Support undoing compound functions

1 files changed, 74 insertions, 20 deletions

diff --git a/src/r.bqn b/src/r.bqn
index dc727069..bc17f5d5 100644
--- a/src/r.bqn
+++ b/src/r.bqn
@@ -557,9 +557,29 @@ ProgressiveIndexOf â†� {ð�•¨âŠ�â—‹((≠∾2Ë™)⥊·â‰�˘⟜OccurrenceCountð�•¨âŠ
 � � FirstCell      ⊘ (ToArray⊸(SelSub _onAxes_ 1))
 ⊑ ↩ (0⊑⥊)          ⊘ Pick
 ◶ ↩ {�((���)⊑�){�}�}  # Same definition, new Pick
+� � {Inverse �}
+
+_repeat_�{
+  n����
+  l�u�0
+  {"�: Repetition numbers in � must be integers"!Int�⋄l↩l⌊�⋄u↩u⌈�}⚇0 n
+  a��⋄_p�{�∘⊣`⟨a⟩∾↕0+�}
+  pos�(�� ⊢)_p u
+  neg�(���⊢)_p-l
+  (|⊑<⟜0⊑pos‿neg˙)⚇0 n
+}
+
+ReshapeT � ⟨∘,⌊,⌽,↑⟩⊑∘�<
+
+� ↩ _repeat_
+⥊ ↩ Deshape        ⊘ Reshape
+⌾ � _under_
+⊒ � OccurrenceCount⊘ ProgressiveIndexOf
+� � ∊⊸/            ⊘ Find
 
 IA � "�: Inverse failed"⊸!
 IX � "�: Inverse does not exist"⊸!
+INF� "�: Inverse not found"!0˙
 _invChk_ � {i����⋄IX �≡��i⋄i}
 GroupIndsInv � {
   IA 1==�
@@ -575,7 +595,11 @@ GroupInv � {
   IA ∧´Nat⌜�
   (⊔�) �⊸�○∾ �
 }
-inverse � {(⊑(0��)�<) ⊑ ((1��)∾⟨"�: Inverse not found"!0˜⟩)˜} � (2∾˜2÷˜≠)⊸⥊ ⟨
+_lookup_ � {
+  s � 2×↕(≠�)÷2
+  (⊑(s��)�<) ⊑ (((1+s)��)∾⟨�⟩)˙
+}
+PrimInverse � INF _lookup_ ⟨
   +, +⊘(-˜)
   -, -
   ×, ⊢⊘(÷˜)
@@ -598,23 +622,53 @@ inverse � {(⊑(0��)�<) ⊑ ((1��)∾⟨"�: Inverse not found"!0
   /, {IA 1==�⋄IA∧´Nat⌜�⋄IX(∧´¯1⊸↓≤1⊸↓)�⋄GroupLen�}⊘(IA∘0)
   ⊔, GroupIndsInv ⊘ GroupInv
 ⟩
-� � {Inverse �}
-
-_repeat_�{
-  n����
-  l�u�0
-  {"�: Repetition numbers in � must be integers"!Int�⋄l↩l⌊�⋄u↩u⌈�}⚇0 n
-  a��⋄_p�{�∘⊣`⟨a⟩∾↕0+�}
-  pos�(�� ⊢)_p u
-  neg�(���⊢)_p-l
-  (|⊑<⟜0⊑pos‿neg˙)⚇0 n
-}
-
-ReshapeT � ⟨∘,⌊,⌽,↑⟩⊑∘�<
-
-� ↩ _repeat_
-⥊ ↩ Deshape        ⊘ Reshape
 ⌜ ↩ {��⌜○ToArray�}
-⌾ � _under_
-⊒ � OccurrenceCount⊘ ProgressiveIndexOf
-� � ∊⊸/            ⊘ Find
+_inv_ � {�⋄���}
+AtopInverse � {(��)⊘(�⟜�)}○{Inverse�}
+Mod1Inverse � INF˙ _lookup_ ⟨
+  ˜, INF _lookup_ ⟨
+    +, ÷⟜2⊘(-˜)
+    -, IA∘0⊘+
+    ×, √⊘(÷˜)
+    ÷, IA∘0⊘×
+    ⋆, IA∘0⊘√
+    √, IA∘0⊘(÷Log)
+    ∧, √⊘(÷˜)
+    ∨, (¬√∘¬)⊘(-˜÷1-⊣)
+    ¬, IA∘0⊘(+-1˙)
+  ⟩
+  ¨, {��¨       ⊣·IA 0<≡∘⊢}
+  ⌜, {��⌜⊘(IA∘0)⊣·IA 0<≡∘⊢}
+  ˘, {��˘       ⊣·IA 0<=∘⊢}
+  `, {(�∾¯1⊸↓��¨1⊸↓)�(1<≠)⊘(IA∘0)}
+⟩ {
+  0⊸⊑ {��}⟜� 1⊸⊑
+}
+IsConstant � (3≤Type)◶⟨1 ⋄ 4‿˙ ≡ 0‿¯1�Decompose⟩
+Mod2Inverse � INF˙ _lookup_ ⟨
+  _inv_, {�⊸⊢�}
+  ∘, AtopInverse
+  ○, {Fi���⋄�� Fi⊘(�⊸Fi)}
+  ⌾, {��⌾�}  # Need to verify for computation Under
+  �, Int∘⊢◶⟨IA∘0˙,{��(-�)}⟩
+  ⊘, {(��)⊘(��)}
+  ⊸, IsConstant∘⊣ ⊣◶{INF⊘�}‿⊢ {�⊸(��)}
+  ⟜, IsConstant∘⊢◶⟨INF˙,{(��˜�⊢)⊘(IA∘0)}⟩
+⟩ {
+  0‿2⊸� {�´�}⟜� 1⊸⊑
+}
+TrainInverse � {
+  f‿g‿h��
+  K�¬IsConstant⊸∧⟜((⊑⟨⊢⟩)⊸=)
+  f K◶⟨{�G�⊢},K˜◶⟨{�G˜�⊢},INF˙⟩⟩ h
+}
+FuncInverse � (⊑ ⊣◶⟨
+  PrimInverse∘⊑⊢                         # 0 primitive
+  ("Cannot currently invert blocks"!0Ë™)Ë™ # 1 block
+  AtopInverse´⊢                          # 2-train
+  TrainInverse                           # 3-train
+  Mod1Inverse                            # 4 1-modifier
+  Mod2Inverse                            # 5 2-modifier
+⟩ 1⊸↓) Decompose
+Inverse � Type◶(3‿1‿2/{⊢⊣�IX∘≡⊢}‿FuncInverse‿("Cannot invert modifier"!0˙))
+� ↩ {� ≠◶⊢‿{�_inv_�} Inverse �}