diff --git a/.travis.yml b/.travis.yml
deleted file mode 100644
--- a/.travis.yml
+++ /dev/null
@@ -1,82 +0,0 @@
-# vim: nospell
-#
-# Basic template to test with GHC=[7.8, 7.10, 8.0]. Caches the 'stack' build
-# directory to speed subsequent compilations.
-#
-# https://docs.travis-ci.com/user/reference/overview/
-#
-language: minimal
-dist: trusty
-sudo: true      # more storage available on sudo-enabled instances
-
-cache:
-  directories:
-    - $HOME/.stack/snapshots
-    - .stack-work/install
-
-before_cache:
-  - rm -rf $(stack path --local-install-root)/doc
-
-addons:
-  apt:
-    sources: &apt_sources
-      - hvr-ghc
-      - ubuntu-toolchain-r-test
-    packages: &apt_packages
-      - libgmp-dev
-      - happy-1.19.5
-      - alex-3.1.7
-
-matrix:
-  include:
-    - env: GHC=7.10.3 CABAL=1.24
-      compiler: "GHC 7.10"
-      addons: { apt: { sources: [ *apt_sources ], packages: [ *apt_packages, cabal-install-1.24 ] }}
-
-    - env: GHC=8.0.2 CABAL=1.24
-      compiler: "GHC 8.0"
-      addons: { apt: { sources: [ *apt_sources ], packages: [ *apt_packages, cabal-install-1.24 ] }}
-
-    - env: GHC=8.2.2 CABAL=2.0
-      compiler: "GHC 8.2"
-      addons: { apt: { sources: [ *apt_sources ], packages: [ *apt_packages, cabal-install-2.0 ] }}
-
-    - env: GHC=8.4.1 CABAL=2.0
-      compiler: "GHC 8.4"
-      addons: { apt: { sources: [ *apt_sources ], packages: [ *apt_packages, cabal-install-2.0 ] }}
-
-    # - env: GHC=head CABAL=head
-    #   compiler: "GHC HEAD"
-    #   addons: { apt: { sources: [ *apt_sources ], packages: [ *apt_packages, ghc-head, cabal-install-head ] }}
-
-  # allow_failures:
-  #   - env: GHC=head CABAL=head
-
-  fast_finish: true
-
-before_install:
-  - export PATH=/opt/cabal/$CABAL/bin:/opt/alex/3.1.7/bin:/opt/happy/1.19.5/bin:$HOME/.cabal/bin:$PATH
-  - source .travis/install-stack.sh
-
-install:
-  - echo "$(ghc --version) [$(ghc --print-project-git-commit-id 2> /dev/null || echo '?')]"
-  - cabal --version
-  - stack --version
-  - stack build --no-terminal --dry-run
-  - travis_retry travis_wait 60 stack build --fast --test --only-dependencies --no-terminal --no-copy-bins
-
-script:
-  - stack build --no-terminal --fast --test --haddock --no-haddock-deps --no-run-tests
-  - stack test
-
-after_success:
-  - source .travis/update-accelerate-buildbot.sh
-
-notifications:
-  irc:
-    channels:
-      - "irc.freenode.org#haskell-lens"
-    skip_join: true
-    template:
-      - "\x0313linear-accelerate\x03/\x0306%{branch}\x03 \x0314%{commit}\x03 %{build_url} %{message}"
-
diff --git a/.vim.custom b/.vim.custom
deleted file mode 100644
--- a/.vim.custom
+++ /dev/null
@@ -1,21 +0,0 @@
-" Add the following to your .vimrc to automatically load this on startup
-" if filereadable(".vim.custom")
-"     so .vim.custom
-" endif
-
-function StripTrailingWhitespace()
-  let myline=line(".")
-  let mycolumn = col(".")
-  silent %s/  *$//
-  call cursor(myline, mycolumn)
-endfunction
-
-syntax on
-set tags=TAGS;/
-set listchars=tab:‗‗,trail:‗
-set list
-
-map <F2> :exec ":!hasktags -x -c --ignore src"<CR><CR>
-
-au BufWritePre *.hs,*.markdown silent! cal StripTrailingWhitespace()
-au BufWritePost *.hs silent! :exec ":!hasktags -x -c --ignore src"
diff --git a/CHANGELOG.markdown b/CHANGELOG.markdown
deleted file mode 100644
--- a/CHANGELOG.markdown
+++ /dev/null
@@ -1,60 +0,0 @@
-# Change Log
-
-Notable changes to the project will be documented in this file.
-
-The format is based on [Keep a Changelog](http://keepachangelog.com/) and the
-project adheres to the [Haskell Package Versioning Policy
-(PVP)](https://pvp.haskell.org)
-
-## [0.6.0.0] - 2018-04-03
-### Changed
-  * update for accelerate-1.2
-
-### Fixed
-  * Disambiguate uses of `fromInteger` and `fromRational`.
-
-## [0.5.0.1] - 2017-09-29
-### Fixed
-  * doctest failure with accelerate-1.1.1.0 ([#10])
-
-## [0.5] - 2017-08-06
-### Fixed
-  * "impossible evaluation" error with accelerate-llvm-native ([#25][acc-llvm#25])
-
-## [0.4.1] - 2017-07-29
-### Added
-  * Support `doctest-0.12`.
-
-## [0.4] - 2017-06-16
-### Changed
-  * Revamp `Setup.hs` to use `cabal-doctest`. This makes `linear-accelerate` build with `Cabal-2.0`.
-  * Re-enable the `doctest`s.
-
-### Fixed
-  * Fix handedness of `(-^)` and `(^-)`.
-
-## [0.3] - 2017-04-01
-### Changed
-  * Expanded API coverage
-
-## [0.2] - 2014-09-15
-### Fixed
-  * Move `Data.Complex` instances into the `accelerate` package ([#1])
-
-## [0.1] - 2014-03-28
-  * Repository initialized
-
-
-[0.6.0.0]:          https://github.com/ekmett/linear-accelerate/compare/v0.5.0.1...v0.6.0.0
-[0.5.0.1]:          https://github.com/ekmett/linear-accelerate/compare/v0.5...v0.5.0.1
-[0.5]:              https://github.com/ekmett/linear-accelerate/compare/v0.4.1...v0.5
-[0.4.1]:            https://github.com/ekmett/linear-accelerate/compare/v0.4...v0.4.1
-[0.4]:              https://github.com/ekmett/linear-accelerate/compare/v0.3...v0.4
-[0.3]:              https://github.com/ekmett/linear-accelerate/compare/v0.2...v0.3
-[0.2]:              https://github.com/ekmett/linear-accelerate/compare/v0.1...v0.2
-[0.1]:              https://github.com/ekmett/linear-accelerate/compare/3db20f05af0a1488fcbc3ea28f8561ce73289b73...v0.1
-
-[#1]:               https://github.com/ekmett/linear-accelerate/issues/1
-[#10]:              https://github.com/ekmett/linear-accelerate/issues/10
-[acc-llvm#25]:      https://github.com/AccelerateHS/accelerate-llvm/issues/25
-
diff --git a/CHANGELOG.md b/CHANGELOG.md
new file mode 100644
--- /dev/null
+++ b/CHANGELOG.md
@@ -0,0 +1,69 @@
+# Change Log
+
+Notable changes to the project will be documented in this file.
+
+The format is based on [Keep a Changelog](http://keepachangelog.com/) and the
+project adheres to the [Haskell Package Versioning Policy
+(PVP)](https://pvp.haskell.org)
+
+## [0.7.0.0] - 2020-08-26
+### Added
+  * embedded pattern synonyms such as `V3_`, etc.
+
+### Changed
+  * Update for accelerate-1.3
+
+## [0.6.0.0] - 2018-04-03
+### Changed
+  * update for accelerate-1.2
+
+### Fixed
+  * Disambiguate uses of `fromInteger` and `fromRational`.
+
+## [0.5.0.1] - 2017-09-29
+### Fixed
+  * doctest failure with accelerate-1.1.1.0 ([#10])
+
+## [0.5] - 2017-08-06
+### Fixed
+  * "impossible evaluation" error with accelerate-llvm-native ([#25][acc-llvm#25])
+
+## [0.4.1] - 2017-07-29
+### Added
+  * Support `doctest-0.12`.
+
+## [0.4] - 2017-06-16
+### Changed
+  * Revamp `Setup.hs` to use `cabal-doctest`. This makes `linear-accelerate` build with `Cabal-2.0`.
+  * Re-enable the `doctest`s.
+
+### Fixed
+  * Fix handedness of `(-^)` and `(^-)`.
+
+## [0.3] - 2017-04-01
+### Changed
+  * Rewritten by Trevor L. McDonell
+  * Expanded API coverage
+
+## [0.2] - 2014-09-15
+### Fixed
+  * Move `Data.Complex` instances into the `accelerate` package ([#1])
+
+## [0.1] - 2014-03-28
+  * Repository initialized
+
+
+[0.7.0.0]:          https://github.com/ekmett/linear-accelerate/compare/v0.6.0.0...v0.7.0.0
+[0.6.0.0]:          https://github.com/ekmett/linear-accelerate/compare/v0.5.0.1...v0.6.0.0
+[0.5.0.1]:          https://github.com/ekmett/linear-accelerate/compare/v0.5...v0.5.0.1
+[0.5]:              https://github.com/ekmett/linear-accelerate/compare/v0.4.1...v0.5
+[0.4.1]:            https://github.com/ekmett/linear-accelerate/compare/v0.4...v0.4.1
+[0.4]:              https://github.com/ekmett/linear-accelerate/compare/v0.3...v0.4
+[0.3]:              https://github.com/ekmett/linear-accelerate/compare/v0.2...v0.3
+[0.2]:              https://github.com/ekmett/linear-accelerate/compare/v0.1...v0.2
+[0.1]:              https://github.com/ekmett/linear-accelerate/compare/3db20f05af0a1488fcbc3ea28f8561ce73289b73...v0.1
+
+[#1]:               https://github.com/ekmett/linear-accelerate/issues/1
+[#10]:              https://github.com/ekmett/linear-accelerate/issues/10
+[acc-llvm#25]:      https://github.com/AccelerateHS/accelerate-llvm/issues/25
+
diff --git a/LICENSE b/LICENSE
--- a/LICENSE
+++ b/LICENSE
@@ -1,4 +1,4 @@
-Copyright 2014 Edward Kmett, Charles Durham
+Copyright 2014 Edward Kmett, Charles Durham, Trevor L. McDonell
 
 All rights reserved.
 
diff --git a/README.markdown b/README.markdown
deleted file mode 100644
--- a/README.markdown
+++ /dev/null
@@ -1,15 +0,0 @@
-linear-accelerate
-=================
-
-[![Hackage](https://img.shields.io/hackage/v/linear-accelerate.svg)](https://hackage.haskell.org/package/linear-accelerate) [![Build Status](https://secure.travis-ci.org/ekmett/linear-accelerate.png?branch=master)](http://travis-ci.org/ekmett/linear-accelerate)
-
-This package provides orphan instances that allows you to use `linear` vector spaces in `accelerate`.
-
-Contact Information
--------------------
-
-Contributions and bug reports are welcome!
-
-Please feel free to contact me through github or on the `#haskell` or `#haskell-lens` IRC channels on `irc.freenode.net`.
-
--Edward Kmett
diff --git a/README.md b/README.md
new file mode 100644
--- /dev/null
+++ b/README.md
@@ -0,0 +1,23 @@
+<div align="center">
+<img width="450" src="https://github.com/AccelerateHS/accelerate/raw/master/images/accelerate-logo-text-v.png?raw=true" alt="henlo, my name is Theia"/>
+
+# linear-accelerate
+
+[![GitHub CI](https://github.com/tmcdonell/linear-accelerate/workflows/CI/badge.svg)](https://github.com/tmcdonell/linear-accelerate/actions)
+[![Gitter](https://img.shields.io/gitter/room/nwjs/nw.js.svg)](https://gitter.im/AccelerateHS/Lobby)
+<br>
+[![Stackage LTS](https://stackage.org/package/linear-accelerate/badge/lts)](https://stackage.org/lts/package/linear-accelerate)
+[![Stackage Nightly](https://stackage.org/package/linear-accelerate/badge/nightly)](https://stackage.org/nightly/package/linear-accelerate)
+[![Hackage](https://img.shields.io/hackage/v/linear-accelerate.svg)](https://hackage.haskell.org/package/linear-accelerate)
+
+</div>
+
+Types and combinators to mix [linear][linear] with [accelerate][accelerate].
+
+Contributions and bug reports are welcome!<br>
+Please feel free to contact me through [GitHub][accelerate] or [gitter.im][gitter.im].
+
+ [linear]:              https://github.com/ekmett/linear
+ [accelerate]:          https://github.com/AccelerateHS/accelerate
+ [gitter.im]:           https://gitter.im/AccelerateHS/Lobby
+
diff --git a/linear-accelerate.cabal b/linear-accelerate.cabal
--- a/linear-accelerate.cabal
+++ b/linear-accelerate.cabal
@@ -1,33 +1,32 @@
 name:          linear-accelerate
-category:      Math, Algebra, Compilers/Interpreters, Concurrency, Data, Parallelism
-version:       0.6.0.0
+category:      Accelerate, Math, Algebra
+version:       0.7.0.0
 license:       BSD3
 cabal-version: >= 1.10
 license-file:  LICENSE
 author:        Edward A. Kmett, Charles Durham, Trevor L. McDonell
-maintainer:    Edward A. Kmett <ekmett@gmail.com>
+maintainer:    Trevor L. McDonell <trevor.mcdonell@gmail.com>
 stability:     provisional
-homepage:      http://github.com/ekmett/linear-accelerate/
-bug-reports:   http://github.com/ekmett/linear-accelerate/issues
+homepage:      http://github.com/tmcdonell/linear-accelerate/
+bug-reports:   http://github.com/tmcdonell/linear-accelerate/issues
 copyright:     Copyright (C) 2014 Edward A. Kmett
 synopsis:      Lifting linear vector spaces into Accelerate
-description:   Lifting linear vector spaces into Accelerate
+description:   Please see the README on GitHub at <https://github.com/tmcdonell/linear-accelerate#readme>
 build-type:    Custom
+
 extra-source-files:
-  .travis.yml
-  .vim.custom
-  CHANGELOG.markdown
-  README.markdown
+  CHANGELOG.md
+  README.md
   Warning.hs
 
 source-repository head
   type:     git
-  location: git://github.com/ekmett/linear-accelerate.git
+  location: git://github.com/tmcdonell/linear-accelerate.git
 
 source-repository this
   type:     git
-  tag:      v0.6.0.0
-  location: git://github.com/ekmett/linear-accelerate.git
+  tag:      v0.7.0.0
+  location: git://github.com/tmcdonell/linear-accelerate.git
 
 custom-setup
   setup-depends:
@@ -38,20 +37,21 @@
 library
   build-depends:
       base              >= 4.5          && < 5
-    , accelerate        >= 1.2
+    , accelerate        >= 1.3
     , distributive      >= 0.2.2        && < 1
     , lens              >= 4            && < 5
-    , linear            >= 1.10         && < 2
+    , linear            >= 1.15         && < 2
 
   exposed-modules:
     Data.Array.Accelerate.Linear
     Data.Array.Accelerate.Linear.Conjugate
     Data.Array.Accelerate.Linear.Epsilon
     Data.Array.Accelerate.Linear.Matrix
-    Data.Array.Accelerate.Linear.Trace
     Data.Array.Accelerate.Linear.Metric
     Data.Array.Accelerate.Linear.Plucker
+    Data.Array.Accelerate.Linear.Projection
     Data.Array.Accelerate.Linear.Quaternion
+    Data.Array.Accelerate.Linear.Trace
     Data.Array.Accelerate.Linear.Type
     Data.Array.Accelerate.Linear.V0
     Data.Array.Accelerate.Linear.V1
@@ -81,7 +81,7 @@
 
   build-depends:
       base              == 4.*
-    , doctest           >= 0.11.1 && < 0.16
+    , doctest           >= 0.11.1 && < 0.17
     , linear-accelerate
 
   default-language:
diff --git a/src/Data/Array/Accelerate/Linear.hs b/src/Data/Array/Accelerate/Linear.hs
--- a/src/Data/Array/Accelerate/Linear.hs
+++ b/src/Data/Array/Accelerate/Linear.hs
@@ -2,10 +2,10 @@
 -- |
 -- Module      : Data.Array.Accelerate.Linear
 -- Copyright   : 2014 Edward Kmett, Charles Durham,
---               [2015..2018] Trevor L. McDonell
+--               [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
diff --git a/src/Data/Array/Accelerate/Linear/Conjugate.hs b/src/Data/Array/Accelerate/Linear/Conjugate.hs
--- a/src/Data/Array/Accelerate/Linear/Conjugate.hs
+++ b/src/Data/Array/Accelerate/Linear/Conjugate.hs
@@ -1,15 +1,16 @@
+{-# LANGUAGE MonoLocalBinds      #-}
 {-# LANGUAGE FlexibleContexts    #-}
 {-# LANGUAGE FlexibleInstances   #-}
+{-# LANGUAGE PatternSynonyms     #-}
 {-# LANGUAGE ScopedTypeVariables #-}
-{-# LANGUAGE ViewPatterns        #-}
 {-# OPTIONS_GHC -fno-warn-orphans #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      : Data.Array.Accelerate.Linear.Conjugate
--- Copyright   : 2018 Trevor L. McDonell
+-- Copyright   : [2018..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
@@ -24,7 +25,7 @@
 ) where
 
 import Data.Array.Accelerate                                        as A
-import Data.Array.Accelerate.Data.Complex                           ( Complex(..) )
+import Data.Array.Accelerate.Data.Complex                           ( pattern (::+),  Complex(..) )
 
 import Linear.Conjugate
 
@@ -38,13 +39,14 @@
 instance Conjugate (Exp Word32)
 instance Conjugate (Exp Word16)
 instance Conjugate (Exp Word8)
-instance Conjugate (Exp Double)
+instance Conjugate (Exp Half)
 instance Conjugate (Exp Float)
+instance Conjugate (Exp Double)
 instance Conjugate (Exp CFloat)
 instance Conjugate (Exp CDouble)
 
 instance (Conjugate (Exp a), A.RealFloat a, Elt (Complex a)) => Conjugate (Exp (Complex a)) where
-  conjugate (unlift -> a :+ b :: Complex (Exp a)) = lift $ conjugate a :+ negate b
+  conjugate (a ::+ b) = conjugate a ::+ negate b
 
 instance TrivialConjugate (Exp Int)
 instance TrivialConjugate (Exp Int64)
@@ -56,8 +58,9 @@
 instance TrivialConjugate (Exp Word32)
 instance TrivialConjugate (Exp Word16)
 instance TrivialConjugate (Exp Word8)
-instance TrivialConjugate (Exp Double)
+instance TrivialConjugate (Exp Half)
 instance TrivialConjugate (Exp Float)
+instance TrivialConjugate (Exp Double)
 instance TrivialConjugate (Exp CFloat)
 instance TrivialConjugate (Exp CDouble)
 
diff --git a/src/Data/Array/Accelerate/Linear/Epsilon.hs b/src/Data/Array/Accelerate/Linear/Epsilon.hs
--- a/src/Data/Array/Accelerate/Linear/Epsilon.hs
+++ b/src/Data/Array/Accelerate/Linear/Epsilon.hs
@@ -5,10 +5,10 @@
 -- |
 -- Module      : Data.Array.Accelerate.Linear.Epsilon
 -- Copyright   : 2014 Edward Kmett, Charles Durham,
---               [2015..2018] Trevor L. McDonell
+--               [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
@@ -24,16 +24,16 @@
 -- | Provides a fairly subjective test to see if a quantity is near zero.
 --
 -- >>> nearZero (1e-11 :: Exp Double)
--- False
+-- (0, ())
 --
 -- >>> nearZero (1e-17 :: Exp Double)
--- True
+-- (1, ())
 --
 -- >>> nearZero (1e-5 :: Exp Float)
--- False
+-- (0, ())
 --
 -- >>> nearZero (1e-7 :: Exp Float)
--- True
+-- (1, ())
 --
 class Num a => Epsilon a where
   -- | Determine if a quantity is near zero.
diff --git a/src/Data/Array/Accelerate/Linear/Lift.hs b/src/Data/Array/Accelerate/Linear/Lift.hs
--- a/src/Data/Array/Accelerate/Linear/Lift.hs
+++ b/src/Data/Array/Accelerate/Linear/Lift.hs
@@ -5,10 +5,10 @@
 -----------------------------------------------------------------------------
 -- |
 -- Module      : Data.Array.Accelerate.Linear.Lift
--- Copyright   : [2015..2018] Trevor L. McDonell
+-- Copyright   : [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Trevor L. McDonell <tmcdonell@cse.unsw.edu.au>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
diff --git a/src/Data/Array/Accelerate/Linear/Matrix.hs b/src/Data/Array/Accelerate/Linear/Matrix.hs
--- a/src/Data/Array/Accelerate/Linear/Matrix.hs
+++ b/src/Data/Array/Accelerate/Linear/Matrix.hs
@@ -1,15 +1,16 @@
 {-# LANGUAGE ConstraintKinds     #-}
 {-# LANGUAGE FlexibleContexts    #-}
+{-# LANGUAGE PatternSynonyms     #-}
 {-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE TypeFamilies        #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      : Data.Array.Accelerate.Linear.Matrix
 -- Copyright   : 2014 Edward Kmett, Charles Durham,
---               [2015..2018] Trevor L. McDonell
+--               [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
@@ -32,8 +33,7 @@
 
 ) where
 
-import Data.Array.Accelerate                    as A hiding ( transpose )
-
+import Data.Array.Accelerate                    as A hiding ( transpose, pattern V2, pattern V3, pattern V4 )
 import Data.Array.Accelerate.Linear.Lift
 import Data.Array.Accelerate.Linear.Trace
 import Data.Array.Accelerate.Linear.Type
@@ -64,7 +64,7 @@
 infixl 7 !*!
 -- | Matrix product. This can compute any combination of sparse and dense multiplication.
 --
--- >>> test $ lift (V2 (V3 1 2 3) (V3 4 5 6) :: M23 Int) !*! lift (V3 (V2 1 2) (V2 3 4) (V2 4 5) :: M32 Int)
+-- >>> test $ (V2_ (V3_ 1 2 3) (V3_ 4 5 6) :: Exp (M23 Int)) !*! (V3_ (V2_ 1 2) (V2_ 3 4) (V2_ 4 5) :: Exp (M32 Int))
 -- V2 (V2 19 25) (V2 43 58)
 --
 (!*!) :: (Functor m, Foldable t, Additive t, Additive n, A.Num a, Box2 m t a, Box2 t n a, Box2 m n a)
@@ -77,7 +77,7 @@
 infixl 6 !+!
 -- | Entry-wise matrix addition.
 --
--- >>> test $ lift (V2 (V3 1 2 3) (V3 4 5 6) :: M23 Int) !+! lift (V2 (V3 7 8 9) (V3 1 2 3) :: M23 Int)
+-- >>> test $ (V2_ (V3_ 1 2 3) (V3_ 4 5 6) :: Exp (M23 Int)) !+! (V2_ (V3_ 7 8 9) (V3_ 1 2 3) :: Exp (M23 Int))
 -- V2 (V3 8 10 12) (V3 5 7 9)
 --
 (!+!) :: (Additive m, Additive n, A.Num a, Box2 m n a)
@@ -90,7 +90,7 @@
 infixl 6 !-!
 -- | Entry-wise matrix subtraction.
 --
--- >>> test $ lift (V2 (V3 1 2 3) (V3 4 5 6) :: M23 Int) !-! lift (V2 (V3 7 8 9) (V3 1 2 3) :: M23 Int)
+-- >>> test $ (V2_ (V3_ 1 2 3) (V3_ 4 5 6) :: Exp (M23 Int)) !-! (V2_ (V3_ 7 8 9) (V3_ 1 2 3) :: Exp (M23 Int))
 -- V2 (V3 (-6) (-6) (-6)) (V3 3 3 3)
 --
 (!-!) :: (Additive m, Additive n, A.Num a, Box2 m n a)
@@ -103,7 +103,7 @@
 infixl 7 !*
 -- | Matrix * column vector
 --
--- >>> test $ lift (V2 (V3 1 2 3) (V3 4 5 6) :: M23 Int) !* lift (V3 7 8 9 :: V3 Int)
+-- >>> test $ (V2_ (V3_ 1 2 3) (V3_ 4 5 6) :: Exp (M23 Int)) !* (V3_ 7 8 9 :: Exp (V3 Int))
 -- V2 50 122
 --
 (!*) :: (Functor m, Foldable r, Additive r, A.Num a, Box2 m r a, Box m a)
@@ -116,7 +116,7 @@
 infixl 7 *!
 -- | Row vector * matrix
 --
--- >>> test $ lift (V2 1 2 :: V2 Int) *! lift (V2 (V3 3 4 5) (V3 6 7 8) :: M23 Int)
+-- >>> test $ (V2_ 1 2 :: Exp (V2 Int)) *! (V2_ (V3_ 3 4 5) (V3_ 6 7 8) :: Exp (M23 Int))
 -- V3 15 18 21
 
 -- (*!) :: (Metric r, Additive n, Num a) => r a -> r (n a) -> n a
@@ -132,7 +132,7 @@
 infixl 7 *!!
 -- | Scalar-matrix product
 --
--- >>> test $ 5 *!! lift (V2 (V2 1 2) (V2 3 4) :: M22 Int)
+-- >>> test $ 5 *!! (V2_ (V2_ 1 2) (V2_ 3 4) :: Exp (M22 Int))
 -- V2 (V2 5 10) (V2 15 20)
 --
 (*!!) :: (Functor m, Functor r, A.Num a, Box2 m r a)
@@ -145,7 +145,7 @@
 infixl 7 !!*
 -- | Matrix-scalar product
 --
--- >>> test $ lift (V2 (V2 1 2) (V2 3 4) :: M22 Int) !!* 5
+-- >>> test $ (V2_ (V2_ 1 2) (V2_ 3 4) :: Exp (M22 Int)) !!* 5
 -- V2 (V2 5 10) (V2 15 20)
 --
 (!!*) :: (Functor m, Functor r, A.Num a, Box2 m r a)
@@ -179,7 +179,7 @@
 
 -- | 'transpose' is just an alias for 'distribute'
 --
--- >>> test $ transpose $ lift (V3 (V2 1 2) (V2 3 4) (V2 5 6) :: M32 Int)
+-- >>> test $ transpose $ (V3_ (V2_ 1 2) (V2_ 3 4) (V2_ 5 6) :: Exp (M32 Int))
 -- V2 (V3 1 3 5) (V3 2 4 6)
 --
 transpose
@@ -259,4 +259,3 @@
 inv44 m =
   let r = L.inv44 (unlift' m)
   in  lift r
-
diff --git a/src/Data/Array/Accelerate/Linear/Metric.hs b/src/Data/Array/Accelerate/Linear/Metric.hs
--- a/src/Data/Array/Accelerate/Linear/Metric.hs
+++ b/src/Data/Array/Accelerate/Linear/Metric.hs
@@ -1,16 +1,17 @@
 {-# LANGUAGE ConstraintKinds     #-}
 {-# LANGUAGE FlexibleContexts    #-}
 {-# LANGUAGE NoImplicitPrelude   #-}
+{-# LANGUAGE PatternSynonyms     #-}
 {-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE TypeFamilies        #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      : Data.Array.Accelerate.Linear.Metric
 -- Copyright   : 2014 Edward Kmett, Charles Durham,
---               [2015..2018] Trevor L. McDonell
+--               [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
@@ -20,7 +21,7 @@
 module Data.Array.Accelerate.Linear.Metric
   where
 
-import Data.Array.Accelerate                    as A
+import Data.Array.Accelerate                    as A hiding ( pattern V2 )
 import Data.Array.Accelerate.Linear.Type
 import Data.Array.Accelerate.Linear.Epsilon
 import Data.Array.Accelerate.Linear.Vector
@@ -28,7 +29,8 @@
 import qualified Linear.Metric                  as L
 
 -- $setup
--- >>> import Data.Array.Accelerate.Linear.V2 ()
+-- >>> :set -XPatternSynonyms
+-- >>> import Data.Array.Accelerate.Linear.V2 ( pattern V2_ )
 -- >>> import Linear.V2
 
 -- | Free and sparse inner product/metric spaces.
@@ -38,7 +40,7 @@
   -- | Compute the inner product of two vectors or (equivalently) convert a
   -- vector @f a@ into a covector @f a -> a@.
   --
-  -- >>> lift (V2 1 2 :: V2 Int) `dot` lift (V2 3 4 :: V2 Int)
+  -- >>> (V2_ 1 2 :: Exp (V2 Int)) `dot` (V2_ 3 4 :: Exp (V2 Int))
   -- 11
   --
   dot :: forall a. (A.Num a, Box f a)
diff --git a/src/Data/Array/Accelerate/Linear/Plucker.hs b/src/Data/Array/Accelerate/Linear/Plucker.hs
--- a/src/Data/Array/Accelerate/Linear/Plucker.hs
+++ b/src/Data/Array/Accelerate/Linear/Plucker.hs
@@ -2,10 +2,14 @@
 {-# LANGUAGE DeriveDataTypeable    #-}
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE FlexibleInstances     #-}
+{-# LANGUAGE GADTs                 #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE PatternSynonyms       #-}
 {-# LANGUAGE RebindableSyntax      #-}
 {-# LANGUAGE ScopedTypeVariables   #-}
 {-# LANGUAGE StandaloneDeriving    #-}
+{-# LANGUAGE TemplateHaskell       #-}
+{-# LANGUAGE TypeApplications      #-}
 {-# LANGUAGE TypeFamilies          #-}
 {-# LANGUAGE UndecidableInstances  #-}
 {-# LANGUAGE ViewPatterns          #-}
@@ -15,10 +19,10 @@
 -- |
 -- Module      : Data.Array.Accelerate.Linear.Plucker
 -- Copyright   : 2014 Edward Kmett, Charles Durham,
---               [2015..2018] Trevor L. McDonell
+--               [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
@@ -27,7 +31,7 @@
 
 module Data.Array.Accelerate.Linear.Plucker (
 
-  Plucker(..),
+  Plucker(..), pattern Plucker_,
 
   squaredError,
   isotropic,
@@ -36,7 +40,7 @@
   plucker3D,
 
   -- * operations on lines
-  LinePass(..),
+  LinePass(..), pattern Clockwise_, pattern Counterclockwise_, pattern Coplanar_,
   parallel,
   intersects,
   passes,
@@ -52,11 +56,10 @@
 
 ) where
 
-import Data.Array.Accelerate                    hiding ( fromInteger )
+import Data.Array.Accelerate                    hiding ( fromInteger, pattern V2, pattern V3, pattern V4 )
 import Data.Array.Accelerate.Data.Functor
 import Data.Array.Accelerate.Smart
-import Data.Array.Accelerate.Product
-import Data.Array.Accelerate.Array.Sugar
+import Data.Array.Accelerate.Unsafe
 
 import Data.Array.Accelerate.Linear.Epsilon
 import Data.Array.Accelerate.Linear.Lift
@@ -123,47 +126,47 @@
   if s > 0      then constant Counterclockwise
                 else constant Clockwise
   where
-    s        = (lift u1 `dot` lift v2) + (lift u2 `dot` lift v1)
-    V2 u1 v1 = toUV a
-    V2 u2 v2 = toUV b
+    s        = (u1 `dot` v2) + (u2 `dot` v1)
+    V2_ u1 v1 = toUV a
+    V2_ u2 v2 = toUV b
 
 -- | Checks if two lines are parallel.
 --
 parallel :: Epsilon a => Exp (Plucker a) -> Exp (Plucker a) -> Exp Bool
-parallel a b = nearZero $ lift u1 `cross` lift u2
+parallel a b = nearZero $ u1 `cross` u2
   where
-    V2 u1 _ = toUV a
-    V2 u2 _ = toUV b
+    V2_ u1 _ = toUV a
+    V2_ u2 _ = toUV b
 
 -- | Represent a Plücker coordinate as a pair of 3-tuples, typically denoted
 -- U and V.
 --
-toUV :: Elt a => Exp (Plucker a) -> V2 (V3 (Exp a))
-toUV (unlift -> Plucker a b c d e f) = V2 (V3 a b c) (V3 d e f)
+toUV :: Elt a => Exp (Plucker a) -> Exp (V2 (V3 a))
+toUV (Plucker_ a b c d e f) = V2_ (V3_ a b c) (V3_ d e f)
 
 -- | The minimum squared distance of a line from the origin.
 --
 quadranceToOrigin :: Fractional a => Exp (Plucker a) -> Exp a
-quadranceToOrigin p = (lift v `dot` lift v) / (lift u `dot` lift u)
+quadranceToOrigin p = (v `dot` v) / (u `dot` u)
   where
-    V2 u v = toUV p
+    V2_ u v = toUV p
 
 -- | The point where a line is closest to the origin.
 --
 closestToOrigin :: Fractional a => Exp (Plucker a) -> Exp (V3 a)
-closestToOrigin p = normalizePoint . lift $ V4 x y z (lift u `dot` lift u)
+closestToOrigin p = normalizePoint $ V4_ x y z (u `dot` u)
   where
-    V2 u v   = toUV p
-    V3 x y z = unlift $ lift v `cross` lift u
+    V2_ u v   = toUV p
+    V3_ x y z = v `cross` u
 
 -- | Not all 6-dimensional points correspond to a line in 3D. This predicate
 -- tests that a Plücker coordinate lies on the Grassmann manifold, and does
 -- indeed represent a 3D line.
 --
 isLine :: Epsilon a => Exp (Plucker a) -> Exp Bool
-isLine p = nearZero $ lift u `dot` lift v
+isLine p = nearZero $ u `dot` v
   where
-    V2 u v = toUV p
+    V2_ u v = toUV p
 
 
 -- | These elements form a basis for the Plücker space, or the Grassmanian
@@ -215,44 +218,21 @@
 
 deriving instance Typeable Plucker
 
+pattern Plucker_ :: Elt a => Exp a -> Exp a -> Exp a -> Exp a -> Exp a -> Exp a -> Exp (Plucker a)
+pattern Plucker_ a b c d e f = Pattern (a,b,c,d,e,f)
+{-# COMPLETE Plucker_ #-}
+
 instance Metric Plucker
 instance Additive Plucker
-
-type instance EltRepr (Plucker a) = EltRepr (a, a, a, a, a, a)
-
-instance Elt a => Elt (Plucker a) where
-  eltType _ = eltType (undefined :: (a,a,a,a,a,a))
-  toElt p = case toElt p of
-     (x, y, z, w, u, v) -> Plucker x y z w u v
-  fromElt (Plucker x y z w u v) = fromElt (x, y, z, w, u, v)
-
-instance cst a => IsProduct cst (Plucker a) where
-  type ProdRepr (Plucker a) = ProdRepr (a,a,a,a,a,a)
-  fromProd p (Plucker x y z w u v) = fromProd p (x, y, z, w, u, v)
-  toProd p t = case toProd p t of
-     (x, y, z, w, u, v) -> Plucker x y z w u v
-  prod p _ = prod p (undefined :: (a,a,a,a,a,a))
+instance Elt a => Elt (Plucker a)
 
 instance (Lift Exp a, Elt (Plain a)) => Lift Exp (Plucker a) where
   type Plain (Plucker a) = Plucker (Plain a)
-  -- lift = Exp . Tuple . F.foldl SnocTup NilTup
   lift (Plucker x y z w u v) =
-    Exp $ Tuple $
-      NilTup `SnocTup` lift x
-             `SnocTup` lift y
-             `SnocTup` lift z
-             `SnocTup` lift w
-             `SnocTup` lift u
-             `SnocTup` lift v
+    Plucker_ (lift x) (lift y) (lift z) (lift w) (lift u) (lift v)
 
 instance Elt a => Unlift Exp (Plucker (Exp a)) where
-  unlift t = Plucker
-    (Exp $ SuccTupIdx (SuccTupIdx (SuccTupIdx (SuccTupIdx (SuccTupIdx ZeroTupIdx)))) `Prj` t)
-    (Exp $ SuccTupIdx (SuccTupIdx (SuccTupIdx (SuccTupIdx ZeroTupIdx))) `Prj` t)
-    (Exp $ SuccTupIdx (SuccTupIdx (SuccTupIdx ZeroTupIdx)) `Prj` t)
-    (Exp $ SuccTupIdx (SuccTupIdx ZeroTupIdx) `Prj` t)
-    (Exp $ SuccTupIdx ZeroTupIdx `Prj` t)
-    (Exp $ ZeroTupIdx `Prj` t)
+  unlift (Plucker_ x y z w u v) = Plucker x y z w u v
 
 instance (Elt a, Elt b) => Each (Exp (Plucker a)) (Exp (Plucker b)) (Exp a) (Exp b) where
   each = liftLens (each :: Traversal (Plucker (Exp a)) (Plucker (Exp b)) (Exp a) (Exp b))
@@ -269,11 +249,11 @@
   min  = pl $$ on min t6
   max  = pl $$ on max t6
 
-t6 :: Elt a => Exp (Plucker a) -> Exp (a,a,a,a,a,a)
-t6 (unlift -> Plucker a b c d e f) = tup6 (a,b,c,d,e,f)
+t6 :: Exp (Plucker a) -> Exp (a, a, a, a, a, a)
+t6 (Exp e) = Exp e
 
-pl :: Elt a => Exp (a,a,a,a,a,a) -> Exp (Plucker a)
-pl (untup6 -> (a,b,c,d,e,f)) = lift (Plucker a b c d e f)
+pl :: Exp (a, a, a, a, a, a) -> Exp (Plucker a)
+pl (Exp e) = Exp e
 
 instance Num a => P.Num (Exp (Plucker a)) where
   (+)           = lift2 ((+) :: Plucker (Exp a) -> Plucker (Exp a) -> Plucker (Exp a))
@@ -313,27 +293,14 @@
   nearZero = nearZero . quadrance
 
 instance Functor Plucker where
-  fmap g (unlift -> Plucker a b c d e f) = lift (Plucker (g a) (g b) (g c) (g d) (g e) (g f))
-  x <$ _                                 = lift (Plucker x x x x x x)
-
-
-type instance EltRepr LinePass = Int8
-
-instance Elt LinePass where
-  eltType _ = eltType (undefined::Int8)
-
-  toElt x = let (==) = (P.==)   -- -XRebindableSyntax hax
-            in  case x of
-                  0 -> Coplanar
-                  1 -> Clockwise
-                  2 -> Counterclockwise
-                  _ -> P.error "LinePass: unhandled constructor"
+  fmap g (Plucker_ a b c d e f) = Plucker_ (g a) (g b) (g c) (g d) (g e) (g f)
+  x <$ _                        = Plucker_ x x x x x x
 
-  fromElt Coplanar         = 0
-  fromElt Clockwise        = 1
-  fromElt Counterclockwise = 2
+instance Elt LinePass
 
 instance Eq LinePass where
-  x == y = bitcast x == (bitcast y :: Exp Int8)
-  x /= y = bitcast x /= (bitcast y :: Exp Int8)
+  x == y = coerce x == (coerce y :: Exp Word8)
+  x /= y = coerce x /= (coerce y :: Exp Word8)
+
+mkPattern ''LinePass
 
diff --git a/src/Data/Array/Accelerate/Linear/Projection.hs b/src/Data/Array/Accelerate/Linear/Projection.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Array/Accelerate/Linear/Projection.hs
@@ -0,0 +1,96 @@
+{-# LANGUAGE RebindableSyntax #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE PatternSynonyms  #-}
+-----------------------------------------------------------------------------
+-- |
+-- Module      : Data.Array.Accelerate.Linear.Projection
+-- Copyright   : [2019..2020] Trevor L. McDonell
+-- License     : BSD-style (see the file LICENSE)
+--
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
+-- Stability   : experimental
+-- Portability : non-portable
+--
+-- Common projection matrices; for example perspective and orthographic
+-- transformation matrices.
+--
+-- @since 0.7.0.0
+----------------------------------------------------------------------------
+
+module Data.Array.Accelerate.Linear.Projection
+  where
+
+import Data.Array.Accelerate                              hiding ( pattern V3, pattern V4 )
+import Data.Array.Accelerate.Smart
+import Data.Array.Accelerate.Linear.Epsilon
+import Data.Array.Accelerate.Linear.Matrix
+import Data.Array.Accelerate.Linear.Metric
+import Data.Array.Accelerate.Linear.V3
+import Data.Array.Accelerate.Linear.V4
+
+import Control.Lens
+import qualified Linear.Projection                        as L
+
+
+-- | Build a look at view matrix
+--
+lookAt
+  :: (Epsilon a, Floating a)
+  => Exp (V3 a)     -- ^ Eye
+  -> Exp (V3 a)     -- ^ Center
+  -> Exp (V3 a)     -- ^ Up
+  -> Exp (M44 a)
+lookAt eye center up = V4_ (V4_ (xa ^. _x)  (xa ^. _y)  (xa ^. _z)  xd)
+                           (V4_ (ya ^. _x)  (ya ^. _y)  (ya ^. _z)  yd)
+                           (V4_ (-za ^. _x) (-za ^. _y) (-za ^. _z) zd)
+                           (V4_ 0           0           0           1)
+ where
+  za = normalize $ center - eye
+  xa = normalize $ cross za up
+  ya = cross xa za
+  xd = -dot xa eye
+  yd = -dot ya eye
+  zd = dot za eye
+
+
+-- | Build a matrix for a symmetric perspective-view frustum
+--
+perspective
+  :: Floating a
+  => Exp a -- ^ FOV
+  -> Exp a -- ^ Aspect ratio
+  -> Exp a -- ^ Near plane
+  -> Exp a -- ^ Far plane
+  -> Exp (M44 a)
+perspective = lift $$$$ L.perspective
+
+
+-- | Build a matrix for a symmetric perspective-view frustum with a far
+-- plane at infinite
+--
+infinitePerspective
+  :: Floating a
+  => Exp a -- ^ FOV
+  -> Exp a -- ^ Aspect Ratio
+  -> Exp a -- ^ Near plane
+  -> Exp (M44 a)
+infinitePerspective = lift $$$ L.infinitePerspective
+
+
+-- | Build an orthographic perspective matrix from 6 clipping planes
+--
+ortho
+  :: Floating a
+  => Exp a -- ^ Left
+  -> Exp a -- ^ Right
+  -> Exp a -- ^ Bottom
+  -> Exp a -- ^ Top
+  -> Exp a -- ^ Near
+  -> Exp a -- ^ Far
+  -> Exp (M44 a)
+ortho = lift $$$$$$ L.ortho
+
+infixr 0 $$$$$$
+($$$$$$) :: (b -> a) -> (c -> d -> e -> f -> g -> h -> b) -> c -> d -> e -> f -> g -> h -> a
+(f $$$$$$ g) x y z u v w = f (g x y z u v w)
+
diff --git a/src/Data/Array/Accelerate/Linear/Quaternion.hs b/src/Data/Array/Accelerate/Linear/Quaternion.hs
--- a/src/Data/Array/Accelerate/Linear/Quaternion.hs
+++ b/src/Data/Array/Accelerate/Linear/Quaternion.hs
@@ -2,20 +2,20 @@
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE FlexibleInstances     #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE PatternSynonyms       #-}
 {-# LANGUAGE RebindableSyntax      #-}
 {-# LANGUAGE ScopedTypeVariables   #-}
 {-# LANGUAGE TypeFamilies          #-}
 {-# LANGUAGE UndecidableInstances  #-}
-{-# LANGUAGE ViewPatterns          #-}
 {-# OPTIONS_GHC -fno-warn-orphans #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      : Data.Array.Accelerate.Linear.Quaternion
 -- Copyright   : 2014 Edward Kmett, Charles Durham,
---               [2015..2018] Trevor L. McDonell
+--               [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
@@ -24,7 +24,7 @@
 
 module Data.Array.Accelerate.Linear.Quaternion (
 
-  Quaternion(..),
+  Quaternion(..), pattern Quaternion_,
 
   slerp,
   asinq,
@@ -40,11 +40,9 @@
 
 ) where
 
-import Data.Array.Accelerate
-import Data.Array.Accelerate.Array.Sugar
+import Data.Array.Accelerate                    hiding ( pattern V3 )
 import Data.Array.Accelerate.Data.Complex       hiding ( conjugate )
 import Data.Array.Accelerate.Data.Functor
-import Data.Array.Accelerate.Product
 import Data.Array.Accelerate.Smart
 
 import Data.Array.Accelerate.Linear.Conjugate
@@ -70,66 +68,66 @@
   where
     dqp = dot q p
     phi = acos cosphi
-    (cosphi, fp) = unlift $ if dqp < 0 then tup2 (-dqp, negate p)
-                                       else tup2 (dqp, p)
+    T2 cosphi fp = if dqp < 0 then T2 (negate dqp) (negate p)
+                              else T2 dqp p
 
 -- | 'asin' with a specified branch cut
 --
 asinq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)
-asinq q@(unlift -> Quaternion e _) u =
+asinq q@(Quaternion_ e _) u =
   if qiq /= 0.0 || e >= -1 && e <= 1
     then asin q
-    else cutWith (asin (lift $ e :+ sqrt qiq)) u
+    else cutWith (asin (e ::+ sqrt qiq)) u
   where
     qiq = qi q
 
 -- | 'acos' with a specified branch cut
 --
 acosq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)
-acosq q@(unlift -> Quaternion e _) u =
+acosq q@(Quaternion_ e _) u =
   if qiq /= 0.0 || e >= -1 && e <= 1
     then acos q
-    else cutWith (acos (lift $ e :+ sqrt qiq)) u
+    else cutWith (acos (e ::+ sqrt qiq)) u
   where
     qiq = qi q
 
 -- | 'atan' with a specified branch cut
 --
 atanq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)
-atanq q@(unlift -> Quaternion e _) u =
+atanq q@(Quaternion_ e _) u =
   if e /= 0.0 || qiq >= -1 && qiq <= 1
     then atan q
-    else cutWith (atan (lift $ e :+ sqrt qiq)) u
+    else cutWith (atan (e ::+ sqrt qiq)) u
   where
     qiq = qi q
 
 -- | 'asinh' with a specified branch cut
 --
 asinhq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)
-asinhq q@(unlift -> Quaternion e _) u =
+asinhq q@(Quaternion_ e _) u =
   if e /= 0.0 || qiq >= -1 && qiq <= 1
     then asinh q
-    else cutWith (asinh (lift $ e :+ sqrt qiq)) u
+    else cutWith (asinh (e ::+ sqrt qiq)) u
   where
     qiq = qi q
 
 -- | 'acosh' with a specified branch cut
 --
 acoshq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)
-acoshq q@(unlift -> Quaternion e _) u =
+acoshq q@(Quaternion_ e _) u =
   if qiq /= 0.0 || e >= 1
     then asinh q
-    else cutWith (acosh (lift $ e :+ sqrt qiq)) u
+    else cutWith (acosh (e ::+ sqrt qiq)) u
   where
     qiq = qi q
 
 -- | 'atanh' with a specified branch cut
 --
 atanhq :: (RealFloat a, Elt (Complex a)) => Exp (Quaternion a) -> Exp (Quaternion a) -> Exp (Quaternion a)
-atanhq q@(unlift -> Quaternion e _) u =
+atanhq q@(Quaternion_ e _) u =
   if qiq /= 0.0 || e > -1 && e < 1
     then atanh q
-    else cutWith (atanh (lift $ e :+ sqrt qiq)) u
+    else cutWith (atanh (e ::+ sqrt qiq)) u
   where
     qiq = qi q
 
@@ -146,15 +144,15 @@
 -- | Apply a rotation to a vector
 --
 rotate :: forall a. (Conjugate (Exp a), RealFloat a) => Exp (Quaternion a) -> Exp (V3 a) -> Exp (V3 a)
-rotate q v = lift ijk
+rotate q v = ijk
   where
-    Quaternion _ ijk = unlift $ q * (lift (Quaternion 0 (unlift v))) * conjugate q :: Quaternion (Exp a)
+    Quaternion_ _ ijk = q * (Quaternion_ 0 v) * conjugate q
 
 -- | @'axisAngle' axis theta@ builds a 'Quaternion' representing a rotation of
 -- @theta@ radians about @axis@.
 --
 axisAngle :: (Epsilon a, Floating a) => Exp (V3 a) -> Exp a -> Exp (Quaternion a)
-axisAngle axis theta = lift $ Quaternion (cos half) (unlift (sin half *^ normalize axis))
+axisAngle axis theta = Quaternion_ (cos half) (sin half *^ normalize axis)
   where
     half = theta / 2
 
@@ -162,38 +160,20 @@
 -- Instances
 -- ---------
 
+pattern Quaternion_ :: Elt a => Exp a -> Exp (V3 a) -> Exp (Quaternion a)
+pattern Quaternion_ x v = Pattern (x,v)
+{-# COMPLETE Quaternion_ #-}
+
 instance Metric Quaternion
 instance Additive Quaternion
-
-type instance EltRepr (Quaternion a) = EltRepr (a, a, a, a)
-
-instance Elt a => Elt (Quaternion a) where
-  eltType _ = eltType (undefined :: (a,a,a,a))
-  toElt p = case toElt p of
-     (x, y, z, w) -> Quaternion x (V3 y z w)
-  fromElt (Quaternion x (V3 y z w)) = fromElt (x, y, z, w)
-
-instance cst a => IsProduct cst (Quaternion a) where
-  type ProdRepr (Quaternion a) = ProdRepr (a,a,a,a)
-  fromProd p (Quaternion x (V3 y z w)) = fromProd p (x,y,z,w)
-  toProd p t = case toProd p t of
-     (x, y, z, w) -> Quaternion x (V3 y z w)
-  prod p _ = prod p (undefined :: (a,a,a,a))
+instance Elt a => Elt (Quaternion a)
 
 instance (Lift Exp a, Elt (Plain a)) => Lift Exp (Quaternion a) where
   type Plain (Quaternion a) = Quaternion (Plain a)
-  --lift = Exp . Tuple . F.foldl SnocTup NilTup
-  lift (Quaternion x (V3 y z w)) = Exp $ Tuple $ NilTup `SnocTup`
-                                   lift x `SnocTup`
-                                   lift y `SnocTup`
-                                   lift z `SnocTup`
-                                   lift w
+  lift (Quaternion x v) = Quaternion_ (lift x) (lift v)
 
 instance Elt a => Unlift Exp (Quaternion (Exp a)) where
-  unlift t = Quaternion (Exp $ SuccTupIdx (SuccTupIdx (SuccTupIdx ZeroTupIdx)) `Prj` t)
-                    (V3 (Exp $ SuccTupIdx (SuccTupIdx ZeroTupIdx) `Prj` t)
-                        (Exp $ SuccTupIdx ZeroTupIdx `Prj` t)
-                        (Exp $ ZeroTupIdx `Prj` t))
+  unlift (Quaternion_ x v) = Quaternion x (unlift v)
 
 instance (Elt a, Elt b) => Each (Exp (Quaternion a)) (Exp (Quaternion b)) (Exp a) (Exp b) where
   each = liftLens (each :: Traversal (Quaternion (Exp a)) (Quaternion (Exp b)) (Exp a) (Exp b))
@@ -211,32 +191,32 @@
   max  = qu $$ on max t4
 
 t4 :: Elt a => Exp (Quaternion a) -> Exp (a,a,a,a)
-t4 (unlift -> Quaternion x (V3 y z w)) = tup4 (x,y,z,w)
+t4 (Quaternion_ x (V3_ y z w)) = T4 x y z w
 
 qu :: Elt a => Exp (a,a,a,a) -> Exp (Quaternion a)
-qu (untup4 -> (x,y,z,w)) = lift (Quaternion x (V3 y z w))
+qu (T4 x y z w) = Quaternion_ x (V3_ y z w)
 
 instance RealFloat a => P.Num (Exp (Quaternion a)) where
   (+)           = lift2 ((+) :: Quaternion (Exp a) -> Quaternion (Exp a) -> Quaternion (Exp a))
   (-)           = lift2 ((-) :: Quaternion (Exp a) -> Quaternion (Exp a) -> Quaternion (Exp a))
   negate        = fmap negate
-  abs z         = lift (Quaternion (norm z) (V3 0 0 0))
-  fromInteger x = lift (Quaternion (fromInteger x) (V3 0 0 0))
+  abs z         = Quaternion_ (norm z) (V3_ 0 0 0)
+  fromInteger x = Quaternion_ (fromInteger x) (V3_ 0 0 0)
 
-  z1 * z2       = let Quaternion s1 v1' = unlift z1; v1 = lift v1'
-                      Quaternion s2 v2' = unlift z2; v2 = lift v2'
-                  in
-                  lift $ Quaternion (s1*s2 - (v1 `dot` v2))
-                                    (unlift ((v1 `cross` v2) + s1*^v2 + s2*^v1))
+  z1 * z2       = let Quaternion_ s1 v1 = z1
+                      Quaternion_ s2 v2 = z2
+                   in
+                   Quaternion_ (s1*s2 - (v1 `dot` v2))
+                               ((v1 `cross` v2) + s1*^v2 + s2*^v1)
 
-  signum q@(unlift -> Quaternion e (V3 i j k)) =
+  signum q@(Quaternion_ e (V3_ i j k)) =
     if m == 0.0                      then q else
     if not (isInfinite m || isNaN m) then q ^/ sqrt m else
     if ne || ni || nj || nk          then qNaN else
-    if not (ii || ij || ik)          then lift $ Quaternion 1 (V3 0 0 0) else
-    if not (ie || ij || ik)          then lift $ Quaternion 0 (V3 1 0 0) else
-    if not (ie || ii || ik)          then lift $ Quaternion 0 (V3 0 1 0) else
-    if not (ie || ii || ij)          then lift $ Quaternion 0 (V3 0 0 1)
+    if not (ii || ij || ik)          then Quaternion_ 1 (V3_ 0 0 0) else
+    if not (ie || ij || ik)          then Quaternion_ 0 (V3_ 1 0 0) else
+    if not (ie || ii || ik)          then Quaternion_ 0 (V3_ 0 1 0) else
+    if not (ie || ii || ij)          then Quaternion_ 0 (V3_ 0 0 1)
                                      else qNaN
     where
       m  = quadrance q
@@ -249,42 +229,44 @@
       nj = isNaN j
       nk = isNaN k
       --
-      qNaN = lift $ Quaternion fNaN (V3 fNaN fNaN fNaN)
+      qNaN = Quaternion_ fNaN (V3_ fNaN fNaN fNaN)
       fNaN = 0/0
 
 instance RealFloat a => P.Fractional (Exp (Quaternion a)) where
   z1 / z2 =
-    let Quaternion q0 (V3 q1 q2 q3) = unlift z1
-        Quaternion r0 (V3 r1 r2 r3) = unlift z2
+    let Quaternion_ q0 (V3_ q1 q2 q3) = z1
+        Quaternion_ r0 (V3_ r1 r2 r3) = z2
     in
-    lift (Quaternion (r0*q0+r1*q1+r2*q2+r3*q3)
-                     (V3 (r0*q1-r1*q0-r2*q3+r3*q2)
-                         (r0*q2+r1*q3-r2*q0-r3*q1)
-                         (r0*q3-r1*q2+r2*q1-r3*q0)))
-      ^/ (r0*r0 + r1*r1 + r2*r2 + r3*r3)
+    Quaternion_
+        (r0 * q0 + r1 * q1 + r2 * q2 + r3 * q3)
+        (V3_ (r0 * q1 - r1 * q0 - r2 * q3 + r3 * q2)
+             (r0 * q2 + r1 * q3 - r2 * q0 - r3 * q1)
+             (r0 * q3 - r1 * q2 + r2 * q1 - r3 * q0)
+        )
+      ^/ (r0 * r0 + r1 * r1 + r2 * r2 + r3 * r3)
 
-  recip q = let Quaternion e v = unlift q :: Quaternion (Exp a)
-            in  lift (Quaternion e (P.fmap negate v)) ^/ quadrance q
+  recip q = let Quaternion_ e v = q
+             in Quaternion_ e (fmap negate v) ^/ quadrance q
 
-  fromRational x = lift (Quaternion (fromRational x) (V3 0 0 0))
+  fromRational x = Quaternion_ (fromRational x) (V3_ 0 0 0)
 
 instance (RealFloat a, Elt (Complex a)) => P.Floating (Exp (Quaternion a)) where
-  pi = lift (Quaternion pi (V3 0 0 0))
+  pi = Quaternion_ pi (V3_ 0 0 0)
 
-  exp q@(unlift -> Quaternion e v) =
+  exp q@(Quaternion_ e v) =
     if qiq == 0
-      then lift (Quaternion exe v)
+      then Quaternion_ exe v
       else reimagine (exe * cos ai) (exe * (sin ai / ai)) q
     where
       qiq = qi q
       ai  = sqrt qiq
       exe = exp e
 
-  log q@(unlift -> Quaternion e v@(V3 _i j k)) =
+  log q@(Quaternion_ e v@(V3_ _i j k)) =
     if qiq == 0
       then if e >= 0
-             then lift $ Quaternion (log e) v
-             else lift $ Quaternion (log (negate e)) (V3 pi j k) -- mmm, pi
+             then Quaternion_ (log e) v
+             else Quaternion_ (log (negate e)) (V3_ pi j k) -- mmm, pi
       else reimagine (log m) (atan2 m e / ai) q
     where
       qiq = qi q
@@ -293,34 +275,34 @@
 
   x ** y = exp (y * log x)
 
-  sqrt q@(unlift -> Quaternion e v) =
+  sqrt q@(Quaternion_ e v) =
     if m   == 0 then q else
     if qiq == 0 then if e > 0
-                        then lift $ Quaternion (sqrt e) (V3 0 0 0)
-                        else lift $ Quaternion 0 (V3 (sqrt (negate e)) 0 0)
-                else lift $ Quaternion (0.5*(m+e)) (unlift (lift v ^* im))
+                        then Quaternion_ (sqrt e) (V3_ 0 0 0)
+                        else Quaternion_ 0 (V3_ (sqrt (negate e)) 0 0)
+                else Quaternion_ (0.5*(m+e)) (v ^* im)
     where
       qiq = qi q
       im  = sqrt (0.5*(m-e)) / sqrt qiq
       m   = sqrte2pqiq e qiq
 
-  cos q@(unlift -> Quaternion e v) =
-    if qiq == 0 then lift $ Quaternion (cos e) v
+  cos q@(Quaternion_ e v) =
+    if qiq == 0 then Quaternion_ (cos e) v
                 else reimagine (cos e * cosh ai) (- sin e / ai / sinh ai) q -- 0.15 bits error
                   -- reimagine (cos e * cosh ai) (- sin e * sinh ai / ai) q -- 13.5 bits worse
     where
       qiq = qi q
       ai  = sqrt qiq
 
-  sin q@(unlift -> Quaternion e v) =
-    if qiq == 0 then lift $ Quaternion (sin e) v
+  sin q@(Quaternion_ e v) =
+    if qiq == 0 then Quaternion_ (sin e) v
                 else reimagine (sin e * cosh ai) (cos e * sinh ai / ai) q
     where
       qiq = qi q
       ai  = sqrt qiq
 
-  tan q@(unlift -> Quaternion e v) =
-    if qiq == 0 then lift $ Quaternion (tan e) v
+  tan q@(Quaternion_ e v) =
+    if qiq == 0 then Quaternion_ (tan e) v
                 else reimagine (ce * sin e / d) (tanrhs sai ai d) q
     where
       qiq = qi q
@@ -329,22 +311,22 @@
       sai = sinh ai
       d   = ce*ce + sai*sai
 
-  sinh q@(unlift -> Quaternion e v) =
-    if qiq == 0 then lift $ Quaternion (sinh e) v
+  sinh q@(Quaternion_ e v) =
+    if qiq == 0 then Quaternion_ (sinh e) v
                 else reimagine (sinh e * cos ai) (cosh e * sin ai / ai) q
     where
       qiq = qi q
       ai  = sqrt qiq
 
-  cosh q@(unlift -> Quaternion e v) =
-    if qiq == 0 then lift $ Quaternion (cosh e) v
+  cosh q@(Quaternion_ e v) =
+    if qiq == 0 then Quaternion_ (cosh e) v
                 else reimagine (cosh e * cos ai) (sin ai * (sinh e / ai)) q
     where
       qiq = qi q
       ai  = sqrt qiq
 
-  tanh q@(unlift -> Quaternion e v) =
-    if qiq == 0 then lift $ Quaternion (tanh e) v
+  tanh q@(Quaternion_ e v) =
+    if qiq == 0 then Quaternion_ (tanh e) v
                 else reimagine (cosh e * se / d) (tanhrhs cai ai d) q
     where
       qiq = qi q
@@ -363,31 +345,31 @@
 
 
 reimagine :: RealFloat a => Exp a -> Exp a -> Exp (Quaternion a) -> Exp (Quaternion a)
-reimagine r s (unlift -> Quaternion _ v) =
+reimagine r s (Quaternion_ _ v) =
   if isNaN s || isInfinite s
     then let aux x = if x == 0 then 0
                                else s * x
-         in lift $ Quaternion r (P.fmap aux v)
-    else    lift $ Quaternion r (unlift (lift v ^* s))
+         in Quaternion_ r (fmap aux v)
+    else    Quaternion_ r (v ^* s)
 
 -- | Helper for calculating with specific branch cuts
 --
 cut :: (RealFloat a, Elt (Complex a)) => (Exp (Complex a) -> Exp (Complex a)) -> Exp (Quaternion a) -> Exp (Quaternion a)
-cut f q@(unlift -> Quaternion e (V3 _ y z)) =
-  if qiq == 0 then lift $ Quaternion a (V3 b y z)
+cut f q@(Quaternion_ e (V3_ _ y z)) =
+  if qiq == 0 then Quaternion_ a (V3_ b y z)
               else reimagine a (b / ai) q
   where
-    qiq    = qi q
-    ai     = sqrt qiq
-    a :+ b = unlift $ f (lift (e :+ ai))
+    qiq     = qi q
+    ai      = sqrt qiq
+    a ::+ b = f (e ::+ ai)
 
 -- | Helper for calculating with specific branch cuts
 --
 cutWith :: (RealFloat a, Elt (Complex a)) => Exp (Complex a) -> Exp (Quaternion a) -> Exp (Quaternion a)
-cutWith (unlift -> r :+ im) q@(unlift -> Quaternion e v) =
+cutWith (r ::+ im) q@(Quaternion_ e v) =
   if e /= 0 || qiq == 0 || isNaN qiq || isInfinite qiq
     then 0/0 -- error "bad cut"  -- TLM: argh
-    else lift $ Quaternion r (unlift (lift v ^* s))
+    else Quaternion_ r (v ^* s)
   where
     qiq = qi q
     s   = im / sqrt qiq
@@ -395,7 +377,7 @@
 -- | quadrance of the imaginary component
 --
 qi :: Num a => Exp (Quaternion a) -> Exp a
-qi (unlift -> Quaternion _ v :: Quaternion (Exp a)) = quadrance (lift v)
+qi (Quaternion_ _ v) = quadrance v
 
 sqrte2pqiq :: (Floating a, Ord a) => Exp a -> Exp a -> Exp a
 sqrte2pqiq e qiq = -- = sqrt (e*e) + qiq
@@ -419,10 +401,9 @@
   nearZero = nearZero . quadrance
 
 instance (RealFloat a, Conjugate (Exp a)) => Conjugate (Exp (Quaternion a)) where
-  conjugate (unlift -> Quaternion e v :: Quaternion (Exp a)) =
-    lift (Quaternion (conjugate e) (unlift (negate (lift v :: Exp (V3 a)))))
+  conjugate (Quaternion_ e v) = (Quaternion_ (conjugate e) (negate v))
 
 instance Functor Quaternion where
-  fmap f (unlift -> Quaternion e v) = lift (Quaternion (f e) (P.fmap f v))
-  x <$ _                            = lift (Quaternion x (V3 x x x))
+  fmap f (Quaternion_ e v) = Quaternion_ (f e) (fmap f v)
+  x <$ _                   = Quaternion_ x (V3_ x x x)
 
diff --git a/src/Data/Array/Accelerate/Linear/Trace.hs b/src/Data/Array/Accelerate/Linear/Trace.hs
--- a/src/Data/Array/Accelerate/Linear/Trace.hs
+++ b/src/Data/Array/Accelerate/Linear/Trace.hs
@@ -5,10 +5,10 @@
 -- |
 -- Module      : Data.Array.Accelerate.Linear.Trace
 -- Copyright   : 2014 Edward Kmett
---               [2015..2018] Trevor L. McDonell
+--               [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
diff --git a/src/Data/Array/Accelerate/Linear/Type.hs b/src/Data/Array/Accelerate/Linear/Type.hs
--- a/src/Data/Array/Accelerate/Linear/Type.hs
+++ b/src/Data/Array/Accelerate/Linear/Type.hs
@@ -4,10 +4,10 @@
 -----------------------------------------------------------------------------
 -- |
 -- Module      : Data.Array.Accelerate.Linear.Type
--- Copyright   : [2015..2018] Trevor L. McDonell
+-- Copyright   : [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 ----------------------------------------------------------------------------
diff --git a/src/Data/Array/Accelerate/Linear/V0.hs b/src/Data/Array/Accelerate/Linear/V0.hs
--- a/src/Data/Array/Accelerate/Linear/V0.hs
+++ b/src/Data/Array/Accelerate/Linear/V0.hs
@@ -1,18 +1,19 @@
 {-# LANGUAGE ConstraintKinds       #-}
+{-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE FlexibleInstances     #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE PatternSynonyms       #-}
 {-# LANGUAGE ScopedTypeVariables   #-}
 {-# LANGUAGE TypeFamilies          #-}
-{-# LANGUAGE UndecidableInstances  #-}
 {-# OPTIONS_GHC -fno-warn-orphans #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      : Data.Array.Accelerate.Linear.V0
 -- Copyright   : 2014 Edward Kmett, Charles Durham,
---               [2015..2018] Trevor L. McDonell
+--               [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
@@ -21,15 +22,13 @@
 
 module Data.Array.Accelerate.Linear.V0 (
 
-  V0(..),
+  V0(..), pattern V0_,
 
 ) where
 
 import Data.Array.Accelerate                    as A
 import Data.Array.Accelerate.Data.Functor       as A
 import Data.Array.Accelerate.Smart
-import Data.Array.Accelerate.Product
-import Data.Array.Accelerate.Array.Sugar
 
 import Data.Array.Accelerate.Linear.Metric
 import Data.Array.Accelerate.Linear.Vector
@@ -43,25 +42,17 @@
 -- Instances
 -- ---------
 
+pattern V0_ :: Elt a => Exp (V0 a)
+pattern V0_ = Pattern ()
+{-# COMPLETE V0_ #-}
+
 instance Metric V0
 instance Additive V0
-
-type instance EltRepr (V0 a) = ()
-
-instance Elt a => Elt (V0 a) where
-  eltType _ = eltType ()
-  toElt () = V0
-  fromElt V0 = ()
-
-instance IsProduct cst (V0 a) where
-  type ProdRepr (V0 a) = ()
-  fromProd _ V0 = ()
-  toProd _ () = V0
-  prod _ _ = ProdRunit
+instance Elt a => Elt (V0 a)
 
 instance Lift Exp (V0 a) where
   type Plain (V0 a) = ()
-  lift V0 = Exp (Tuple NilTup)
+  lift _ = Exp (SmartExp Nil)
 
 instance Unlift Exp (V0 a) where
   unlift _ = V0
diff --git a/src/Data/Array/Accelerate/Linear/V1.hs b/src/Data/Array/Accelerate/Linear/V1.hs
--- a/src/Data/Array/Accelerate/Linear/V1.hs
+++ b/src/Data/Array/Accelerate/Linear/V1.hs
@@ -2,19 +2,19 @@
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE FlexibleInstances     #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE PatternSynonyms       #-}
 {-# LANGUAGE ScopedTypeVariables   #-}
 {-# LANGUAGE TypeFamilies          #-}
 {-# LANGUAGE UndecidableInstances  #-}
-{-# LANGUAGE ViewPatterns          #-}
 {-# OPTIONS_GHC -fno-warn-orphans #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      : Data.Array.Accelerate.Linear.V1
 -- Copyright   : 2014 Edward Kmett, Charles Durham,
---               [2015..2018] Trevor L. McDonell
+--               [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
@@ -23,16 +23,14 @@
 
 module Data.Array.Accelerate.Linear.V1 (
 
-  V1(..), R1(..), ex,
+  V1(..), pattern V1_,
+  R1(..),
+  ex,
 
 ) where
 
 import Data.Array.Accelerate                    as A
 import Data.Array.Accelerate.Data.Functor       as A
-import Data.Array.Accelerate.Array.Sugar
-import Data.Array.Accelerate.Product
-import Data.Array.Accelerate.Smart
-import Data.Array.Accelerate.Type
 
 import Data.Array.Accelerate.Linear.Epsilon
 import Data.Array.Accelerate.Linear.Lift
@@ -57,10 +55,10 @@
 --
 class L.R1 t => R1 t where
   -- |
-  -- >>> test $ lift (V1 2 :: V1 Int) ^._x
+  -- >>> test $ (V1_ 2 :: Exp (V1 Int)) ^. _x
   -- 2
   --
-  -- >>> test $ lift (V1 2 :: V1 Int) & _x .~ 3
+  -- >>> test $ (V1_ 2 :: Exp (V1 Int)) & _x .~ 3
   -- V1 3
   --
   _x :: (Elt a, Box t a) => Lens' (Exp (t a)) (Exp a)
@@ -74,48 +72,40 @@
 -- Instances
 -- ---------
 
+pattern V1_ :: Elt a => Exp a -> Exp (V1 a)
+pattern V1_ x = Pattern x
+{-# COMPLETE V1_ #-}
+
 instance Metric V1
 instance Additive V1
 instance R1 V1
-
-type instance EltRepr (V1 a) = ((), EltRepr a)
-
-instance Elt a => Elt (V1 a) where
-  eltType _ = TypeRpair TypeRunit (eltType (undefined :: a))
-  toElt ((), x) = V1 (toElt x)
-  fromElt (V1 x) = ((), fromElt x)
-
-instance cst a => IsProduct cst (V1 a) where
-  type ProdRepr (V1 a) = ((), a)
-  fromProd _ (V1 x) = ((), x)
-  toProd _ ((), x) = V1 x
-  prod _ _ = ProdRsnoc ProdRunit
+instance Elt a => Elt (V1 a)
 
 instance (Lift Exp a, Elt (Plain a)) => Lift Exp (V1 a) where
   type Plain (V1 a) = V1 (Plain a)
-  lift (V1 x) = Exp . Tuple $ NilTup `SnocTup` lift x
+  lift (V1 x) = V1_ (lift x)
 
 instance Elt a => Unlift Exp (V1 (Exp a)) where
-  unlift t = V1 $ Exp $ ZeroTupIdx `Prj` t
+  unlift (V1_ x) = V1 x
 
 instance (Elt a, Elt b) => Each (Exp (V1 a)) (Exp (V1 b)) (Exp a) (Exp b) where
   each = liftLens (each :: Traversal (V1 (Exp a)) (V1 (Exp b)) (Exp a) (Exp b))
 
 instance A.Eq a => A.Eq (V1 a) where
-  (unlift -> V1 x) == (unlift -> V1 y) = x A.== y
-  (unlift -> V1 x) /= (unlift -> V1 y) = x A./= y
+  V1_ x == V1_ y = x A.== y
+  V1_ x /= V1_ y = x A./= y
 
 instance A.Ord a => A.Ord (V1 a) where
-  (unlift -> V1 x) <  (unlift -> V1 y) = x A.< y
-  (unlift -> V1 x) >  (unlift -> V1 y) = x A.> y
-  (unlift -> V1 x) >= (unlift -> V1 y) = x A.>= y
-  (unlift -> V1 x) <= (unlift -> V1 y) = x A.<= y
-  min (unlift -> V1 x) (unlift -> V1 y) = lift $ V1 (A.min x y)
-  max (unlift -> V1 x) (unlift -> V1 y) = lift $ V1 (A.max x y)
+  V1_ x <  V1_ y = x A.< y
+  V1_ x >  V1_ y = x A.> y
+  V1_ x >= V1_ y = x A.>= y
+  V1_ x <= V1_ y = x A.<= y
+  min (V1_ x) (V1_ y) = V1_ (A.min x y)
+  max (V1_ x) (V1_ y) = V1_ (A.max x y)
 
 instance A.Bounded a => P.Bounded (Exp (V1 a)) where
-  minBound = lift (V1 (minBound :: Exp a))
-  maxBound = lift (V1 (maxBound :: Exp a))
+  minBound = V1_ minBound
+  maxBound = V1_ maxBound
 
 instance A.Num a => P.Num (Exp (V1 a)) where
   (+)             = lift2 ((+) :: V1 (Exp a) -> V1 (Exp a) -> V1 (Exp a))
@@ -124,15 +114,15 @@
   negate          = lift1 (negate :: V1 (Exp a) -> V1 (Exp a))
   signum          = lift1 (signum :: V1 (Exp a) -> V1 (Exp a))
   abs             = lift1 (signum :: V1 (Exp a) -> V1 (Exp a))
-  fromInteger x   = lift (P.fromInteger x :: V1 (Exp a))
+  fromInteger x   = V1_ (P.fromInteger x)
 
 instance A.Floating a => P.Fractional (Exp (V1 a)) where
   (/)             = lift2 ((/) :: V1 (Exp a) -> V1 (Exp a) -> V1 (Exp a))
   recip           = lift1 (recip :: V1 (Exp a) -> V1 (Exp a))
-  fromRational x  = lift (P.fromRational x :: V1 (Exp a))
+  fromRational x  = V1_ (P.fromRational x)
 
 instance A.Floating a => P.Floating (Exp (V1 a)) where
-  pi              = lift (pi :: V1 (Exp a))
+  pi              = V1_ pi
   log             = lift1 (log :: V1 (Exp a) -> V1 (Exp a))
   exp             = lift1 (exp :: V1 (Exp a) -> V1 (Exp a))
   sin             = lift1 (sin :: V1 (Exp a) -> V1 (Exp a))
@@ -149,9 +139,9 @@
   atanh           = lift1 (atanh :: V1 (Exp a) -> V1 (Exp a))
 
 instance Epsilon a => Epsilon (V1 a) where
-  nearZero (unlift -> V1 x) = nearZero x
+  nearZero (V1_ x) = nearZero x
 
 instance A.Functor V1 where
-  fmap f (unlift -> V1 x) = lift (V1 (f x))
-  x <$ _                  = lift (V1 x)
+  fmap f (V1_ x) = V1_ (f x)
+  x <$ _         = V1_ x
 
diff --git a/src/Data/Array/Accelerate/Linear/V2.hs b/src/Data/Array/Accelerate/Linear/V2.hs
--- a/src/Data/Array/Accelerate/Linear/V2.hs
+++ b/src/Data/Array/Accelerate/Linear/V2.hs
@@ -2,19 +2,19 @@
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE FlexibleInstances     #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE PatternSynonyms       #-}
 {-# LANGUAGE ScopedTypeVariables   #-}
 {-# LANGUAGE TypeFamilies          #-}
 {-# LANGUAGE UndecidableInstances  #-}
-{-# LANGUAGE ViewPatterns          #-}
 {-# OPTIONS_GHC -fno-warn-orphans #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      : Data.Array.Accelerate.Linear.V2
 -- Copyright   : 2014 Edward Kmett, Charles Durham,
---               [2015..2018] Trevor L. McDonell
+--               [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
@@ -23,18 +23,18 @@
 
 module Data.Array.Accelerate.Linear.V2 (
 
-  V2(..), R1(..), R2(..),
+  V2(..), pattern V2_,
+  R1(..),
+  R2(..),
   _yx,
   ex, ey,
   perp, angle,
 
 ) where
 
-import Data.Array.Accelerate                    as A
+import Data.Array.Accelerate                    as A hiding ( pattern V2 )
 import Data.Array.Accelerate.Data.Functor       as A
 import Data.Array.Accelerate.Smart
-import Data.Array.Accelerate.Product
-import Data.Array.Accelerate.Array.Sugar
 
 import Data.Array.Accelerate.Linear.Epsilon
 import Data.Array.Accelerate.Linear.Lift
@@ -59,7 +59,7 @@
 
 -- | the counter-clockwise perpendicular vector
 --
--- >>> test $ perp $ lift (V2 10 20 :: V2 Int)
+-- >>> test $ perp $ (V2_ 10 20 :: Exp (V2 Int))
 -- V2 (-20) 10
 --
 perp :: forall a. A.Num a => Exp (V2 a) -> Exp (V2 a)
@@ -77,10 +77,10 @@
 --
 class (L.R2 t, R1 t) => R2 t where
   -- |
-  -- >>> test $ lift (V2 1 2 :: V2 Int) ^._y
+  -- >>> test $ (V2_ 1 2 :: Exp (V2 Int)) ^. _y
   -- 2
   --
-  -- >>> test $ lift (V2 1 2 :: V2 Int) & _y .~ 3
+  -- >>> test $ (V2_ 1 2 :: Exp (V2 Int)) & _y .~ 3
   -- V2 1 3
   --
   _y :: (Elt a, Box t a) => Lens' (Exp (t a)) (Exp a)
@@ -91,7 +91,7 @@
 
 
 -- |
--- >>> test $ lift (V2 1 2 :: V2 Int) ^. _yx
+-- >>> test $ (V2_ 1 2 :: Exp (V2 Int)) ^. _yx
 -- V2 2 1
 --
 _yx :: forall t a. (R2 t, Elt a, Box t a) => Lens' (Exp (t a)) (Exp (V2 a))
@@ -105,33 +105,22 @@
 -- Instances
 -- ---------
 
+pattern V2_ :: Elt a => Exp a -> Exp a -> Exp (V2 a)
+pattern V2_ x y = Pattern (x,y)
+{-# COMPLETE V2_ #-}
+
 instance Metric V2
 instance Additive V2
 instance R1 V2
 instance R2 V2
-
-type instance EltRepr (V2 a) = EltRepr (a, a)
-
-instance Elt a => Elt (V2 a) where
-  eltType _ = eltType (undefined :: (a,a))
-  toElt p = case toElt p of
-     (x, y) -> V2 x y
-  fromElt (V2 x y) = fromElt (x, y)
-
-instance cst a => IsProduct cst (V2 a) where
-  type ProdRepr (V2 a) = ProdRepr (a,a)
-  fromProd p (V2 x y) = fromProd p (x,y)
-  toProd p t = case toProd p t of
-     (x, y) -> V2 x y
-  prod p _ = prod p (undefined :: (a,a))
+instance Elt a => Elt (V2 a)
 
 instance (Lift Exp a, Elt (Plain a)) => Lift Exp (V2 a) where
   type Plain (V2 a) = V2 (Plain a)
-  lift (V2 x y) = Exp $ Tuple $ NilTup `SnocTup` lift x `SnocTup` lift y
+  lift (V2 x y) = V2_ (lift x) (lift y)
 
 instance Elt a => Unlift Exp (V2 (Exp a)) where
-  unlift t = V2 (Exp $ SuccTupIdx ZeroTupIdx `Prj` t)
-                (Exp $ ZeroTupIdx `Prj` t)
+  unlift (V2_ x y) = V2 x y
 
 instance (Elt a, Elt b) => Each (Exp (V2 a)) (Exp (V2 b)) (Exp a) (Exp b) where
   each = liftLens (each :: Traversal (V2 (Exp a)) (V2 (Exp b)) (Exp a) (Exp b))
@@ -148,15 +137,15 @@
   min  = v2 $$ on A.min t2
   max  = v2 $$ on A.max t2
 
-t2 :: Elt a => Exp (V2 a) -> Exp (a,a)
-t2 (unlift -> V2 x y) = tup2 (x,y)
+t2 :: Exp (V2 a) -> Exp (a, a)
+t2 (Exp e) = Exp e
 
-v2 :: Elt a => Exp (a,a) -> Exp (V2 a)
-v2 (untup2 -> (x,y)) = lift (V2 x y)
+v2 :: Exp (a, a) -> Exp (V2 a)
+v2 (Exp e) = Exp e
 
 instance A.Bounded a => P.Bounded (Exp (V2 a)) where
-  minBound = lift (V2 (minBound :: Exp a) (minBound :: Exp a))
-  maxBound = lift (V2 (maxBound :: Exp a) (maxBound :: Exp a))
+  minBound = V2_ minBound minBound
+  maxBound = V2_ maxBound maxBound
 
 instance A.Num a => P.Num (Exp (V2 a)) where
   (+)             = lift2 ((+) :: V2 (Exp a) -> V2 (Exp a) -> V2 (Exp a))
@@ -193,6 +182,6 @@
   nearZero = nearZero . quadrance
 
 instance A.Functor V2 where
-  fmap f (unlift -> V2 x y) = lift (V2 (f x) (f y))
-  x <$ _                    = lift (V2 x x)
+  fmap f (V2_ x y) = V2_ (f x) (f y)
+  x <$ _           = V2_ x x
 
diff --git a/src/Data/Array/Accelerate/Linear/V3.hs b/src/Data/Array/Accelerate/Linear/V3.hs
--- a/src/Data/Array/Accelerate/Linear/V3.hs
+++ b/src/Data/Array/Accelerate/Linear/V3.hs
@@ -2,19 +2,19 @@
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE FlexibleInstances     #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE PatternSynonyms       #-}
 {-# LANGUAGE ScopedTypeVariables   #-}
 {-# LANGUAGE TypeFamilies          #-}
 {-# LANGUAGE UndecidableInstances  #-}
-{-# LANGUAGE ViewPatterns          #-}
 {-# OPTIONS_GHC -fno-warn-orphans #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      : Data.Array.Accelerate.Linear.V3
 -- Copyright   : 2014 Edward Kmett, Charles Durham,
---               [2015..2018] Trevor L. McDonell
+--               [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
@@ -23,7 +23,8 @@
 
 module Data.Array.Accelerate.Linear.V3 (
 
-  V3(..), cross, triple,
+  V3(..), pattern V3_,
+  cross, triple,
   R1(..),
   R2(..),
   _yx,
@@ -34,11 +35,9 @@
 
 ) where
 
-import Data.Array.Accelerate                    as A
+import Data.Array.Accelerate                    as A hiding ( pattern V2, pattern V3 )
 import Data.Array.Accelerate.Data.Functor       as A
 import Data.Array.Accelerate.Smart
-import Data.Array.Accelerate.Product
-import Data.Array.Accelerate.Array.Sugar
 
 import Data.Array.Accelerate.Linear.Epsilon
 import Data.Array.Accelerate.Linear.Lift
@@ -78,10 +77,10 @@
 --
 class (L.R3 t, R2 t) => R3 t where
   -- |
-  -- >>> test $ lift (V3 1 2 3 :: V3 Int) ^. _z
+  -- >>> test $ (V3_ 1 2 3 :: Exp (V3 Int)) ^. _z
   -- 3
   --
-  -- >>> test $ lift (V3 1 2 3 :: V3 Int) & _z .~ 42
+  -- >>> test $ (V3_ 1 2 3 :: Exp (V3 Int)) & _z .~ 42
   -- V3 1 2 42
   --
   _z :: forall a. (Elt a, Box t a) => Lens' (Exp (t a)) (Exp a)
@@ -112,35 +111,23 @@
 -- Instances
 -- ---------
 
+pattern V3_ :: Elt a => Exp a -> Exp a -> Exp a -> Exp (V3 a)
+pattern V3_ x y z = Pattern (x,y,z)
+{-# COMPLETE V3_ #-}
+
 instance Metric V3
 instance Additive V3
 instance R1 V3
 instance R2 V3
 instance R3 V3
-
-type instance EltRepr (V3 a) = EltRepr (a, a, a)
-
-instance Elt a => Elt (V3 a) where
-  eltType _ = eltType (undefined :: (a,a,a))
-  toElt p = case toElt p of
-     (x, y, z) -> V3 x y z
-  fromElt (V3 x y z) = fromElt (x, y, z)
-
-instance cst a => IsProduct cst (V3 a) where
-  type ProdRepr (V3 a) = ProdRepr (a,a,a)
-  fromProd p (V3 x y z) = fromProd p (x,y,z)
-  toProd p t = case toProd p t of
-     (x, y, z) -> V3 x y z
-  prod p _ = prod p (undefined :: (a,a,a))
+instance Elt a => Elt (V3 a)
 
 instance (Lift Exp a, Elt (Plain a)) => Lift Exp (V3 a) where
   type Plain (V3 a) = V3 (Plain a)
-  lift (V3 x y z) = Exp $ Tuple $ NilTup `SnocTup` lift x `SnocTup` lift y `SnocTup` lift z
+  lift (V3 x y z) = V3_ (lift x) (lift y) (lift z)
 
 instance Elt a => Unlift Exp (V3 (Exp a)) where
-  unlift t = V3 (Exp $ SuccTupIdx (SuccTupIdx ZeroTupIdx) `Prj` t)
-                (Exp $ SuccTupIdx ZeroTupIdx `Prj` t)
-                (Exp $ ZeroTupIdx `Prj` t)
+  unlift (V3_ x y z) = V3 x y z
 
 instance (Elt a, Elt b) => Each (Exp (V3 a)) (Exp (V3 b)) (Exp a) (Exp b) where
   each = liftLens (each :: Traversal (V3 (Exp a)) (V3 (Exp b)) (Exp a) (Exp b))
@@ -157,15 +144,15 @@
   min  = v3 $$ on A.min t3
   max  = v3 $$ on A.max t3
 
-t3 :: Elt a => Exp (V3 a) -> Exp (a,a,a)
-t3 (unlift -> V3 x y z) = tup3 (x,y,z)
+t3 :: Exp (V3 a) -> Exp (a, a, a)
+t3 (Exp e) = Exp e
 
-v3 :: Elt a => Exp (a,a,a) -> Exp (V3 a)
-v3 (untup3 -> (x,y,z)) = lift (V3 x y z)
+v3 :: Exp (a, a, a) -> Exp (V3 a)
+v3 (Exp e) = Exp e
 
 instance A.Bounded a => P.Bounded (Exp (V3 a)) where
-  minBound = lift (V3 (minBound :: Exp a) (minBound :: Exp a) (minBound :: Exp a))
-  maxBound = lift (V3 (maxBound :: Exp a) (maxBound :: Exp a) (maxBound :: Exp a))
+  minBound = V3_ minBound minBound minBound
+  maxBound = V3_ maxBound maxBound maxBound
 
 instance A.Num a => P.Num (Exp (V3 a)) where
   (+)             = lift2 ((+) :: V3 (Exp a) -> V3 (Exp a) -> V3 (Exp a))
@@ -202,8 +189,8 @@
   nearZero = nearZero . quadrance
 
 instance A.Functor V3 where
-  fmap f (unlift -> V3 x y z) = lift (V3 (f x) (f y) (f z))
-  x <$ _                      = lift (V3 x x x)
+  fmap f (V3_ x y z) = V3_ (f x) (f y) (f z)
+  x <$ _             = V3_ x x x
 
 -- $liftAcc
 --
diff --git a/src/Data/Array/Accelerate/Linear/V4.hs b/src/Data/Array/Accelerate/Linear/V4.hs
--- a/src/Data/Array/Accelerate/Linear/V4.hs
+++ b/src/Data/Array/Accelerate/Linear/V4.hs
@@ -2,19 +2,19 @@
 {-# LANGUAGE FlexibleContexts      #-}
 {-# LANGUAGE FlexibleInstances     #-}
 {-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE PatternSynonyms       #-}
 {-# LANGUAGE ScopedTypeVariables   #-}
 {-# LANGUAGE TypeFamilies          #-}
 {-# LANGUAGE UndecidableInstances  #-}
-{-# LANGUAGE ViewPatterns          #-}
 {-# OPTIONS_GHC -fno-warn-orphans #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      : Data.Array.Accelerate.Linear.V4
 -- Copyright   : 2014 Edward Kmett, Charles Durham,
---               [2015..2018] Trevor L. McDonell
+--               [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
@@ -23,7 +23,8 @@
 
 module Data.Array.Accelerate.Linear.V4 (
 
-  V4(..), vector, point, normalizePoint,
+  V4(..), pattern V4_,
+  vector, point, normalizePoint,
   R1(..),
   R2(..),
   _yx,
@@ -41,11 +42,9 @@
 
 ) where
 
-import Data.Array.Accelerate                    as A
+import Data.Array.Accelerate                    as A hiding ( pattern V2, pattern V3, pattern V4 )
 import Data.Array.Accelerate.Data.Functor       as A
 import Data.Array.Accelerate.Smart
-import Data.Array.Accelerate.Product
-import Data.Array.Accelerate.Array.Sugar
 
 import Data.Array.Accelerate.Linear.Epsilon
 import Data.Array.Accelerate.Linear.Lift
@@ -95,10 +94,10 @@
 --
 class (L.R4 t, R3 t) => R4 t where
   -- |
-  -- >>> test $ lift (V4 1 2 3 4 :: V4 Int) ^._w
+  -- >>> test $ (V4_ 1 2 3 4 :: Exp (V4 Int)) ^. _w
   -- 4
   --
-  -- >>> test $ lift (V4 1 2 3 4 :: V4 Int) & _w .~ 42
+  -- >>> test $ (V4_ 1 2 3 4 :: Exp (V4 Int)) & _w .~ 42
   -- V4 1 2 3 42
   --
   _w :: forall a. (Elt a, Box t a) => Lens' (Exp (t a)) (Exp a)
@@ -176,41 +175,24 @@
 -- Instances
 -- ---------
 
+pattern V4_ :: Elt a => Exp a -> Exp a -> Exp a -> Exp a -> Exp (V4 a)
+pattern V4_ x y z w = Pattern (x,y,z,w)
+{-# COMPLETE V4_ #-}
+
 instance Metric V4
 instance Additive V4
 instance R1 V4
 instance R2 V4
 instance R3 V4
 instance R4 V4
-
-type instance EltRepr (V4 a) = EltRepr (a, a, a, a)
-
-instance Elt a => Elt (V4 a) where
-  eltType _ = eltType (undefined :: (a,a,a,a))
-  toElt p = case toElt p of
-     (x, y, z, w) -> V4 x y z w
-  fromElt (V4 x y z w) = fromElt (x, y, z, w)
-
-instance cst a => IsProduct cst (V4 a) where
-  type ProdRepr (V4 a) = ProdRepr (a,a,a,a)
-  fromProd p (V4 x y z w) = fromProd p (x,y,z,w)
-  toProd p t = case toProd p t of
-     (x, y, z, w) -> V4 x y z w
-  prod p _ = prod p (undefined :: (a,a,a,a))
+instance Elt a => Elt (V4 a)
 
 instance (Lift Exp a, Elt (Plain a)) => Lift Exp (V4 a) where
   type Plain (V4 a) = V4 (Plain a)
-  lift (V4 x y z w) =
-    Exp $ Tuple $ NilTup `SnocTup` lift x
-                         `SnocTup` lift y
-                         `SnocTup` lift z
-                         `SnocTup` lift w
+  lift (V4 x y z w) = V4_ (lift x) (lift y) (lift z) (lift w)
 
 instance Elt a => Unlift Exp (V4 (Exp a)) where
-  unlift t = V4 (Exp $ SuccTupIdx (SuccTupIdx (SuccTupIdx ZeroTupIdx)) `Prj` t)
-                (Exp $ SuccTupIdx (SuccTupIdx ZeroTupIdx) `Prj` t)
-                (Exp $ SuccTupIdx ZeroTupIdx `Prj` t)
-                (Exp $ ZeroTupIdx `Prj` t)
+  unlift (V4_ x y z w) = V4 x y z w
 
 instance (Elt a, Elt b) => Each (Exp (V4 a)) (Exp (V4 b)) (Exp a) (Exp b) where
   each = liftLens (each :: Traversal (V4 (Exp a)) (V4 (Exp b)) (Exp a) (Exp b))
@@ -227,15 +209,15 @@
   min  = v4 $$ on A.min t4
   max  = v4 $$ on A.max t4
 
-t4 :: Elt a => Exp (V4 a) -> Exp (a,a,a,a)
-t4 (unlift -> V4 x y z w) = tup4 (x,y,z,w)
+t4 :: Exp (V4 a) -> Exp (a, a, a, a)
+t4 (Exp e) = Exp e
 
-v4 :: Elt a => Exp (a,a,a,a) -> Exp (V4 a)
-v4 (untup4 -> (x,y,z,w)) = lift (V4 x y z w)
+v4 :: Exp (a, a, a, a) -> Exp (V4 a)
+v4 (Exp e) = Exp e
 
 instance A.Bounded a => P.Bounded (Exp (V4 a)) where
-  minBound = lift (V4 (minBound :: Exp a) (minBound :: Exp a) (minBound :: Exp a) (minBound :: Exp a))
-  maxBound = lift (V4 (maxBound :: Exp a) (maxBound :: Exp a) (maxBound :: Exp a) (maxBound :: Exp a))
+  minBound = V4_ minBound minBound minBound minBound
+  maxBound = V4_ maxBound maxBound maxBound maxBound
 
 instance A.Num a => P.Num (Exp (V4 a)) where
   (+)             = lift2 ((+) :: V4 (Exp a) -> V4 (Exp a) -> V4 (Exp a))
@@ -272,6 +254,5 @@
   nearZero = nearZero . quadrance
 
 instance A.Functor V4 where
-  fmap f (unlift -> V4 x y z w) = lift (V4 (f x) (f y) (f z) (f w))
-  x <$ _                        = lift (V4 x x x x)
-
+  fmap f (V4_ x y z w) = V4_ (f x) (f y) (f z) (f w)
+  x <$ _               = V4_ x x x x
diff --git a/src/Data/Array/Accelerate/Linear/Vector.hs b/src/Data/Array/Accelerate/Linear/Vector.hs
--- a/src/Data/Array/Accelerate/Linear/Vector.hs
+++ b/src/Data/Array/Accelerate/Linear/Vector.hs
@@ -1,17 +1,17 @@
 {-# LANGUAGE ConstraintKinds     #-}
 {-# LANGUAGE FlexibleContexts    #-}
+{-# LANGUAGE PatternSynonyms     #-}
 {-# LANGUAGE RankNTypes          #-}
 {-# LANGUAGE ScopedTypeVariables #-}
 {-# LANGUAGE TypeFamilies        #-}
-{-# LANGUAGE ViewPatterns        #-}
 -----------------------------------------------------------------------------
 -- |
 -- Module      : Data.Array.Accelerate.Linear.Vector
 -- Copyright   : 2014 Edward Kmett, Charles Durham,
---               [2015..2018] Trevor L. McDonell
+--               [2015..2020] Trevor L. McDonell
 -- License     : BSD-style (see the file LICENSE)
 --
--- Maintainer  : Edward Kmett <ekmett@gmail.com>
+-- Maintainer  : Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   : experimental
 -- Portability : non-portable
 --
@@ -21,7 +21,7 @@
 module Data.Array.Accelerate.Linear.Vector
   where
 
-import Data.Array.Accelerate                    as A
+import Data.Array.Accelerate                    as A hiding ( pattern V2 )
 import Data.Array.Accelerate.Linear.Type
 
 import Control.Lens
@@ -32,8 +32,9 @@
 infixl 7 ^*, *^, ^/, /^
 
 -- $setup
+-- >>> :set -XPatternSynonyms
 -- >>> import Linear.V2
--- >>> import Data.Array.Accelerate.Linear.V2 ()
+-- >>> import Data.Array.Accelerate.Linear.V2 ( pattern V2_ )
 -- >>> import Data.Array.Accelerate.Interpreter
 -- >>> :{
 --   let test :: Elt e => Exp e -> e
@@ -53,7 +54,7 @@
 
   -- | Compute the sum of two vectors
   --
-  -- >>> test $ lift (V2 1 2 :: V2 Int) ^+^ lift (V2 3 4 :: V2 Int)
+  -- >>> test $ (V2_ 1 2 :: Exp (V2 Int)) ^+^ (V2_ 3 4 :: Exp (V2 Int))
   -- V2 4 6
   --
   (^+^) :: forall a. (A.Num a, Box f a)
@@ -64,7 +65,7 @@
 
   -- | Compute the difference between two vectors
   --
-  -- >>> test $ lift (V2 4 5 :: V2 Int) ^-^ lift (V2 3 1 :: V2 Int)
+  -- >>> test $ (V2_ 4 5 :: Exp (V2 Int)) ^-^ (V2_ 3 1 :: Exp (V2 Int))
   -- V2 1 4
   --
   (^-^) :: forall a. (A.Num a, Box f a)
@@ -95,7 +96,7 @@
 
 -- | Compute the negation of a vector
 --
--- >>> test $ negated (lift (V2 2 4 :: V2 Int))
+-- >>> test $ negated (V2_ 2 4 :: Exp (V2 Int))
 -- V2 (-2) (-4)
 --
 negated
@@ -106,7 +107,7 @@
 
 -- | Compute the left scalar product
 --
--- >>> test $ 2 *^ lift (V2 3 4 :: V2 Int)
+-- >>> test $ 2 *^ (V2_ 3 4 :: Exp (V2 Int))
 -- V2 6 8
 --
 (*^) :: forall f a. (Functor f, A.Num a, Box f a)
@@ -117,7 +118,7 @@
 
 -- | Compute the right scalar product
 --
--- >>> test $ lift (V2 3 4 :: V2 Int) ^* 2
+-- >>> test $ (V2_ 3 4 :: Exp (V2 Int)) ^* 2
 -- V2 6 8
 --
 (^*) :: forall f a. (Functor f, A.Num a, Box f a)
@@ -128,7 +129,7 @@
 
 -- | Compute division by a scalar on the right
 --
--- >>> test $ lift (V2 4 6 :: V2 Double) ^/ 2
+-- >>> test $ (V2_ 4 6 :: Exp (V2 Double)) ^/ 2
 -- V2 2.0 3.0
 --
 (^/) :: forall f a. (Functor f, A.Fractional a, Box f a)
@@ -139,7 +140,7 @@
 
 -- | Compute division of a scalar on the left
 --
--- >>> test $ 4 /^ lift (V2 2 4 :: V2 Double)
+-- >>> test $ 4 /^ (V2_ 2 4 :: Exp (V2 Double))
 -- V2 2.0 1.0
 --
 (/^) :: forall f a. (Functor f, A.Fractional a, Box f a)
@@ -150,7 +151,7 @@
 
 -- | Addition with a scalar on the left
 --
--- >>> test $ 2 +^ lift (V2 3 4 :: V2 Int)
+-- >>> test $ 2 +^ (V2_ 3 4 :: Exp (V2 Int))
 -- V2 5 6
 --
 (+^) :: forall f a. (Functor f, A.Num a, Box f a)
@@ -161,7 +162,7 @@
 
 -- | Addition with a scalar on the right
 --
--- >>> test $ lift (V2 1 2 :: V2 Int) ^+ 3
+-- >>> test $ (V2_ 1 2 :: Exp (V2 Int)) ^+ 3
 -- V2 4 5
 --
 (^+) :: forall f a. (Functor f, A.Num a, Box f a)
@@ -172,7 +173,7 @@
 
 -- | Subtraction with a scalar on the left
 --
--- >>> test $ 2 -^ lift (V2 3 4 :: V2 Int)
+-- >>> test $ 2 -^ (V2_ 3 4 :: Exp (V2 Int))
 -- V2 (-1) (-2)
 --
 (-^) :: forall f a. (Functor f, A.Num a, Box f a)
@@ -183,7 +184,7 @@
 
 -- | Subtraction with a scalar on the right
 --
--- >>> test $ lift (V2 1 2 :: V2 Int) ^- 3
+-- >>> test $ (V2_ 1 2 :: Exp (V2 Int)) ^- 3
 -- V2 (-2) (-1)
 --
 (^-) :: forall f a. (Functor f, A.Num a, Box f a)
diff --git a/tests/doctests.hs b/tests/doctests.hs
--- a/tests/doctests.hs
+++ b/tests/doctests.hs
@@ -3,7 +3,7 @@
 -- Module      :  Main (doctests)
 -- Copyright   :  (C) 2012-14 Edward Kmett
 -- License     :  BSD-style (see the file LICENSE)
--- Maintainer  :  Edward Kmett <ekmett@gmail.com>
+-- Maintainer  :  Trevor L. McDonell <trevor.mcdonell@gmail.com>
 -- Stability   :  provisional
 -- Portability :  portable
 --