diff --git a/src/Stlc.lagda b/src/Stlc.lagda index da75264e..e8c9b400 100644 --- a/src/Stlc.lagda +++ b/src/Stlc.lagda @@ -113,12 +113,30 @@ data Term : Set where if_then_else_ : Term → Term → Term → Term \end{code} -A NOTE ON : AND ∶ +#### Unicode -USE OF ` FOR var +We use the following unicode characters + ` U+0060: GRAVE ACCENT + λ U+03BB GREEK SMALL LETTER LAMBDA + ∶ U+2236 RATIO + · U+00B7: MIDDLE DOT +In particular, ∶ (U+2236 RATIO) is not the same as : (U+003A COLON). +Colon is reserved in Agda for declaring types. Everywhere that we +declare a type in the object language rather than Agda we will use +ratio in place of colon, otherwise our code will not parse. Recall +that in Agda one may treat square brackets `[]` as ordinary symbols, +while round parentheses `()` and curly braces `{}` have special +meaning. +Using ratio is arguably a bad idea, because one must use context +rather than sight to distinguish it from colon. Arguably, it might be +better to use a different symbol, such as `∈` or `::`. We reserve `∈` +for use later to indicate that a variable appears free in a term, and +don't use `::` because we consider it too ugly. + +#### Examples Here are a couple of example terms, `not` of type `𝔹 ⇒ 𝔹`, which complements its argument, and `two` of type @@ -140,13 +158,18 @@ currying. This is made more convenient by declaring `_⇒_` to associate to the right and `_·_` to associate to the left. Thus, - `(𝔹 ⇒ 𝔹) ⇒ 𝔹 ⇒ 𝔹` abbreviates `(𝔹 ⇒ 𝔹) ⇒ (𝔹 ⇒ 𝔹)`, +> `(𝔹 ⇒ 𝔹) ⇒ 𝔹 ⇒ 𝔹` abbreviates `(𝔹 ⇒ 𝔹) ⇒ (𝔹 ⇒ 𝔹)`, and similarly, - `two · not · true` abbreviates `(two · not) · true`. +> `two · not · true` abbreviates `(two · not) · true`. -SCOPE OF λ OR if +We choose the binding strength for abstractions and conditionals +to be weaker than application. For instance, + +> `` λ[ f ∶ 𝔹 ⇒ 𝔹 ] λ[ x ∶ 𝔹 ] ` f · (` f · ` x) `` abbreviates +> `` (λ[ f ∶ 𝔹 ⇒ 𝔹 ] (λ[ x ∶ 𝔹 ] (` f · (` f · ` x)))) `` and not +> `` (λ[ f ∶ 𝔹 ⇒ 𝔹 ] (λ[ x ∶ 𝔹 ] ` f)) · (` f · ` x) ``. \begin{code} example₁ : (𝔹 ⇒ 𝔹) ⇒ 𝔹 ⇒ 𝔹 ≡ (𝔹 ⇒ 𝔹) ⇒ (𝔹 ⇒ 𝔹) @@ -155,7 +178,8 @@ example₁ = refl example₂ : two · not · true ≡ (two · not) · true example₂ = refl -example₃ : λ[ f ∶ 𝔹 ⇒ 𝔹 ] λ[ x ∶ 𝔹 ] ` f · (` f · ` x) ≡ (λ[ f ∶ 𝔹 ⇒ 𝔹 ] (λ[ x ∶ 𝔹 ] (` f · (` f · ` x)))) +example₃ : λ[ f ∶ 𝔹 ⇒ 𝔹 ] λ[ x ∶ 𝔹 ] ` f · (` f · ` x) + ≡ (λ[ f ∶ 𝔹 ⇒ 𝔹 ] (λ[ x ∶ 𝔹 ] (` f · (` f · ` x)))) example₃ = refl \end{code}