From 2486155f3f3dc8c0aa19ac44646ec42f6a871d07 Mon Sep 17 00:00:00 2001
From: Jeremy Siek <jsiek@indiana.edu>
Date: Sun, 29 Mar 2020 16:51:25 -0400
Subject: [PATCH] doh! got Church and Scott mixed up, unfixing
---
src/plfa/part2/Untyped.lagda.md | 18 +++++++-----------
1 file changed, 7 insertions(+), 11 deletions(-)
diff --git a/src/plfa/part2/Untyped.lagda.md b/src/plfa/part2/Untyped.lagda.md
index be787cf2..28a1f5de 100644
--- a/src/plfa/part2/Untyped.lagda.md
+++ b/src/plfa/part2/Untyped.lagda.md
@@ -681,7 +681,7 @@ Here is the representation of naturals encoded with de Bruijn indexes:
`zero = ƛ ƛ (# 0)
`suc_ : ∀ {Γ} → (Γ ⊢ ★) → (Γ ⊢ ★)
-`suc_ M = (ƛ ƛ ƛ (# 1 · (# 2 · # 1 · # 0))) · M
+`suc_ M = (ƛ ƛ ƛ (# 1 · # 2)) · M
case : ∀ {Γ} → (Γ ⊢ ★) → (Γ ⊢ ★) → (Γ , ★ ⊢ ★) → (Γ ⊢ ★)
case L M N = L · (ƛ N) · M
@@ -691,21 +691,17 @@ definitions. The successor branch expects an additional variable to
be in scope (as indicated by its type), so it is converted to an
ordinary term using lambda abstraction.
-Applying successor to the zero indeed reduces to the Church numeral
+Applying successor to the zero indeed reduces to the Scott numeral
for one.
```
_ : eval (gas 100) (`suc_ {∅} `zero) ≡
steps
- ((ƛ (ƛ (ƛ (` (S Z)) · ((` (S (S Z))) · (` (S Z)) · (` Z))))) · (ƛ (ƛ (` Z)))
- —→⟨ β ⟩
- ƛ (ƛ (` (S Z)) · ((ƛ (ƛ (` Z))) · (` (S Z)) · (` Z)))
- —→⟨ ζ (ζ (ξ₂ (ξ₁ β))) ⟩
- ƛ (ƛ (` (S Z)) · ((ƛ (` Z)) · (` Z)))
- —→⟨ ζ (ζ (ξ₂ β)) ⟩
- ƛ (ƛ (` (S Z)) · (` Z))
- ∎)
- (done (ƛ (ƛ (′ (` (S Z)) · (′ (` Z))))))
+ ((ƛ (ƛ (ƛ # 1 · # 2))) · (ƛ (ƛ # 0))
+ —→⟨ β ⟩
+ ƛ (ƛ # 1 · (ƛ (ƛ # 0)))
+ ∎)
+ (done (ƛ (ƛ (′ (` (S Z)) · (ƛ (ƛ (′ (` Z))))))))
_ = refl
```