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Merge branch 'dev' of github.com:plfa/plfa.github.io into dev

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wadler 2018-07-06 10:12:48 -03:00
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11
src/plfa/Induction.lagda
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@ -314,7 +314,7 @@ For the base case, we must show:
zero + zero ≡ zero zero + zero ≡ zero
Simplifying with the base case of of addition, this is straightforward. Simplifying with the base case of addition, this is straightforward.
For the inductive case, we must show: For the inductive case, we must show:
@ -385,7 +385,7 @@ For the base case, we must show:
zero + suc n ≡ suc (zero + n) zero + suc n ≡ suc (zero + n)
Simplifying with the base case of of addition, this is straightforward. Simplifying with the base case of addition, this is straightforward.
For the inductive case, we must show: For the inductive case, we must show:
@ -497,9 +497,10 @@ time we are concerned with judgements asserting associativity.
Now, we apply the rules to all the judgements we know about. The base Now, we apply the rules to all the judgements we know about. The base
case tells us that `(zero + n) + p ≡ zero + (n + p)` for every natural case tells us that `(zero + n) + p ≡ zero + (n + p)` for every natural
`n` and `p`. The inductive case tells us that if `(m + n) + p ≡ m + `n` and `p`. The inductive case tells us that if `(m + n) + p ≡ m +
(n + p)` (on the day before today) then `(suc m + n) + p ≡ suc m + (n (n + p)` (on the day before today) then
+ p)` (today). We didn't know any judgments about associativity `(suc m + n) + p ≡ suc m + (n + p)` (today).
before today, so that rule doesn't give us any new judgments. We didn't know any judgments about associativity before today, so that
rule doesn't give us any new judgments.
-- on the first day, we know about associativity of 0 -- on the first day, we know about associativity of 0
(0 + 0) + 0 ≡ 0 + (0 + 0) ... (0 + 4) + 5 ≡ 0 + (4 + 5) ... (0 + 0) + 0 ≡ 0 + (0 + 0) ... (0 + 4) + 5 ≡ 0 + (4 + 5) ...