diff --git a/.envrc b/.envrc
new file mode 100644
--- /dev/null
+++ b/.envrc
@@ -0,0 +1,1 @@
+use flake
diff --git a/COPYING b/COPYING
deleted file mode 100644
--- a/COPYING
+++ /dev/null
@@ -1,674 +0,0 @@
-                    GNU GENERAL PUBLIC LICENSE
-                       Version 3, 29 June 2007
-
- Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
- Everyone is permitted to copy and distribute verbatim copies
- of this license document, but changing it is not allowed.
-
-                            Preamble
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-PURPOSE.  THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM
-IS WITH YOU.  SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF
-ALL NECESSARY SERVICING, REPAIR OR CORRECTION.
-
-  16. Limitation of Liability.
-
-  IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING
-WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
-THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
-GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
-USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
-DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
-PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
-EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
-SUCH DAMAGES.
-
-  17. Interpretation of Sections 15 and 16.
-
-  If the disclaimer of warranty and limitation of liability provided
-above cannot be given local legal effect according to their terms,
-reviewing courts shall apply local law that most closely approximates
-an absolute waiver of all civil liability in connection with the
-Program, unless a warranty or assumption of liability accompanies a
-copy of the Program in return for a fee.
-
-                     END OF TERMS AND CONDITIONS
-
-            How to Apply These Terms to Your New Programs
-
-  If you develop a new program, and you want it to be of the greatest
-possible use to the public, the best way to achieve this is to make it
-free software which everyone can redistribute and change under these terms.
-
-  To do so, attach the following notices to the program.  It is safest
-to attach them to the start of each source file to most effectively
-state the exclusion of warranty; and each file should have at least
-the "copyright" line and a pointer to where the full notice is found.
-
-    <one line to give the program's name and a brief idea of what it does.>
-    Copyright (C) <year>  <name of author>
-
-    This program is free software: you can redistribute it and/or modify
-    it under the terms of the GNU General Public License as published by
-    the Free Software Foundation, either version 3 of the License, or
-    (at your option) any later version.
-
-    This program is distributed in the hope that it will be useful,
-    but WITHOUT ANY WARRANTY; without even the implied warranty of
-    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
-    GNU General Public License for more details.
-
-    You should have received a copy of the GNU General Public License
-    along with this program.  If not, see <http://www.gnu.org/licenses/>.
-
-Also add information on how to contact you by electronic and paper mail.
-
-  If the program does terminal interaction, make it output a short
-notice like this when it starts in an interactive mode:
-
-    <program>  Copyright (C) <year>  <name of author>
-    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
-    This is free software, and you are welcome to redistribute it
-    under certain conditions; type `show c' for details.
-
-The hypothetical commands `show w' and `show c' should show the appropriate
-parts of the General Public License.  Of course, your program's commands
-might be different; for a GUI interface, you would use an "about box".
-
-  You should also get your employer (if you work as a programmer) or school,
-if any, to sign a "copyright disclaimer" for the program, if necessary.
-For more information on this, and how to apply and follow the GNU GPL, see
-<http://www.gnu.org/licenses/>.
-
-  The GNU General Public License does not permit incorporating your program
-into proprietary programs.  If your program is a subroutine library, you
-may consider it more useful to permit linking proprietary applications with
-the library.  If this is what you want to do, use the GNU Lesser General
-Public License instead of this License.  But first, please read
-<http://www.gnu.org/philosophy/why-not-lgpl.html>.
diff --git a/Makefile b/Makefile
new file mode 100644
--- /dev/null
+++ b/Makefile
@@ -0,0 +1,44 @@
+override REPL_OPTIONS += -ignore-dot-ghci
+
+cabal := $(wildcard *.cabal)
+package := $(notdir ./$(cabal:.cabal=))
+version := $(shell sed -ne 's/^version: *\(.*\)/\1/p' $(cabal))
+project := $(patsubst %.cabal,%,$(cabal))
+
+all: build
+build:
+	cabal build $(CABAL_BUILD_FLAGS)
+clean c:
+	cabal clean
+repl:
+	cabal repl $(CABAL_REPL_FLAGS) $(project)
+ghcid:
+	ghcid -c 'cabal repl $(CABAL_REPL_FLAGS) $(project) --repl-options "$(REPL_OPTIONS)"' --reverse-errors
+
+doc:
+	cabal haddock --haddock-css ocean --haddock-hyperlink-source
+
+tag:
+	git tag --merged | grep -Fqx "$(package)-$(version)" || \
+	git tag -f -s -m "$(package) v$(version)" $(package)-$(version)
+
+tar:
+	cabal sdist
+	cabal haddock --haddock-for-hackage --enable-doc
+upload: LANG=C
+upload: tar
+	cabal upload $(CABAL_UPLOAD_FLAGS) dist-newstyle/sdist/$(package)-$(version).tar.gz
+	cabal upload $(CABAL_UPLOAD_FLAGS) --documentation dist-newstyle/$(package)-$(version)-docs.tar.gz
+%/publish: CABAL_UPLOAD_FLAGS+=--publish
+%/publish: %
+	
+publish: upload/publish
+
+nix-build:
+	nix -L build
+nix-relock:
+	nix flake update --recreate-lock-file
+nix-repl:
+	nix -L develop --command cabal repl $(CABAL_REPL_FLAGS)
+nix-shell:
+	nix -L develop
diff --git a/cabal.project b/cabal.project
new file mode 100644
--- /dev/null
+++ b/cabal.project
@@ -0,0 +1,1 @@
+packages:.
diff --git a/default.nix b/default.nix
new file mode 100644
--- /dev/null
+++ b/default.nix
@@ -0,0 +1,27 @@
+{ pkgs ? import <nixpkgs> {}
+, ghc ? null
+, withHoogle ? false
+}:
+let
+  haskellPackages =
+    if ghc == null
+    then pkgs.haskellPackages
+    else pkgs.haskell.packages.${ghc};
+  hs = haskellPackages.extend (with pkgs.haskell.lib; hself: hsuper: {
+      symantic-base = buildFromSdist (hself.callCabal2nix "symantic-base" ./. {});
+  });
+in hs.symantic-base // {
+  shell = hs.shellFor {
+    doBenchmark = true;
+    packages = p: [ p.symantic-base ];
+    nativeBuildInputs = [
+      hs.cabal-install
+      hs.ghcid
+      hs.haskell-language-server
+      hs.hlint
+    ];
+    buildInputs = [
+    ];
+    inherit withHoogle;
+  };
+}
diff --git a/flake.lock b/flake.lock
new file mode 100644
--- /dev/null
+++ b/flake.lock
@@ -0,0 +1,38 @@
+{
+  "nodes": {
+    "flake-utils": {
+      "locked": {
+        "lastModified": 1623875721,
+        "narHash": "sha256-A8BU7bjS5GirpAUv4QA+QnJ4CceLHkcXdRp4xITDB0s=",
+        "owner": "numtide",
+        "repo": "flake-utils",
+        "rev": "f7e004a55b120c02ecb6219596820fcd32ca8772",
+        "type": "github"
+      },
+      "original": {
+        "owner": "numtide",
+        "repo": "flake-utils",
+        "type": "github"
+      }
+    },
+    "nixpkgs": {
+      "locked": {
+        "narHash": "sha256-3C35/g5bJ3KH67fOpxTkqDpfJ1CHYrO2bbl+fPgqfMQ=",
+        "path": "/nix/store/6g7dgkinzm4rvwmpfp9avklsb4hiqals-nixpkgs-patched",
+        "type": "path"
+      },
+      "original": {
+        "id": "nixpkgs",
+        "type": "indirect"
+      }
+    },
+    "root": {
+      "inputs": {
+        "flake-utils": "flake-utils",
+        "nixpkgs": "nixpkgs"
+      }
+    }
+  },
+  "root": "root",
+  "version": 7
+}
diff --git a/flake.nix b/flake.nix
new file mode 100644
--- /dev/null
+++ b/flake.nix
@@ -0,0 +1,13 @@
+{
+inputs.nixpkgs.url = "flake:nixpkgs";
+#inputs.nixpkgs.url = "github:NixOS/nixpkgs";
+inputs.flake-utils.url = "github:numtide/flake-utils";
+outputs = inputs:
+  inputs.flake-utils.lib.eachDefaultSystem (system: let
+    pkgs = inputs.nixpkgs.legacyPackages.${system};
+    in {
+      defaultPackage = import ./default.nix { inherit pkgs; };
+      devShell = (import ./default.nix { inherit pkgs; }).shell;
+    }
+  );
+}
diff --git a/src/Symantic/Base.hs b/src/Symantic/Base.hs
deleted file mode 100644
--- a/src/Symantic/Base.hs
+++ /dev/null
@@ -1,17 +0,0 @@
-module Symantic.Base
- ( module Symantic.Base.ADT
- , module Symantic.Base.Algebrable
- , module Symantic.Base.Composable
- , module Symantic.Base.CurryN
- , module Symantic.Base.Fixity
- , module Symantic.Base.Permutable
- , module Symantic.Base.Routable
- ) where
-
-import Symantic.Base.ADT
-import Symantic.Base.Algebrable
-import Symantic.Base.Composable
-import Symantic.Base.CurryN
-import Symantic.Base.Fixity
-import Symantic.Base.Permutable
-import Symantic.Base.Routable
diff --git a/src/Symantic/Base/ADT.hs b/src/Symantic/Base/ADT.hs
deleted file mode 100644
--- a/src/Symantic/Base/ADT.hs
+++ /dev/null
@@ -1,198 +0,0 @@
-{-# LANGUAGE AllowAmbiguousTypes #-}
-{-# LANGUAGE DataKinds #-}
-{-# LANGUAGE ConstraintKinds #-}
-{-# LANGUAGE InstanceSigs #-}
-{-# LANGUAGE EmptyCase #-}
-{-# LANGUAGE PolyKinds #-}
-{-# LANGUAGE UndecidableInstances #-}
--- | EOT (Either of Tuples) to/from ADT (Algebraic Data Type).
--- to produce or consume custom ADT with @('<:>')@ and @('<+>')@.
---
--- This is like what is done in @generic-sop@:
--- https://hackage.haskell.org/package/generics-sop-0.5.1.0/docs/src/Generics.SOP.GGP.html#gSumFrom
--- but using directly 'Either' and 'Tuples'
--- instead of passing by the intermediary GADTs @NP@ and @NS@.
-module Symantic.Base.ADT where
-
-import Data.Either (Either(..))
-import Data.Void (Void, absurd)
-import Data.Function (($), (.), id, const)
-import GHC.Generics as Generics
-
--- * Type family 'EoT'
--- Return an 'Either' of 'Tuples' from the given 'ADT',
--- matching the nesting occuring when using @('<:>')@ and ('<+>')@
--- and their associativity and precedence,
--- with no parenthesis messing around.
-type family EoT (adt :: [[*]]) :: * where
-  -- This is 'absurd'
-  EoT '[] = Void
-  -- There Is No Alternative
-  EoT '[ ps ] = Tuples ps
-  -- The right associativity of @('<+>')@
-  -- puts leaves on 'Left' and nodes on 'Right'
-  EoT (ps ': ss) = Either (Tuples ps) (EoT ss)
-
--- * Type family 'Tuples'
--- | Return the type of 'snd'-nested 2-tuples
--- from the given list of types.
-type family Tuples (as :: [*]) :: (r :: *) where
-  Tuples '[] = ()
-  Tuples '[a] = a
-  Tuples (a ': rest) = (a, Tuples rest)
-
--- * Type 'ADT'
--- | Normalized type-level representation of an Algebraic Data Type.
-type ADT (adt :: *) = ListOfRepSums (Rep adt) '[]
-
--- ** Type family 'ListOfRepSums'
--- | Collect the alternatives in a continuation passing-style.
-type family ListOfRepSums (a :: * -> *) (ss :: [[*]]) :: [[*]]
-type instance ListOfRepSums (a:+:b)     ss = ListOfRepSums a (ListOfRepSums b ss)
--- | Meta-information for datatypes
-type instance ListOfRepSums (M1 D _c a) ss = ListOfRepSums a ss
--- | Meta-information for constructors
-type instance ListOfRepSums (M1 C _c a) ss = ListOfRepProducts a '[] ': ss
--- | Empty datatypes
-type instance ListOfRepSums V1          ss = ss
-
--- ** Type family 'ListOfRepProducts'
--- | Collect the records in a continuation passing-style.
-type family ListOfRepProducts (a :: * -> *) (ps :: [*]) :: [*]
-type instance ListOfRepProducts (a:*:b)     ps = ListOfRepProducts a (ListOfRepProducts b ps)
--- | Meta-information for record selectors
-type instance ListOfRepProducts (M1 S _c a) ps = TypeOfRepField a ': ps
--- | Constructor without fields
-type instance ListOfRepProducts U1          ps = ps
-
--- ** Type family 'TypeOfRepField'
-type family TypeOfRepField (a :: * -> *) :: *
-type instance TypeOfRepField (K1 _i a) = a
-
--- * Class 'RepOfEoT'
-type RepOfEoT a = RepOfEithers (Rep a) '[]
-
--- | Morph the 'Either' of 'Tuples' corresponding to an 'ADT'
--- into a constructor of this 'ADT'.
--- This is the reverse of 'eotOfadt'.
-adtOfeot :: Generic a => RepOfEoT a => EoT (ADT a) -> a
-adtOfeot eot = Generics.to $ repOfEithers @_ @'[] eot id absurd
-
--- ** Class 'RepOfEithers'
-class RepOfEithers (a :: * -> *) ss where
-  -- | Parse the 'Either' (list-like) binary tree of 'EoT'
-  -- into the @(':+:')@ (balanced) binary tree of 'Rep',
-  -- using continuation passing-style for performance.
-  repOfEithers ::
-   EoT (ListOfRepSums a ss) ->
-   -- the 'a' 'Rep' is the current alternative in the 'EoT'
-   (a x -> r) ->
-   -- the 'a' 'Rep' is a following alternative in the 'EoT'
-   (EoT ss -> r) ->
-   r
-instance (RepOfEithers a (ListOfRepSums b ss), RepOfEithers b ss) => RepOfEithers (a:+:b) ss where
-  repOfEithers eot ok ko =
-    -- try to parse 'a' on the current 'eot'
-    repOfEithers @a @(ListOfRepSums b ss) eot
-     (ok . L1)
-     (\next ->
-      -- parsing 'a' failed
-      -- try to parse 'b' on the 'Right' of the current 'eot'
-      repOfEithers @b @ss next
-       (ok . R1)
-       ko -- parsing 'b' failed: backtrack
-     )
-instance RepOfEithers a ss => RepOfEithers (M1 D c a) ss where
-  repOfEithers eot ok = repOfEithers @a @ss eot (ok . M1)
-instance RepOfTuples a '[] => RepOfEithers (M1 C c a) (ps ': ss) where
-  repOfEithers eot ok ko =
-    case eot of
-     -- 'EoT' is a leaf, and 'Rep' too: parsing succeeds
-     Left ts -> ok $ M1 $ repOfTuples @a @'[] ts const
-     -- 'EoT' is a node, but 'Rep' is a leaf: parsing fails
-     Right ss -> ko ss
-instance RepOfTuples a '[] => RepOfEithers (M1 C c a) '[] where
-  repOfEithers eot ok _ko = ok $ M1 $ repOfTuples @_ @'[] eot const
-instance RepOfEithers V1 ss where
-  repOfEithers eot _ok ko = ko eot
-
--- ** Class 'RepOfTuples'
-class RepOfTuples (a :: * -> *) (xs::[*]) where
-  -- | Parse the 'Tuples' (list-like) binary tree of 'EoT'
-  -- into the @(':*:')@ (balanced) binary tree of 'Rep',
-  -- using continuation passing-style for performance.
-  repOfTuples ::
-   Tuples (ListOfRepProducts a xs) ->
-   (a x -> Tuples xs -> r) -> r
-instance (RepOfTuples a (ListOfRepProducts b ps), RepOfTuples b ps) => RepOfTuples (a:*:b) ps where
-  repOfTuples ts k =
-    -- uncons 'a'
-    repOfTuples @a @(ListOfRepProducts b ps) ts
-     (\a ts' ->
-      -- uncons 'b'
-      repOfTuples @b @ps ts'
-        (\b -> k (a:*:b)))
-instance RepOfField a => RepOfTuples (M1 S c a) (p ': ps) where
-  repOfTuples (a, ts) k = k (M1 (repOfField a)) ts
-instance RepOfField a => RepOfTuples (M1 S c a) '[] where
-  repOfTuples a k = k (M1 (repOfField a)) ()
-instance RepOfTuples U1 ps where
-  repOfTuples ts k = k U1 ts
-
--- ** Class 'RepOfField'
-class RepOfField (a :: * -> *) where
-  repOfField :: TypeOfRepField a -> a x
-instance RepOfField (K1 i a) where
-  repOfField = K1
-
--- * Class 'EoTOfRep'
-type EoTOfRep a = EithersOfRep (Rep a) '[]
-
--- | Morph the constructor of an 'ADT'
--- into the corresponding 'Either' of 'Tuples' of this 'ADT'.
--- This is the reverse of 'adtOfeot'.
-eotOfadt :: Generic a => EoTOfRep a => a -> EoT (ADT a)
-eotOfadt = eithersOfRepL @_ @'[] . Generics.from
-
--- ** Class 'EithersOfRep'
-class EithersOfRep (a :: * -> *) ss where
-  eithersOfRepL :: a x    -> EoT (ListOfRepSums a ss)
-  eithersOfRepR :: EoT ss -> EoT (ListOfRepSums a ss)
-instance (EithersOfRep a (ListOfRepSums b ss), EithersOfRep b ss) =>
- EithersOfRep (a:+:b) ss where
-  eithersOfRepL = \case
-   L1 a -> eithersOfRepL @a @(ListOfRepSums b ss) a
-   R1 b -> eithersOfRepR @a @(ListOfRepSums b ss) (eithersOfRepL @b @ss b)
-  eithersOfRepR ss = eithersOfRepR @a @(ListOfRepSums b ss) (eithersOfRepR @b @ss ss)
-instance EithersOfRep a ss => EithersOfRep (M1 D c a) ss where
-  eithersOfRepL (M1 a) = eithersOfRepL @a @ss a
-  eithersOfRepR = eithersOfRepR @a @ss
-instance TuplesOfRep a '[] => EithersOfRep (M1 C c a) '[] where
-  eithersOfRepL (M1 a) = tuplesOfRep @_ @'[] a ()
-  eithersOfRepR = absurd
-instance TuplesOfRep a '[] => EithersOfRep (M1 C c a) (ps ': ss) where
-  eithersOfRepL (M1 a) = Left $ tuplesOfRep @_ @'[] a ()
-  eithersOfRepR = Right
-instance EithersOfRep V1 ss where
-  eithersOfRepL = \case {}
-  eithersOfRepR = id
-
--- ** Class 'TuplesOfRep'
-class TuplesOfRep (a :: * -> *) (ps::[*]) where
-  tuplesOfRep :: a x -> Tuples ps -> Tuples (ListOfRepProducts a ps)
-instance (TuplesOfRep a (ListOfRepProducts b ps), TuplesOfRep b ps) => TuplesOfRep (a:*:b) ps where
-  tuplesOfRep (a:*:b) ps =
-    tuplesOfRep @a @(ListOfRepProducts b ps) a
-     (tuplesOfRep @b @ps b ps)
-instance TuplesOfRep U1 ps where
-  tuplesOfRep U1 xs = xs
-instance FieldOfRep a => TuplesOfRep (M1 S c a) (x ': ps) where
-  tuplesOfRep (M1 a) xs = (fieldOfRep a, xs)
-instance FieldOfRep a => TuplesOfRep (M1 S c a) '[] where
-  tuplesOfRep (M1 a) _xs = fieldOfRep a
-
--- ** Class 'FieldOfRep'
-class FieldOfRep (a :: * -> *) where
-  fieldOfRep :: a x -> TypeOfRepField a
-instance FieldOfRep (K1 i a) where
-  fieldOfRep (K1 a) = a
diff --git a/src/Symantic/Base/Algebrable.hs b/src/Symantic/Base/Algebrable.hs
deleted file mode 100644
--- a/src/Symantic/Base/Algebrable.hs
+++ /dev/null
@@ -1,128 +0,0 @@
-module Symantic.Base.Algebrable where
-
-import Data.Either (Either)
-import Data.Function ((.))
-import Data.Maybe (Maybe(..))
-import Data.Proxy (Proxy(..))
-import GHC.Generics (Generic)
-
-import Symantic.Base.ADT
-import Symantic.Base.CurryN
-import Symantic.Base.Composable
-
--- | @('adt' @@SomeADT some_expr)@
--- wrap\/unwrap @(some_expr)@ input\/output value
--- to\/from the Algebraic Data Type @(SomeADT)@.
--- @(SomeADT)@ must have a 'Generic' instance
--- (using the @DeriveGeneric@ language extension to GHC).
-adt ::
- forall adt repr k.
- Dimapable repr =>
- Generic adt =>
- RepOfEoT adt =>
- EoTOfRep adt =>
- repr (EoT (ADT adt) -> k) k ->
- repr (adt -> k) k
-adt = dimap adtOfeot eotOfadt
-
--- * Class 'Tupable'
-class Tupable repr where
-  default (<:>) :: Transformable repr => Tupable (UnTrans repr) =>
-           repr (a->k) k -> repr (b->k) k -> repr ((a,b)->k) k
-  (<:>) :: repr (a->k) k -> repr (b->k) k -> repr ((a,b)->k) k
-  (<:>) = trans2 (<:>)
-infixr 4 <:>
-
--- ** Class 'Unitable'
-class Unitable repr where
-  default unit :: Transformable repr => Unitable (UnTrans repr) =>
-          repr (() -> k) k
-  unit :: repr (() -> k) k
-  unit = noTrans unit
-
--- ** Class 'Constant'
-class Constant repr where
-  default constant :: Transformable repr => Constant (UnTrans repr) =>
-              a -> repr (a -> k) k
-  constant :: a -> repr (a -> k) k
-  constant = noTrans . constant
-
--- * Class 'Eitherable'
-class Eitherable repr where
-  default (<+>) :: Transformable repr => Eitherable (UnTrans repr) =>
-           repr (a->k) k -> repr (b->k) k -> repr (Either a b -> k) k
-  (<+>) :: repr (a->k) k -> repr (b->k) k -> repr (Either a b->k) k
-  (<+>) = trans2 (<+>)
--- NOTE: yes infixr, not infixl like <|>,
--- in order to run left-most checks first.
-infixr 3 <+>
-
--- ** Class 'Emptyable'
-class Emptyable repr where
-  default empty :: Transformable repr => Emptyable (UnTrans repr) =>
-           repr k k
-  empty :: repr k k
-  empty = noTrans empty
-
--- ** Class 'Optionable'
-class Optionable repr where
-  default option :: Transformable repr => Optionable (UnTrans repr) =>
-            repr k k -> repr k k
-  option :: repr k k -> repr k k
-  option = trans1 option
-  default optional :: Transformable repr => Optionable (UnTrans repr) =>
-              repr (a->k) k -> repr (Maybe a->k) k
-  optional :: repr (a->k) k -> repr (Maybe a->k) k
-  optional = trans1 optional
-
--- * Class 'Repeatable'
-class Repeatable repr where
-  default many0 :: Transformable repr => Repeatable (UnTrans repr) =>
-           repr (a->k) k -> repr ([a]->k) k
-  many0 :: repr (a->k) k -> repr ([a]->k) k
-  many0 = trans1 many0
-  default many1 :: Transformable repr => Repeatable (UnTrans repr) =>
-           repr (a->k) k -> repr ([a]->k) k
-  many1 :: repr (a->k) k -> repr ([a]->k) k
-  many1 = trans1 many1
-
--- * Class 'Substractable'
-class Substractable repr where
-  default (<->) :: Transformable repr => Substractable (UnTrans repr) =>
-           repr a k -> repr k' k' -> repr a k
-  (<->) :: repr a k -> repr k' k' -> repr a k
-  (<->) = trans2 (<->)
-infixr 3 <->
-
--- * Class 'Dicurryable'
-class Dicurryable repr where
-  dicurry ::
-   CurryN args =>
-   proxy args ->
-   (args-..->r) -> -- construction
-   (r->Tuples args) -> -- destruction
-   repr (args-..->k) k ->
-   repr (r->k) k
-  default dicurry ::
-   Transformable repr =>
-   Dicurryable (UnTrans repr) =>
-   CurryN args =>
-   proxy args ->
-   (args-..->r) ->
-   (r->Tuples args) ->
-   repr (args-..->k) k ->
-   repr (r->k) k
-  dicurry args constr destr = trans1 (dicurry args constr destr)
-
-construct ::
- forall args a k repr.
- Dicurryable repr =>
- Generic a =>
- EoTOfRep a =>
- CurryN args =>
- Tuples args ~ EoT (ADT a) =>
- (args ~ Args (args-..->a)) =>
- (args-..->a) ->
- repr (args-..->k) k ->
- repr (a -> k) k
-construct f = dicurry (Proxy::Proxy args) f eotOfadt
diff --git a/src/Symantic/Base/Composable.hs b/src/Symantic/Base/Composable.hs
deleted file mode 100644
--- a/src/Symantic/Base/Composable.hs
+++ /dev/null
@@ -1,61 +0,0 @@
-module Symantic.Base.Composable where
-
-import Data.Function ((.))
-
--- * Class 'Composable'
-class Composable repr where
-  default (<.>) :: Transformable repr => Composable (UnTrans repr) =>
-           repr a b -> repr b c -> repr a c
-  (<.>) :: repr a b -> repr b c -> repr a c
-  (<.>) = trans2 (<.>)
-infixr 4 <.>
-
--- * Class 'Voidable'
-class Voidable repr where
-  default void :: Transformable repr => Voidable (UnTrans repr) =>
-          a -> repr (a -> b) k -> repr b k
-  void :: a -> repr (a -> b) k -> repr b k
-  void a = trans1 (void a)
-
--- * Class 'Transformable'
--- | Used with @DefaultSignatures@ and default methods,
--- in the symantics class definition,
--- it then avoids on an interpreter instance
--- to define unused methods.
-class Transformable repr where
-  -- | The underlying representation that @(repr)@ transforms.
-  type UnTrans repr :: * -> * -> *
-  -- | Lift the underlying representation to @(repr)@.
-  -- Useful to define a combinator that does nothing 
-  -- in a transformation.
-  noTrans :: UnTrans repr a b -> repr a b
-  -- | Unlift a representation. Useful when a transformation
-  -- combinator needs to access the 'UnTrans'formed representation,
-  -- or at the end to get the underlying 'UnTrans'formed representation
-  -- from the inferred @(repr)@ value.
-  unTrans :: repr a b -> UnTrans repr a b
-  -- | Convenient helper lifing an unary operator,
-  -- but also enables to identify unary operators.
-  trans1 :: (UnTrans repr a b -> UnTrans repr c d) -> repr a b -> repr c d
-  trans1 f = noTrans . f . unTrans
-  -- | Convenient helper lifting a binary operator,
-  -- but also enables to identify binary operators.
-  trans2 :: (UnTrans repr a b -> UnTrans repr c d -> UnTrans repr e f) -> repr a b -> repr c d -> repr e f
-  trans2 f x y = noTrans (f (unTrans x) (unTrans y))
-
--- ** Type 'IdentityTrans'
--- | A 'Transformable' that does nothing.
-newtype IdentityTrans repr a k
- =      IdentityTrans
- {    unIdentityTrans :: repr a k }
-instance Transformable (IdentityTrans repr) where
-  type UnTrans (IdentityTrans repr) = repr
-  noTrans = IdentityTrans
-  unTrans = unIdentityTrans
-
--- * Class 'Dimapable'
-class Dimapable repr where
-  default dimap :: Transformable repr => Dimapable (UnTrans repr) =>
-           (a->b) -> (b->a) -> repr (a->k) k -> repr (b->k) k
-  dimap :: (a->b) -> (b->a) -> repr (a->k) k -> repr (b->k) k
-  dimap a2b b2a = trans1 (dimap a2b b2a)
diff --git a/src/Symantic/Base/CurryN.hs b/src/Symantic/Base/CurryN.hs
deleted file mode 100644
--- a/src/Symantic/Base/CurryN.hs
+++ /dev/null
@@ -1,40 +0,0 @@
-{-# LANGUAGE AllowAmbiguousTypes #-}
-{-# LANGUAGE DataKinds #-}
-module Symantic.Base.CurryN where
-
-import Data.Function (($), (.))
-
-import Symantic.Base.ADT (Tuples)
-
--- * Class 'CurryN'
--- | Produce and consume 'Tuples'.
--- Not actually useful for the Generic side of this module,
--- but related through the use of 'Tuples'.
-class CurryN args where
-  -- Like 'curry' but for an arbitrary number of nested 2-tuples.
-  curryN :: (Tuples args -> res) -> args-..->res
-  -- Like 'uncurry' but for an arbitrary number of nested 2-tuples.
-  uncurryN :: (args-..->res) -> Tuples args -> res
-  -- Like 'fmap' on @('->')@ but for an arbitrary number of arguments.
-  mapresultN :: (a->b) -> (args-..->a) -> args-..->b
-instance CurryN '[a] where
-  curryN = ($)
-  uncurryN = ($)
-  mapresultN = (.)
-instance CurryN (b ': as) => CurryN (a ': b ': as) where
-  curryN f x = curryN @(b ': as) (\xs -> f (x, xs))
-  uncurryN f (x, xs) = uncurryN @(b ': as) (f x) xs
-  mapresultN f as2r = mapresultN @(b ': as) f . as2r
-
--- ** Type family ('-..->')
-type family (args :: [*]) -..-> (r :: *) :: * where
-  '[]        -..-> r = r
-  (a : args) -..-> r = a -> args -..-> r
--- ** Type family 'Args'
-type family Args (f :: *) :: [*] where
-  Args (a -> r) = a : Args r
-  Args r = '[]
--- ** Type family 'Result'
-type family Result (as :: *) :: * where
-  Result (a -> r) = Result r
-  Result r = r
diff --git a/src/Symantic/Base/Fixity.hs b/src/Symantic/Base/Fixity.hs
deleted file mode 100644
--- a/src/Symantic/Base/Fixity.hs
+++ /dev/null
@@ -1,115 +0,0 @@
-module Symantic.Base.Fixity where
-
-import Data.Bool
-import Data.Eq (Eq(..))
-import Data.Function ((.))
-import Data.Int (Int)
-import Data.Maybe (Maybe(..))
-import Data.Ord (Ord(..))
-import Data.Semigroup
-import Data.String (String, IsString(..))
-import Text.Show (Show(..))
-
--- * Type 'Fixity'
-data Fixity
- =   Fixity1 Unifix
- |   Fixity2 Infix
- deriving (Eq, Show)
-
--- ** Type 'Unifix'
-data Unifix
- =   Prefix  { unifix_precedence :: Precedence }
- |   Postfix { unifix_precedence :: Precedence }
- deriving (Eq, Show)
-
--- ** Type 'Infix'
-data Infix
- =   Infix
- {   infix_associativity :: Maybe Associativity
- ,   infix_precedence    :: Precedence
- } deriving (Eq, Show)
-
-infixL :: Precedence -> Infix
-infixL = Infix (Just AssocL)
-
-infixR :: Precedence -> Infix
-infixR = Infix (Just AssocR)
-
-infixB :: Side -> Precedence -> Infix
-infixB = Infix . Just . AssocB
-
-infixN :: Precedence -> Infix
-infixN = Infix Nothing
-
-infixN0 :: Infix
-infixN0 = infixN 0
-
-infixN5 :: Infix
-infixN5 = infixN 5
-
--- | Given 'Precedence' and 'Associativity' of its parent operator,
--- and the operand 'Side' it is in,
--- return whether an 'Infix' operator
--- needs to be enclosed by a 'Pair'.
-isPairNeeded :: (Infix, Side) -> Infix -> Bool
-isPairNeeded (po, lr) op =
-  infix_precedence op < infix_precedence po
-  || infix_precedence op == infix_precedence po
-  && not associate
-  where
-  associate =
-    case (lr, infix_associativity po) of
-     (_, Just AssocB{})   -> True
-     (SideL, Just AssocL) -> True
-     (SideR, Just AssocR) -> True
-     _ -> False
-
--- | If 'isPairNeeded' is 'True',
--- enclose the given 'IsString' by given 'Pair',
--- otherwise returns the same 'IsString'.
-pairIfNeeded ::
- Semigroup s => IsString s =>
- Pair -> (Infix, Side) -> Infix ->
- s -> s
-pairIfNeeded (o,c) po op s =
-  if isPairNeeded po op
-  then fromString o <> s <> fromString c
-  else s
-
--- * Type 'Precedence'
-type Precedence = Int
-
--- ** Class 'PrecedenceOf'
-class PrecedenceOf a where
-  precedence :: a -> Precedence
-instance PrecedenceOf Fixity where
-  precedence (Fixity1 uni) = precedence uni
-  precedence (Fixity2 inf) = precedence inf
-instance PrecedenceOf Unifix where
-  precedence = unifix_precedence
-instance PrecedenceOf Infix where
-  precedence = infix_precedence
-
--- * Type 'Associativity'
-data Associativity
- =   AssocL      -- ^ Associate to the left:  @a ¹ b ² c == (a ¹ b) ² c@
- |   AssocR      -- ^ Associate to the right: @a ¹ b ² c == a ¹ (b ² c)@
- |   AssocB Side -- ^ Associate to both sides, but to 'Side' when reading.
- deriving (Eq, Show)
-
--- ** Type 'Side'
-data Side
- =   SideL -- ^ Left
- |   SideR -- ^ Right
- deriving (Eq, Show)
-
--- ** Type 'Pair'
-type Pair = (String, String)
-pairAngle   :: Pair
-pairBrace   :: Pair
-pairBracket :: Pair
-pairParen   :: Pair
-pairAngle   = ("<",">")
-pairBrace   = ("{","}")
-pairBracket = ("[","]")
-pairParen   = ("(",")")
diff --git a/src/Symantic/Base/Permutable.hs b/src/Symantic/Base/Permutable.hs
deleted file mode 100644
--- a/src/Symantic/Base/Permutable.hs
+++ /dev/null
@@ -1,73 +0,0 @@
-{-# LANGUAGE TypeFamilyDependencies #-}
-{-# LANGUAGE UndecidableInstances #-}
-module Symantic.Base.Permutable where
-
-import Data.Function ((.))
-import Data.Maybe (Maybe(..), fromJust)
-
-import Symantic.Base.Composable
-import Symantic.Base.Algebrable
-
--- * Class 'Permutable'
-class Permutable repr where
-  -- Use @TypeFamilyDependencies@ to help type-inference infer @(repr)@.
-  type Permutation (repr:: * -> * -> *) = (r :: * -> * -> *) | r -> repr
-  type Permutation repr = Permutation (UnTrans repr)
-  permutable :: Permutation repr (a->k) k -> repr (a->k) k
-  perm :: repr (a->k) k -> Permutation repr (a->k) k
-  noPerm :: Permutation repr k k
-  permWithDefault :: a -> repr (a->k) k -> Permutation repr (a->k) k
-  optionalPerm ::
-   Eitherable repr => Dimapable repr => Permutable repr =>
-   repr (a->k) k -> Permutation repr (Maybe a -> k) k
-  optionalPerm = permWithDefault Nothing . dimap Just fromJust
-
-(<&>) ::
- Permutable repr =>
- Tupable (Permutation repr) =>
- repr (a->k) k ->
- Permutation repr (b->k) k ->
- Permutation repr ((a,b)->k) k
-x <&> y = perm x <:> y
-
-(<?&>) ::
- Eitherable repr =>
- Dimapable repr =>
- Permutable repr =>
- Tupable (Permutation repr) =>
- repr (a->k) k ->
- Permutation repr (b->k) k ->
- Permutation repr ((Maybe a,b)->k) k
-x <?&> y = optionalPerm x <:> y
-
-(<*&>) ::
- Eitherable repr =>
- Repeatable repr =>
- Dimapable repr =>
- Permutable repr =>
- Tupable (Permutation repr) =>
- repr (a->k) k ->
- Permutation repr (b->k) k ->
- Permutation repr (([a],b)->k) k
-x <*&> y = permWithDefault [] (many1 x) <:> y
-
-(<+&>) ::
- Eitherable repr =>
- Repeatable repr =>
- Dimapable repr =>
- Permutable repr =>
- Tupable (Permutation repr) =>
- repr (a->k) k ->
- Permutation repr (b->k) k ->
- Permutation repr (([a],b)->k) k
-x <+&> y = perm (many1 x) <:> y
-
-infixr 4 <&>
-infixr 4 <?&>
-infixr 4 <*&>
-infixr 4 <+&>
-
-{-# INLINE (<&>)  #-}
-{-# INLINE (<?&>) #-}
-{-# INLINE (<*&>) #-}
-{-# INLINE (<+&>) #-}
diff --git a/src/Symantic/Base/Routable.hs b/src/Symantic/Base/Routable.hs
deleted file mode 100644
--- a/src/Symantic/Base/Routable.hs
+++ /dev/null
@@ -1,20 +0,0 @@
-module Symantic.Base.Routable where
-
-import Data.Eq (Eq)
-import Text.Show (Show)
-
-import Symantic.Base.Composable
-
--- * Class 'Routable'
-class Routable repr where
-  (<!>) = trans2 (<!>)
-  default (<!>) :: Transformable repr => Routable (UnTrans repr) =>
-           repr a k -> repr b k -> repr (a:!:b) k
-  (<!>) :: repr a k -> repr b k -> repr (a:!:b) k
-infixr 3 <!>
-
--- ** Type (':!:')
--- | Like @(,)@ but @infixr@.
-data (:!:) a b = a:!:b
- deriving (Eq,Show)
-infixr 3 :!:
diff --git a/src/Symantic/Dityped.hs b/src/Symantic/Dityped.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Dityped.hs
@@ -0,0 +1,7 @@
+module Symantic.Dityped
+ ( module Symantic.Dityped.Derive
+ , module Symantic.Dityped.Lang
+ ) where
+
+import Symantic.Dityped.Derive
+import Symantic.Dityped.Lang
diff --git a/src/Symantic/Dityped/ADT.hs b/src/Symantic/Dityped/ADT.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Dityped/ADT.hs
@@ -0,0 +1,198 @@
+{-# LANGUAGE AllowAmbiguousTypes #-}
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE ConstraintKinds #-}
+{-# LANGUAGE InstanceSigs #-}
+{-# LANGUAGE EmptyCase #-}
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE UndecidableInstances #-}
+-- | EOT (Either of Tuples) to/from ADT (Algebraic Data Type).
+-- to produce or consume custom ADT with @('<:>')@ and @('<+>')@.
+--
+-- This is like what is done in @generic-sop@:
+-- https://hackage.haskell.org/package/generics-sop-0.5.1.0/docs/src/Generics.SOP.GGP.html#gSumFrom
+-- but using directly 'Either' and 'Tuples'
+-- instead of passing by the intermediary GADTs @NP@ and @NS@.
+module Symantic.Dityped.ADT where
+
+import Data.Either (Either(..))
+import Data.Void (Void, absurd)
+import Data.Function (($), (.), id, const)
+import GHC.Generics as Generics
+
+-- * Type family 'EoT'
+-- Return an 'Either' of 'Tuples' from the given 'ADT',
+-- matching the nesting occuring when using @('<:>')@ and ('<+>')@
+-- and their associativity and precedence,
+-- with no parenthesis messing around.
+type family EoT (adt :: [[*]]) :: * where
+  -- This is 'absurd'
+  EoT '[] = Void
+  -- There Is No Alternative
+  EoT '[ ps ] = Tuples ps
+  -- The right associativity of @('<+>')@
+  -- puts leaves on 'Left' and nodes on 'Right'
+  EoT (ps ': ss) = Either (Tuples ps) (EoT ss)
+
+-- * Type family 'Tuples'
+-- | Return the type of 'snd'-nested 2-tuples
+-- from the given list of types.
+type family Tuples (as :: [*]) :: (r :: *) where
+  Tuples '[] = ()
+  Tuples '[a] = a
+  Tuples (a ': rest) = (a, Tuples rest)
+
+-- * Type 'ADT'
+-- | Normalized type-level representation of an Algebraic Data Type.
+type ADT (adt :: *) = ListOfRepSums (Rep adt) '[]
+
+-- ** Type family 'ListOfRepSums'
+-- | Collect the alternatives in a continuation passing-style.
+type family ListOfRepSums (a :: * -> *) (ss :: [[*]]) :: [[*]]
+type instance ListOfRepSums (a:+:b)     ss = ListOfRepSums a (ListOfRepSums b ss)
+-- | Meta-information for datatypes
+type instance ListOfRepSums (M1 D _c a) ss = ListOfRepSums a ss
+-- | Meta-information for constructors
+type instance ListOfRepSums (M1 C _c a) ss = ListOfRepProducts a '[] ': ss
+-- | Empty datatypes
+type instance ListOfRepSums V1          ss = ss
+
+-- ** Type family 'ListOfRepProducts'
+-- | Collect the records in a continuation passing-style.
+type family ListOfRepProducts (a :: * -> *) (ps :: [*]) :: [*]
+type instance ListOfRepProducts (a:*:b)     ps = ListOfRepProducts a (ListOfRepProducts b ps)
+-- | Meta-information for record selectors
+type instance ListOfRepProducts (M1 S _c a) ps = TypeOfRepField a ': ps
+-- | Constructor without fields
+type instance ListOfRepProducts U1          ps = ps
+
+-- ** Type family 'TypeOfRepField'
+type family TypeOfRepField (a :: * -> *) :: *
+type instance TypeOfRepField (K1 _i a) = a
+
+-- * Class 'RepOfEoT'
+type RepOfEoT a = RepOfEithers (Rep a) '[]
+
+-- | Morph the 'Either' of 'Tuples' corresponding to an 'ADT'
+-- into a constructor of this 'ADT'.
+-- This is the reverse of 'eotOfadt'.
+adtOfeot :: Generic a => RepOfEoT a => EoT (ADT a) -> a
+adtOfeot eot = Generics.to $ repOfEithers @_ @'[] eot id absurd
+
+-- ** Class 'RepOfEithers'
+class RepOfEithers (a :: * -> *) ss where
+  -- | Parse the 'Either' (list-like) binary tree of 'EoT'
+  -- into the @(':+:')@ (balanced) binary tree of 'Rep',
+  -- using continuation passing-style for performance.
+  repOfEithers ::
+   EoT (ListOfRepSums a ss) ->
+   -- the 'a' 'Rep' is the current alternative in the 'EoT'
+   (a x -> r) ->
+   -- the 'a' 'Rep' is a following alternative in the 'EoT'
+   (EoT ss -> r) ->
+   r
+instance (RepOfEithers a (ListOfRepSums b ss), RepOfEithers b ss) => RepOfEithers (a:+:b) ss where
+  repOfEithers eot ok ko =
+    -- try to parse 'a' on the current 'eot'
+    repOfEithers @a @(ListOfRepSums b ss) eot
+     (ok . L1)
+     (\next ->
+      -- parsing 'a' failed
+      -- try to parse 'b' on the 'Right' of the current 'eot'
+      repOfEithers @b @ss next
+       (ok . R1)
+       ko -- parsing 'b' failed: backtrack
+     )
+instance RepOfEithers a ss => RepOfEithers (M1 D c a) ss where
+  repOfEithers eot ok = repOfEithers @a @ss eot (ok . M1)
+instance RepOfTuples a '[] => RepOfEithers (M1 C c a) (ps ': ss) where
+  repOfEithers eot ok ko =
+    case eot of
+     -- 'EoT' is a leaf, and 'Rep' too: parsing succeeds
+     Left ts -> ok $ M1 $ repOfTuples @a @'[] ts const
+     -- 'EoT' is a node, but 'Rep' is a leaf: parsing fails
+     Right ss -> ko ss
+instance RepOfTuples a '[] => RepOfEithers (M1 C c a) '[] where
+  repOfEithers eot ok _ko = ok $ M1 $ repOfTuples @_ @'[] eot const
+instance RepOfEithers V1 ss where
+  repOfEithers eot _ok ko = ko eot
+
+-- ** Class 'RepOfTuples'
+class RepOfTuples (a :: * -> *) (xs::[*]) where
+  -- | Parse the 'Tuples' (list-like) binary tree of 'EoT'
+  -- into the @(':*:')@ (balanced) binary tree of 'Rep',
+  -- using continuation passing-style for performance.
+  repOfTuples ::
+   Tuples (ListOfRepProducts a xs) ->
+   (a x -> Tuples xs -> r) -> r
+instance (RepOfTuples a (ListOfRepProducts b ps), RepOfTuples b ps) => RepOfTuples (a:*:b) ps where
+  repOfTuples ts k =
+    -- uncons 'a'
+    repOfTuples @a @(ListOfRepProducts b ps) ts
+     (\a ts' ->
+      -- uncons 'b'
+      repOfTuples @b @ps ts'
+        (\b -> k (a:*:b)))
+instance RepOfField a => RepOfTuples (M1 S c a) (p ': ps) where
+  repOfTuples (a, ts) k = k (M1 (repOfField a)) ts
+instance RepOfField a => RepOfTuples (M1 S c a) '[] where
+  repOfTuples a k = k (M1 (repOfField a)) ()
+instance RepOfTuples U1 ps where
+  repOfTuples ts k = k U1 ts
+
+-- ** Class 'RepOfField'
+class RepOfField (a :: * -> *) where
+  repOfField :: TypeOfRepField a -> a x
+instance RepOfField (K1 i a) where
+  repOfField = K1
+
+-- * Class 'EoTOfRep'
+type EoTOfRep a = EithersOfRep (Rep a) '[]
+
+-- | Morph the constructor of an 'ADT'
+-- into the corresponding 'Either' of 'Tuples' of this 'ADT'.
+-- This is the reverse of 'adtOfeot'.
+eotOfadt :: Generic a => EoTOfRep a => a -> EoT (ADT a)
+eotOfadt = eithersOfRepL @_ @'[] . Generics.from
+
+-- ** Class 'EithersOfRep'
+class EithersOfRep (a :: * -> *) ss where
+  eithersOfRepL :: a x    -> EoT (ListOfRepSums a ss)
+  eithersOfRepR :: EoT ss -> EoT (ListOfRepSums a ss)
+instance (EithersOfRep a (ListOfRepSums b ss), EithersOfRep b ss) =>
+ EithersOfRep (a:+:b) ss where
+  eithersOfRepL = \case
+   L1 a -> eithersOfRepL @a @(ListOfRepSums b ss) a
+   R1 b -> eithersOfRepR @a @(ListOfRepSums b ss) (eithersOfRepL @b @ss b)
+  eithersOfRepR ss = eithersOfRepR @a @(ListOfRepSums b ss) (eithersOfRepR @b @ss ss)
+instance EithersOfRep a ss => EithersOfRep (M1 D c a) ss where
+  eithersOfRepL (M1 a) = eithersOfRepL @a @ss a
+  eithersOfRepR = eithersOfRepR @a @ss
+instance TuplesOfRep a '[] => EithersOfRep (M1 C c a) '[] where
+  eithersOfRepL (M1 a) = tuplesOfRep @_ @'[] a ()
+  eithersOfRepR = absurd
+instance TuplesOfRep a '[] => EithersOfRep (M1 C c a) (ps ': ss) where
+  eithersOfRepL (M1 a) = Left $ tuplesOfRep @_ @'[] a ()
+  eithersOfRepR = Right
+instance EithersOfRep V1 ss where
+  eithersOfRepL = \case {}
+  eithersOfRepR = id
+
+-- ** Class 'TuplesOfRep'
+class TuplesOfRep (a :: * -> *) (ps::[*]) where
+  tuplesOfRep :: a x -> Tuples ps -> Tuples (ListOfRepProducts a ps)
+instance (TuplesOfRep a (ListOfRepProducts b ps), TuplesOfRep b ps) => TuplesOfRep (a:*:b) ps where
+  tuplesOfRep (a:*:b) ps =
+    tuplesOfRep @a @(ListOfRepProducts b ps) a
+     (tuplesOfRep @b @ps b ps)
+instance TuplesOfRep U1 ps where
+  tuplesOfRep U1 xs = xs
+instance FieldOfRep a => TuplesOfRep (M1 S c a) (x ': ps) where
+  tuplesOfRep (M1 a) xs = (fieldOfRep a, xs)
+instance FieldOfRep a => TuplesOfRep (M1 S c a) '[] where
+  tuplesOfRep (M1 a) _xs = fieldOfRep a
+
+-- ** Class 'FieldOfRep'
+class FieldOfRep (a :: * -> *) where
+  fieldOfRep :: a x -> TypeOfRepField a
+instance FieldOfRep (K1 i a) where
+  fieldOfRep (K1 a) = a
diff --git a/src/Symantic/Dityped/CurryN.hs b/src/Symantic/Dityped/CurryN.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Dityped/CurryN.hs
@@ -0,0 +1,40 @@
+{-# LANGUAGE AllowAmbiguousTypes #-}
+{-# LANGUAGE DataKinds #-}
+module Symantic.Dityped.CurryN where
+
+import Data.Function (($), (.))
+
+import Symantic.Dityped.ADT (Tuples)
+
+-- * Class 'CurryN'
+-- | Produce and consume 'Tuples'.
+-- Not actually useful for the Generic side of this module,
+-- but related through the use of 'Tuples'.
+class CurryN args where
+  -- Like 'curry' but for an arbitrary number of nested 2-tuples.
+  curryN :: (Tuples args -> res) -> args-..->res
+  -- Like 'uncurry' but for an arbitrary number of nested 2-tuples.
+  uncurryN :: (args-..->res) -> Tuples args -> res
+  -- Like 'fmap' on @('->')@ but for an arbitrary number of arguments.
+  mapresultN :: (a->b) -> (args-..->a) -> args-..->b
+instance CurryN '[a] where
+  curryN = ($)
+  uncurryN = ($)
+  mapresultN = (.)
+instance CurryN (b ': as) => CurryN (a ': b ': as) where
+  curryN f x = curryN @(b ': as) (\xs -> f (x, xs))
+  uncurryN f (x, xs) = uncurryN @(b ': as) (f x) xs
+  mapresultN f as2r = mapresultN @(b ': as) f . as2r
+
+-- ** Type family ('-..->')
+type family (args :: [*]) -..-> (r :: *) :: * where
+  '[]        -..-> r = r
+  (a : args) -..-> r = a -> args -..-> r
+-- ** Type family 'Args'
+type family Args (f :: *) :: [*] where
+  Args (a -> r) = a : Args r
+  Args r = '[]
+-- ** Type family 'Result'
+type family Result (as :: *) :: * where
+  Result (a -> r) = Result r
+  Result r = r
diff --git a/src/Symantic/Dityped/Derive.hs b/src/Symantic/Dityped/Derive.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Dityped/Derive.hs
@@ -0,0 +1,87 @@
+{-# LANGUAGE ConstraintKinds #-} -- For type class synonyms
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE DefaultSignatures #-} -- For adding LiftDerived* constraints
+module Symantic.Dityped.Derive where
+
+import Data.Function ((.))
+import Data.Kind (Type)
+
+-- * Type family 'Derived'
+-- | The representation that @(repr)@ derives to.
+type family Derived (repr :: Type -> Type -> Type) :: Type -> Type -> Type
+
+-- * Class 'Derivable'
+-- | Derivable an interpreter to a another interpreter
+-- determined by the 'Derived' open type family.
+-- This is mostly useful when running the interpreter stack,
+-- but also when going back from an initial encoding to a final one.
+--
+-- Note that 'derive' and 'liftDerived' are not necessarily reciprocical functions.
+class Derivable repr where
+  derive :: repr a ka -> Derived repr a ka
+
+-- * Class 'LiftDerived'
+-- | Lift the 'Derived' interpreter of an interpreter, to that interpreter.
+-- This is mostly useful to give default values to class methods
+-- in order to skip their definition for interpreters
+-- where 'liftDerived' can already apply the right semantic.
+--
+-- Note that 'derive' and 'liftDerived' are not necessarily reciprocical functions.
+class LiftDerived repr where
+  liftDerived :: Derived repr a ka -> repr a ka
+
+-- * Class 'LiftDerived1'
+-- | Convenient wrapper of 'derive' and 'liftDerived' for functions with a single argument.
+class LiftDerived1 repr where
+  liftDerived1 ::
+    (Derived repr a ka -> Derived repr b kb) ->
+    repr a ka -> repr b kb
+  liftDerived1 f = liftDerived . f . derive
+  default liftDerived1 ::
+    LiftDerived repr => Derivable repr =>
+    (Derived repr a ka -> Derived repr b kb) ->
+    repr a ka -> repr b kb
+
+-- * Class 'LiftDerived2'
+-- | Convenient wrapper of 'derive' and 'liftDerived' for functions with two arguments.
+class LiftDerived2 repr where
+  liftDerived2 ::
+    (Derived repr a ka -> Derived repr b kb -> Derived repr c kc) ->
+    repr a ka -> repr b kb -> repr c kc
+  liftDerived2 f a b = liftDerived (f (derive a) (derive b))
+  default liftDerived2 ::
+    LiftDerived repr => Derivable repr =>
+    (Derived repr a ka -> Derived repr b kb -> Derived repr c kc) ->
+    repr a ka -> repr b kb -> repr c kc
+
+-- * Class 'LiftDerived3'
+-- | Convenient wrapper of 'derive' and 'liftDerived' for functions with three arguments.
+class LiftDerived3 repr where
+  liftDerived3 ::
+    (Derived repr a ka -> Derived repr b kb -> Derived repr c kc -> Derived repr d kd) ->
+    repr a ka -> repr b kb -> repr c kc -> repr d kd
+  liftDerived3 f a b c = liftDerived (f (derive a) (derive b) (derive c))
+  default liftDerived3 ::
+    LiftDerived repr => Derivable repr =>
+    (Derived repr a ka -> Derived repr b kb -> Derived repr c kc -> Derived repr d kd) ->
+    repr a ka -> repr b kb -> repr c kc -> repr d kd
+
+-- * Class 'LiftDerived4'
+-- | Convenient wrapper of 'derive' and 'liftDerived' for functions with three arguments.
+class LiftDerived4 repr where
+  liftDerived4 ::
+    (Derived repr a ka -> Derived repr b kb -> Derived repr c kc -> Derived repr d kd -> Derived repr e ke) ->
+    repr a ka -> repr b kb -> repr c kc -> repr d kd -> repr e ke
+  liftDerived4 f a b c d = liftDerived (f (derive a) (derive b) (derive c) (derive d))
+  default liftDerived4 ::
+    LiftDerived repr => Derivable repr =>
+    (Derived repr a ka -> Derived repr b kb -> Derived repr c kc -> Derived repr d kd -> Derived repr e ke) ->
+    repr a ka -> repr b kb -> repr c kc -> repr d kd -> repr e ke
+
+-- * Type synonyms @FromDerived*@
+-- | Convenient type synonym for using 'liftDerived' on symantic class @(sym)@.
+type FromDerived  sym repr = ( LiftDerived  repr, sym (Derived repr) )
+type FromDerived1 sym repr = ( LiftDerived1 repr, sym (Derived repr) )
+type FromDerived2 sym repr = ( LiftDerived2 repr, sym (Derived repr) )
+type FromDerived3 sym repr = ( LiftDerived3 repr, sym (Derived repr) )
+type FromDerived4 sym repr = ( LiftDerived4 repr, sym (Derived repr) )
diff --git a/src/Symantic/Dityped/Lang.hs b/src/Symantic/Dityped/Lang.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Dityped/Lang.hs
@@ -0,0 +1,246 @@
+{-# LANGUAGE TypeFamilyDependencies #-} -- For Permutation
+{-# LANGUAGE UndecidableInstances #-} -- For Permutation
+module Symantic.Dityped.Lang where
+
+import Data.Either (Either)
+import Data.Eq (Eq)
+import Data.Function ((.))
+import Data.Maybe (Maybe(..), fromJust)
+import Data.Proxy (Proxy(..))
+import GHC.Generics (Generic)
+import Text.Show (Show)
+
+import Symantic.Dityped.ADT
+import Symantic.Dityped.CurryN
+import Symantic.Dityped.Derive
+
+-- * Class 'Composable'
+class Composable repr where
+  (<.>) :: repr a b -> repr b c -> repr a c
+  (<.>) = liftDerived2 (<.>)
+  default (<.>) ::
+    FromDerived2 Composable repr =>
+    repr a b -> repr b c -> repr a c
+infixr 4 <.>
+
+-- ** Class 'Constant'
+class Constant repr where
+  constant :: a -> repr (a -> k) k
+  constant = liftDerived . constant
+  default constant ::
+    FromDerived Constant repr =>
+    a -> repr (a -> k) k
+
+-- * Class 'Dicurryable'
+class Dicurryable repr where
+  dicurry ::
+    CurryN args =>
+    proxy args ->
+    (args-..->r) -> -- construction
+    (r->Tuples args) -> -- destruction
+    repr (args-..->k) k ->
+    repr (r->k) k
+  dicurry args constr destr = liftDerived1 (dicurry args constr destr)
+  default dicurry ::
+    FromDerived1 Dicurryable repr =>
+    CurryN args =>
+    proxy args ->
+    (args-..->r) ->
+    (r->Tuples args) ->
+    repr (args-..->k) k ->
+    repr (r->k) k
+
+construct ::
+  forall args a k repr.
+  Dicurryable repr =>
+  Generic a =>
+  EoTOfRep a =>
+  CurryN args =>
+  Tuples args ~ EoT (ADT a) =>
+  (args ~ Args (args-..->a)) =>
+  (args-..->a) ->
+  repr (args-..->k) k ->
+  repr (a -> k) k
+construct f = dicurry (Proxy::Proxy args) f eotOfadt
+
+-- * Class 'Dimapable'
+class Dimapable repr where
+  dimap :: (a->b) -> (b->a) -> repr (a->k) k -> repr (b->k) k
+  dimap a2b b2a = liftDerived1 (dimap a2b b2a)
+  default dimap ::
+    FromDerived1 Dimapable repr =>
+    (a->b) -> (b->a) -> repr (a->k) k -> repr (b->k) k
+
+-- * Class 'Eitherable'
+class Eitherable repr where
+  (<+>) :: repr (a->k) k -> repr (b->k) k -> repr (Either a b->k) k
+  (<+>) = liftDerived2 (<+>)
+  default (<+>) ::
+    FromDerived2 Eitherable repr =>
+    repr (a->k) k -> repr (b->k) k -> repr (Either a b -> k) k
+-- NOTE: yes infixr, not infixl like <|>,
+-- in order to run left-most checks first.
+infixr 3 <+>
+
+-- | @('adt' @@SomeADT some_expr)@
+-- wrap\/unwrap @(some_expr)@ input\/output value
+-- to\/from the Algebraic Data Type @(SomeADT)@.
+-- @(SomeADT)@ must have a 'Generic' instance
+-- (using the @DeriveGeneric@ language extension to GHC).
+adt ::
+  forall adt repr k.
+  Dimapable repr =>
+  Generic adt =>
+  RepOfEoT adt =>
+  EoTOfRep adt =>
+  repr (EoT (ADT adt) -> k) k ->
+  repr (adt -> k) k
+adt = dimap adtOfeot eotOfadt
+
+-- ** Class 'Emptyable'
+class Emptyable repr where
+  empty :: repr k k
+  empty = liftDerived empty
+  default empty ::
+    FromDerived Emptyable repr =>
+    repr k k
+
+-- ** Class 'Optionable'
+class Optionable repr where
+  option :: repr k k -> repr k k
+  optional :: repr (a->k) k -> repr (Maybe a->k) k
+  option = liftDerived1 option
+  optional = liftDerived1 optional
+  default option ::
+    FromDerived1 Optionable repr =>
+    repr k k -> repr k k
+  default optional ::
+    FromDerived1 Optionable repr =>
+    repr (a->k) k -> repr (Maybe a->k) k
+
+-- * Class 'Permutable'
+class Permutable repr where
+  -- Use @TypeFamilyDependencies@ to help type-inference infer @(repr)@.
+  type Permutation (repr:: * -> * -> *) = (r :: * -> * -> *) | r -> repr
+  type Permutation repr = Permutation (Derived repr)
+  permutable :: Permutation repr (a->k) k -> repr (a->k) k
+  perm :: repr (a->k) k -> Permutation repr (a->k) k
+  noPerm :: Permutation repr k k
+  permWithDefault :: a -> repr (a->k) k -> Permutation repr (a->k) k
+  optionalPerm ::
+    Eitherable repr => Dimapable repr => Permutable repr =>
+    repr (a->k) k -> Permutation repr (Maybe a -> k) k
+  optionalPerm = permWithDefault Nothing . dimap Just fromJust
+
+(<&>) ::
+  Permutable repr =>
+  Tupable (Permutation repr) =>
+  repr (a->k) k ->
+  Permutation repr (b->k) k ->
+  Permutation repr ((a,b)->k) k
+x <&> y = perm x <:> y
+
+(<?&>) ::
+  Eitherable repr =>
+  Dimapable repr =>
+  Permutable repr =>
+  Tupable (Permutation repr) =>
+  repr (a->k) k ->
+  Permutation repr (b->k) k ->
+  Permutation repr ((Maybe a,b)->k) k
+x <?&> y = optionalPerm x <:> y
+
+(<*&>) ::
+  Eitherable repr =>
+  Repeatable repr =>
+  Dimapable repr =>
+  Permutable repr =>
+  Tupable (Permutation repr) =>
+  repr (a->k) k ->
+  Permutation repr (b->k) k ->
+  Permutation repr (([a],b)->k) k
+x <*&> y = permWithDefault [] (many1 x) <:> y
+
+(<+&>) ::
+  Eitherable repr =>
+  Repeatable repr =>
+  Dimapable repr =>
+  Permutable repr =>
+  Tupable (Permutation repr) =>
+  repr (a->k) k ->
+  Permutation repr (b->k) k ->
+  Permutation repr (([a],b)->k) k
+x <+&> y = perm (many1 x) <:> y
+
+infixr 4 <&>
+infixr 4 <?&>
+infixr 4 <*&>
+infixr 4 <+&>
+
+{-# INLINE (<&>)  #-}
+{-# INLINE (<?&>) #-}
+{-# INLINE (<*&>) #-}
+{-# INLINE (<+&>) #-}
+
+-- * Class 'Repeatable'
+class Repeatable repr where
+  many0 :: repr (a->k) k -> repr ([a]->k) k
+  many1 :: repr (a->k) k -> repr ([a]->k) k
+  many0 = liftDerived1 many0
+  many1 = liftDerived1 many1
+  default many0 ::
+    FromDerived1 Repeatable repr =>
+    repr (a->k) k -> repr ([a]->k) k
+  default many1 ::
+    FromDerived1 Repeatable repr =>
+    repr (a->k) k -> repr ([a]->k) k
+
+-- * Class 'Routable'
+class Routable repr where
+  (<!>) :: repr a k -> repr b k -> repr (a:!:b) k
+  (<!>) = liftDerived2 (<!>)
+  default (<!>) ::
+    FromDerived2 Routable repr =>
+    repr a k -> repr b k -> repr (a:!:b) k
+infixr 3 <!>
+
+-- ** Type (':!:')
+-- | Like @(,)@ but @infixr@.
+-- Mostly useful for clarity when using 'Routable'.
+data (:!:) a b = a:!:b
+ deriving (Eq, Show)
+infixr 3 :!:
+
+-- * Class 'Substractable'
+class Substractable repr where
+  (<->) :: repr a k -> repr k' k' -> repr a k
+  (<->) = liftDerived2 (<->)
+  default (<->) ::
+    FromDerived2 Substractable repr =>
+    repr a k -> repr k' k' -> repr a k
+infixr 3 <->
+
+-- * Class 'Tupable'
+class Tupable repr where
+  (<:>) :: repr (a->k) k -> repr (b->k) k -> repr ((a,b)->k) k
+  (<:>) = liftDerived2 (<:>)
+  default (<:>) ::
+    FromDerived2 Tupable repr =>
+    repr (a->k) k -> repr (b->k) k -> repr ((a,b)->k) k
+infixr 4 <:>
+
+-- ** Class 'Unitable'
+class Unitable repr where
+  unit :: repr (() -> k) k
+  unit = liftDerived unit
+  default unit ::
+    FromDerived Unitable repr =>
+    repr (() -> k) k
+
+-- * Class 'Voidable'
+class Voidable repr where
+  default void ::
+    FromDerived1 Voidable repr =>
+    a -> repr (a -> b) k -> repr b k
+  void :: a -> repr (a -> b) k -> repr b k
+  void a = liftDerived1 (void a)
diff --git a/src/Symantic/Typed.hs b/src/Symantic/Typed.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Typed.hs
@@ -0,0 +1,17 @@
+module Symantic.Typed
+ ( module Symantic.Typed.Data
+ , module Symantic.Typed.Derive
+ , module Symantic.Typed.Lang
+ , module Symantic.Typed.ObserveSharing
+ , module Symantic.Typed.Optimize
+ , module Symantic.Typed.Reify
+ , module Symantic.Typed.View
+ ) where
+
+import Symantic.Typed.Data
+import Symantic.Typed.Derive
+import Symantic.Typed.Lang
+import Symantic.Typed.ObserveSharing
+import Symantic.Typed.Optimize
+import Symantic.Typed.Reify
+import Symantic.Typed.View
diff --git a/src/Symantic/Typed/Data.hs b/src/Symantic/Typed/Data.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Typed/Data.hs
@@ -0,0 +1,211 @@
+{-# LANGUAGE ConstraintKinds #-}
+{-# LANGUAGE DataKinds #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE KindSignatures #-}
+{-# LANGUAGE LambdaCase #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE PatternSynonyms #-}
+{-# LANGUAGE RankNTypes #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE StandaloneDeriving #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE ViewPatterns #-}
+module Symantic.Typed.Data where
+
+import Data.Bool (Bool)
+import Data.Either (Either)
+import Data.Kind (Constraint, Type)
+import Data.Maybe (Maybe)
+import Type.Reflection (Typeable, (:~~:)(..), eqTypeRep, typeRep)
+import qualified Data.Eq as Eq
+import qualified Data.Maybe as Maybe
+import qualified Data.Function as Fun
+
+import Symantic.Typed.Lang
+import Symantic.Typed.Derive
+
+-- * Type 'SomeData'
+data SomeData repr a =
+  forall able.
+  ( Derivable (Data able repr)
+  , Typeable able
+  ) => SomeData (Data able repr a)
+
+type instance Derived (SomeData repr) = repr
+instance Derivable (SomeData repr) where
+  derive (SomeData x) = derive x
+
+-- ** Type 'TypedRepr'
+type TypedRepr = Type -> Type
+
+-- ** Type 'Data'
+-- TODO: neither data families nor data instances
+-- can have phantom roles with GHC-9's RoleAnnotations,
+-- hence 'Data.Coerce.coerce' cannot be used on them for now.
+-- https://gitlab.haskell.org/ghc/ghc/-/issues/8177
+-- https://gitlab.haskell.org/ghc/ghc/-/wikis/roles#proposal-roles-for-type-families
+data family Data
+  (able :: TypedRepr -> Constraint)
+  :: TypedRepr -> TypedRepr
+type instance Derived (Data able repr) = repr
+
+-- | Convenient utility to pattern-match a 'SomeData'.
+pattern Data :: Typeable able => Data able repr a -> SomeData repr a
+pattern Data x <- (unSomeData -> Maybe.Just x)
+
+-- | @(unSomeData c :: 'Maybe' ('Data' able repr a))@
+-- extract the data-constructor from the given 'SomeData'
+-- iif. it belongs to the @('Data' able repr a)@ data-instance.
+unSomeData ::
+  forall able repr a.
+  Typeable able =>
+  SomeData repr a -> Maybe (Data able repr a)
+unSomeData (SomeData (c::Data c repr a)) =
+  case typeRep @able `eqTypeRep` typeRep @c of
+    Maybe.Just HRefl -> Maybe.Just c
+    Maybe.Nothing -> Maybe.Nothing
+
+-- Abstractable
+data instance Data Abstractable repr a where
+  (:@) :: SomeData repr (a->b) -> SomeData repr a -> Data Abstractable repr b
+  Lam :: (SomeData repr a -> SomeData repr b) -> Data Abstractable repr (a->b)
+  Lam1 :: (SomeData repr a -> SomeData repr b) -> Data Abstractable repr (a->b)
+  Var :: repr a -> Data Abstractable repr a
+  -- FIXME: add constructors
+instance
+  ( Abstractable repr
+  ) => Derivable (Data Abstractable repr) where
+  derive = \case
+    f :@ x -> derive f .@ derive x
+    Lam f -> lam (\x -> derive (f (SomeData (Var x))))
+    Lam1 f -> lam1 (\x -> derive (f (SomeData (Var x))))
+    Var x -> var x
+instance
+  ( Abstractable repr
+  ) => Abstractable (SomeData repr) where
+  f .@ x = SomeData (f :@ x)
+  lam f = SomeData (Lam f)
+  lam1 f = SomeData (Lam1 f)
+  var = Fun.id
+  ($) = lam1 (\f -> lam1 (\x -> f .@ x))
+  (.) = lam1 (\f -> lam1 (\g -> lam1 (\x -> f .@ (g .@ x))))
+  const = lam1 (\x -> lam1 (\_y -> x))
+  flip = lam1 (\f -> lam1 (\x -> lam1 (\y -> f .@ y .@ x)))
+  id = lam1 (\x -> x)
+
+-- Anythingable
+data instance Data Anythingable repr a where
+  Anything :: repr a -> Data Anythingable repr a
+instance
+  ( Anythingable repr
+  ) =>
+  Derivable (Data Anythingable repr) where
+  derive = \case
+    Anything x -> anything x
+instance Anythingable (SomeData repr)
+instance Anythingable (Data Anythingable repr)
+
+-- Bottomable
+data instance Data Bottomable repr a where
+  Bottom :: Data Bottomable repr a
+instance Bottomable repr => Derivable (Data Bottomable repr) where
+  derive Bottom{} = bottom
+
+-- Constantable
+data instance Data (Constantable c) repr a where
+  Constant :: {-Typeable c =>-} c -> Data (Constantable c) repr c
+instance Constantable c repr => Derivable (Data (Constantable c) repr) where
+  derive = \case
+    Constant x -> constant x
+instance
+  ( Constantable c repr
+  , Typeable c
+  ) => Constantable c (SomeData repr) where
+  constant c = SomeData (Constant c)
+instance {-Typeable c =>-} Constantable c (Data (Constantable c) repr) where
+  constant = Constant
+
+-- Eitherable
+data instance Data Eitherable repr a where
+  Left :: Data Eitherable repr (l -> Either l r)
+  Right :: Data Eitherable repr (r -> Either l r)
+instance Eitherable repr => Derivable (Data Eitherable repr) where
+  derive = \case
+    Left -> left
+    Right -> right
+instance
+  ( Eitherable repr
+  ) => Eitherable (SomeData repr) where
+  left = SomeData Left
+  right = SomeData Right
+instance Eitherable (Data Eitherable repr) where
+  left = Left
+  right = Right
+
+-- Equalable
+data instance Data Equalable repr a where
+  Equal :: Eq.Eq a => Data Equalable repr (a -> a -> Bool)
+instance Equalable repr => Derivable (Data Equalable repr) where
+  derive = \case
+    Equal -> equal
+instance
+  ( Equalable repr
+  ) => Equalable (SomeData repr) where
+  equal = SomeData Equal
+instance Equalable (Data Equalable repr) where
+  equal = Equal
+
+-- IfThenElseable
+data instance Data IfThenElseable repr a where
+  IfThenElse ::
+    SomeData repr Bool ->
+    SomeData repr a ->
+    SomeData repr a ->
+    Data IfThenElseable repr a
+instance IfThenElseable repr => Derivable (Data IfThenElseable repr) where
+  derive = \case
+    IfThenElse test ok ko -> ifThenElse (derive test) (derive ok) (derive ko)
+instance
+  ( IfThenElseable repr
+  ) => IfThenElseable (SomeData repr) where
+  ifThenElse test ok ko = SomeData (IfThenElse test ok ko)
+instance IfThenElseable repr => IfThenElseable (Data IfThenElseable repr) where
+  ifThenElse test ok ko = IfThenElse (SomeData test) (SomeData ok) (SomeData ko)
+
+-- Listable
+data instance Data Listable repr a where
+  Cons :: Data Listable repr (a -> [a] -> [a])
+  Nil :: Data Listable repr [a]
+infixr 4 `Cons`
+instance Listable repr => Derivable (Data Listable repr) where
+  derive = \case
+    Cons -> cons
+    Nil -> nil
+instance
+  ( Listable repr
+  ) => Listable (SomeData repr) where
+  cons = SomeData Cons
+  nil = SomeData Nil
+instance Listable (Data Listable repr) where
+  cons = Cons
+  nil = Nil
+
+-- Maybeable
+data instance Data Maybeable repr a where
+  Nothing :: Data Maybeable repr (Maybe a)
+  Just :: Data Maybeable repr (a -> Maybe a)
+instance Maybeable repr => Derivable (Data Maybeable repr) where
+  derive = \case
+    Nothing -> nothing
+    Just -> just
+instance
+  ( Maybeable repr
+  ) => Maybeable (SomeData repr) where
+  nothing = SomeData Nothing
+  just = SomeData Just
+instance Maybeable (Data Maybeable repr) where
+  nothing = Nothing
+  just = Just
diff --git a/src/Symantic/Typed/Derive.hs b/src/Symantic/Typed/Derive.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Typed/Derive.hs
@@ -0,0 +1,87 @@
+{-# LANGUAGE ConstraintKinds #-} -- For type class synonyms
+{-# LANGUAGE PolyKinds #-}
+{-# LANGUAGE DefaultSignatures #-} -- For adding LiftDerived* constraints
+module Symantic.Typed.Derive where
+
+import Data.Function ((.))
+import Data.Kind (Type)
+
+-- * Type family 'Derived'
+-- | The representation that @(repr)@ derives to.
+type family Derived (repr :: Type -> Type) :: Type -> Type
+
+-- * Class 'Derivable'
+-- | Derivable an interpreter to a another interpreter
+-- determined by the 'Derived' open type family.
+-- This is mostly useful when running the interpreter stack,
+-- but also when going back from an initial encoding to a final one.
+--
+-- Note that 'derive' and 'liftDerived' are not necessarily reciprocical functions.
+class Derivable repr where
+  derive :: repr a -> Derived repr a
+
+-- * Class 'LiftDerived'
+-- | Lift the 'Derived' interpreter of an interpreter, to that interpreter.
+-- This is mostly useful to give default values to class methods
+-- in order to skip their definition for interpreters
+-- where 'liftDerived' can already apply the right semantic.
+--
+-- Note that 'derive' and 'liftDerived' are not necessarily reciprocical functions.
+class LiftDerived repr where
+  liftDerived :: Derived repr a -> repr a
+
+-- * Class 'LiftDerived1'
+-- | Convenient wrapper of 'derive' and 'liftDerived' for functions with a single argument.
+class LiftDerived1 repr where
+  liftDerived1 ::
+    (Derived repr a -> Derived repr b) ->
+    repr a -> repr b
+  liftDerived1 f = liftDerived . f . derive
+  default liftDerived1 ::
+    LiftDerived repr => Derivable repr =>
+    (Derived repr a -> Derived repr b) ->
+    repr a -> repr b
+
+-- * Class 'LiftDerived2'
+-- | Convenient wrapper of 'derive' and 'liftDerived' for functions with two arguments.
+class LiftDerived2 repr where
+  liftDerived2 ::
+    (Derived repr a -> Derived repr b -> Derived repr c) ->
+    repr a -> repr b -> repr c
+  liftDerived2 f a b = liftDerived (f (derive a) (derive b))
+  default liftDerived2 ::
+    LiftDerived repr => Derivable repr =>
+    (Derived repr a -> Derived repr b -> Derived repr c) ->
+    repr a -> repr b -> repr c
+
+-- * Class 'LiftDerived3'
+-- | Convenient wrapper of 'derive' and 'liftDerived' for functions with three arguments.
+class LiftDerived3 repr where
+  liftDerived3 ::
+    (Derived repr a -> Derived repr b -> Derived repr c -> Derived repr d) ->
+    repr a -> repr b -> repr c -> repr d
+  liftDerived3 f a b c = liftDerived (f (derive a) (derive b) (derive c))
+  default liftDerived3 ::
+    LiftDerived repr => Derivable repr =>
+    (Derived repr a -> Derived repr b -> Derived repr c -> Derived repr d) ->
+    repr a -> repr b -> repr c -> repr d
+
+-- * Class 'LiftDerived4'
+-- | Convenient wrapper of 'derive' and 'liftDerived' for functions with three arguments.
+class LiftDerived4 repr where
+  liftDerived4 ::
+    (Derived repr a -> Derived repr b -> Derived repr c -> Derived repr d -> Derived repr e) ->
+    repr a -> repr b -> repr c -> repr d -> repr e
+  liftDerived4 f a b c d = liftDerived (f (derive a) (derive b) (derive c) (derive d))
+  default liftDerived4 ::
+    LiftDerived repr => Derivable repr =>
+    (Derived repr a -> Derived repr b -> Derived repr c -> Derived repr d -> Derived repr e) ->
+    repr a -> repr b -> repr c -> repr d -> repr e
+
+-- * Type synonyms @FromDerived*@
+-- | Convenient type synonym for using 'liftDerived' on symantic class @(sym)@.
+type FromDerived  sym repr = ( LiftDerived  repr, sym (Derived repr) )
+type FromDerived1 sym repr = ( LiftDerived1 repr, sym (Derived repr) )
+type FromDerived2 sym repr = ( LiftDerived2 repr, sym (Derived repr) )
+type FromDerived3 sym repr = ( LiftDerived3 repr, sym (Derived repr) )
+type FromDerived4 sym repr = ( LiftDerived4 repr, sym (Derived repr) )
diff --git a/src/Symantic/Typed/Fixity.hs b/src/Symantic/Typed/Fixity.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Typed/Fixity.hs
@@ -0,0 +1,115 @@
+module Symantic.Typed.Fixity where
+
+import Data.Bool
+import Data.Eq (Eq(..))
+import Data.Function ((.))
+import Data.Int (Int)
+import Data.Maybe (Maybe(..))
+import Data.Ord (Ord(..))
+import Data.Semigroup
+import Data.String (String, IsString(..))
+import Text.Show (Show(..))
+
+-- * Type 'Fixity'
+data Fixity
+ =   Fixity1 Unifix
+ |   Fixity2 Infix
+ deriving (Eq, Show)
+
+-- ** Type 'Unifix'
+data Unifix
+ =   Prefix  { unifix_precedence :: Precedence }
+ |   Postfix { unifix_precedence :: Precedence }
+ deriving (Eq, Show)
+
+-- ** Type 'Infix'
+data Infix
+ =   Infix
+ {   infix_associativity :: Maybe Associativity
+ ,   infix_precedence    :: Precedence
+ } deriving (Eq, Show)
+
+infixL :: Precedence -> Infix
+infixL = Infix (Just AssocL)
+
+infixR :: Precedence -> Infix
+infixR = Infix (Just AssocR)
+
+infixB :: Side -> Precedence -> Infix
+infixB = Infix . Just . AssocB
+
+infixN :: Precedence -> Infix
+infixN = Infix Nothing
+
+infixN0 :: Infix
+infixN0 = infixN 0
+
+infixN5 :: Infix
+infixN5 = infixN 5
+
+-- | Given 'Precedence' and 'Associativity' of its parent operator,
+-- and the operand 'Side' it is in,
+-- return whether an 'Infix' operator
+-- needs to be enclosed by a 'Pair'.
+isPairNeeded :: (Infix, Side) -> Infix -> Bool
+isPairNeeded (po, lr) op =
+  infix_precedence op < infix_precedence po
+  || infix_precedence op == infix_precedence po
+  && not associate
+  where
+  associate =
+    case (lr, infix_associativity po) of
+     (_, Just AssocB{})   -> True
+     (SideL, Just AssocL) -> True
+     (SideR, Just AssocR) -> True
+     _ -> False
+
+-- | If 'isPairNeeded' is 'True',
+-- enclose the given 'IsString' by given 'Pair',
+-- otherwise returns the same 'IsString'.
+pairIfNeeded ::
+ Semigroup s => IsString s =>
+ Pair -> (Infix, Side) -> Infix ->
+ s -> s
+pairIfNeeded (o,c) po op s =
+  if isPairNeeded po op
+  then fromString o <> s <> fromString c
+  else s
+
+-- * Type 'Precedence'
+type Precedence = Int
+
+-- ** Class 'PrecedenceOf'
+class PrecedenceOf a where
+  precedence :: a -> Precedence
+instance PrecedenceOf Fixity where
+  precedence (Fixity1 uni) = precedence uni
+  precedence (Fixity2 inf) = precedence inf
+instance PrecedenceOf Unifix where
+  precedence = unifix_precedence
+instance PrecedenceOf Infix where
+  precedence = infix_precedence
+
+-- * Type 'Associativity'
+data Associativity
+ =   AssocL      -- ^ Associate to the left:  @a ¹ b ² c == (a ¹ b) ² c@
+ |   AssocR      -- ^ Associate to the right: @a ¹ b ² c == a ¹ (b ² c)@
+ |   AssocB Side -- ^ Associate to both sides, but to 'Side' when reading.
+ deriving (Eq, Show)
+
+-- ** Type 'Side'
+data Side
+ =   SideL -- ^ Left
+ |   SideR -- ^ Right
+ deriving (Eq, Show)
+
+-- ** Type 'Pair'
+type Pair = (String, String)
+pairAngle   :: Pair
+pairBrace   :: Pair
+pairBracket :: Pair
+pairParen   :: Pair
+pairAngle   = ("<",">")
+pairBrace   = ("{","}")
+pairBracket = ("[","]")
+pairParen   = ("(",")")
diff --git a/src/Symantic/Typed/Lang.hs b/src/Symantic/Typed/Lang.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Typed/Lang.hs
@@ -0,0 +1,154 @@
+{-# LANGUAGE ConstraintKinds #-}
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE DefaultSignatures #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE NoMonomorphismRestriction #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE NoImplicitPrelude #-}
+module Symantic.Typed.Lang where
+
+import Data.Char (Char)
+import Data.Bool (Bool(..))
+import Data.Either (Either(..))
+import Data.Eq (Eq)
+import Data.Maybe (Maybe(..))
+import qualified Data.Function as Fun
+
+import Symantic.Typed.Derive
+
+-- * Class 'Abstractable'
+class Abstractable repr where
+  -- | Application, aka. unabstract.
+  (.@) :: repr (a->b) -> repr a -> repr b; infixl 9 .@
+  -- | Lambda term abstraction, in HOAS (Higher-Order Abstract Syntax) style.
+  lam :: (repr a -> repr b) -> repr (a->b)
+  -- | Like 'lam' but whose argument is used only once,
+  -- hence safe to beta-reduce (inline) without duplicating work.
+  lam1 :: (repr a -> repr b) -> repr (a->b)
+  const :: repr (a -> b -> a)
+  flip :: repr ((a -> b -> c) -> b -> a -> c)
+  id :: repr (a->a)
+  (.) :: repr ((b->c) -> (a->b) -> a -> c); infixr 9 .
+  ($) :: repr ((a->b) -> a -> b); infixr 0 $
+  var :: repr a -> repr a
+  (.@) = liftDerived2 (.@)
+  lam f = liftDerived (lam (derive Fun.. f Fun.. liftDerived))
+  lam1 f = liftDerived (lam1 (derive Fun.. f Fun.. liftDerived))
+  const = liftDerived const
+  flip = liftDerived flip
+  id = liftDerived id
+  (.) = liftDerived (.)
+  ($) = liftDerived ($)
+  var = liftDerived1 var
+  default (.@) ::
+    FromDerived2 Abstractable repr =>
+    repr (a->b) -> repr a -> repr b
+  default lam ::
+    FromDerived Abstractable repr => Derivable repr =>
+    (repr a -> repr b) -> repr (a->b)
+  default lam1 ::
+    FromDerived Abstractable repr => Derivable repr =>
+    (repr a -> repr b) -> repr (a->b)
+  default const ::
+    FromDerived Abstractable repr =>
+    repr (a -> b -> a)
+  default flip ::
+    FromDerived Abstractable repr =>
+    repr ((a -> b -> c) -> b -> a -> c)
+  default id ::
+    FromDerived Abstractable repr =>
+    repr (a->a)
+  default (.) ::
+    FromDerived Abstractable repr =>
+    repr ((b->c) -> (a->b) -> a -> c)
+  default ($) ::
+    FromDerived Abstractable repr =>
+    repr ((a->b) -> a -> b)
+  default var ::
+    FromDerived1 Abstractable repr =>
+    repr a -> repr a
+
+-- * Class 'Anythingable'
+class Anythingable repr where
+  anything :: repr a -> repr a
+  anything = Fun.id
+
+-- * Class 'Bottomable'
+class Bottomable repr where
+  bottom :: repr a
+
+-- * Class 'Constantable'
+class Constantable c repr where
+  constant :: c -> repr c
+  constant = liftDerived Fun.. constant
+  default constant ::
+    FromDerived (Constantable c) repr =>
+    c -> repr c
+
+bool :: Constantable Bool repr => Bool -> repr Bool
+bool = constant @Bool
+char :: Constantable Char repr => Char -> repr Char
+char = constant @Char
+unit :: Constantable () repr => repr ()
+unit = constant @() ()
+
+-- * Class 'Eitherable'
+class Eitherable repr where
+  left :: repr (l -> Either l r)
+  right :: repr (r -> Either l r)
+  left = liftDerived left
+  right = liftDerived right
+  default left ::
+    FromDerived Eitherable repr =>
+    repr (l -> Either l r)
+  default right ::
+    FromDerived Eitherable repr =>
+    repr (r -> Either l r)
+
+-- * Class 'Equalable'
+class Equalable repr where
+  equal :: Eq a => repr (a -> a -> Bool)
+  equal = liftDerived equal
+  default equal ::
+    FromDerived Equalable repr =>
+    Eq a => repr (a -> a -> Bool)
+
+infix 4 `equal`, ==
+(==) :: (Abstractable repr, Equalable repr, Eq a) => repr (a -> a -> Bool)
+(==) = lam (\x -> lam (\y -> equal .@ x .@ y))
+
+-- * Class 'IfThenElseable'
+class IfThenElseable repr where
+  ifThenElse :: repr Bool -> repr a -> repr a -> repr a
+  ifThenElse = liftDerived3 ifThenElse
+  default ifThenElse ::
+    FromDerived3 IfThenElseable repr =>
+    repr Bool -> repr a -> repr a -> repr a
+
+-- * Class 'Listable'
+class Listable repr where
+  cons :: repr (a -> [a] -> [a])
+  nil :: repr [a]
+  cons = liftDerived cons
+  nil = liftDerived nil
+  default cons ::
+    FromDerived Listable repr =>
+    repr (a -> [a] -> [a])
+  default nil ::
+    FromDerived Listable repr =>
+    repr [a]
+
+-- * Class 'Maybeable'
+class Maybeable repr where
+  nothing :: repr (Maybe a)
+  just :: repr (a -> Maybe a)
+  nothing = liftDerived nothing
+  just = liftDerived just
+  default nothing ::
+    FromDerived Maybeable repr =>
+    repr (Maybe a)
+  default just ::
+    FromDerived Maybeable repr =>
+    repr (a -> Maybe a)
diff --git a/src/Symantic/Typed/ObserveSharing.hs b/src/Symantic/Typed/ObserveSharing.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Typed/ObserveSharing.hs
@@ -0,0 +1,330 @@
+{-# LANGUAGE AllowAmbiguousTypes #-} -- For ShowLetName
+{-# LANGUAGE BangPatterns #-} -- For makeSharingName
+{-# LANGUAGE DataKinds #-} -- For ShowLetName
+{-# LANGUAGE DefaultSignatures #-}
+{-# LANGUAGE ExistentialQuantification #-} -- For SharingName
+-- {-# LANGUAGE MagicHash #-} -- For unsafeCoerce#
+module Symantic.Typed.ObserveSharing where
+
+import Control.Applicative (Applicative(..))
+import Control.Monad (Monad(..))
+import Data.Bool (Bool(..))
+import Data.Eq (Eq(..))
+import Data.Foldable (foldMap)
+import Data.Function (($), (.))
+import Data.Functor ((<$>))
+import Data.Functor.Compose (Compose(..))
+import Data.HashMap.Strict (HashMap)
+import Data.HashSet (HashSet)
+import Data.Hashable (Hashable, hashWithSalt, hash)
+import Data.Int (Int)
+import Data.Maybe (Maybe(..), isNothing)
+import Data.Monoid (Monoid(..))
+import Data.Ord (Ord(..))
+import Data.String (String)
+-- import GHC.Exts (Int(..))
+-- import GHC.Prim (unsafeCoerce#)
+import GHC.StableName (StableName(..), makeStableName, hashStableName, eqStableName)
+-- import Numeric (showHex)
+import Prelude ((+), error)
+import System.IO (IO)
+import System.IO.Unsafe (unsafePerformIO)
+import Text.Show (Show(..))
+import qualified Control.Monad.Trans.Class as MT
+import qualified Control.Monad.Trans.Reader as MT
+import qualified Control.Monad.Trans.State as MT
+import qualified Control.Monad.Trans.Writer as MT
+import qualified Data.HashMap.Strict as HM
+import qualified Data.HashSet as HS
+
+import Symantic.Typed.Derive
+
+-- * Class 'Letable'
+-- | This class is not for end-users like usual symantic operators,
+-- here 'shareable' and 'ref' are introduced by 'observeSharing'.
+class Letable letName repr where
+  -- | @('ref' isRec letName)@ is a reference to @(letName)@.
+  -- @(isRec)@ is 'True' iif. this 'ref'erence is recursive,
+  -- ie. is reachable within its 'shareable' definition.
+  ref :: Bool -> letName -> repr a
+  ref isRec n = liftDerived (ref isRec n)
+  default ref ::
+    FromDerived (Letable letName) repr =>
+    Bool -> letName -> repr a
+
+  -- | @('shareable' letName x)@ let-binds @(letName)@ to be equal to @(x)@.
+  shareable :: letName -> repr a -> repr a
+  shareable n = liftDerived1 (shareable n)
+  default shareable ::
+    FromDerived1 (Letable letName) repr =>
+    letName -> repr a -> repr a
+
+-- * Class 'MakeLetName'
+class MakeLetName letName where
+  makeLetName :: SharingName -> IO letName
+
+-- ** Type 'ShowLetName'
+-- | Useful on golden unit tests because 'StableName'
+-- change often when changing unrelated source code
+-- or even changing basic GHC or executable flags.
+class ShowLetName (showName::Bool) letName where
+  showLetName :: letName -> String
+-- | Like 'Show'.
+instance Show letName => ShowLetName 'True letName where
+  showLetName = show
+-- | Always return @"<hidden>"@,
+instance ShowLetName 'False letName where
+  showLetName _p = "<hidden>"
+
+-- * Type 'SharingName'
+-- | Note that the observable sharing enabled by 'StableName'
+-- is not perfect as it will not observe all the sharing explicitely done.
+--
+-- Note also that the observed sharing could be different between ghc and ghci.
+data SharingName = forall a. SharingName (StableName a)
+-- | @('makeSharingName' x)@ is like @('makeStableName' x)@ but it also forces
+-- evaluation of @(x)@ to ensure that the 'StableName' is correct first time,
+-- which avoids to produce a tree bigger than needed.
+--
+-- Note that this function uses 'unsafePerformIO' instead of returning in 'IO',
+-- this is apparently required to avoid infinite loops due to unstable 'StableName'
+-- in compiled code, and sometimes also in ghci.
+--
+-- Note that maybe [pseq should be used here](https://gitlab.haskell.org/ghc/ghc/-/issues/2916).
+makeSharingName :: a -> SharingName
+makeSharingName !x = SharingName $ unsafePerformIO $ makeStableName x
+
+instance Eq SharingName where
+  SharingName x == SharingName y = eqStableName x y
+instance Hashable SharingName where
+  hash (SharingName n) = hashStableName n
+  hashWithSalt salt (SharingName n) = hashWithSalt salt n
+{-
+instance Show SharingName where
+  showsPrec _ (SharingName n) = showHex (I# (unsafeCoerce# n))
+-}
+
+-- * Type 'ObserveSharing'
+newtype ObserveSharing letName repr a = ObserveSharing { unObserveSharing ::
+  MT.ReaderT (HashSet SharingName)
+             (MT.State (ObserveSharingState letName))
+             (FinalizeSharing letName repr a) }
+
+-- | Interpreter detecting some (Haskell embedded) @let@ definitions used at
+-- least once and/or recursively, in order to replace them
+-- with the 'shareable' and 'ref' combinators.
+-- See [Type-safe observable sharing in Haskell](https://doi.org/10.1145/1596638.1596653)
+--
+-- Beware not to apply 'observeSharing' more than once on the same term
+-- otherwise some 'shareable' introduced by the first call
+-- would be removed by the second call.
+observeSharing ::
+  Eq letName =>
+  Hashable letName =>
+  Show letName =>
+  ObserveSharing letName repr a ->
+  WithSharing letName repr a
+observeSharing (ObserveSharing m) =
+  let (fs, st) = MT.runReaderT m mempty `MT.runState`
+        ObserveSharingState
+          { oss_refs = HM.empty
+          , oss_recs = HS.empty
+          } in
+  let refs = HS.fromList $
+        (`foldMap` oss_refs st) $ (\(letName, refCount) ->
+          if refCount > 0 then [letName] else []) in
+  --trace (show refs) $
+  MT.runWriter $
+    (`MT.runReaderT` refs) $
+      unFinalizeSharing fs
+
+-- ** Type 'SomeLet'
+data SomeLet repr = forall a. SomeLet (repr a)
+
+-- ** Type 'WithSharing'
+type WithSharing letName repr a =
+  (repr a, HM.HashMap letName (SomeLet repr))
+{-
+-- * Type 'WithSharing'
+data WithSharing letName repr a = WithSharing
+  { lets :: HM.HashMap letName (SomeLet repr)
+  , body :: repr a
+  }
+mapWithSharing ::
+  (forall v. repr v -> repr v) ->
+  WithSharing letName repr a ->
+  WithSharing letName repr a
+mapWithSharing f ws = WithSharing
+  { lets = (\(SomeLet repr) -> SomeLet (f repr)) <$> lets ws
+  , body = f (body ws)
+  }
+-}
+
+-- ** Type 'ObserveSharingState'
+data ObserveSharingState letName = ObserveSharingState
+  { oss_refs :: HashMap SharingName (letName, Int)
+  , oss_recs :: HashSet SharingName
+    -- ^ TODO: unused so far, will it be useful somewhere at a later stage?
+  }
+
+observeSharingNode ::
+  Eq letName =>
+  Hashable letName =>
+  Show letName =>
+  Letable letName repr =>
+  MakeLetName letName =>
+  ObserveSharing letName repr a ->
+  ObserveSharing letName repr a
+observeSharingNode (ObserveSharing m) = ObserveSharing $ do
+  let nodeName = makeSharingName m
+  st <- MT.lift MT.get
+  ((letName, before), preds) <- getCompose $ HM.alterF (\before ->
+    Compose $ case before of
+      Nothing -> do
+        let letName = unsafePerformIO $ makeLetName nodeName
+        return ((letName, before), Just (letName, 0))
+      Just (letName, refCount) -> do
+        return ((letName, before), Just (letName, refCount + 1))
+    ) nodeName (oss_refs st)
+  parentNames <- MT.ask
+  if nodeName `HS.member` parentNames
+  then do
+    MT.lift $ MT.put st
+      { oss_refs = preds
+      , oss_recs = HS.insert nodeName (oss_recs st)
+      }
+    return $ ref True letName
+  else do
+    MT.lift $ MT.put st{ oss_refs = preds }
+    if isNothing before
+      then MT.local (HS.insert nodeName) (shareable letName <$> m)
+      else return $ ref False letName
+
+type instance Derived (ObserveSharing letName repr) = FinalizeSharing letName repr
+instance
+  ( Letable letName repr
+  , MakeLetName letName
+  , Eq letName
+  , Hashable letName
+  , Show letName
+  ) => LiftDerived (ObserveSharing letName repr) where
+  liftDerived = observeSharingNode . ObserveSharing . return
+instance
+  ( Letable letName repr
+  , MakeLetName letName
+  , Eq letName
+  , Hashable letName
+  , Show letName
+  ) => LiftDerived1 (ObserveSharing letName repr) where
+  liftDerived1 f x = observeSharingNode $ ObserveSharing $
+    f <$> unObserveSharing x
+instance
+  ( Letable letName repr
+  , MakeLetName letName
+  , Eq letName
+  , Hashable letName
+  , Show letName
+  ) => LiftDerived2 (ObserveSharing letName repr) where
+  liftDerived2 f x y = observeSharingNode $ ObserveSharing $
+    f <$> unObserveSharing x
+      <*> unObserveSharing y
+instance
+  ( Letable letName repr
+  , MakeLetName letName
+  , Eq letName
+  , Hashable letName
+  , Show letName
+  ) => LiftDerived3 (ObserveSharing letName repr) where
+  liftDerived3 f x y z = observeSharingNode $ ObserveSharing $
+    f <$> unObserveSharing x
+      <*> unObserveSharing y
+      <*> unObserveSharing z
+instance Letable letName (ObserveSharing letName repr) where
+  shareable = error "[BUG]: observeSharing MUST NOT be applied twice"
+  ref = error "[BUG]: observeSharing MUST NOT be applied twice"
+instance Letsable letName (ObserveSharing letName repr) where
+  lets = error "[BUG]: observeSharing MUST NOT be applied twice"
+
+-- * Type 'FinalizeSharing'
+-- | Remove 'shareable' when non-recursive or unused
+-- or replace it by 'ref', moving 'shareable's to the top.
+newtype FinalizeSharing letName repr a = FinalizeSharing { unFinalizeSharing ::
+  MT.ReaderT (HS.HashSet letName)
+    (MT.Writer (LetBindings letName repr))
+      (repr a) }
+
+-- ** Type 'LetBindings'
+type LetBindings letName repr = HM.HashMap letName (SomeLet repr)
+
+type instance Derived (FinalizeSharing _letName repr) = repr
+instance
+  ( Eq letName
+  , Hashable letName
+  ) => LiftDerived (FinalizeSharing letName repr) where
+  liftDerived = FinalizeSharing . pure
+instance
+  ( Eq letName
+  , Hashable letName
+  ) => LiftDerived1 (FinalizeSharing letName repr) where
+  liftDerived1 f x = FinalizeSharing $ f <$> unFinalizeSharing x
+instance
+  ( Eq letName
+  , Hashable letName
+  ) => LiftDerived2 (FinalizeSharing letName repr) where
+  liftDerived2 f x y = FinalizeSharing $
+    f <$> unFinalizeSharing x
+      <*> unFinalizeSharing y
+instance
+  ( Eq letName
+  , Hashable letName
+  ) => LiftDerived3 (FinalizeSharing letName repr) where
+  liftDerived3 f x y z = FinalizeSharing $
+    f <$> unFinalizeSharing x
+      <*> unFinalizeSharing y
+      <*> unFinalizeSharing z
+instance
+  ( Letable letName repr
+  , Eq letName
+  , Hashable letName
+  , Show letName
+  ) => Letable letName (FinalizeSharing letName repr) where
+  shareable name x = FinalizeSharing $ do
+    refs <- MT.ask
+    if name `HS.member` refs
+      -- This 'shareable' is 'ref'erenced, move it into the result,
+      -- to put it in scope even when some 'ref' to it exists outside of 'x'
+      -- (which can happen when a sub-expression is shared),
+      -- and replace it by a 'ref'.
+      then do
+        let (repr, defs) = MT.runWriter $ MT.runReaderT (unFinalizeSharing x) refs
+        MT.lift $ MT.tell $ HM.insert name (SomeLet repr) defs
+        return $ ref False name
+      -- Remove 'shareable'.
+      else
+        unFinalizeSharing x
+
+-- * Class 'Letsable'
+class Letsable letName repr where
+  -- | @('lets' defs x)@ let-binds @(defs)@ in @(x)@.
+  lets :: LetBindings letName repr -> repr a -> repr a
+  lets defs = liftDerived1 (lets ((\(SomeLet val) -> SomeLet (derive val)) <$> defs))
+  default lets ::
+    Derivable repr =>
+    FromDerived1 (Letsable letName) repr =>
+    LetBindings letName repr -> repr a -> repr a
+{-
+-- | Not used but can be written nonetheless.
+instance
+  ( Letsable letName repr
+  , Eq letName
+  , Hashable letName
+  , Show letName
+  ) => Letsable letName (FinalizeSharing letName repr) where
+  lets defs x = FinalizeSharing $ do
+    ds <- traverse (\(SomeLet v) -> do
+      r <- unFinalizeSharing v
+      return (SomeLet r)
+      ) defs
+    MT.lift $ MT.tell ds
+    unFinalizeSharing x
+-}
diff --git a/src/Symantic/Typed/Optimize.hs b/src/Symantic/Typed/Optimize.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Typed/Optimize.hs
@@ -0,0 +1,41 @@
+module Symantic.Typed.Optimize where
+
+import Data.Bool (Bool)
+import qualified Data.Function as Fun
+
+import Symantic.Typed.Lang
+import Symantic.Typed.Data
+
+-- | Beta-reduce the left-most outer-most lambda abstraction (aka. normal-order reduction),
+-- but to avoid duplication of work, only those manually marked
+-- as using their variable at most once.
+--
+-- DOC: Demonstrating Lambda Calculus Reduction, Peter Sestoft, 2001,
+-- https://www.itu.dk/people/sestoft/papers/sestoft-lamreduce.pdf
+normalOrderReduction :: forall repr a.
+  Abstractable repr =>
+  IfThenElseable repr =>
+  SomeData repr a -> SomeData repr a
+normalOrderReduction = nor
+  where
+  -- | normal-order reduction
+  nor :: SomeData repr b -> SomeData repr b
+  nor = \case
+    Data (Lam f) -> lam (nor Fun.. f)
+    Data (Lam1 f) -> lam1 (nor Fun.. f)
+    Data (x :@ y) -> case whnf x of
+      Data (Lam1 f) -> nor (f y)
+      x' -> nor x' .@ nor y
+    Data (IfThenElse test ok ko) ->
+      case nor test of
+        Data (Constant b :: Data (Constantable Bool) repr Bool) ->
+          if b then nor ok else nor ko
+        t -> ifThenElse (nor t) (nor ok) (nor ko)
+    x -> x
+  -- | weak-head normal-form
+  whnf :: SomeData repr b -> SomeData repr b
+  whnf = \case
+    Data (x :@ y) -> case whnf x of
+      Data (Lam1 f) -> whnf (f y)
+      x' -> x' .@ y
+    x -> x
diff --git a/src/Symantic/Typed/Reify.hs b/src/Symantic/Typed/Reify.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Typed/Reify.hs
@@ -0,0 +1,68 @@
+{-# LANGUAGE TemplateHaskell #-}
+{-# OPTIONS_GHC -Wno-incomplete-patterns #-} -- For reifyTH
+-- | Reify an Haskell value using type-directed normalisation-by-evaluation (NBE).
+module Symantic.Typed.Reify where
+
+import Control.Monad (Monad(..))
+import qualified Data.Function as Fun
+import qualified Language.Haskell.TH as TH
+
+import Symantic.Typed.Lang (Abstractable(..))
+
+-- | 'ReifyReflect' witnesses the duality between @meta@ and @(repr a)@.
+--  It indicates which type variables in @a@ are not to be instantiated
+--  with the arrow type, and instantiates them to @(repr _)@ in @meta@.
+--  This is directly taken from: http://okmij.org/ftp/tagless-final/course/TDPE.hs
+--
+-- * @meta@ instantiates polymorphic types of the original Haskell expression
+--   with @(repr _)@ types, according to how 'ReifyReflect' is constructed
+--   using 'base' and @('-->')@. This is obviously not possible
+--   if the orignal expression uses monomorphic types (like 'Int'),
+--   but remains possible with constrained polymorphic types (like @(Num i => i)@),
+--   because @(i)@ can still be inferred to @(repr _)@,
+--   whereas the finally chosen @(repr)@
+--   (eg. 'E', or 'Identity', or 'TH.CodeQ', or ...)
+--   can have a 'Num' instance.
+-- * @(repr a)@ is the symantic type as it would have been,
+--   had the expression been written with explicit 'lam's
+--   instead of bare haskell functions.
+-- DOC: http://okmij.org/ftp/tagless-final/cookbook.html#TDPE
+-- DOC: http://okmij.org/ftp/tagless-final/NBE.html
+-- DOC: https://www.dicosmo.org/Articles/2004-BalatDiCosmoFiore-Popl.pdf
+data ReifyReflect repr meta a = ReifyReflect
+  { -- | 'reflect' converts from a *represented* Haskell term of type @a@
+    -- to an object *representing* that value of type @a@.
+    reify   :: meta -> repr a
+    -- | 'reflect' converts back an object *representing* a value of type @a@,
+    -- to the *represented* Haskell term of type @a@.
+  , reflect :: repr a -> meta
+  }
+
+-- | The base of induction : placeholder for a type which is not the arrow type.
+base :: ReifyReflect repr (repr a) a
+base = ReifyReflect{reify = Fun.id, reflect = Fun.id}
+
+-- | The inductive case : the arrow type.
+-- 'reify' and 'reflect' are built together inductively.
+infixr 8 -->
+(-->) :: Abstractable repr =>
+         ReifyReflect repr m1 o1 -> ReifyReflect repr m2 o2 ->
+         ReifyReflect repr (m1 -> m2) (o1 -> o2)
+r1 --> r2 = ReifyReflect
+  { reify   = \meta -> lam (reify r2 Fun.. meta Fun.. reflect r1)
+  , reflect = \repr -> reflect r2 Fun.. (.@) repr Fun.. reify r1
+  }
+
+-- * Using TemplateHaskell to fully auto-generate 'ReifyReflect'
+
+-- | @$(reifyTH 'Foo.bar)@ calls 'reify' on 'Foo.bar'
+-- with an 'ReifyReflect' generated from the infered type of 'Foo.bar'.
+reifyTH :: TH.Name -> TH.Q TH.Exp
+reifyTH name = do
+  info <- TH.reify name
+  case info of
+    TH.VarI n (TH.ForallT _vs _ctx ty) _dec ->
+      [| reify $(genReifyReflect ty) $(return (TH.VarE n)) |]
+    where
+    genReifyReflect (TH.AppT (TH.AppT TH.ArrowT a) b) = [| $(genReifyReflect a) --> $(genReifyReflect b) |]
+    genReifyReflect TH.VarT{} = [| base |]
diff --git a/src/Symantic/Typed/View.hs b/src/Symantic/Typed/View.hs
new file mode 100644
--- /dev/null
+++ b/src/Symantic/Typed/View.hs
@@ -0,0 +1,116 @@
+{-# LANGUAGE FlexibleContexts #-}
+{-# LANGUAGE FlexibleInstances #-}
+{-# LANGUAGE GADTs #-}
+{-# LANGUAGE ImplicitPrelude #-}
+{-# LANGUAGE LambdaCase #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE OverloadedStrings #-}
+{-# LANGUAGE PatternSynonyms #-}
+{-# LANGUAGE ScopedTypeVariables #-}
+{-# LANGUAGE TypeApplications #-}
+{-# LANGUAGE TypeFamilies #-}
+{-# LANGUAGE UndecidableInstances #-} -- For Show (SomeData a)
+module Symantic.Typed.View where
+
+import Data.Int (Int)
+import Data.String
+import Text.Show
+import qualified Data.Function as Fun
+import qualified Prelude
+
+import Symantic.Typed.Fixity
+import Symantic.Typed.Lang
+import Symantic.Typed.Data
+import Symantic.Typed.Derive
+
+data View a where
+  View :: (ViewEnv -> ShowS) -> View a
+  ViewUnifix :: Unifix -> String -> String -> View (a -> b)
+  ViewInfix :: Infix -> String -> String -> View (a -> b -> c)
+  ViewApp :: View (b -> a) -> View b -> View a
+
+runView :: View a -> ViewEnv -> ShowS
+runView (View v) env = v env
+runView (ViewInfix _op name _infixName) _env = showString name
+runView (ViewUnifix _op name _unifixName) _env = showString name
+runView (ViewApp f x) env =
+  pairView env op Fun.$
+    runView f env{viewEnv_op = (op, SideL) } Fun..
+    showString " " Fun..
+    runView x env{viewEnv_op = (op, SideR) }
+  where op = infixN 10
+
+-- | Unusual, but enables to leverage default definition of methods.
+type instance Derived View = View
+instance LiftDerived View where
+  liftDerived = Fun.id
+
+instance IsString (View a) where
+  fromString s = View Fun.$ \_env -> showString s
+instance Show (View a) where
+  showsPrec p = (`runView` ViewEnv
+    { viewEnv_op = (infixN p, SideL)
+    , viewEnv_pair = pairParen
+    , viewEnv_lamDepth = 1
+    })
+instance Show (SomeData View a) where
+  showsPrec p (SomeData x) = showsPrec p (derive x :: View a)
+
+data ViewEnv
+  = ViewEnv
+  { viewEnv_op :: (Infix, Side)
+  , viewEnv_pair :: Pair
+  , viewEnv_lamDepth :: Int
+  }
+
+pairView :: ViewEnv -> Infix -> ShowS -> ShowS
+pairView env op s =
+  if isPairNeeded (viewEnv_op env) op
+  then showString o Fun.. s Fun.. showString c
+  else s
+  where (o,c) = viewEnv_pair env
+
+instance Abstractable View where
+  var = Fun.id
+  lam f = viewLam "x" f
+  lam1 f = viewLam "u" f
+  ViewInfix op _name infixName .@ ViewApp x y = View Fun.$ \env ->
+    pairView env op Fun.$
+      runView x env{viewEnv_op=(op, SideL)} Fun..
+      showString " " Fun.. showString infixName Fun.. showString " " Fun..
+      runView y env{viewEnv_op=(op, SideR)}
+  ViewInfix op name _infixName .@ x = View Fun.$ \env ->
+    showParen Prelude.True Fun.$
+      runView x env{viewEnv_op=(op, SideL)} Fun..
+      showString " " Fun.. showString name
+  f .@ x = ViewApp f x
+viewLam :: String -> (View a -> View b) -> View (a -> b)
+viewLam varPrefix f = View Fun.$ \env ->
+  pairView env op Fun.$
+    let x = showString varPrefix Fun..
+            showsPrec 0 (viewEnv_lamDepth env) in
+    -- showString "Lam1 (" .
+    showString "\\" Fun.. x Fun.. showString " -> " Fun..
+    runView (f (View (\_env -> x))) env
+      { viewEnv_op = (op, SideL)
+      , viewEnv_lamDepth = Prelude.succ (viewEnv_lamDepth env)
+      }
+    -- . showString ")"
+  where
+  op = infixN 0
+instance Anythingable View
+instance Bottomable View where
+  bottom = "<hidden>"
+instance Show c => Constantable c View where
+  constant c = View Fun.$ \_env -> shows c
+instance Eitherable View where
+  left = "Left"
+  right = "Right"
+instance Equalable View where
+  equal = ViewInfix (infixN 4) "(==)" "=="
+instance Listable View where
+  cons = ViewInfix (infixR 5) "(:)" ":"
+  nil = "[]"
+instance Maybeable View where
+  nothing = "Nothing"
+  just = "Just"
diff --git a/stack.yaml b/stack.yaml
deleted file mode 100644
--- a/stack.yaml
+++ /dev/null
@@ -1,1 +0,0 @@
-resolver: lts-15.4
diff --git a/stack.yaml.lock b/stack.yaml.lock
deleted file mode 100644
--- a/stack.yaml.lock
+++ /dev/null
@@ -1,12 +0,0 @@
-# This file was autogenerated by Stack.
-# You should not edit this file by hand.
-# For more information, please see the documentation at:
-#   https://docs.haskellstack.org/en/stable/lock_files
-
-packages: []
-snapshots:
-- completed:
-    size: 491163
-    url: https://raw.githubusercontent.com/commercialhaskell/stackage-snapshots/master/lts/15/4.yaml
-    sha256: bc60043a06b58902b533baa80fb566c0ec495c41e428bc0f8c1e8c15b2a4c468
-  original: lts-15.4
diff --git a/symantic-base.cabal b/symantic-base.cabal
--- a/symantic-base.cabal
+++ b/symantic-base.cabal
@@ -1,43 +1,93 @@
+cabal-version: 3.0
+license: AGPL-3.0-or-later
 name: symantic-base
 -- PVP:  +-+------- breaking API changes
 --       | | +----- non-breaking API additions
 --       | | | +--- code changes with no API change
-version: 0.0.2.20200708
+version: 0.1.0.20210703
 category: Data Structures
-synopsis: Basic symantics for writing Embedded Domain-Specific Languages (EDSL).
-description: A collection of basic tagless-final combinators.
-extra-doc-files:
-license: GPL-3
-license-file: COPYING
+synopsis: Commonly useful symantics for Embedded Domain-Specific Languages (EDSL)
+description:
+  This is a work-in-progress collection of basic tagless-final combinators,
+  along with some advanced utilities to exploit them.
+
+  * @Symantic.Typed@
+    is for combinators indexed by a single type.
+  * @Symantic.Dityped@
+    is for combinators indexed by an extensible function type,
+    used for typed formatting, enabling type safe dual interpreters à la printf and scanf.
+    Inspired by Oleg Kiselyov's [PrintScanF.hs](http://okmij.org/ftp/tagless-final/course/PrintScanF.hs).
+    For an example, see [symantic-http](https://hackage.haskell.org/package/symantic-http).
+  * @Symantic.{Typed,Dityped}.Lang@
+    gather commonly used tagless-final combinators
+    (the syntax part of symantics).
+  * @Symantic.Typed.Data@ is an interpreter enabling to pattern-match on combinators,
+    while keeping their extensibility.
+  * @Symantic.{Typed,Dityped}.Derive@
+    enable to give a default value to combinators which avoids boilerplate code
+    when implementing combinators for an interpreter is factorizable.
+  * @Symantic.Typed.ObserveSharing@
+    enables to observe Haskell @let@ definitions,
+    turning infinite values into finite ones,
+    which is useful to inspect and optimize recursive grammars for example.
+    Inspired by Andy Gill's [Type-safe observable sharing in Haskell](https://doi.org/10.1145/1596638.1596653).
+    For an example, see [symantic-parser](https://hackage.haskell.org/package/symantic-parser).
+  * @Symantic.Typed.Reify@
+    enables the lifting to any interpreter
+    of any Haskell functions taking as arguments
+    only polymorphic types (possibly constrained)
+    or functions using such types.
+    Inspired by Oleg Kiselyov's [TDPE.hs](http://okmij.org/ftp/tagless-final/course/TDPE.hs).
+  * @Symantic.Typed.View@
+    is an interpreter enabling to turn combinators into a human-readable string.
+  * @Symantic.Dityped.ADT@
+    enables to define formats à la printf-scanf
+    using data-constructors instead of @Either@s of tuples.
+    For an example, see [symantic-atom](https://hackage.haskell.org/package/symantic-atom).
+  * @Symantic.Dityped.CurryN@
+    gather utilities for currying or uncurrying tuples
+    of size greater or equal to 2.
+  * @Symantic.Typed.Fixity@
+    gathers utilities for parsing or viewing
+    infix, prefix and postfix combinators.
 stability: experimental
-author:      Julien Moutinho <julm+symantic-base@sourcephile.fr>
-maintainer:  Julien Moutinho <julm+symantic-base@sourcephile.fr>
-bug-reports: Julien Moutinho <julm+symantic-base@sourcephile.fr>
--- homepage:
+author: Julien Moutinho <julm+symantic-base@sourcephile.fr>
+maintainer: Julien Moutinho <julm+symantic-base@sourcephile.fr>
+bug-reports: https://mails.sourcephile.fr/inbox/symantic-base
+copyright: Julien Moutinho <julm+symantic-base@sourcephile.fr>
 
 build-type: Simple
-cabal-version: 1.24
-tested-with: GHC==8.8.3
+tested-with: GHC==8.10.4
 extra-source-files:
-  stack.yaml
-  stack.yaml.lock
+  cabal.project
+  default.nix
+  .envrc
+  flake.lock
+  flake.nix
+  Makefile
 extra-tmp-files:
 
-Source-Repository head
+source-repository head
+  type: git
   location: git://git.sourcephile.fr/haskell/symantic-base
-  type:     git
 
-Library
+library
   hs-source-dirs: src
   exposed-modules:
-    Symantic.Base
-    Symantic.Base.ADT
-    Symantic.Base.Algebrable
-    Symantic.Base.Composable
-    Symantic.Base.CurryN
-    Symantic.Base.Fixity
-    Symantic.Base.Permutable
-    Symantic.Base.Routable
+    Symantic.Dityped
+    Symantic.Dityped.ADT
+    Symantic.Dityped.CurryN
+    Symantic.Dityped.Derive
+    Symantic.Dityped.Lang
+    Symantic.Typed
+    Symantic.Typed.Data
+    Symantic.Typed.Derive
+    Symantic.Typed.Fixity
+    Symantic.Typed.Lang
+    Symantic.Typed.ObserveSharing
+    Symantic.Typed.Optimize
+    Symantic.Typed.Reify
+    Symantic.Typed.View
   default-language: Haskell2010
   default-extensions:
     DefaultSignatures
@@ -58,6 +108,12 @@
     -Wall
     -Wincomplete-uni-patterns
     -Wincomplete-record-updates
-    -- -fhide-source-paths
+    -Wpartial-fields
+    -fprint-potential-instances
   build-depends:
-      base >= 4.10 && < 5
+      base >= 4.10 && < 5,
+      containers,
+      hashable,
+      template-haskell,
+      transformers,
+      unordered-containers