diff --git a/src/plfa/part3/Denotational.lagda.md b/src/plfa/part3/Denotational.lagda.md index 453cb4fb..83346b39 100644 --- a/src/plfa/part3/Denotational.lagda.md +++ b/src/plfa/part3/Denotational.lagda.md @@ -400,14 +400,11 @@ id-app-id : ∀ {u : Value} → `∅ ⊢ id · id ↓ (u ↦ u) id-app-id {u} = ↦-elim (↦-intro var) (↦-intro var) ``` -Next we revisit the Church numeral two. - - ƛ ƛ (# 1 · (# 1 · # 0)) - -This function has two parameters: a function and an arbitrary value -`u`, and it applies the function twice. So the function must map `u` -to some value, which we'll name `v`. Then for the second application, -it must map `v` to some value. Let's name it `w`. So the function's +Next we revisit the Church numeral two: `λ f. λ u. (f (f u))`. +This function has two parameters: a function `f` and an arbitrary value +`u`, and it applies `f` twice. So `f` must map `u` to some value, which +we'll name `v`. Then for the second application, +`f` must map `v` to some value. Let's name it `w`. So the function's table must include two entries, both `u ↦ v` and `v ↦ w`. For each application of the table, we extract the appropriate entry from it using the `sub` rule. In particular, we use the ⊑-conj-R1 and