Properly handling variance for arrays to avoid invalid subtyping.

37 files changed, 325 insertions, 172 deletions

diff --git a/.github/workflows/setup_aedifex/action.yml b/.github/workflows/setup_aedifex/action.yml
index bc848c2f0..fa70014a3 100644
--- a/.github/workflows/setup_aedifex/action.yml
+++ b/.github/workflows/setup_aedifex/action.yml
@@ -1,3 +1,5 @@
+# https://cardinalby.github.io/blog/post/github-actions/dry-reusing-code-in-github-actions/
+# https://docs.github.com/en/actions/creating-actions/creating-a-composite-action
 name: 'Setup Aedifex'
 runs:
   using: "composite"
@@ -8,7 +10,8 @@ runs:
         distribution: 'temurin'
         java-version: '17'
     
-    - uses: actions/checkout@v2
+    # Presumably, whoever invokes this action already has done a checkout.
+    # - uses: actions/checkout@v2
     
     - run: wget https://github.com/LuxLang/lux/releases/download/0.6.5/aedifex_do_not_touch_3.jar && mv aedifex_do_not_touch_3.jar aedifex.jar
       shell: bash
diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index f8b31badd..740da5621 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -4,11 +4,13 @@ jobs:
   test_stdlib_on_jvm:
     runs-on: ubuntu-latest
     steps:
+      - uses: actions/checkout@v2
       - uses: ./.github/workflows/setup_aedifex
       - run: cd ./stdlib/ && ../lux.sh with jvm with bibliotheca test
   test_stdlib_on_node_js:
     runs-on: ubuntu-latest
     steps:
+      - uses: actions/checkout@v2
       - uses: ./.github/workflows/setup_aedifex
       # https://github.com/actions/setup-node
       - uses: actions/setup-node@v2
diff --git a/documentation/bookmark/arithmetic.md b/documentation/bookmark/arithmetic.md
deleted file mode 100644
index e4a3ddd07..000000000
--- a/documentation/bookmark/arithmetic.md
+++ /dev/null
@@ -1,12 +0,0 @@
-# Saturation
-
-1. [Saturation arithmetic](https://en.wikipedia.org/wiki/Saturation_arithmetic)
-
-# Interval
-
-1. [Interval Arithmetic: Not All Intervals are Created Equal](https://samlikes.pizza/pluto_interval_blog.jl.html)
-1. [Growing a Language, by Guy Steele](https://www.youtube.com/watch?v=_ahvzDzKdB0&t=2214s)
-1. [Yet another alternative to floating-point numbers](https://wordsandbuttons.online/yet_another_alternative_to_floating_point_numbers.html)
-1. [Interval arithmetic](https://en.wikipedia.org/wiki/Interval_arithmetic)
-1. [How do you compute the midpoint of an interval?](https://hal.archives-ouvertes.fr/file/index/docid/576641/filename/computing-midpoint.pdf)
-
diff --git a/documentation/bookmark/back_end/c++.md b/documentation/bookmark/back_end/c++.md
index 8cbb088d5..e86d2672d 100644
--- a/documentation/bookmark/back_end/c++.md
+++ b/documentation/bookmark/back_end/c++.md
@@ -1,5 +1,10 @@
+# Optimization
+
+0. [C and C++ coding style for best performance](https://www.ibm.com/docs/en/aix/7.1?topic=implementation-c-c-coding-style-best-performance)
+
 # Reference
 
+0. [Constant references are not always your friends](https://belaycpp.com/2022/02/15/constant-references-are-not-always-your-friends/)
 0. [Unionizing for Profit: How to Exploit the Power of Unions in C++](https://dev-discuss.pytorch.org/t/unionizing-for-profit-how-to-exploit-the-power-of-unions-in-c/444)
 0. [std::any: How, when, and why](https://devblogs.microsoft.com/cppblog/stdany-how-when-and-why/)
 0. [Using C Libraries in your Modern C++ Embedded Project - Michael Caisse - CppCon 2021](https://www.youtube.com/watch?v=Ototzy-nP4M)
diff --git a/documentation/bookmark/bloat.md b/documentation/bookmark/bloat.md
new file mode 100644
index 000000000..e1091256c
--- /dev/null
+++ b/documentation/bookmark/bloat.md
@@ -0,0 +1,4 @@
+# Reference
+
+0. [Nibbler: Debloating Binary Shared Libraries](https://cs.brown.edu/~vpk/papers/nibbler.acsac19.pdf)
+
diff --git a/documentation/bookmark/business/management.md b/documentation/bookmark/business/management.md
index b7205f1d0..aa7b63070 100644
--- a/documentation/bookmark/business/management.md
+++ b/documentation/bookmark/business/management.md
@@ -1,4 +1,5 @@
 # Reference
 
+0. [First, Let’s Fire All the Managers](https://hbr.org/2011/12/first-lets-fire-all-the-managers)
 0. [Value Add Disease](https://boz.com/articles/vad)
 
diff --git a/documentation/bookmark/business/model.md b/documentation/bookmark/business/model.md
new file mode 100644
index 000000000..7857523b8
--- /dev/null
+++ b/documentation/bookmark/business/model.md
@@ -0,0 +1,4 @@
+# Reference
+
+0. [Reciprocity as a Business Model: What motivates people to pay for services they receive?](https://briefthoughts.substack.com/p/reciprocity-as-a-business-model?s=r)
+
diff --git a/documentation/bookmark/business/negotiation.md b/documentation/bookmark/business/negotiation.md
index 636bcbbfe..32b092b3d 100644
--- a/documentation/bookmark/business/negotiation.md
+++ b/documentation/bookmark/business/negotiation.md
@@ -1,4 +1,5 @@
 # Reference
 
+0. [A Better Way to Divide the Pie](https://insights.som.yale.edu/insights/better-way-to-divide-the-pie)
 0. [Rethinking Negotiation: A smarter way to split the pie](https://hbr.org/2021/11/rethinking-negotiation)
 
diff --git a/documentation/bookmark/community/onboarding.md b/documentation/bookmark/community/onboarding.md
new file mode 100644
index 000000000..8407ed4cd
--- /dev/null
+++ b/documentation/bookmark/community/onboarding.md
@@ -0,0 +1,4 @@
+# Reference
+
+0. [The Ultimate Guide to Onboarding Software Engineers](https://leadership.garden/onboarding-engineers/)
+
diff --git a/documentation/bookmark/mixin.md b/documentation/bookmark/composition/mixin.md
index bdcc7ae9c..bdcc7ae9c 100644
--- a/documentation/bookmark/mixin.md
+++ b/documentation/bookmark/composition/mixin.md
diff --git a/documentation/bookmark/recursion_schemes.md b/documentation/bookmark/composition/recursion_schemes.md
index 31a013123..31a013123 100644
--- a/documentation/bookmark/recursion_schemes.md
+++ b/documentation/bookmark/composition/recursion_schemes.md
diff --git a/documentation/bookmark/concurrency/disruptor.md b/documentation/bookmark/concurrency/disruptor.md
new file mode 100644
index 000000000..159a380f6
--- /dev/null
+++ b/documentation/bookmark/concurrency/disruptor.md
@@ -0,0 +1,4 @@
+# Reference
+
+0. [LMAX Disruptor: High performance alternative to bounded queues for exchanging data between concurrent threads](https://lmax-exchange.github.io/disruptor/disruptor.html)
+
diff --git a/documentation/bookmark/concurrency/Engine.md b/documentation/bookmark/concurrency/engine.md
index 33d036863..33d036863 100644
--- a/documentation/bookmark/concurrency/Engine.md
+++ b/documentation/bookmark/concurrency/engine.md
diff --git a/documentation/bookmark/concurrency/lock_free_programming.md b/documentation/bookmark/concurrency/lock_free_programming.md
index 1ee123951..d904c8841 100644
--- a/documentation/bookmark/concurrency/lock_free_programming.md
+++ b/documentation/bookmark/concurrency/lock_free_programming.md
@@ -1,5 +1,6 @@
 # Reference
 
+0. [Nonblocking Algorithms and Scalable Multicore Programming: Exploring some alternatives to lock-based synchronization](https://queue.acm.org/detail.cfm?id=2492433)
 0. [Design and Implementation of Highly Scalable Quantifiable Data Structures in C++ - CppCon 2021](https://www.youtube.com/watch?v=ECWsLj0pgbI)
 0. [Building a Lock-free Multi-producer, Multi-consumer Queue for Tcmalloc - Matt Kulukundis - CppCon 21](https://www.youtube.com/watch?v=_qaKkHuHYE0)
 0. [Fear and Loathing in Lock-Free Programming](https://medium.com/@tylerneely/fear-and-loathing-in-lock-free-programming-7158b1cdd50c)
diff --git a/documentation/bookmark/foreign_function_interface.md b/documentation/bookmark/foreign_function_interface.md
index eca9fe747..ce86904db 100644
--- a/documentation/bookmark/foreign_function_interface.md
+++ b/documentation/bookmark/foreign_function_interface.md
@@ -1,4 +1,5 @@
 # Reference
 
+0. [Rust - Python FFI From Scratch](https://i.hsfzxjy.site/2022-03-12-rust-python-ffi-from-scratch/)
 0. [Porting libffi to pure WebAssembly](https://www.tweag.io/blog/2022-03-17-libffi-wasm32/)
 
diff --git a/documentation/bookmark/graphic/3D.md b/documentation/bookmark/graphic/3d.md
index a4d7702f0..a4d7702f0 100644
--- a/documentation/bookmark/graphic/3D.md
+++ b/documentation/bookmark/graphic/3d.md
diff --git a/documentation/bookmark/graphic/svg.md b/documentation/bookmark/graphic/svg.md
new file mode 100644
index 000000000..36b7efe43
--- /dev/null
+++ b/documentation/bookmark/graphic/svg.md
@@ -0,0 +1,4 @@
+# Reference
+
+0. [Optimizing SVG Patterns to Their Smallest Size](https://css-tricks.com/optimizing-svg-patterns/)
+
diff --git a/documentation/bookmark/math/arithmetic.md b/documentation/bookmark/math/arithmetic.md
new file mode 100644
index 000000000..93e4a97ee
--- /dev/null
+++ b/documentation/bookmark/math/arithmetic.md
@@ -0,0 +1,12 @@
+# Saturation
+
+0. [Saturation arithmetic](https://en.wikipedia.org/wiki/Saturation_arithmetic)
+
+# Interval
+
+0. [Interval Arithmetic: Not All Intervals are Created Equal](https://samlikes.pizza/pluto_interval_blog.jl.html)
+0. [Growing a Language, by Guy Steele](https://www.youtube.com/watch?v=_ahvzDzKdB0&t=2214s)
+0. [Yet another alternative to floating-point numbers](https://wordsandbuttons.online/yet_another_alternative_to_floating_point_numbers.html)
+0. [Interval arithmetic](https://en.wikipedia.org/wiki/Interval_arithmetic)
+0. [How do you compute the midpoint of an interval?](https://hal.archives-ouvertes.fr/file/index/docid/576641/filename/computing-midpoint.pdf)
+
diff --git a/documentation/bookmark/music/language.md b/documentation/bookmark/music/language.md
new file mode 100644
index 000000000..f7fb95dd6
--- /dev/null
+++ b/documentation/bookmark/music/language.md
@@ -0,0 +1,4 @@
+# Reference
+
+0. [glicol](https://glicol.org/)
+
diff --git a/documentation/bookmark/resource_management.md b/documentation/bookmark/resource_management.md
index 3b353ccab..ef459b9f0 100644
--- a/documentation/bookmark/resource_management.md
+++ b/documentation/bookmark/resource_management.md
@@ -1,5 +1,6 @@
 # Reference
 
-1. [Understanding ResourceT](https://www.fpcomplete.com/blog/2017/06/understanding-resourcet/)
-1. [Composable resource management in Scala](https://bszwej.medium.com/composable-resource-management-in-scala-ce902bda48b2)
+0. [Vale's Higher RAII, the pattern that saved me a vital 5 hours in the 7DRL Challenge](https://verdagon.dev/blog/higher-raii-7drl)
+0. [Understanding ResourceT](https://www.fpcomplete.com/blog/2017/06/understanding-resourcet/)
+0. [Composable resource management in Scala](https://bszwej.medium.com/composable-resource-management-in-scala-ce902bda48b2)
 
diff --git a/documentation/bookmark/text/unicode.md b/documentation/bookmark/text/unicode.md
new file mode 100644
index 000000000..f58b09aac
--- /dev/null
+++ b/documentation/bookmark/text/unicode.md
@@ -0,0 +1,4 @@
+# Reference
+
+0. [How Unicode helps to ruin your software](https://blog.typeable.io/posts/2021-08-17-unicode.html)
+
diff --git a/documentation/bookmark/text/utf8.md b/documentation/bookmark/text/utf8.md
new file mode 100644
index 000000000..4def76b75
--- /dev/null
+++ b/documentation/bookmark/text/utf8.md
@@ -0,0 +1,9 @@
+# Reference
+
+0. [A Branchless UTF-8 Decoder](https://nullprogram.com/blog/2017/10/06/)
+0. [skeeto/branchless-utf8](https://github.com/skeeto/branchless-utf8/blob/master/utf8.h)
+0. [trivial-utf-8](https://gitlab.common-lisp.net/trivial-utf-8/trivial-utf-8)
+0. [utf8: Unicode Text Processing](https://rdrr.io/cran/utf8/)
+0. [Encoding character strings in R](https://rstudio-pubs-static.s3.amazonaws.com/279354_f552c4c41852439f910ad620763960b6.html)
+0. [Any Encoding, Ever - ztd.text and Unicode for C++](https://thephd.dev/any-encoding-ever-ztd-text-unicode-cpp)
+
diff --git a/documentation/bookmark/type_theory/unit.md b/documentation/bookmark/type_theory/unit.md
index cf23e396c..1a82ddf66 100644
--- a/documentation/bookmark/type_theory/unit.md
+++ b/documentation/bookmark/type_theory/unit.md
@@ -1,5 +1,6 @@
 # Reference
 
-1. https://en.wikipedia.org/wiki/Metric_prefix#Metric_units
-1. [unittyped: An extendable library for type-safe computations including units.](https://hackage.haskell.org/package/unittyped)
+0. [mp-units - A Units Library for C++](https://github.com/mpusz/units)
+0. https://en.wikipedia.org/wiki/Metric_prefix#Metric_units
+0. [unittyped: An extendable library for type-safe computations including units.](https://hackage.haskell.org/package/unittyped)
 
diff --git a/documentation/bookmark/unicode.md b/documentation/bookmark/unicode.md
deleted file mode 100644
index 706b3791d..000000000
--- a/documentation/bookmark/unicode.md
+++ /dev/null
@@ -1,4 +0,0 @@
-# Reference
-
-1. [How Unicode helps to ruin your software](https://blog.typeable.io/posts/2021-08-17-unicode.html)
-
diff --git a/documentation/bookmark/utf8.md b/documentation/bookmark/utf8.md
deleted file mode 100644
index 3dd68e828..000000000
--- a/documentation/bookmark/utf8.md
+++ /dev/null
@@ -1,9 +0,0 @@
-# Reference
-
-1. [A Branchless UTF-8 Decoder](https://nullprogram.com/blog/2017/10/06/)
-1. [skeeto/branchless-utf8](https://github.com/skeeto/branchless-utf8/blob/master/utf8.h)
-1. [trivial-utf-8](https://gitlab.common-lisp.net/trivial-utf-8/trivial-utf-8)
-1. [utf8: Unicode Text Processing](https://rdrr.io/cran/utf8/)
-1. [Encoding character strings in R](https://rstudio-pubs-static.s3.amazonaws.com/279354_f552c4c41852439f910ad620763960b6.html)
-1. [Any Encoding, Ever - ztd.text and Unicode for C++](https://thephd.dev/any-encoding-ever-ztd-text-unicode-cpp)
-
diff --git a/lux-bootstrapper/src/lux/analyser/proc/jvm.clj b/lux-bootstrapper/src/lux/analyser/proc/jvm.clj
index 38310e60c..0cfa8c873 100644
--- a/lux-bootstrapper/src/lux/analyser/proc/jvm.clj
+++ b/lux-bootstrapper/src/lux/analyser/proc/jvm.clj
@@ -206,7 +206,7 @@
 
     (&/$GenericArray param)
     (|do [=param (generic-class->type env param)]
-      (return (&/$Primitive &host-type/array-data-tag (&/|list =param))))
+      (return (&type/Array =param)))
 
     (&/$GenericWildcard _)
     (return (&/$ExQ &/$End (&/$Parameter 1)))
@@ -568,7 +568,7 @@
                    &&a-parser/parse-gclass)
           gtype-env &/get-type-env
           =gclass (&host-type/instance-gtype &type/existential gtype-env gclass)
-          :let [array-type (&/$Primitive &host-type/array-data-tag (&/|list =gclass))]
+          :let [array-type (&type/Array =gclass)]
           =length (&&/analyse-1 analyse length-type length)
           _ (&type/check exo-type array-type)
           _location &/location]
@@ -578,11 +578,14 @@
   (defn- analyse-jvm-aaload [analyse exo-type ?values]
     (|do [:let [(&/$Item array (&/$Item idx (&/$End))) ?values]
           =array (&&/analyse-1+ analyse array)
-          [arr-class arr-params] (ensure-object (&&/expr-type* =array))
+          array-type (&type/normal (&&/expr-type* =array))
+          [arr-class arr-params] (ensure-object array-type)
           _ (&/assert! (= &host-type/array-data-tag arr-class) (str "[Analyser Error] Expected array. Instead got: " arr-class))
-          :let [(&/$Item inner-arr-type (&/$End)) arr-params]
+          :let [(&/$Item mutable_type (&/$End)) arr-params
+                (&/$Primitive "#Mutable" (&/$Item type_variance (&/$End))) mutable_type
+                (&/$Function write_type read_type) type_variance]
           =idx (&&/analyse-1 analyse idx-type idx)
-          _ (&type/check exo-type inner-arr-type)
+          _ (&type/check exo-type read_type)
           _location &/location]
       (return (&/|list (&&/|meta exo-type _location
                                  (&&/$proc (&/T ["jvm" "aaload"]) (&/|list =array =idx) (&/|list)))))))
@@ -590,12 +593,14 @@
   (defn- analyse-jvm-aastore [analyse exo-type ?values]
     (|do [:let [(&/$Item array (&/$Item idx (&/$Item elem (&/$End)))) ?values]
           =array (&&/analyse-1+ analyse array)
-          :let [array-type (&&/expr-type* =array)]
+          array-type (&type/normal (&&/expr-type* =array))
           [arr-class arr-params] (ensure-object array-type)
           _ (&/assert! (= &host-type/array-data-tag arr-class) (str "[Analyser Error] Expected array. Instead got: " arr-class))
-          :let [(&/$Item inner-arr-type (&/$End)) arr-params]
+          :let [(&/$Item mutable_type (&/$End)) arr-params
+                (&/$Primitive "#Mutable" (&/$Item type_variance (&/$End))) mutable_type
+                (&/$Function write_type read_type) type_variance]
           =idx (&&/analyse-1 analyse idx-type idx)
-          =elem (&&/analyse-1 analyse inner-arr-type elem)
+          =elem (&&/analyse-1 analyse write_type elem)
           _ (&type/check exo-type array-type)
           _location &/location]
       (return (&/|list (&&/|meta exo-type _location
diff --git a/lux-bootstrapper/src/lux/compiler/jvm/proc/host.clj b/lux-bootstrapper/src/lux/compiler/jvm/proc/host.clj
index a455be83a..619e4b6f9 100644
--- a/lux-bootstrapper/src/lux/compiler/jvm/proc/host.clj
+++ b/lux-bootstrapper/src/lux/compiler/jvm/proc/host.clj
@@ -777,7 +777,11 @@
               ;; (&/$End) special-args
               ]
         ^MethodVisitor *writer* &/get-writer
-        array-type (&host/->java-sig (&a/expr-type* ?array))
+        normal_array_type (&type/normal (&a/expr-type* ?array))
+        :let [(&/$Primitive "#Array" (&/$Item mutable_type (&/$End))) normal_array_type
+              (&/$Primitive "#Mutable" (&/$Item type_variance (&/$End))) mutable_type
+              (&/$Function write_type read_type) type_variance]
+        array-type (&host/->java-sig (&/$Primitive "#Array" (&/|list read_type)))
         _ (compile ?array)
         :let [_ (.visitTypeInsn *writer* Opcodes/CHECKCAST array-type)]
         _ (compile ?idx)
@@ -792,7 +796,11 @@
               ;; (&/$End) special-args
               ]
         ^MethodVisitor *writer* &/get-writer
-        array-type (&host/->java-sig (&a/expr-type* ?array))
+        normal_array_type (&type/normal (&a/expr-type* ?array))
+        :let [(&/$Primitive "#Array" (&/$Item mutable_type (&/$End))) normal_array_type
+              (&/$Primitive "#Mutable" (&/$Item type_variance (&/$End))) mutable_type
+              (&/$Function write_type read_type) type_variance]
+        array-type (&host/->java-sig (&/$Primitive "#Array" (&/|list write_type)))
         _ (compile ?array)
         :let [_ (.visitTypeInsn *writer* Opcodes/CHECKCAST array-type)]
         :let [_ (.visitInsn *writer* Opcodes/DUP)]
@@ -809,7 +817,15 @@
               ;; (&/$End) special-args
               ]
         ^MethodVisitor *writer* &/get-writer
-        array-type (&host/->java-sig (&a/expr-type* ?array))
+        normal_array_type (&type/normal (&a/expr-type* ?array))
+        array-type (|case normal_array_type
+                     (&/$Primitive ?name (&/$End))
+                     (&host/->java-sig normal_array_type)
+
+                     (&/$Primitive "#Array" (&/$Item mutable_type (&/$End)))
+                     (|let [(&/$Primitive "#Mutable" (&/$Item type_variance (&/$End))) mutable_type
+                            (&/$Function write_type read_type) type_variance]
+                       (&host/->java-sig (&/$Primitive "#Array" (&/|list read_type)))))
         _ (compile ?array)
         :let [_ (.visitTypeInsn *writer* Opcodes/CHECKCAST array-type)]
         :let [_ (doto *writer*
diff --git a/lux-bootstrapper/src/lux/host.clj b/lux-bootstrapper/src/lux/host.clj
index 7b114a772..0abba888a 100644
--- a/lux-bootstrapper/src/lux/host.clj
+++ b/lux-bootstrapper/src/lux/host.clj
@@ -42,13 +42,19 @@
 (def ->package ->module-class)
 
 (defn unfold-array
-  "(-> Type (, Int Type))"
+  "(-> Type [Nat Type])"
   [type]
   (|case type
-    (&/$Primitive "#Array" (&/$Item param (&/$End)))
+    (&/$Primitive "#Array" (&/$Item (&/$Primitive "#Mutable" (&/$Item (&/$Function _ param)
+                                                                      (&/$End)))
+                                    (&/$End)))
     (|let [[count inner] (unfold-array param)]
       (&/T [(inc count) inner]))
 
+    (&/$Primitive "#Array" (&/$Item param (&/$End)))
+    (|let [[count inner] (unfold-array param)]
+      (&/T [(inc count) inner]))
+    
     _
     (&/T [0 type])))
 
@@ -59,7 +65,8 @@
     [^objects type]
     (|case type
       (&/$Primitive ?name params)
-      (cond (= &host-type/array-data-tag ?name) (|do [:let [[level base] (unfold-array type)]
+      (cond (= &host-type/array-data-tag ?name) (|do [normal_type (&type/normal type)
+                                                      :let [[level base] (unfold-array normal_type)]
                                                       base-sig (|case base
                                                                  (&/$Primitive base-class _)
                                                                  (return (&host-generics/->type-signature base-class))
diff --git a/lux-bootstrapper/src/lux/type.clj b/lux-bootstrapper/src/lux/type.clj
index e1e229ce9..657eb3077 100644
--- a/lux-bootstrapper/src/lux/type.clj
+++ b/lux-bootstrapper/src/lux/type.clj
@@ -40,8 +40,7 @@
 (def Text (&/$Named (&/T [&/prelude "Text"]) (&/$Primitive "#Text" &/$End)))
 (def Ident (&/$Named (&/T [&/prelude "Ident"]) (&/$Product Text Text)))
 
-(defn Array [elemT]
-  (&/$Primitive "#Array" (&/|list elemT)))
+(def Array &&host/Array)
 
 (def Nothing
   (&/$Named (&/T [&/prelude "Nothing"])
@@ -924,3 +923,25 @@
 
     _
     (return type)))
+
+(defn normal
+  "(-> Type Type)"
+  [it]
+  (|case it
+    (&/$Named _ ?it)
+    (normal ?it)
+
+    (&/$Primitive ?name ?parameters)
+    (|do [=parameters (&/map% normal ?parameters)]
+      (return (&/$Primitive ?name =parameters)))
+
+    (&/$Apply ?parameter ?abstraction)
+    (|do [reification (apply-type ?abstraction ?parameter)]
+      (normal reification))
+
+    (&/$Var id)
+    (|do [referenced (deref id)]
+      (normal referenced))
+
+    _
+    (return it)))
diff --git a/lux-bootstrapper/src/lux/type/host.clj b/lux-bootstrapper/src/lux/type/host.clj
index 692062f50..0ea72c98f 100644
--- a/lux-bootstrapper/src/lux/type/host.clj
+++ b/lux-bootstrapper/src/lux/type/host.clj
@@ -64,7 +64,11 @@
                     (&/$Parameter 1))))
 
 ;; [Exports]
+(def mutable-data-tag "#Mutable")
 (def array-data-tag "#Array")
+(defn Array [item]
+  (&/$Primitive array-data-tag (&/|list (&/$Primitive mutable-data-tag (&/|list (&/$Function item item))))))
+
 (def null-data-tag "#Null")
 (def i64-data-tag "#I64")
 (def nat-data-tag "#Nat")
@@ -135,7 +139,7 @@
           (let [base (or arr-obase simple-base (jprim->lprim arr-pbase))]
             (if (.equals "void" base)
               Any
-              (reduce (fn [inner _] (&/$Primitive array-data-tag (&/|list inner)))
+              (reduce (fn [inner _] (Array inner))
                       (&/$Primitive base (try (-> (Class/forName base) .getTypeParameters
                                                   seq count (repeat (&/$Primitive "java.lang.Object" &/$End))
                                                   &/->list)
@@ -152,7 +156,7 @@
 
         (instance? GenericArrayType refl-type)
         (|do [inner-type (instance-param existential matchings (.getGenericComponentType ^GenericArrayType refl-type))]
-          (return (&/$Primitive array-data-tag (&/|list inner-type))))
+          (return (Array inner-type)))
         
         (instance? ParameterizedType refl-type)
         (|do [:let [refl-type* ^ParameterizedType refl-type]
@@ -183,7 +187,11 @@
           (if (type= Any class-type)
             "V"
             (|case class-type
-              (&/$Primitive "#Array" (&/$Item (&/$Primitive class-name _) (&/$End)))
+              (&/$Primitive "#Array"
+                            (&/$Item (&/$Primitive "#Mutable"
+                                                   (&/$Item (&/$Function _ (&/$Primitive class-name _))
+                                                            (&/$End)))
+                                     (&/$End)))
               (str "[" (&host-generics/->type-signature class-name))
 
               (&/$Primitive class-name _)
@@ -211,7 +219,7 @@
   (|case gtype
     (&/$GenericArray component-type)
     (|do [inner-type (instance-gtype existential matchings component-type)]
-      (return (&/$Primitive array-data-tag (&/|list inner-type))))
+      (return (Array inner-type)))
     
     (&/$GenericClass type-name type-params)
     ;; When referring to type-parameters during class or method
diff --git a/stdlib/source/library/lux/data/collection/array.lux b/stdlib/source/library/lux/data/collection/array.lux
index 4a931cfae..eb0cf93b0 100644
--- a/stdlib/source/library/lux/data/collection/array.lux
+++ b/stdlib/source/library/lux/data/collection/array.lux
@@ -9,13 +9,18 @@
     [predicate {"+" Predicate}]]
    [data
     [collection
-     ["[0]" list]]]]]
+     ["[0]" list]]]
+   [type
+    [variance {"+"}]]]]
  ["!" \\unsafe])
 
 (def: .public type_name
   Text
   !.type)
 
+(type: .public Array'
+  !.Array')
+
 (type: .public Array
   !.Array)
 
@@ -24,73 +29,73 @@
   (|>> !.empty))
 
 (def: .public size
-  (All (_ a) (-> (Array a) Nat))
+  (All (_ r w) (-> (Array' r w) Nat))
   (|>> !.size))
 
 (def: .public (item index array)
-  (All (_ a)
-    (-> Nat (Array a) (Maybe a)))
+  (All (_ r w)
+    (-> Nat (Array' r w) (Maybe r)))
   (if (!.lacks? index array)
     {.#None}
     {.#Some (!.item index array)}))
 
 (def: .public (has! index value array)
-  (All (_ a)
-    (-> Nat a (Array a) (Array a)))
+  (All (_ r w)
+    (-> Nat w (Array' r w) (Array' r w)))
   (!.has! index value array))
 
 (def: .public (lacks! index array)
-  (All (_ a)
-    (-> Nat (Array a) (Array a)))
+  (All (_ r w)
+    (-> Nat (Array' r w) (Array' r w)))
   (!.lacks! index array))
 
 (def: .public (lacks? index array)
-  (All (_ a)
-    (-> Nat (Array a) Bit))
+  (All (_ r w)
+    (-> Nat (Array' r w) Bit))
   (!.lacks? index array))
 
 (def: .public (has? index array)
-  (All (_ a)
-    (-> Nat (Array a) Bit))
+  (All (_ r w)
+    (-> Nat (Array' r w) Bit))
   (!.has? index array))
 
 (def: .public (revised! index $ array)
-  (All (_ a)
-    (-> Nat (-> a a) (Array a) (Array a)))
+  (All (_ r w)
+    (-> Nat (-> r w) (Array' r w) (Array' r w)))
   (!.revised! index $ array))
 
 (def: .public (upsert! index default transform array)
-  (All (_ a)
-    (-> Nat a (-> a a) (Array a) (Array a)))
+  (All (_ r w)
+    (-> Nat r (-> r w) (Array' r w) (Array' r w)))
   (!.upsert! index default transform array))
 
 (def: .public (copy! length src_start src_array dest_start dest_array)
-  (All (_ a)
-    (-> Nat Nat (Array a) Nat (Array a)
-        (Array a)))
+  (All (_ r w)
+    (-> Nat Nat (Array' w Nothing) Nat (Array' r w)
+        (Array' r w)))
   (!.copy! length src_start src_array dest_start dest_array))
 
 (def: .public occupancy
-  (All (_ a) (-> (Array a) Nat))
+  (All (_ r w) (-> (Array' r w) Nat))
   (|>> !.occupancy))
 
 (def: .public vacancy
-  (All (_ a) (-> (Array a) Nat))
+  (All (_ r w) (-> (Array' r w) Nat))
   (|>> !.vacancy))
 
 (def: .public (only! ? it)
-  (All (_ a)
-    (-> (Predicate a) (Array a) (Array a)))
+  (All (_ r w)
+    (-> (Predicate r) (Array' r w) (Array' r w)))
   (!.only! ? it))
 
 (def: .public (example ? it)
-  (All (_ a)
-    (-> (Predicate a) (Array a) (Maybe a)))
+  (All (_ r w)
+    (-> (Predicate r) (Array' r w) (Maybe r)))
   (!.example ? it))
 
 (def: .public (example' ? it)
-  (All (_ a)
-    (-> (-> Nat a Bit) (Array a) (Maybe [Nat a])))
+  (All (_ r w)
+    (-> (-> Nat r Bit) (Array' r w) (Maybe [Nat r])))
   (!.example' ? it))
 
 (def: .public clone
@@ -102,11 +107,11 @@
   (|>> !.of_list))
 
 (def: .public (list default array)
-  (All (_ a) (-> (Maybe a) (Array a) (List a)))
+  (All (_ r w) (-> (Maybe r) (Array' r w) (List r)))
   (!.list default array))
 
 (implementation: .public (equivalence //)
-  (All (_ a) (-> (Equivalence a) (Equivalence (Array a))))
+  (All (_ r) (-> (Equivalence r) (Equivalence (Ex (_ w) (Array' r w)))))
   
   (def: (= left/* right/*)
     (!.= // left/* right/*)))
@@ -120,7 +125,7 @@
     (!.composite left/* right/*)))
 
 (implementation: .public mix
-  (Mix Array)
+  (Mix (All (_ r) (Array' r Nothing)))
   
   (def: (mix $ init it)
     (!.mix (function (_ index partial total)
@@ -134,17 +139,17 @@
   (def: (each $ input)
     (!.each $ input)))
 
-(def: .public (every? ? it)
-  (All (_ a)
-    (-> (Predicate a) (Predicate (Array a))))
-  (!.every? ? it))
+(template [<safe> <unsafe>]
+  [(def: .public (<safe> ? it)
+     (All (_ r w)
+       (-> (Predicate r) (Predicate (Array' r w))))
+     (<unsafe> ? it))]
 
-(def: .public (any? ? it)
-  (All (_ a)
-    (-> (Predicate a) (Predicate (Array a))))
-  (!.any? ? it))
+  [every? !.every?]
+  [any? !.any?]
+  )
 
 (def: .public (one ? it)
-  (All (_ a b)
-    (-> (-> a (Maybe b)) (Array a) (Maybe b)))
+  (All (_ r r' w)
+    (-> (-> r (Maybe r')) (Array' r w) (Maybe r')))
   (!.one ? it))
diff --git a/stdlib/source/library/lux/ffi.jvm.lux b/stdlib/source/library/lux/ffi.jvm.lux
index 2428f6bb2..2441cf387 100644
--- a/stdlib/source/library/lux/ffi.jvm.lux
+++ b/stdlib/source/library/lux/ffi.jvm.lux
@@ -382,8 +382,7 @@
                    (` {.#Primitive (~ (code.text (..reflection (jvm.array elementT)))) {.#End}})
                    
                    {.#None}
-                   (` {.#Primitive (~ (code.text array.type_name))
-                                   {.#Item (~ (value_type elementT)) {.#End}}}))]))
+                   (` ((~! array.Array) (~ (value_type elementT)))))]))
           ... else
           (undefined)
           )))
@@ -1691,8 +1690,9 @@
                     [jvm.double  "jvm array new double"]
                     [jvm.char    "jvm array new char"]))
               ... else
-              (in (list (` (.is (~ (value_type {#ManualPrM} (jvm.array type)))
-                                ("jvm array new object" (~ g!size))))))))))
+              (in (list (` (.as ((~! array.Array) (~ (value_type {#ManualPrM} type)))
+                                (.is (~ (value_type {#ManualPrM} (jvm.array type)))
+                                     ("jvm array new object" (~ g!size)))))))))))
 
 (exception: .public (cannot_convert_to_jvm_type [type .Type])
   (exception.report
@@ -1743,9 +1743,9 @@
 
                   (text#= array.type_name name)
                   (case params
-                    {.#Item elementLT {.#End}}
+                    {.#Item {.#Apply writeLT {.#Apply readLT _Mutable}} {.#End}}
                     (# meta.monad each jvm.array
-                       (lux_type->jvm_type context elementLT))
+                       (lux_type->jvm_type context readLT))
 
                     _
                     <failure>)
diff --git a/stdlib/source/library/lux/ffi.old.lux b/stdlib/source/library/lux/ffi.old.lux
index ce9e50959..32844a7d7 100644
--- a/stdlib/source/library/lux/ffi.old.lux
+++ b/stdlib/source/library/lux/ffi.old.lux
@@ -1727,5 +1727,5 @@
 (syntax: .public (type [type (..generic_type^ (list))])
   (in (list (..class_type {#ManualPrM} (list) type))))
 
-(template: .public (as type term)
+(template: .public (is type term)
   [(.as type term)])
diff --git a/stdlib/source/library/lux/target/jvm/reflection.lux b/stdlib/source/library/lux/target/jvm/reflection.lux
index 55b6a4185..4fe60fd37 100644
--- a/stdlib/source/library/lux/target/jvm/reflection.lux
+++ b/stdlib/source/library/lux/target/jvm/reflection.lux
@@ -183,8 +183,8 @@
         {.#Some reflection}
         ... TODO: Instead of having single lower/upper bounds, should
         ... allow for multiple ones.
-        (case [(array.read! 0 (java/lang/reflect/WildcardType::getLowerBounds reflection))
-               (array.read! 0 (java/lang/reflect/WildcardType::getUpperBounds reflection))]
+        (case [(array.item 0 (java/lang/reflect/WildcardType::getLowerBounds reflection))
+               (array.item 0 (java/lang/reflect/WildcardType::getUpperBounds reflection))]
           (^.template [<pattern> <kind>]
             [<pattern>
              (case (ffi.as java/lang/reflect/GenericArrayType bound)
diff --git a/stdlib/source/library/lux/tool/compiler/language/lux/phase/extension/analysis/jvm.lux b/stdlib/source/library/lux/tool/compiler/language/lux/phase/extension/analysis/jvm.lux
index 95915309c..6d7804b9a 100644
--- a/stdlib/source/library/lux/tool/compiler/language/lux/phase/extension/analysis/jvm.lux
+++ b/stdlib/source/library/lux/tool/compiler/language/lux/phase/extension/analysis/jvm.lux
@@ -65,7 +65,9 @@
    ["/[1]" // "_"
     [generation
      [jvm
-      ["[0]" runtime]]]
+      ["[0]" runtime]
+      ["[0]" function "_"
+       ["[1]" abstract]]]]
     ["/[1]" // "_"
      ["[0]" generation]
      ["[0]" directive]
@@ -387,6 +389,9 @@
             [(reflection.reflection reflection.char)    [box.char jvm.char]])
       (dictionary.of_list text.hash)))
 
+(template: (lux_array_type :read: :write:)
+  [{.#Primitive (static array.type_name) (list {.#Apply :write: {.#Apply :read: _Mutable}})}])
+
 (def: (jvm_type luxT)
   (-> .Type (Operation (Type Value)))
   (case luxT
@@ -401,7 +406,7 @@
       {.#None}
       (/////analysis.except ..non_jvm_type luxT))
 
-    (pattern {.#Primitive (static array.type_name) (list elemT)})
+    (pattern (lux_array_type elemT _))
     (phase#each jvm.array (jvm_type elemT))
 
     {.#Primitive class parametersT}
@@ -432,6 +437,9 @@
 
     {.#Ex _}
     (phase#in (jvm.class ..object_class (list)))
+
+    {.#Function _}
+    (phase#in function.class)
     
     _
     (/////analysis.except ..non_jvm_type luxT)))
@@ -467,13 +475,16 @@
     (case args
       (pattern (list arrayC))
       (<| typeA.with_var
-          (function (_ [@var :var:]))
+          (function (_ [@read :read:]))
+          typeA.with_var
+          (function (_ [@write :write:]))
           (do phase.monad
             [_ (typeA.inference ..int)
-             arrayA (<| (typeA.expecting (.type (array.Array :var:)))
+             arrayA (<| (typeA.expecting (.type (array.Array' :read: :write:)))
                         (analyse archive arrayC))
-             :var: (typeA.check (check.clean (list) :var:))
-             arrayJT (jvm_array_type (.type (array.Array :var:)))]
+             :read: (typeA.check (check.clean (list) :read:))
+             :write: (typeA.check (check.clean (list) :write:))
+             arrayJT (jvm_array_type (.type (array.Array' :read: :write:)))]
             (in {/////analysis.#Extension extension_name (list (/////analysis.text (..signature arrayJT))
                                                                arrayA)})))
 
@@ -520,8 +531,7 @@
 (def: (check_parameter objectT)
   (-> .Type (Operation (Type Parameter)))
   (case objectT
-    (pattern {.#Primitive (static array.type_name)
-                          (list elementT)})
+    (pattern (lux_array_type elementT _))
     (/////analysis.except ..non_parameter objectT)
     
     {.#Primitive name parameters}
@@ -573,6 +583,9 @@
       {.#None}
       (/////analysis.except ..non_parameter objectT))
 
+    {.#Function _}
+    (phase#in function.class)
+
     _
     (/////analysis.except ..non_parameter objectT)))
 
@@ -613,9 +626,8 @@
 
               ... else
               (phase#in (jvm.class name (list)))))
-    
-    (pattern {.#Primitive (static array.type_name)
-                          (list elementT)})
+
+    (pattern (lux_array_type elementT _))
     (|> elementT
         check_jvm
         (phase#each jvm.array))
@@ -701,15 +713,18 @@
     (case args
       (pattern (list idxC arrayC))
       (<| typeA.with_var
-          (function (_ [@var :var:]))
+          (function (_ [@read :read:]))
+          typeA.with_var
+          (function (_ [@write :write:]))
           (do phase.monad
-            [_ (typeA.inference :var:)
-             arrayA (<| (typeA.expecting (.type (array.Array :var:)))
+            [_ (typeA.inference :read:)
+             arrayA (<| (typeA.expecting (.type (array.Array' :read: :write:)))
                         (analyse archive arrayC))
-             :var: (typeA.check (check.clean (list) :var:))
-             arrayJT (jvm_array_type (.type (array.Array :var:)))
              idxA (<| (typeA.expecting ..int)
-                      (analyse archive idxC))]
+                      (analyse archive idxC))
+             :read: (typeA.check (check.clean (list) :read:))
+             :write: (typeA.check (check.clean (list) :write:))
+             arrayJT (jvm_array_type (.type (array.Array' :read: :write:)))]
             (in {/////analysis.#Extension extension_name (list (/////analysis.text (..signature arrayJT))
                                                                idxA
                                                                arrayA)})))
@@ -745,17 +760,20 @@
     (case args
       (pattern (list idxC valueC arrayC))
       (<| typeA.with_var
-          (function (_ [@var :var:]))
+          (function (_ [@read :read:]))
+          typeA.with_var
+          (function (_ [@write :write:]))
           (do phase.monad
-            [_ (typeA.inference (.type (array.Array :var:)))
-             arrayA (<| (typeA.expecting (.type (array.Array :var:)))
+            [_ (typeA.inference (.type (array.Array' :read: :write:)))
+             arrayA (<| (typeA.expecting (.type (array.Array' :read: :write:)))
                         (analyse archive arrayC))
-             :var: (typeA.check (check.clean (list) :var:))
-             arrayJT (jvm_array_type (.type (array.Array :var:)))
              idxA (<| (typeA.expecting ..int)
                       (analyse archive idxC))
-             valueA (<| (typeA.expecting :var:)
-                        (analyse archive valueC))]
+             valueA (<| (typeA.expecting :write:)
+                        (analyse archive valueC))
+             :read: (typeA.check (check.clean (list) :read:))
+             :write: (typeA.check (check.clean (list) :write:))
+             arrayJT (jvm_array_type (.type (array.Array' :read: :write:)))]
             (in {/////analysis.#Extension extension_name (list (/////analysis.text (..signature arrayJT))
                                                                idxA
                                                                valueA
diff --git a/stdlib/source/library/lux/type/variance.lux b/stdlib/source/library/lux/type/variance.lux
index 00d2d931e..93f80356a 100644
--- a/stdlib/source/library/lux/type/variance.lux
+++ b/stdlib/source/library/lux/type/variance.lux
@@ -1,6 +1,8 @@
 (.using
-  [library
-   [lux "*"]])
+ [library
+  [lux "*"
+   [meta
+    ["[0]" symbol]]]])
 
 (type: .public (Co it)
   (-> Any it))
@@ -10,3 +12,32 @@
 
 (type: .public (In it)
   (-> it it))
+
+(type: .public (Mutable r w)
+  (Primitive "#Mutable" [(-> w r)]))
+
+(template [<name> <type>]
+  [(template: .public (<name> it)
+     [((.is (.All (_ r w) <type>)
+            (.|>> .as_expected))
+       it)])]
+
+  [read (.-> (..Mutable r w) r)]
+  [write (.-> w (..Mutable r w))]
+  )
+
+(type: .public (Read_Only a)
+  (Mutable a Nothing))
+
+(type: .public (Write_Only a)
+  (Mutable Any a))
+
+(template [<name> <type>]
+  [(template: .public (<name> it)
+     [((.is (.All (_ r w) <type>)
+            (.|>>))
+       it)])]
+
+  [read_only (.-> (..Mutable r w) (..Read_Only r))]
+  [write_only (.-> (..Mutable r w) (..Write_Only w))]
+  )
diff --git a/stdlib/source/unsafe/lux/data/collection/array.lux b/stdlib/source/unsafe/lux/data/collection/array.lux
index e66d3ca3b..0a44efcf8 100644
--- a/stdlib/source/unsafe/lux/data/collection/array.lux
+++ b/stdlib/source/unsafe/lux/data/collection/array.lux
@@ -6,17 +6,23 @@
     ["[0]" functor]]
    [data
     [collection
-     ["[0]" list]]]]])
+     ["[0]" list]]]
+   [type
+    ["[0]" variance]]]])
 
 (def: .public type
   "#Array")
 
-(type: .public (Array a)
-  {.#Primitive ..type {.#Item a {.#End}}})
+(template [<item> <array>]
+  [(type: .public <array>
+     {.#Primitive ..type {.#Item <item> {.#End}}})]
+
+  [(variance.Mutable r w) (Array' r w)]
+  [(variance.Mutable a a) (Array a)]
+  )
 
 (with_expansions [<index_type> (.Primitive "java.lang.Long")
-                  <elem_type> (.Primitive "java.lang.Object")
-                  <array_type> (.type (..Array <elem_type>))]
+                  <item_type> (.Primitive "java.lang.Object")]
   (for @.jvm (template: (jvm_int value)
                [(.|> value
                      (.as <index_type>)
@@ -33,7 +39,7 @@
                        (~~ (.static @.jvm))
                        (|> (~~ (..jvm_int size))
                            "jvm array new object"
-                           (.is <array_type>)
+                           (.is (..Array <item_type>))
                            .as_expected)
 
                        (~~ (.static @.js)) ("js array new" size)
@@ -45,14 +51,13 @@
           <size>)]))
 
   (`` (template: .public (size <array>)
-        [((.is (.All (_ a) (.-> (..Array a) .Nat))
+        [((.is (.All (_ r w) (.-> (..Array' r w) .Nat))
                (.function (size array)
                  (.for (~~ (.static @.old))
                        ("jvm arraylength" array)
 
                        (~~ (.static @.jvm))
                        (.|> array
-                            (.as <array_type>)
                             "jvm array length object"
                             "jvm conversion int-to-long"
                             "jvm object cast"
@@ -71,8 +76,8 @@
     [(<null?> (<read!> index array))])
 
   (`` (template: .public (lacks? <index> <array>)
-        [((.is (.All (_ a)
-                 (.-> .Nat (..Array a) .Bit))
+        [((.is (.All (_ r w)
+                 (.-> .Nat (..Array' r w) .Bit))
                (.function (lacks? index array)
                  (.let [size (..size array)]
                    (.if ("lux i64 <" (.int size) (.int index))
@@ -81,7 +86,6 @@
 
                            (~~ (.static @.jvm))
                            (.|> array
-                                (.as <array_type>)
                                 ("jvm array read object" (~~ (jvm_int index)))
                                 "jvm object null?")
 
@@ -98,15 +102,14 @@
     [(.not (..lacks? index array))])
 
   (`` (template: .public (item <index> <array>)
-        [((.is (.All (_ a)
-                 (.-> .Nat (..Array a) a))
+        [((.is (.All (_ r w)
+                 (.-> .Nat (..Array' r w) r))
                (.function (item index array)
                  (.for (~~ (.static @.old))
                        ("jvm aaload" array index)
 
                        (~~ (.static @.jvm))
                        (.|> array
-                            (.as <array_type>)
                             ("jvm array read object" (~~ (jvm_int index)))
                             .as_expected)
 
@@ -119,16 +122,15 @@
           <index> <array>)]))
 
   (`` (template: .public (has! <index> <value> <array>)
-        [((.is (.All (_ a)
-                 (.-> .Nat a (..Array a) (..Array a)))
+        [((.is (.All (_ r w)
+                 (.-> .Nat w (..Array' r w) (..Array' r w)))
                (.function (has! index value array)
                  (.for (~~ (.static @.old))
                        ("jvm aastore" array index value)
 
                        (~~ (.static @.jvm))
                        (.|> array
-                            (.as <array_type>)
-                            ("jvm array write object" (~~ (jvm_int index)) (.as <elem_type> value))
+                            ("jvm array write object" (~~ (jvm_int index)) value)
                             .as_expected)
 
                        (~~ (.static @.js)) ("js array write" index value array)
@@ -140,8 +142,8 @@
           <index> <value> <array>)]))
 
   (`` (template: .public (lacks! <index> <array>)
-        [((.is (.All (_ a)
-                 (.-> .Nat (..Array a) (..Array a)))
+        [((.is (.All (_ r w)
+                 (.-> .Nat (..Array' r w) (..Array' r w)))
                (.function (lacks! index array)
                  (.let [size (..size array)]
                    (.if ("lux i64 <" (.int size) (.int index))
@@ -149,7 +151,7 @@
                            (..has! index (.as_expected ("jvm object null")) array)
                            
                            (~~ (.static @.jvm))
-                           (..has! index (.as_expected (is <elem_type> ("jvm object null"))) array)
+                           (..has! index (.as_expected (is <item_type> ("jvm object null"))) array)
 
                            (~~ (.static @.js)) ("js array delete" index array)
                            (~~ (.static @.python)) ("python array delete" index array)
@@ -162,8 +164,8 @@
   )
 
 (template: .public (revised! <index> <$> <array>)
-  [((.is (.All (_ a)
-           (.-> .Nat (.-> a a) (..Array a) (..Array a)))
+  [((.is (.All (_ r w)
+           (.-> .Nat (.-> r w) (..Array' r w) (..Array' r w)))
          (.function (revised! index $ array)
            (.if (..lacks? index array)
              array
@@ -171,8 +173,8 @@
     <index> <$> <array>)])
 
 (template: .public (upsert! <index> <default> <$> <array>)
-  [((.is (.All (_ a)
-           (.-> .Nat a (.-> a a) (..Array a) (..Array a)))
+  [((.is (.All (_ r w)
+           (.-> .Nat r (.-> r w) (..Array' r w) (..Array' r w)))
          (.function (upsert! index default $ array)
            (..has! index
                    ($ (.if (..lacks? index array)
@@ -182,9 +184,9 @@
     <index> <default> <$> <array>)])
 
 (template: .public (copy! <length> <src_start> <src_array> <dest_start> <dest_array>)
-  [((.is (.All (_ a)
-           (.-> .Nat .Nat (..Array a) .Nat (..Array a)
-                (..Array a)))
+  [((.is (.All (_ r w)
+           (.-> .Nat .Nat (..Array' w .Nothing) .Nat (..Array' r w)
+                (..Array' r w)))
          (.function (copy! length src_start src_array dest_start dest_array)
            (.loop (again [offset 0])
              (.if ("lux i64 <" (.int length) (.int offset))
@@ -200,7 +202,7 @@
 
 (template [<name> <when_lacks> <when_has>]
   [(template: .public (<name> <array>)
-     [((.is (.All (_ a) (.-> (..Array a) .Nat))
+     [((.is (.All (_ r w) (.-> (..Array' r w) .Nat))
             (.function (occupancy array)
               (.let [size (..size array)]
                 (.loop (again [index 0
@@ -217,8 +219,8 @@
   )
 
 (template: .public (only! <?> <it>)
-  [((.is (.All (_ a)
-           (.-> (.-> a .Bit) (..Array a) (..Array a)))
+  [((.is (.All (_ r w)
+           (.-> (.-> r .Bit) (..Array' r w) (..Array' r w)))
          (.function (only! ? it)
            (.let [size (..size it)]
              (.loop (again [index 0])
@@ -235,8 +237,8 @@
 
 (template [<name> <predicate> <test> <type> <term>]
   [(template: .public (<name> <?> <it>)
-     [((.is (.All (_ a)
-              (.-> <predicate> (..Array a) (.Maybe <type>)))
+     [((.is (.All (_ r w)
+              (.-> <predicate> (..Array' r w) (.Maybe <type>)))
             (.function (<name> ? it)
               (.let [size (..size it)]
                 (.loop (again [index 0])
@@ -250,8 +252,8 @@
                     {.#None})))))
        <?> <it>)])]
 
-  [example (.-> a .Bit) (? it) a it]
-  [example' (.-> Nat a .Bit) (? index it) [Nat a] [index it]]
+  [example (.-> r .Bit) (? it) r it]
+  [example' (.-> Nat r .Bit) (? index it) [Nat r] [index it]]
   )
 
 (template: .public (clone <it>)
@@ -283,7 +285,7 @@
   (-- 0))
 
 (`` (template: (list|-default <empty> <array>)
-      [((.is (.All (_ a) (.-> (.List a) (..Array a) (.List a)))
+      [((.is (.All (_ r w) (.-> (.List r) (..Array' r w) (.List r)))
              (.function (list|-default empty array)
                (.loop (again [index ("lux i64 -" 1 (..size array))
                               output empty])
@@ -296,7 +298,7 @@
         <empty> <array>)]))
 
 (`` (template: (list|+default <default> <array>)
-      [((.is (.All (_ a) (.-> a (..Array a) (.List a)))
+      [((.is (.All (_ r w) (.-> r (..Array' r w) (.List r)))
              (.function (list|+default default array)
                (.loop (again [index ("lux i64 -" 1 (..size array))
                               output (`` (.is (.List (~~ (.these (~~ (.type_of default)))))
@@ -311,7 +313,7 @@
         <default> <array>)]))
 
 (`` (template: .public (list <default> <array>)
-      [((.is (.All (_ a) (.-> (.Maybe a) (..Array a) (.List a)))
+      [((.is (.All (_ r w) (.-> (.Maybe r) (..Array' r w) (.List r)))
              (.function (list default array)
                (.case default
                  {.#Some default}
@@ -322,7 +324,7 @@
         <default> <array>)]))
 
 (template: .public (= <//#=> <left/*> <right/*>)
-  [((.is (.All (_ a) (.-> (.-> a a .Bit) (..Array a) (..Array a) .Bit))
+  [((.is (.All (_ r w0 w1) (.-> (.-> r r .Bit) (..Array' r w0) (..Array' r w1) .Bit))
          (.function (= //#= left/* right/*)
            (.let [size (..size left/*)]
              (.and ("lux i64 =" (..size right/*) size)
@@ -339,7 +341,7 @@
     <//#=> <left/*> <right/*>)])
 
 (template: .public (composite <left/*> <right/*>)
-  [((.is (.All (_ a) (.-> (..Array a) (..Array a) (..Array a)))
+  [((.is (.All (_ a) (.-> (..Array' a .Nothing) (..Array' a .Nothing) (..Array a)))
          (.function (composite left/* right/*)
            (.let [|left| (..size left/*)
                   |right| (..size right/*)]
@@ -349,8 +351,8 @@
     <left/*> <right/*>)])
 
 (template: .public (mix <$> <init> <it>)
-  [((.is (.All (_ a b)
-           (.-> (.-> Nat b a a) a (..Array b) a))
+  [((.is (.All (_ r w s)
+           (.-> (.-> Nat r s s) s (..Array' r w) s))
          (.function (mix $ init it)
            (.let [size (..size it)]
              (.loop (again [index 0
@@ -373,9 +375,9 @@
 
 (template [<name> <init> <op>]
   [(template: .public (<name> <?> <it>)
-     [((.is (.All (_ a)
-              (.-> (.-> a .Bit)
-                   (.-> (..Array a) .Bit)))
+     [((.is (.All (_ r w)
+              (.-> (.-> r .Bit)
+                   (.-> (..Array' r w) .Bit)))
             (.function (<name> ? it)
               (.let [size (..size it)]
                 (.loop (again [index 0])
@@ -392,8 +394,8 @@
   )
 
 (template: .public (one <?> <it>)
-  [((.is (.All (_ a b)
-           (.-> (.-> a (.Maybe b)) (..Array a) (.Maybe b)))
+  [((.is (.All (_ r r' w)
+           (.-> (.-> r (.Maybe r')) (..Array' r w) (.Maybe r')))
          (.function (one ? it)
            (.let [size (..size it)]
              (.loop (again [index 0])