to Martin
Löf, and was published in 1975. An older form is due to Leibniz, and
The form of asserting equality that we have used is due to Martin-Löf,
and was published in 1975. An older form is due to Leibniz, and
was published in 1686. Leibniz asserted the _identity of
indiscernibles_: two objects are equal if and only if they satisfy the
same properties. This principle sometimes goes by the name Leibniz'
Law, and is closely related to Spock's Law, "A difference that makes
no difference is no difference". Here we define Leibniz equality,
and show that two terms satisfy Leibniz equality if and only if they
satisfy Martin Löf equality.
satisfy Martin-Löf equality.
Leibniz equality is usually formalised to state that `x ≐ y` holds if
every property `P` that holds of `x` also holds of `y`. Perhaps
@ -593,7 +593,7 @@ implies `P x`. To do so, we instantiate the equality with a predicate
is trivial by reflexivity, and hence `Q y` follows from `x ≐ y`. But
`Q y` is exactly a proof of what we require, that `P y` implies `P x`.
We now show that Martin Löf equality implies
We now show that Martin-Löf equality implies
Leibniz equality, and vice versa. In the forward direction, if we know
`x ≡ y` we need for any `P` to take evidence of `P x` to evidence of `P y`,
which is easy since equality of `x` and `y` implies that any proof
@ -625,7 +625,7 @@ to a proof of `P y` we need to show `x ≡ y`:
```
The proof is similar to that for symmetry of Leibniz equality. We take
`Q` to be the predicate that holds of `z` if `x ≡ z`. Then `Q x` is
trivial by reflexivity of Martin Löf equality, and hence `Q y`
trivial by reflexivity of Martin-Löf equality, and hence `Q y`
follows from `x ≐ y`. But `Q y` is exactly a proof of what we
require, that `x ≡ y`.

View file

@ -290,7 +290,7 @@ hypothesis:
Reading the chain of equations in the inductive case of the proof, the
top and bottom of the chain match the two sides of the equation to be
shown, and reading down from the top and up from the bottom takes us
to the simplified equation above. The remaining equation, does not follow
to the simplified equation above. The remaining equation does not follow
from simplification alone, so we use an additional operator for chain
reasoning, `_≡⟨_⟩_`, where a justification for the equation appears
within angle brackets. The justification given is:

View file

@ -1314,7 +1314,7 @@ We can fill in the hole by typing C-c C-r again:
And again:
⊢suc = ⊢ƛ (⊢suc (⊢` { }3))
⊢suc = ⊢ƛ (⊢suc (⊢` { }3))
?3 : ∅ , "n" ⦂ ` ∋ "n" ⦂ `
A further attempt with C-c C-r yields the message:
@ -1323,7 +1323,7 @@ A further attempt with C-c C-r yields the message:
We can fill in `Z` by hand. If we type C-c C-space, Agda will confirm we are done:
⊢suc = ⊢ƛ (⊢suc (⊢` Z))
⊢suc = ⊢ƛ (⊢suc (⊢` Z))
The entire process can be automated using Agsy, invoked with C-c C-a.
@ -1415,6 +1415,7 @@ This chapter uses the following unicode:
⇒ U+21D2 RIGHTWARDS DOUBLE ARROW (\=>)
ƛ U+019B LATIN SMALL LETTER LAMBDA WITH STROKE (\Gl-)
· U+00B7 MIDDLE DOT (\cdot)
≟ U+225F QUESTIONED EQUAL TO (\?=)
— U+2014 EM DASH (\em)
↠ U+21A0 RIGHTWARDS TWO HEADED ARROW (\rr-)
ξ U+03BE GREEK SMALL LETTER XI (\Gx or \xi)