Merge pull request #55 from razetime/master

Simple help pages for Primitive Symbols 

63 files changed, 1631 insertions, 0 deletions

diff --git a/help/abs_modulus.md b/help/abs_modulus.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/abs_modulus.html).*
+
+# Pipe (`|`)
+    
+## `| 𝕩`: Absolute Value  
+    
+Absolute Value of `𝕩`.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          | ¯2
+
+          | 1‿3‿¯4‿3
+
+    
+    
+## `𝕨 | 𝕩`: Modulus
+    
+Remainder of `𝕩` divided by `𝕨`.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 | 3
+
+          2 | 3‿4‿5
+
+    
diff --git a/help/after_bindright.md b/help/after_bindright.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/after_bindright.html).*
+
+# Left Multimap (`⟜`)
+    
+## `𝔽⟜𝕘 𝕩`: Bind 
+    
+Supply `𝕘` as a right argument to `𝔽` (`𝕩 𝔽 𝕘`).
+    
+## `𝕘` must be a value, `F` must be dyadic.
+    
+           -⟜3 9
+
+           - 3 9
+
+           9 - 3
+
+    
+    
+## `𝔽⟜𝔾 𝕩`: After
+    
+Apply `𝔾` to `𝕩`, and supply it as a right argument to `𝔽` (`𝕩 𝔽 (𝔾 𝕩)`). 
+    
+`𝔽` must be dyadic, `𝔾` must be monadic.
+    
+           ×⟜- 9
+
+           × - 9
+
+           9 × (- 9)
+
+    
+    
+## `𝕨 𝔽⟜𝔾 𝕩`: Dyadic After
+    
+Apply `𝔾` to `𝕩`, and supply it as a right argument to `𝔽` (`𝕨 𝔽 (𝔾 𝕩)`). 
+    
+`𝔽` must be dyadic, `𝔾` must be monadic.
+    
+           2 ×⟜- 1
+
+           2 × (- 1)
+
+    
diff --git a/help/assert_assertwithmsg.md b/help/assert_assertwithmsg.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/assert_assertwithmsg.html).*
+
+# Exclamation Mark (`!`)
+    
+## `! 𝕩`: Assert
+    
+Throw an error if `𝕩` is not 1.
+    
+           ! 1
+
+           ! 2
+
+           ! "hello"
+
+
+    
+    
+## `𝕨 ! 𝕩`: Dyad
+    
+Throw an error with message `𝕨` if `𝕩` is not 1.
+    
+           "hi" ! 1
+
+           "two" ! 2
+
+           "hello error" ! "hello"
+
+
+    
diff --git a/help/atop.md b/help/atop.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/atop.html).*
+
+# Ring Operator (`∘`)
+    
+## `𝔽∘𝔾 𝕩`: Atop
+    
+Apply `𝔾` to `𝕩`, then apply `𝔽` (`𝔽 𝔾 𝕩`).
+    
+`𝔽` and `𝔾` must be monadic.
+    
+           -∘- 5
+
+           - - 5
+
+    
+    
+## `𝕨 𝔽∘𝔾 𝕩`: Dyadic Atop
+    
+Apply `𝔾` to `𝕨` and `𝕩`, then apply `𝔽` (`𝔽 (𝕨 𝔾 𝕩)`).
+    
+#`𝔽` must be monadic, and `𝔾` must be dyadic.
+    
+           1 -∘+ 2
+
+           1 - + 2
+
+           - 1 + 2
+
+    
diff --git a/help/before_bindleft.md b/help/before_bindleft.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/before_bindleft.html).*
+
+# Multimap (`⊸`)
+    
+## `𝕗⊸𝔾 𝕩`: Bind Left
+    
+Supply `𝕗` as a left argument to `𝔾` (`𝕗 𝔾 𝕩`).
+    
+## `𝕗` must be a value, `𝔾` must be dyadic.
+    
+           3⊸- 9
+
+           3 - 9
+
+    
+    
+## `𝔽⊸𝔾 𝕩`: Before
+    
+Apply `𝔽` to `𝕩`, and supply it as a left argument to `𝔾` (`(𝔽 𝕩) 𝔾 𝕩`). 
+    
+`𝔽` must be monadic, `𝔾` must be dyadic.
+    
+           -⊸+ 9
+
+           - + 9
+
+           (- 9) + 9
+
+    
+    
+## `𝕨 𝔽⊸𝔾 𝕩`: Dyadic Before
+    
+Apply `𝔽` to `𝕨`, and supply it as a left argument to `𝔾` (`(𝔽 𝕨) 𝔾 𝕩`).
+    
+`𝔽` must be monadic, `𝔾` must be dyadic.
+    
+           2 -⊸+ 1
+
+           2 - + 1
+
+           (- 2) + 1
+
+    
diff --git a/help/catch.md b/help/catch.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/catch.html).*
+
+# Circled Triangle Down (`⎊`)
+    
+## `𝔽⎊𝔾 𝕩`, `𝕨 𝔽⎊𝔾 𝕩`: Catch
+    
+Apply `𝔽` to the arguments. 
+    
+If an error happens when `𝔽` is applied, cancel its execution, apply `𝔾` to the arguments and return the results. 
+    
+Otherwise, return the results of `𝔽`.
+    
+           ∾⎊{"error occurred with argument: "∾•Fmt 𝕩} 1
+
+           ∾⎊{"error occurred with argument: "∾•Fmt 𝕩} ⟨⟨1,2⟩, ⟨3,4⟩⟩
+
+    
diff --git a/help/ceiling_maximum.md b/help/ceiling_maximum.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/ceiling_maximum.html).*
+
+# Left Ceiling (`⌈`)
+    
+## `⌈ 𝕩`: Ceiling  
+    
+Round `𝕩` up.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          ⌈ 1.2‿π‿3‿7.89
+
+    
+    
+## `𝕨 ⌈ 𝕩`: Maximum
+    
+Maximum of `𝕨` and `𝕩`.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 ⌈ 2
+
+          2‿3 ⌈ 4‿2
+
+    
diff --git a/help/cells.md b/help/cells.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/cells.html).*
+
+# Breve (`˘`)
+    
+## `𝔽˘ 𝕩`, `𝕨 𝔽˘ 𝕩`: Cells
+    
+Apply `𝔽` to/between the major cells of the arguments. (`𝔽⎉¯1`)
+    
+           a ← 3‿3 ⥊ ↕9
+
+
+           <˘ a
+
+           a ≍˘ a
+
+
+    
diff --git a/help/choose.md b/help/choose.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/choose.html).*
+
+# Circle with Lower Right Quadrant (`◶`)
+    
+## `𝔽◶𝕘 𝕩`, `𝕨 𝔽◶𝕘 𝕩`: Choose
+    
+Apply `𝔽` to the arguments and pick a function from list `𝕘`. Apply the picked function to the arguments.
+    
+           F ← ⊢◶+‿-‿÷‿×
+
+           F 0
+
+           F 1
+
+           F 2
+
+           F 3
+
+    
diff --git a/help/classify_indexof.md b/help/classify_indexof.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/classify_indexof.html).*
+
+# Square Original Of (`⊐`)
+    
+## `⊐ 𝕩`: Classify  
+    
+First index of each major cell of `𝕩` in `𝕩`.
+    
+           ⊐ 5‿6‿2‿2‿5‿1
+
+           a ← 3‿3 ⥊ 0‿1‿2‿9‿0‿9‿0‿1‿2
+
+           ⊐ a
+
+    
+    
+## `𝕨 ⊐ 𝕩`: Index Of
+    
+First index of each major cell of `𝕩` in `𝕨`. Rank of `𝕩` must be at least cell rank of 𝕨`.
+    
+If a cell is not found in `𝕨`, that position will contain the length of `𝕨` (`≠𝕨`). 
+    
+           5‿6‿2‿2‿5‿1 ⊐ 5‿2‿1‿6
+
+           a ← 3‿3 ⥊ 0‿1‿2‿9‿0‿9‿0‿1‿2
+
+           a ⊐ ⟨9‿0‿9⟩
+
+
+    
diff --git a/help/conjugate_add.md b/help/conjugate_add.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/conjugate_add.html).*
+
+# Plus (`+`)
+    
+## `+ 𝕩`: Conjugate
+    
+          + 1
+
+          + ¯1
+
+    
+## `𝕨 + 𝕩`: Add
+    
+`𝕨` added to `𝕩`. Either `𝕨` or `𝕩` can be a character, and if so, the other has to be an integer.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 + 2
+
+          1 + 2‿3‿4
+
+          'a' + 4
+
+    
diff --git a/help/constant.md b/help/constant.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/constant.html).*
+
+# Dot Above (`˙`)
+    
+## `𝔽˙ 𝕩`, `𝕨 𝔽˙ 𝕩`: Constant
+    
+Returns a function that will always return `𝕗`.
+    
+           "hello" (1 ˙) 2
+
+           "hello" ({𝕨+𝕩} ˙) 2
+
+    
diff --git a/help/deduplicate_find.md b/help/deduplicate_find.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/deduplicate_find.html).*
+
+# Epsilon Underbar (`⍷`)
+    
+## `⍷ 𝕩`: Deduplicate
+    
+Unique major cells of `𝕩`.
+    
+           ⍷ 4‿5‿6‿6‿4‿7‿5
+
+           a ← 3‿3 ⥊ ↕6
+
+           ⍷ a
+
+    
+    
+## `𝕨 ⍷ 𝕩`: Find
+    
+Mark the top left location of the occurrences of `𝕨` in `𝕩` with a 1, and other locations with 0.
+    
+Result is the same shape as `(≢𝕨)↕x`.
+    
+           "string" ⍷ "substring"
+
+           "loooooong" ⍷ "short"
+
+           a ← 7 (4|⋆˜)⌜○↕ 9
+
+           b ← (0‿3‿0≍0‿1‿0)
+
+           b ⍷ a
+
+    
diff --git a/help/depth.md b/help/depth.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/depth.html).*
+
+# Circle With Two Dots (`⚇`)
+    
+## `𝔽⚇𝕘 𝕩`, `𝕨 𝔽⚇𝕘 𝕩`: Depth
+    
+Apply `𝔽` to the cells of the arguments at depth given in `𝕘`.
+    
+    
+           1⊸↓⚇1 ⟨⟨1,2,3⟩, ⟨4,5,6⟩⟩
+
+           1 ↓⚇1 ⟨⟨1,2,3⟩, ⟨4,5,6⟩⟩
+
+    
diff --git a/help/depth_match.md b/help/depth_match.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/depth_match.html).*
+
+# Identical To (`≡`)
+    
+## `≡ 𝕩`: Depth
+    
+Highest level of nesting in `𝕩`.
+    
+          ≡ 2‿3‿4
+
+          ≡ ⟨2,<3,4,<<<5⟩
+
+          ≡ 9
+
+    
+    
+## `𝕨 ≡ 𝕩`: Match
+    
+Does `𝕨` exactly match `𝕩`?
+    
+          1 ≡ ⟨1⟩
+
+          ⟨1⟩ ≡ ⟨1⟩
+
+    
diff --git a/help/deshape_reshape.md b/help/deshape_reshape.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/deshape_reshape.html).*
+
+# Barb (`⥊`)
+        
+## `⥊ 𝕩`: Deshape  
+        
+Put all elements of `𝕩` in a rank 1 array, converting to array if necessary.
+        
+              ⥊ 1
+    
+              ⥊ 1‿2 ≍ 3‿4
+    
+        
+        
+## `𝕨 ⥊ 𝕩`: Reshape
+        
+Put all elements of `𝕩` in an array of shape `𝕨`, adding or removing elements if necessary.
+        
+A single element in `𝕩` can be a function, which will be replaced with an appropriate length:
+- `∘` Exact fit
+- `⌊` Round length down, discarding elements
+- `⌽` Round length up
+- `↑` Round length up, and use element fill to add extra elements.
+        
+              3‿3 ⥊ 3
+    
+              2‿⌽‿2 ⥊ 1‿2‿3
+    
+              2‿↑‿2 ⥊ 1‿2‿3
+    
+        
diff --git a/help/each.md b/help/each.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/each.html).*
+
+# Diaresis (`¨`)
+    
+## `𝔽¨ 𝕩`, `𝕨 𝔽¨ 𝕩`: Each
+    
+Apply `𝔽` to/between the major elements of the arguments. (`𝔽⚇¯1`)
+    
+           <¨ 1‿2‿3
+
+           4‿5‿6 ∾¨ 1‿2‿3
+
+    
diff --git a/help/enclose_less.md b/help/enclose_less.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/enclose_less.html).*
+
+# Lesser Than (`<`)
+    
+## `< 𝕩`: Enclose  
+    
+Create a unit array containing `𝕩`. (`(≢𝕩) ≡ ⟨⟩`)
+    
+    
+          <1
+
+        
+          ≢<1
+
+    
+    
+## `𝕨 < 𝕩`: Lesser Than
+    
+`𝕨` and `𝕩` can both be either numbers or characters.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 < 3
+
+          2‿3‿0 < 3‿1‿0
+
+    
diff --git a/help/enlist_pair.md b/help/enlist_pair.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/enlist_pair.html).*
+
+# Bow Tie (`⋈`)
+    
+## `⋈ 𝕩`: Enlist 
+    
+Put `𝕩` in a single element list. (`⟨𝕩⟩`)
+    
+          ⋈ 1
+
+          ⋈ 4‿4 ⥊ 3‿67‿8‿0
+
+    
+    
+## `𝕨 ⋈ 𝕩`: Pair
+    
+Put `𝕨` and `𝕩` in a two element list. (`⟨𝕨, 𝕩⟩`)
+    
+          1 ⋈ 2
+
+          1 ⋈ "dsdasdas"
+
+          (3‿3 ⥊ 3) ⋈ 67‿'a'‿"example"
+
+    
diff --git a/help/exponential_power.md b/help/exponential_power.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/exponential_power.html).*
+
+# Star (`⋆`)
+    
+## `⋆ 𝕩`: Exponential  
+    
+`e` (Euler's constant) to the power of `𝕩`.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          ⋆ 0‿1‿2‿3
+
+    
+    
+## `𝕨 ⋆ 𝕩`: Power
+    
+`𝕨` to the power of `𝕩`.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          2 ⋆ 5
+
+          8‿5‿9 ⋆ 2
+
+          2‿3 ⋆ 3‿¯4
+
+    
diff --git a/help/first_pick.md b/help/first_pick.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/first_pick.html).*
+
+# Square Image Of Or Equal To (`⊑`)
+    
+## `⊑ 𝕩`: First
+    
+First element of `𝕩`.
+    
+           ⊑ ⟨1, 2, 3⟩
+
+           a ← 3‿3 ⥊ ↕9
+
+           ⊑ a
+
+    
+    
+## `𝕨 ⊑ 𝕩`: Pick
+    
+Pick the element of `𝕨` at index `𝕩`.
+    
+           2 ⊑ ⟨1, 2, 3⟩
+
+           a ← 3‿3 ⥊ ↕9
+
+           2‿0 ⊑ a
+
+    
diff --git a/help/firstcell_select.md b/help/firstcell_select.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/firstcell_select.html).*
+
+# Square Image Of (`⊏`)
+    
+## `⊏ 𝕩`: First Cell
+    
+First major cell of `𝕩`.
+    
+           ⊏ ⟨1, 2, 3⟩
+
+           a ← 3‿3 ⥊ ↕9
+
+           ⊏ a
+
+    
+    
+## `𝕨 ⊏ 𝕩`: Select
+    
+Select the major cells of `𝕨` at the indices in `𝕩`.
+    
+           2‿0 ⊏ ⟨1, 2, 3⟩
+
+           a ← 3‿3 ⥊ ↕9
+
+           2‿0 ⊏ a
+
+    
diff --git a/help/floor_minimum.md b/help/floor_minimum.md
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+++ b/help/floor_minimum.md
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+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/floor_minimum.html).*
+
+# Left Floor (`⌊`)
+    
+## `⌊ 𝕩`: Floor  
+    
+Round `𝕩` down.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          ⌊ 1.2‿π‿3‿7.89
+
+    
+    
+## `𝕨 ⌊ 𝕩`: Minimum
+    
+Minimum of `𝕨` and `𝕩`.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 ⌊ 2
+
+          2‿3 ⌊ 4‿2
+
+    
diff --git a/help/fold.md b/help/fold.md
new file mode 100644
index 00000000..3684d96c
--- /dev/null
+++ b/help/fold.md
@@ -0,0 +1,30 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/fold.html).*
+
+# Acute Accent (`´`)
+    
+## `𝔽´ 𝕩`: Fold
+    
+Fold over `𝕩` with `𝔽` from right to left i.e. Insert `𝔽` between the elements of `𝕩`.
+    
+           +´ 1‿2‿3
+
+           1+2+3
+
+           -´ 1‿2‿3
+
+           1-2-3
+
+    
+## `𝕨 𝔽´ 𝕩`: Fold With initial
+    
+Monadic fold, but use `𝕨` as initial right argument.
+    
+           5 +´ 1‿2‿3
+
+           1+2+3+5
+
+           5 -´ 1‿2‿3
+
+           1-2-3-5
+
+    
diff --git a/help/gradedown_binsdown.md b/help/gradedown_binsdown.md
new file mode 100644
index 00000000..f3906c00
--- /dev/null
+++ b/help/gradedown_binsdown.md
@@ -0,0 +1,29 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/gradedown_binsdown.html).*
+
+# Del Stile (`⍒`)
+    
+## `⍒ 𝕩`: Grade Down
+    
+Indices of `𝕩` that would sort its major cells in descending order.
+    
+           a ← 1‿2‿3
+
+           ⍒ a
+
+           (⍒a) ⊏ a
+
+    
+    
+## `𝕨 ⍒ 𝕩`: Bins Down
+    
+Binary search for each element of `𝕩` in `𝕨`, and return the index found, if any. 
+    
+`𝕨` must be sorted in descending order.
+    
+[Right Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+           7‿5‿4‿3 ⍒ 2
+
+           7‿5‿4‿3 ⍒ 2‿6
+
+    
diff --git a/help/gradeup_binsup.md b/help/gradeup_binsup.md
new file mode 100644
index 00000000..7a73116d
--- /dev/null
+++ b/help/gradeup_binsup.md
@@ -0,0 +1,28 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/gradeup_binsup.html).*
+
+# Delta Stile (`⍋`)
+    
+## `⍋ 𝕩`: Grade Up
+    
+Indices of `𝕩` that would sort its major cells in ascending order.
+    
+           a ← 3‿2‿1
+
+           ⍋ a
+
+           (⍋a) ⊏ a
+
+           
+    
+    
+## `𝕨 ⍋ 𝕩`: Bins Up
+    
+Binary search for each element of `𝕩` in `𝕨`, and return the index found, if any. 
+    
+`𝕨` must be sorted in ascending order.
+    
+           3‿4‿5‿7 ⍋ 2
+
+           3‿4‿5‿7 ⍋ 2‿6
+
+    
diff --git a/help/greatequal.md b/help/greatequal.md
new file mode 100644
index 00000000..1772cbaf
--- /dev/null
+++ b/help/greatequal.md
@@ -0,0 +1,15 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/greatequal.html).*
+
+# Greater Than or Equal To (`≥`)
+    
+## `𝕨 ≥ 𝕩`: Greater Than or Equal To
+    
+`𝕨` and `𝕩` can both be either numbers or characters.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 ≥ 3
+
+          2‿3‿0 ≥ 3‿1‿0
+
+    
diff --git a/help/groupindices_group.md b/help/groupindices_group.md
new file mode 100644
index 00000000..ee0e9762
--- /dev/null
+++ b/help/groupindices_group.md
@@ -0,0 +1,31 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/groupindices_group.html).*
+
+# Square Cup (`⊔`)
+    
+## `⊔ 𝕩`: Group Indices
+    
+Group the indices of the major cells of `𝕩` by their respective values.
+    
+## `𝕩` must consist of integers. Groups start from 0. 
+    
+           ⊔ 4‿5‿6‿6‿4‿7‿5
+
+           (↕8) ≍ ⊔ 4‿5‿6‿6‿4‿7‿5
+
+    
+    
+## `𝕨 ⊔ 𝕩`: Group
+    
+Group the major cells of `𝕩` by their respective indices in `𝕨`.
+    
+If an element corresponds to `¯1`, it is excluded from grouping.
+    
+An extra element can be added to the end of `𝕨` to specify length of the result.
+    
+           1‿0‿1‿2‿2‿3‿3  ⊔ 4‿5‿6‿6‿4‿7‿5
+
+           1‿0‿1‿¯1‿¯1‿3‿3  ⊔ 4‿5‿6‿6‿4‿7‿5
+
+           1‿0‿1‿¯1‿¯1‿3‿3‿10  ⊔ 4‿5‿6‿6‿4‿7‿5
+
+    
diff --git a/help/identity_left.md b/help/identity_left.md
new file mode 100644
index 00000000..dabe6cc7
--- /dev/null
+++ b/help/identity_left.md
@@ -0,0 +1,21 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/identity_left.html).*
+
+# Left Tack (`⊣`)
+    
+## `⊣ 𝕩`: 
+    
+Return `𝕩`.
+    
+          ⊣ 5
+
+    
+    
+## `𝕨 ⊣ 𝕩`: Left
+    
+Return `𝕨`.
+    
+          5 ⊣ 8
+
+          'a' ⊣ 1‿2‿3
+
+    
diff --git a/help/identity_right.md b/help/identity_right.md
new file mode 100644
index 00000000..a0844a8f
--- /dev/null
+++ b/help/identity_right.md
@@ -0,0 +1,21 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/identity_right.html).*
+
+# Right Tack (`⊢`)
+    
+## `⊢ 𝕩`: 
+    
+Return `𝕩`.
+    
+          ⊢ 5
+
+    
+    
+## `𝕨 ⊢ 𝕩`: Right
+    
+Return `𝕩`.
+    
+          5 ⊢ 8
+
+          'a' ⊢ 1‿2‿3
+
+    
diff --git a/help/indices_replicate.md b/help/indices_replicate.md
new file mode 100644
index 00000000..9ffad842
--- /dev/null
+++ b/help/indices_replicate.md
@@ -0,0 +1,25 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/indices_replicate.html).*
+
+# Solidus (`/`)
+    
+## `/ 𝕩`: Indices
+    
+Repeat the index of each element in `𝕩` by the element's value. `𝕩` must be rank 1.
+    
+           / 1‿2‿3
+
+           / 1‿0‿1
+
+    
+    
+## `𝕨 / 𝕩`: Replicate
+    
+Repeat each major cell in `𝕩` by the corresponding element in `𝕨`.
+    
+Atomic `𝕨` applies to all elements.
+    
+           3 / "copy"
+
+           1‿0‿1 / 1‿2‿3
+
+    
diff --git a/help/join_jointo.md b/help/join_jointo.md
new file mode 100644
index 00000000..13419744
--- /dev/null
+++ b/help/join_jointo.md
@@ -0,0 +1,31 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/join_jointo.html).*
+
+# Lazy S (`∾`)
+    
+## `∾ 𝕩`: Join  
+    
+Join all elements of `𝕩` together.
+    
+Element ranks must be compatible.
+    
+           ∾ ⟨1‿2, 3, 4‿5⟩
+
+           m ← (3‿1≍⌜4‿2‿5) ⥊¨ 2‿3⥊↕6
+
+           ∾ m
+
+    
+    
+## `𝕨 ∾ 𝕩`: Join
+    
+Join `𝕨` to `𝕩` along the first axis.
+    
+           "abcd" ∾ "EFG"
+
+           a ← 3‿3 ⥊ ↕9
+
+           c ← 4‿3 ⥊ ↕12 
+
+           a∾c
+
+    
diff --git a/help/length_notequal.md b/help/length_notequal.md
new file mode 100644
index 00000000..057247c9
--- /dev/null
+++ b/help/length_notequal.md
@@ -0,0 +1,32 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/length_notequal.html).*
+
+# Not Equal (`≠`)
+    
+## `≠ 𝕩`: Length
+    
+Length of the first dimension of `𝕩`.
+    
+    
+          ≠ 3
+
+          ≠ ⟨1, 2, 3⟩
+
+          ≠ 3‿4‿5⥊0
+
+          ≠ 1‿4‿5⥊0
+
+          ≠ 4‿4‿5⥊0
+
+    
+    
+## `𝕨 ≠ 𝕩`: Not Equal To
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 ≠ 3
+
+          2‿3‿0 ≠ 3‿1‿0
+
+          'a' ≠ 'a'
+
+    
diff --git a/help/lessequal.md b/help/lessequal.md
new file mode 100644
index 00000000..8fc0000b
--- /dev/null
+++ b/help/lessequal.md
@@ -0,0 +1,15 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/lessequal.html).*
+
+# Lesser Than or Equal To (`≤`)
+    
+## `𝕨 ≤ 𝕩`: Lesser Than or Equal To
+    
+`𝕨` and `𝕩` can both be either numbers or characters.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 ≤ 3
+
+          2‿3‿0 ≤ 3‿1‿0
+
+    
diff --git a/help/markfirst_memberof.md b/help/markfirst_memberof.md
new file mode 100644
index 00000000..228d6a50
--- /dev/null
+++ b/help/markfirst_memberof.md
@@ -0,0 +1,29 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/markfirst_memberof.html).*
+
+# Element Of (`∊`)
+    
+## `∊ 𝕩`: Unique Mask
+    
+Mark the first occurrence of each major cell in `𝕩` with a 1, and all other occurrences with a 0.
+    
+           ∊ 4‿5‿6‿6‿4‿7‿5
+
+           a ← 3‿3 ⥊ ↕9
+
+           ∊ a
+
+    
+    
+## `𝕨 ∊ 𝕩`: Member Of
+    
+Is each element in `𝕨` a major cell of `𝕩`?
+    
+           ⟨1⟩ ∊ ↕9
+
+           a ← 3‿3 ⥊ ↕9
+
+           ⟨0‿1‿2⟩ ∊ a
+
+           ⟨1‿3 ⥊ 0‿1‿2⟩ ∊ a
+
+    
diff --git a/help/merge_great.md b/help/merge_great.md
new file mode 100644
index 00000000..c91b3b8b
--- /dev/null
+++ b/help/merge_great.md
@@ -0,0 +1,37 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/merge_great.html).*
+
+# Greater Than (`>`)
+    
+## `> 𝕩`: Merge  
+    
+Add the rank of an element of `𝕩` to the rank of `𝕩`.
+    
+All elements must have the same rank.
+    
+Returns atomic values as is.
+    
+    
+          a ← ⟨⟨1, 2⟩, ⟨3, 4⟩⟩
+
+          >a
+
+          ≢a
+
+          ≢>a
+
+          
+    
+    
+## `𝕨 > 𝕩`: Greater Than
+    
+`𝕨` and `𝕩` can both be either numbers or characters.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 > 3
+
+          2‿3‿0 > 3‿1‿0
+
+          'a' > 'b'
+
+    
diff --git a/help/negate_subtract.md b/help/negate_subtract.md
new file mode 100644
index 00000000..8a70e1bf
--- /dev/null
+++ b/help/negate_subtract.md
@@ -0,0 +1,30 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/negate_subtract.html).*
+
+# Minus (`-`)
+    
+## `- 𝕩`: Negate
+    
+Additive Inverse of `𝕩`.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          - 1
+
+          - ¯1
+
+    
+## `𝕨 - 𝕩`: Subtract
+    
+Subtract `𝕩` from `𝕨`. `𝕨` and `𝕩` can be characters or integers.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 - 2
+
+          1 - 2‿3‿4
+
+          'a' - 4
+
+          'b' - 'a'
+
+    
diff --git a/help/not_span.md b/help/not_span.md
new file mode 100644
index 00000000..7b099699
--- /dev/null
+++ b/help/not_span.md
@@ -0,0 +1,27 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/not_span.html).*
+
+# Not (`¬`)
+    
+## `¬ 𝕩`: Logical Not  
+    
+Logical Not of `𝕩`.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          ¬ 0
+
+          ¬ 1‿0
+
+    
+    
+## `𝕨 ¬ 𝕩`: Span
+    
+Count of numbers in the inclusive range from `𝕩` to `𝕨`.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          3 ¬ 1
+
+          3‿4 ¬ 0‿2
+
+    
diff --git a/help/occcount_progindex.md b/help/occcount_progindex.md
new file mode 100644
index 00000000..649869c8
--- /dev/null
+++ b/help/occcount_progindex.md
@@ -0,0 +1,23 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/occcount_progindex.html).*
+
+# Square Original Of or Equal To (`⊒`)
+    
+## `⊒ 𝕩`: Occurrence Count
+    
+Number of times each major cell of `𝕩` appears before itself.
+    
+            ⊒   2‿7‿1‿8‿1‿7‿1‿8‿2‿8‿4
+
+            ≍⟜⊒ 2‿7‿1‿8‿1‿7‿1‿8‿2‿8‿4
+
+    
+    
+## `𝕨 ⊒ 𝕩`: Progressive Index Of
+    
+Index of the first unused match of each major cell of `𝕩` in `𝕨`. If there are no more matches left, length of `𝕨` is placed in that position.
+    
+            "aaa" ⊒ "aaaaa"
+
+            "aaabb" ⊒ "ababababab"
+
+    
diff --git a/help/over.md b/help/over.md
new file mode 100644
index 00000000..38795145
--- /dev/null
+++ b/help/over.md
@@ -0,0 +1,29 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/over.html).*
+
+# Circle (`○`)
+    
+## `𝔽○𝔾 𝕩`: Atop
+    
+Apply `𝔾` to `𝕩`, then apply `𝔽` (`𝔽 𝔾 𝕩`).
+    
+`𝔽` and `𝔾` must be monadic.
+    
+           -○- 5
+
+           - - 5
+
+    
+    
+## `𝕨 𝔽○𝔾 𝕩`: Over
+    
+Apply `𝔾` to `𝕨` and `𝕩`, then apply `𝔽` to them (`(𝔾 𝕨) 𝔽 (𝔾 𝕩)`).
+    
+`𝔽` must be dyadic, `𝔾` must be monadic.
+    
+           1 +○- 2
+
+           1 + - 2
+
+           (- 1) + (- 2)
+
+    
diff --git a/help/prefixes_take.md b/help/prefixes_take.md
new file mode 100644
index 00000000..636574fa
--- /dev/null
+++ b/help/prefixes_take.md
@@ -0,0 +1,35 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/prefixes_take.html).*
+
+# Up Arrow (`↑`)
+    
+## `↑ 𝕩`: Prefixes
+    
+Prefixes of array `𝕩` along its first axis.
+    
+           ↑ 1‿2‿3‿4
+
+           a ← 3‿3 ⥊ ↕9
+
+           ↑ a
+
+    
+    
+## `𝕨 ↑ 𝕩`: Take
+    
+For each integer in `𝕨`, take that many elements from each dimension of `𝕩`.
+    
+Negative numbers take from the end.
+    
+If any of the elements in `𝕨` are greater than the length of their respective dimension, the dimension is extended with a fill value.
+    
+          3 ↑ 1‿3‿5‿67
+
+          a ← 4‿4 ⥊ ↕16
+
+          3‿3 ↑ a
+
+          5‿5 ↑ a
+
+          3‿¯3 ↑ a
+
+    
diff --git a/help/range_windows.md b/help/range_windows.md
new file mode 100644
index 00000000..d4f82a1c
--- /dev/null
+++ b/help/range_windows.md
@@ -0,0 +1,27 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/range_windows.html).*
+
+# Up Down Arrow (`↕`)
+    
+## `↕ 𝕩`: Range  
+    
+Return all indices to index into an array of shape `𝕩`, in the shape described by `𝕩`.
+    
+When given a single number, range from 0 to `𝕩-1`.
+    
+           ↕ 4
+
+           ↕ 4‿5
+
+    
+    
+## `𝕨 ↕ 𝕩`: Windows
+    
+Overlapping slices of `𝕩` which are of shape `𝕨`.
+    
+           5 ↕ "abcdefg"
+
+           a ← 3‿3⥊↕9
+
+           2‿2 ↕ a
+
+    
diff --git a/help/rank.md b/help/rank.md
new file mode 100644
index 00000000..0bbab822
--- /dev/null
+++ b/help/rank.md
@@ -0,0 +1,20 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/rank.html).*
+
+# Circled Horizontal Bar With Notch (`⎉`)
+    
+## `𝔽⎉𝕘 𝕩`, `𝕨 𝔽⎉𝕘 𝕩`: Rank
+    
+Apply `𝔽` to cells at ranks given in `𝕘`.
+    
+The ranks applied are given by the following:
+    
+- `⎉ c`    Rank-c cells of `𝕩` (monadic) or both arguments (dyadic)
+- `⎉ b‿c`   ⍝ Rank-b cells of `𝕨` and rank-c cells of `𝕩` (dyadic)
+- `⎉ a‿b‿c`   ⍝ Rank-a cells of `𝕩` (monadic), b-cells of `𝕨` and c-cells of `𝕩` (dyadic)
+    
+    
+           a ← 3‿2‿4⥊"ABCDEFGHIJKLMNOPQRSTUVWXYZ"
+
+           ⌽⎉2 a
+
+    
diff --git a/help/rank_equal.md b/help/rank_equal.md
new file mode 100644
index 00000000..1663df7d
--- /dev/null
+++ b/help/rank_equal.md
@@ -0,0 +1,30 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/rank_equal.html).*
+
+# Equal (`=`)
+    
+## `= 𝕩`: Rank
+    
+Returns the number of dimensions in `𝕩`.
+    
+    
+          = 0
+
+          = 3⥊0
+
+          = 3‿3⥊0
+
+          3‿3‿3 ⥊ ⟨⟨0⟩⟩
+
+    
+    
+## `𝕨 = 𝕩`: Equal To
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 = 3
+
+          2‿3‿0 = 3‿1‿0
+
+          'a' = 'a'
+
+    
diff --git a/help/reciprocal_divide.md b/help/reciprocal_divide.md
new file mode 100644
index 00000000..c7d8374c
--- /dev/null
+++ b/help/reciprocal_divide.md
@@ -0,0 +1,26 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/reciprocal_divide.html).*
+
+# Divide (`÷`)
+    
+## `÷ 𝕩`: Reciprocal  
+    
+Gives `1 ÷ 𝕩`.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          ÷ 5
+
+    
+    
+## `𝕨 ÷ 𝕩`: Divide
+    
+`𝕨` divided by `𝕩`.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+
+        5 ÷ 4
+
+        14 ÷ 7
+    
+
+    
diff --git a/help/repeat.md b/help/repeat.md
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--- /dev/null
+++ b/help/repeat.md
@@ -0,0 +1,17 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/repeat.html).*
+
+# Circle Star (`⍟`)
+    
+## `𝔽⍟𝔾 𝕩`, `𝕨 𝔽⍟𝔾 𝕩`: Repeat
+    
+Apply `𝔾` to `𝕨` and `𝕩` and apply `𝔽` to `𝕩` that may times. If `𝕨` is given, keep it as a constant left argument.
+    
+If `𝔾` returns an array, give `𝔽⍟𝕩` for each element.
+    
+           1 +⍟⊢ 4
+
+           1 +⍟1‿2‿3 4
+
+           3 ∾⍟{≠𝕩} ⟨4,5,6⟩
+
+    
diff --git a/help/reverse_rotate.md b/help/reverse_rotate.md
new file mode 100644
index 00000000..a7ec430b
--- /dev/null
+++ b/help/reverse_rotate.md
@@ -0,0 +1,27 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/reverse_rotate.html).*
+
+# Circle Stile (`⌽`)
+    
+## `⌽ 𝕩`: Reverse  
+    
+Reverse the first axis of `𝕩`.
+    
+           ⌽ 1‿2‿3
+
+           a ← 3‿3 ⥊ ↕9
+
+           ⌽ a
+
+    
+    
+## `𝕨 ⌽ 𝕩`: Dyad
+    
+Move the first `𝕨` elements of `𝕩` to its end. Negative `𝕨` reverses the direction of rotation.
+    
+           2 ⌽ 1‿2‿3
+
+           a ← 3‿3 ⥊ ↕9
+
+           2 ⌽ a
+
+    
diff --git a/help/scan.md b/help/scan.md
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--- /dev/null
+++ b/help/scan.md
@@ -0,0 +1,31 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/scan.html).*
+
+# Grave (`` ` ``)
+    
+## ``𝔽` 𝕩``: Fold
+    
+Scan over `𝕩` with `𝔽` from left to right, producing intermediate values.
+    
+    
+           +` 1‿2‿3
+
+           ⟨1, 1+2, (1+2)+3⟩
+
+           -` 1‿2‿3
+
+           ⟨1, 1-2, (1-2)-3⟩
+
+    
+## ``𝕨 𝔽` 𝕩``: Scan With initial
+    
+Monadic scan, but use `𝕨` as initial left argument.
+    
+           5 +` 1‿2‿3
+
+           ⟨5+1, (5+1)+2, ((5+1)+2)+3⟩
+
+           5 -` 1‿2‿3
+
+           ⟨5-1, (5-1)-2, ((5-1)-2)-3⟩
+
+    
diff --git a/help/self_swap.md b/help/self_swap.md
new file mode 100644
index 00000000..fdd4dcc8
--- /dev/null
+++ b/help/self_swap.md
@@ -0,0 +1,23 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/self_swap.html).*
+
+# Small Tilde (`˜`)
+    
+## `𝔽˜ 𝕩`: Self
+    
+Supplies `𝕩` as a left argument to `𝔽` (`𝕩 𝔽 𝕩`).
+    
+           1 + 1
+
+           +˜ 1
+
+    
+    
+## `𝕨 𝔽˜ 𝕩`: Swap
+    
+Swaps the arguments of `𝔽` (`𝕩 𝔽 𝕨`).
+    
+           1 - 2
+
+           1 -˜ 2
+
+    
diff --git a/help/shape_notmatch.md b/help/shape_notmatch.md
new file mode 100644
index 00000000..663d1d61
--- /dev/null
+++ b/help/shape_notmatch.md
@@ -0,0 +1,25 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/shape_notmatch.html).*
+
+# Not Identical To (`≢`)
+    
+## `≢ 𝕩`: Shape
+    
+Length of each dimension of x.
+    
+          ≢ 1
+
+          ≢ 1‿2
+
+          ≢ 1‿2 ≍ 3‿4
+
+    
+    
+## `𝕨 ≢ 𝕩`: Not Match
+    
+Does `𝕨` not exactly match `𝕩`?
+    
+          1 ≢ ⟨1⟩
+
+          ⟨1⟩ ≢ ⟨1⟩
+
+    
diff --git a/help/shiftafter.md b/help/shiftafter.md
new file mode 100644
index 00000000..08e42a89
--- /dev/null
+++ b/help/shiftafter.md
@@ -0,0 +1,27 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/shiftafter.html).*
+
+# Right Pointing Double Angle Quotation (`»`)
+    
+## `» 𝕩`: Shift After
+    
+Remove the last element of `𝕩`, add a cell of fill values to the start of the first axis of `𝕩`.
+    
+           » 1‿2‿3
+
+           » 3‿3 ⥊ 9
+
+    
+    
+## `𝕨 » 𝕩`: Shift After
+    
+Remove the last `≠𝕨` (length) major cells from `𝕩`, join `𝕨` to the start of `𝕩`. Ranks must match.
+    
+           78 » 1‿2‿3
+
+           1‿2 » 1‿2‿3
+
+           a ← 3‿3 ⥊ 9
+
+           1‿2‿3 » a
+
+    
diff --git a/help/shiftbefore.md b/help/shiftbefore.md
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index 00000000..ca32833f
--- /dev/null
+++ b/help/shiftbefore.md
@@ -0,0 +1,27 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/shiftbefore.html).*
+
+# Left Pointing Double Angle Quotation (`«`)
+    
+## `« 𝕩`: Shift Before
+    
+Remove the first element of `𝕩`,  add a cell of fill values to the end of the first axis of `𝕩`.
+    
+           78 « 1‿2‿3
+
+           « 1‿2‿3
+
+           « 3‿3 ⥊ 9
+
+    
+    
+## `𝕨 « 𝕩`: Shift Before
+    
+Remove the first `≠𝕨` (length) major cells from `𝕩`, join `𝕨` to the end of `𝕩`. Ranks must match.
+    
+           8‿5 « 1‿2‿3
+
+           a ← 3‿3 ⥊ 9
+
+           1‿2‿3 « a
+
+    
diff --git a/help/sign_multiply.md b/help/sign_multiply.md
new file mode 100644
index 00000000..3b8fa8de
--- /dev/null
+++ b/help/sign_multiply.md
@@ -0,0 +1,28 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/sign_multiply.html).*
+
+# Times (`×`)
+    
+## `× 𝕩`: Sign  
+    
+Sign of `𝕩`.
+- `¯1` if `𝕩 < 0`
+- `0` if `𝕩 = 0`
+- `1` if `𝕩 > 0`
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          × ¯5‿0‿5‿1
+
+    
+    
+## `𝕨 × 𝕩`: Multiply
+    
+`𝕨` multiplied by `𝕩`.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 × 2
+
+          2 × 2‿3‿4
+
+    
diff --git a/help/solo_couple.md b/help/solo_couple.md
new file mode 100644
index 00000000..ac66e5c2
--- /dev/null
+++ b/help/solo_couple.md
@@ -0,0 +1,33 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/solo_couple.html).*
+
+# Tape (`≍`)
+    
+## `≍ 𝕩`: Solo 
+    
+Add a dimension to `𝕩`.
+    
+          ≍ 1
+
+          
+          ≍≍ 1
+
+          
+         ≍≍≍ 1
+
+          
+         ≍≍ 1‿2‿3‿4
+
+          
+         ≍≍≍ 1‿2‿3‿4
+
+    
+    
+## `𝕨 ≍ 𝕩`: Couple
+    
+Join `𝕨` and `𝕩` along a newly created axis.
+    
+           1 ≍ 3
+
+           1‿2 ≍ 2‿3
+
+    
diff --git a/help/sortdown_or.md b/help/sortdown_or.md
new file mode 100644
index 00000000..03982acd
--- /dev/null
+++ b/help/sortdown_or.md
@@ -0,0 +1,25 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/sortdown_or.html).*
+
+# Logical Or (`∨`)
+    
+## `∨ 𝕩`: Sort Down
+    
+Sort array `𝕩` in descending order.
+    
+          ∨ 3‿1‿4‿1‿5
+
+    
+    
+## `𝕨 ∨ 𝕩`: Logical Or
+    
+Logical Or of `𝕨` and `𝕩`. 
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 ∨ 0
+
+          1‿0 ∨ 1‿1
+
+          0 ∨ 0
+
+    
diff --git a/help/sortup_and.md b/help/sortup_and.md
new file mode 100644
index 00000000..bf727848
--- /dev/null
+++ b/help/sortup_and.md
@@ -0,0 +1,23 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/sortup_and.html).*
+
+# Logical And (`∧`)
+    
+## `∧ 𝕩`: Sort Up
+    
+Sort array `𝕩` in ascending order.
+    
+          ∧ 3‿1‿4‿1‿5
+
+    
+    
+## `𝕨 ∧ 𝕩`: Logical And
+    
+Logical And of `𝕨` and `𝕩`. 
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          1 ∧ 1
+
+          1‿0 ∧ 1‿1
+
+    
diff --git a/help/squareroot_root.md b/help/squareroot_root.md
new file mode 100644
index 00000000..c97c92c5
--- /dev/null
+++ b/help/squareroot_root.md
@@ -0,0 +1,23 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/squareroot_root.html).*
+
+# Root (`√`)
+    
+## `√ 𝕩`: Square root  
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          √ 2
+
+    
+    
+## `𝕨 √ 𝕩`: Root
+    
+`𝕨`th root of `𝕩`.
+    
+[Pervasive.](https://mlochbaum.github.io/BQN/doc/arithmetic.html#pervasion)
+    
+          2 √ 2
+
+          1‿2‿3‿4 √ 4  
+
+    
diff --git a/help/suffixes_drop.md b/help/suffixes_drop.md
new file mode 100644
index 00000000..10c93520
--- /dev/null
+++ b/help/suffixes_drop.md
@@ -0,0 +1,34 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/suffixes_drop.html).*
+
+# Down Arrow (`↓`)
+    
+## `↓ 𝕩`: Suffixes
+    
+Suffixes of array `𝕩` along its first axis.
+    
+           ↓ 1‿2‿3‿4
+
+           a ← 3‿3 ⥊ ↕9
+
+           ↓ a
+
+    
+    
+## `𝕨 ↓ 𝕩`: Drop
+    
+For each integer in `𝕨`, drop that many elements from the beginning of each dimension of `𝕩`.
+    
+Negative numbers drop from the end.
+    
+           3 ↓ 1‿3‿5‿67
+
+           a ← 4‿4 ⥊ ↕16
+
+           3‿3 ↓ a
+
+           5‿5 ↓ a
+
+
+           3‿¯3 ↓ a
+
+    
diff --git a/help/table.md b/help/table.md
new file mode 100644
index 00000000..dd190660
--- /dev/null
+++ b/help/table.md
@@ -0,0 +1,13 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/table.html).*
+
+# Top Left Corner (`⌜`)
+    
+## `𝕨 𝔽⌜ 𝕩`: Each
+    
+Apply `𝔽` between every possible pair of the elements of the arguments.
+    
+           1‿2‿3‿4 +⌜ 4‿5‿6‿7
+
+           "abc" ∾⌜ "xyz"
+
+    
diff --git a/help/transpose_dyadtranspose.md b/help/transpose_dyadtranspose.md
new file mode 100644
index 00000000..d3db90ab
--- /dev/null
+++ b/help/transpose_dyadtranspose.md
@@ -0,0 +1,27 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/transpose_dyadtranspose.html).*
+
+# Circle Backslash (`⍉`)
+    
+## `⍉ 𝕩`: Transpose 
+    
+Move the first axis of `𝕩` to the end.
+    
+           a ← 3‿3 ⥊ ↕9
+
+           ⍉ a
+
+           b ← 1‿2‿3 ⥊ ↕6
+
+           ≢⍉ b
+
+    
+    
+## `𝕨 ⍉ 𝕩`: Dyad
+    
+Rearrange the axes of `𝕩` as per the axis indices in `𝕨`.
+    
+           ≢ a ← 2‿3‿4‿5‿6 ⥊1
+
+           ≢ 1‿3‿2‿0‿4 ⍉ a
+
+    
diff --git a/help/under.md b/help/under.md
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--- /dev/null
+++ b/help/under.md
@@ -0,0 +1,22 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/under.html).*
+
+# Circle Jot (`⌾`)
+    
+## `𝔽⌾𝔾 𝕩`, `𝕨 𝔽⌾𝔾 𝕩`: Under
+    
+- Apply transformation `𝔾` to all arguments
+- Apply `𝔽` to the transformed arguments
+- Undo transformation `𝔾`
+    
+Where `𝔾` must be 
+    
+1. A function invertible by `⁼` (Undo)
+2. A structural modification
+    
+           9⌾(1⊸⊑) 1‿2‿3
+
+           √⁼ (√1) + (√9)
+
+           1 +⌾√ 9
+
+    
diff --git a/help/undo.md b/help/undo.md
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index 00000000..0daa6469
--- /dev/null
+++ b/help/undo.md
@@ -0,0 +1,22 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/undo.html).*
+
+# Superscript Equals Sign (`⁼`)
+    
+## `𝔽⁼ 𝕩`, `𝕨 𝔽⁼ 𝕩`: Undo
+    
+Invert the function `𝔽`, or use its defined inverse. Not all functions have inverses.
+    
+    
+           1 - 2
+
+           1 -⁼ 2
+
+           √ 16
+
+           √⁼ 4
+
+           ⋆ 1
+
+           ⋆⁼ 2.718281828459045
+
+    
diff --git a/help/valences.md b/help/valences.md
new file mode 100644
index 00000000..d7ef83b8
--- /dev/null
+++ b/help/valences.md
@@ -0,0 +1,23 @@
+*View this file with results and syntax highlighting [here](https://mlochbaum.github.io/BQN/help/valences.html).*
+
+# Circled Division Slash (`⊘`)
+    
+## `𝔽⊘𝔾 𝕩`: Valences
+    
+Apply `𝔽` to `𝕩`.
+    
+           +⊘- 5
+
+           -⊘+ 5
+
+    
+    
+## `𝕨 𝔽⊘𝔾 𝕩`: Valences
+    
+Apply `𝔾` to `𝕨` and `𝕩`.
+    
+           4 +⊘- 5
+
+           4 -⊘+ 5
+
+