abstract out the kind of environment classifiers (ECKind)

[coq-hetmet.git] / src / HaskKinds.v

diff --git a/src/HaskKinds.v b/src/HaskKinds.v
index 583bb86..2200f51 100644 (file)
--- a/src/HaskKinds.v
+++ b/src/HaskKinds.v
@@ -12,30 +12,46 @@ Variable Note                : Type.                         Extract Inlined Con
 Variable natToString         : nat         -> string.        Extract Inlined Constant natToString => "natToString".
 Instance NatToStringInstance : ToString nat := { toString := natToString }.
 
-(* Figure 7: production κ, ι *)
 Inductive Kind : Type := 
-  | KindType          : Kind                      (* ★  - the kind of coercions and the kind of types inhabited by [boxed] values *)
-  | KindTypeFunction  : Kind  -> Kind  -> Kind    (* ⇛  - type-function-space; things of kind X⇛Y are NOT inhabited by expressions*)
+  | KindStar          : Kind                      (* ★  - the kind of coercions and the kind of types inhabited by [boxed] values *)
+  | KindArrow         : Kind  -> Kind  -> Kind    (* ⇛  - type-function-space; things of kind X⇛Y are NOT inhabited by expressions*)
   | KindUnliftedType  : Kind                      (* not in the paper - this is the kind of unboxed non-tuple types *)
   | KindUnboxedTuple  : Kind                      (* not in the paper - this is the kind of unboxed tuples *)
-  | KindArgType       : Kind                      (* not in the paper - this is the lub of KindType and KindUnliftedType *)
-  | KindOpenType      : Kind                      (* not in the paper - kind of all types (lifted, boxed, whatever) *).
+  | KindArgType       : Kind                      (* not in the paper - this is the lub of KindStar and KindUnliftedType *)
+  | KindOpenType      : Kind                      (* not in the paper - kind of all types (lifted, boxed, whatever) *)
+  .
 
 Open Scope string_scope.
 Fixpoint kindToString (k:Kind) : string :=
   match k with
-  | KindType                     => "*"
-  | KindTypeFunction KindType k2 => "*=>"+++kindToString k2
-  | KindTypeFunction k1 k2       => "("+++kindToString k1+++")=>"+++kindToString k2
+  | KindStar                     => "*"
+  | KindArrow KindStar k2        => "*=>"+++kindToString k2
+  | KindArrow k1 k2              => "("+++kindToString k1+++")=>"+++kindToString k2
   | KindUnliftedType             => "#"
   | KindUnboxedTuple             => "(#)"
-  | KindArgType                  => "?"
+  | KindArgType                  => "??"
   | KindOpenType                 => "?"
   end.
 Instance KindToString : ToString Kind := { toString := kindToString }.
 
-Notation "'★'"   := KindType.
-Notation "a ⇛ b" := (KindTypeFunction a b).
+Notation "'★'"   := KindStar.
+Notation "a ⇛ b" := (KindArrow a b).
+
+(* the kind of environment classifiers *)
+Definition ECKind := ★ .  
+Opaque ECKind.
+
+Fixpoint kindToLatexMath (k:Kind) : LatexMath :=
+  match k with
+  | ★                            => rawLatexMath "\star"
+  | ★  ⇛ k2                      => (rawLatexMath "\star\Rightarrow ")+++kindToLatexMath k2
+  | k1 ⇛ k2                      => (rawLatexMath "(")+++kindToLatexMath k1+++(rawLatexMath ")\Rightarrow ")+++kindToLatexMath k2
+  | KindUnliftedType             => rawLatexMath "\text{\tt{\#}}"
+  | KindUnboxedTuple             => rawLatexMath "\text{\tt{(\#)}}"
+  | KindArgType                  => rawLatexMath "\text{\tt{??}}"
+  | KindOpenType                 => rawLatexMath "\text{\tt{?}}"
+  end.
+Instance KindToLatexMath : ToLatexMath Kind := { toLatexMath := kindToLatexMath }.
 
 Instance KindEqDecidable : EqDecidable Kind.
   apply Build_EqDecidable.
@@ -50,3 +66,10 @@ Instance KindEqDecidable : EqDecidable Kind.
     destruct v2; try (right; intro q; inversion q; fail) ; left ; auto.
   Defined.
 
+(* splits a kind into a list of arguments and a result *)
+Fixpoint splitKind (k:Kind) : ((list Kind) * Kind) :=
+  match k with
+    | a ⇛ b => let (args,res) := splitKind b in ((a::args),res)
+    | _     => (nil, k)
+  end.
+