+-- Can the given core expression be applied to something? This is true for
+-- applying to a value as well as a type.
+is_applicable :: CoreSyn.CoreExpr -> Bool
+is_applicable expr = is_fun expr || is_poly expr
+
+-- Does the given CoreExpr have any free type vars?
+has_free_tyvars :: CoreSyn.CoreExpr -> Bool
+has_free_tyvars = not . VarSet.isEmptyVarSet . (CoreFVs.exprSomeFreeVars Var.isTyVar)
+
+-- Turns a Var CoreExpr into the Id inside it. Will of course only work for
+-- simple Var CoreExprs, not complexer ones.
+exprToVar :: CoreSyn.CoreExpr -> Var.Id
+exprToVar (CoreSyn.Var id) = id