Pro-functor member/traversal (part 8 of optics).

documentation/bookmark/biological_programming.md

@@ -1,5 +1,6 @@
 # Reference
 
+0. [A motor for cell-free metabolism: Researchers have developed the first cell-free system in which genetic information and metabolism work together](https://www.mpg.de/22163540/0703-terr-a-motor-for-cell-free-metabolism-153410-x)
 0. [New tools for programming biology](https://centuryofbio.com/p/new-tools-for-programming-biology)
 0. [Open Genes: Structured data on human genes associated with aging: functions, evolution, the influence of gene activity on lifespan, age-related changes in gene expression, associations of allelic variants of genes with longevity and age-related phenotype.](https://open-genes.com/genes)
 0. [Axial Discovery - Cell reprogramming](https://discoverybio.substack.com/p/axial-discovery-cell-reprogramming)

stdlib/source/library/lux.lux

@@ -1729,6 +1729,7 @@
                 _
                 (failure ..wrong_syntax))))
 
+(the' .public per Macro ..left_associative)
 (the' .public all Macro ..right_associative)
 
 ... (every (Monad m)

stdlib/source/library/lux/abstract/functor/pro.lux

@@ -5,33 +5,44 @@
  [library
   [lux (.except)]])
 
-(every .public (Functor it)
+(every .public (Functor =>)
   (Interface
    (is (for_any (_ cause effect
                    cause' effect')
          (-> (<- cause cause') (-> effect effect')
-             (-> (it cause effect)
-                 (it cause' effect'))))
+             (-> (=> cause effect)
+                 (=> cause' effect'))))
        each)))
 
-(every .public (Cartesian it)
+(every .public (Cartesian =>)
   (Interface
-   (is (for_any (_ cause effect extra)
-         (-> (it cause effect)
-             (it (And cause extra) (And effect extra))))
+   (is (for_any (_ head head' tail)
+         (-> (=> head head')
+             (=> (And head tail) (And head' tail))))
        in_left)
-   (is (for_any (_ cause effect extra)
-         (-> (it cause effect)
-             (it (And extra cause) (And extra effect))))
+   (is (for_any (_ tail tail' head)
+         (-> (=> tail tail')
+             (=> (And head tail) (And head tail'))))
        in_right)))
 
-(every .public (Co_Cartesian it)
+(every .public (Co_Cartesian =>)
   (Interface
-   (is (for_any (_ cause effect extra)
-         (-> (it cause effect)
-             (it (Or cause extra) (Or effect extra))))
+   (is (for_any (_ head head' tail)
+         (-> (=> head head')
+             (=> (Or head tail) (Or head' tail))))
        when_left)
-   (is (for_any (_ cause effect extra)
-         (-> (it cause effect)
-             (it (Or extra cause) (Or extra effect))))
+   (is (for_any (_ tail tail' head)
+         (-> (=> tail tail')
+             (=> (Or head tail) (Or head tail'))))
        when_right)))
+
+(every .public (Monoidal =>)
+  (Interface
+   (is (for_any (_ head head'
+                   tail tail')
+         (-> (=> head head')
+             (=> tail tail')
+             (=> [head tail] [head' tail'])))
+       in_parallel)
+   (is (=> Any Any)
+       empty)))

stdlib/source/library/lux/aspect.lux

@@ -1,105 +1,11 @@
 ... This Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0.
 ... If a copy of the MPL was not distributed with this file, You can obtain one at https://mozilla.org/MPL/2.0/.
 
+... [Profunctor Optics: Modular Data Accessors](https://arxiv.org/abs/1703.10857)
 (.using
  [library
-  [lux (.except all with)
-   [abstract
-    [functor (.only Functor)
-     ["[0]" pro]]]
-   [type
-    ["[0]" nominal]]
-   ["[0]" function]
-   [data
-    ["[0]" product]]]])
+  [lux (.except)]])
 
-(every .public (Aspect it context context' aspect aspect')
-  (-> (it aspect aspect')
-      (it context context')))
-
-... TODO: Make this nominal type unnecessary.
-(nominal.every .public (Membership one all)
-  (Variant
-   {#All all}
-   {#One one (Membership one (-> one all))})
-
-  (the outer
-    (for_any (_ one all)
-      (-> (Membership one all)
-          (Or all (And one (Membership one (-> one all))))))
-    (|>> nominal.as))
-
-  (the inner
-    (for_any (_ one all)
-      (-> (Or all (And one (Membership one (-> one all))))
-          (Membership one all)))
-    (|>> nominal.of))
-
-  (the .public membership_functor
-    (for_any (_ one)
-      (Functor (Membership one)))
-    (implementation
-     (the (each value it)
-       (nominal.of
-        (.when (nominal.as it)
-          {#All all}
-          {#All (value all)}
-
-          {#One one next}
-          {#One one (each (function (_ before)
-                            (|>> before
-                                 value))
-                          next)}))
-       )))
-
-  (every .public (Apply context)
-    (Interface
-     (is (Functor context)
-         functor)
-     (is (for_any (_ it)
-           (-> it
-               (context it)))
-         pure)
-     (is (for_any (_ it it')
-           (-> (context (-> it it'))
-               (-> (context it)
-                   (context it'))))
-         with)))
-
-  (the .public membership_apply
-    (for_any (_ one)
-      (Apply (Membership one)))
-    (implementation
-     (the functor ..membership_functor)
-     (the pure (|>> {#All} nominal.of))
-     (the (with internal_effect internal_cause)
-       (.when (nominal.as internal_effect)
-         {#All internal_effect}
-         (by ..membership_functor each internal_effect internal_cause)
-
-         {#One one internal_effect}
-         (nominal.of
-          {#One one (with (by ..membership_functor each function.flipped internal_effect)
-                      internal_cause)})))))
-
-  (the .public (one it)
-    (for_any (_ it)
-      (-> it
-          (Membership it it)))
-    (nominal.of {#One it (nominal.of {#All (|>>)})}))
-
-  (the .public (all it)
-    (for_any (_ one all)
-      (-> (Membership one all)
-          all))
-    (.when (nominal.as it)
-      {#All it}
-      it
-
-      {#One one next}
-      ((all next) one)))
-
-  (every .public (Member all one)
-    (-> all
-        (Membership one all)))
-  )
+(every .public (Aspect => context context' aspect aspect')
+  (-> (=> aspect aspect')
+      (=> context context')))

stdlib/source/library/lux/aspect/case.lux

@@ -1,6 +1,7 @@
 ... This Source Code Form is subject to the terms of the Mozilla Public License, v. 2.0.
 ... If a copy of the MPL was not distributed with this file, You can obtain one at https://mozilla.org/MPL/2.0/.
 
+... [Profunctor Optics: Modular Data Accessors](https://arxiv.org/abs/1703.10857)
 (.using
  [library
   [lux (.except macro
@@ -78,9 +79,9 @@
   )
 
 (every .public (Aspect context context' case case')
-  (for_any (_ it)
-    (-> [(pro.Functor it) (pro.Co_Cartesian it)]
-        (//.Aspect it context context' case case'))))
+  (for_any (_ =>)
+    (-> [(pro.Functor =>) (pro.Co_Cartesian =>)]
+        (//.Aspect => context context' case case'))))
 
 (the functor
   (for_any (_ case case')
@@ -117,12 +118,12 @@
       (|>> when_right
            (each /#when (sum.either function.identity /#some)))))
 
-(the .public (of_aspect it)
+(the .public (of_aspect =>)
   (for_any (_ context context' case case')
     (-> (Aspect context context' case case' (for_any (_ context context')
                                               (Case' context context'
                                                      case case')))
         (Case' context context' case case')))
-  (it [..functor ..co_cartesian]
+  (=> [..functor ..co_cartesian]
       [#when sum.right
        #some function.identity]))