From ea42753758afead48455446d056514a51144f8b8 Mon Sep 17 00:00:00 2001
From: Jeremy Siek <jsiek@indiana.edu>
Date: Sat, 18 Jan 2020 21:38:42 -0500
Subject: [PATCH] added hints to Bin-isomorphism exercise
---
src/plfa/part1/Quantifiers.lagda.md | 18 ++++++++++++++++++
1 file changed, 18 insertions(+)
diff --git a/src/plfa/part1/Quantifiers.lagda.md b/src/plfa/part1/Quantifiers.lagda.md
index 545626d9..559560ce 100644
--- a/src/plfa/part1/Quantifiers.lagda.md
+++ b/src/plfa/part1/Quantifiers.lagda.md
@@ -463,6 +463,24 @@ And to establish the following properties:
Using the above, establish that there is an isomorphism between `ℕ` and
`∃[ b ](Can b)`.
+We recommend proving following lemmas which show that, for a given
+binary number `b`, there is only one proof of `One b` and similarly
+for `Can b`.
+
+ ≡One : ∀{b : Bin} (o o' : One b) → o ≡ o'
+
+ ≡Can : ∀{b : Bin} (cb : Can b) (cb' : Can b) → cb ≡ cb'
+
+The proof of `to∘from` is tricky. We recommend proving the following lemma
+
+ to∘from-aux : ∀ (b : Bin) (cb : Can b) → to (from b) ≡ b
+ → _≡_ {_} {∃[ b ](Can b)} ⟨ to (from b) , canon-to (from b) ⟩ ⟨ b , cb ⟩
+
+You cannot immediately use `≡Can` to equate `canon-to (from b)` and
+`cb` because they have different types: `Can (to (from b))` and `Can b`
+respectively. You must first get their types to be equal, which
+can be done by changing the type of `cb` using `rewrite`.
+
```
-- Your code goes here
```