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

docs/about/progress.md

@@ -1,11 +1,9 @@
-# draft of presentation
-
-## sappho short
+# sappho short
 	- sappho types intro
 	- a quick look at msph and spho
 
 
-### The types
+## The types
 
 We take a look at the grammar for sappho types
 
@@ -15,7 +13,7 @@ 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)
@@ -30,7 +28,7 @@ n ∈ nominal
 a ∈ opname
 ```
 
-The type `t <: s` would be expressive sugar for `box (t => s)`
+The type `t <: s` would be syntactic sugar for `box (t => s)`
 
 ### msph and spho
 
@@ -60,7 +58,7 @@ Thoughts
 * maybe eventually add a basic term language and interpreter
 * can we use external software/libraries for proof search?
 
-## interpretation of types
+# interpretation of types
 	- example programs in `msph`
 		- unified syntax for types and bounded polymorphism
 		- example: self typing
@@ -75,7 +73,8 @@ Check formalities.md.
 	- simple rules
 	- type constructor rules
 	- recursion and cyclic proofs
-* next steps?
+
+# next steps?
 	- formals:
 		- formulate theorems
 			- if we use semantic subtyping, isn't it enough to
@@ -85,3 +84,4 @@ Check formalities.md.
 		- simple rules, should be fairly simple
 		- type constructors, straightforward hopefully
 		- recursion and cyclic proofs... `¯\_(ツ)_/¯`
+	- describe use of language with type system (interpretation of types)