fixing parsing

docs/about/formalities.md

@@ -8,7 +8,7 @@ s, t ::= s | t              (disjunction, a.k.a. union)
        | s => t             (implication)
        | s -> t             (arrow, a.k.a. function)
        | forall x . t       (forall, polymorphic)
-       | box t              (box, c.f. modular logic)
+       | box t              (box, c.f. modal logic)
        | a [t..]            (type operator application)
        | x                  (variable)
        | n                  (nominal)
@@ -37,23 +37,23 @@ s, γ ⊢ s, δ
 ---- [false-left]
 false, γ ⊢ δ
 
-// trace pairs: none
+// trace pairs: none?
 s, t, γ ⊢ δ
 ---- [conj-left]
 s & t, γ ⊢ δ
 
-// trace pairs: none
+// trace pairs: none?
 γ ⊢ s, t, δ
 ---- [disj-right]
 γ ⊢ s | t, δ
 
-// trace pairs: none
+// trace pairs: none?
 s, γ ⊢ δ
 t, γ ⊢ δ
 ---- [disj-left]
 s | t, γ ⊢ δ
 
-// trace pairs: none
+// trace pairs: none?
 γ ⊢ s, δ
 γ ⊢ t, δ
 ---- [conj-right]
@@ -61,12 +61,12 @@ s | t, γ ⊢ δ
 
 // XXX
 // remove s => t? always make progress
-// trace pairs: none
+// trace pairs: none?
 s => t, s, t, γ ⊢ δ
 ---- [impl-left]
 s => t, s, γ ⊢ δ
 
-// trace pairs: none
+// trace pairs: none?
 s, γ ⊢ t, δ
 ---- [impl-right]
 γ ⊢ s => t, δ
@@ -89,7 +89,7 @@ box t, γ ⊢ δ
 // to exclude typedefs like
 // type A = A
 // Or that our cycle detection excludes paths between "identical" states.
-// trace pairs: none
+// trace pairs: none?
 γ ⊢ expand(a[t..]), δ
 ----
 γ ⊢ a[t..], δ
@@ -114,6 +114,7 @@ n fresh
 ---- [forall]
 γ ⊢ δ
 
+// TODO can we choose a simpler rule instead?
 // 1 + n! premises
 // trace pairs: i ∈ [1..(n! + 1)], premise[i] -- conclusion
 c, γ*  ⊢ a_1, ..., a_n, δ*
@@ -122,9 +123,10 @@ c, γ*  ⊢ a_1, ..., a_n, δ*
 	OR
 	{ b_i | i ∈ ¬I }, γ* ⊢ d, δ*
 ---- [loads-of-fun]
-a_1 -> b_1, ..., a_n -> b_n, γ ⊢ c -> d, δ
+a_1 -> b_1, ..., a_n -> b_n, γ    ⊢    c -> d, δ
 ```
 
+
 ### context operators
 
 * box filtering