[package]
name = "Printiest"
version = "0.1"
lean_version = "leanprover/lean4:nightly-2021-04-26"

# What is this?
A general algebraic [pretty-printer](https://en.wikipedia.org/wiki/Prettyprint#Programming_code_formatting) for [Lean 4](https://github.com/leanprover/lean4) using ideas from Jean-Philippe Bernardy's [Prettiest](https://github.com/jyp/prettiest). Bernardy also acknowledges work by Podkopaev, Boulytchev, Azero, and Swierstra in the addendum to [his paper](https://jyp.github.io/pdf/Prettiest.pdf). Broadly, the idea with this style of printer is that the library can save the user a lot of guesswork by doing some measuring/calculating to figure out the most optimal way to render a document, according to three very general principles:
```
1. Visibility: The printer will fit its output within the specified render width*
2. Legibility: The printer will respect the user's layout choices (groups)
3. Frugality: The printer will use as few lines as possible while respecting 1 and 2.
* The printer won't break up individual strings given by the user, so if you pass an 80 character string and specify a render width of 10, principle 1 will be violated (though only in that one spot)
```
Bernardy's insight was that while a naive implementation runs in exponential time, clever (but not complicated) pruning of the space of possible layouts makes things more or less linear (see the paper for details/graphs about this).
--- 
This implementation adds a third (optional) group choice for laying out segments of human-language text, and changes the implementation of the measuring and rendering so that the two phases are completely separate, which allows the final output to be written directly to an output stream rather than building up the whole output string in memory, then writing the string somewhere. 
Much of the Lean community (myself included) has yet to really explore the performance characteristics of Lean 4 and the language primitives, but the compiled version of this already performs very well compared to a very similar Rust implementation and Bernardy's Haskell version (which has more implementation differences, so a little bit apples to oranges).
## How do I use it?
Full examples of the printer's use can be found in the `Tests` module. Conceptually, the thing you want to print is built up by combining `Doc` elements which you then render to either a string with `Doc.renderString <width : Nat>`, or to an output stream with `Doc.renderStream <width : Nat> <stream>`.
There are three infix operators:
```
x <> y -- concatenate x and y
x <+> y -- concatenate x and y, with a space between
x <n> y -- vertically concatenate x and y
```
The main ways in which this (and Prettiest) differs from something like a Wadler/Leijen style printer is that the `Group` node does more of the work for you (you can still force a node to render as a certain orientation if you want), and for docs > 1 line in height, concatenation is "tetris-like". For existing programs that depend on "classic" concatenation, you can still achieve the same results by changing the manner in which the doc is built up in your program.
## Future work
+ Adding an annotation system.
+ Figuring out what API/integration to offer for external code or document formatters.
+ Figuring out the best way to make use of buffered streams/writers in Lean 4.
+ While work on verification is sort of blocked until well-founded recursion is implemented and the `partial` functions can be removed, it would be interesting to have a verified pretty-printer. It seems like the relevant correctness properties are:
1. That all of the Text nodes in a Doc tree are present in the output
2. That the rendered text appears in the correct order 
As long as you can show that all of the intended text made it into the output string, and did so in the right order, it seems like everything else is just a matter of taste, but if anyone knows more about this hit me up. 
## Examples
The full set of examples can be seen in the `Tests` module. The real strength of this printer is the versatility and ease of use of the `Group` node, and the way it automatically adjusts the rendering to fit the desired render width (users can still exert manual control over group rendering when they want to). For example, function for rendering generic S-expressions is extremely simple...:
```
partial def Sexpr.pretty : Sexpr -> Doc
| atom s => Doc.Text s
| list es => 
  let inner := Doc.group (es.map pretty) " "
  "(" <> inner <> ")"
```
But it will produce nice outputs automatically for different render widths, while leaving users the option of forcing a horizontal/vertical orientation to accomodate things like code formatters.
```
-- render width := 80 
((abcde ((a b c d) (a b c d) (a b c d) (a b c d)))
 (abcdefgh ((a b c d) (a b c d) (a b c d) (a b c d))))
-- render width := 40 
((abcde ((a b c d)
         (a b c d)
         (a b c d)
         (a b c d)))
 (abcdefgh ((a b c d)
            (a b c d)
            (a b c d)
            (a b c d))))
-- render width := 15
((abcde
  ((a b c d)
   (a b c d)
   (a b c d)
   (a b c d)))
 (abcdefgh
  ((a b c d)
   (a b c d)
   (a b c d)
   (a b c d))))
```
Recreating a portion of the `git --help` output, showing the ability to render a CLI in a manner suited to a user's detected terminal width.
```
-- render width := 80
usage: git [--version] [--help] [-C <path>] [-c <name>=<value>]
           [--exec-path[=<path>]] [--html-path] [--man-path] [--info-path]
           [--p|--paginate|-P|--no-pager] [--no-replace-objects] [--bare]
       <command>
       [<args>]
'git help -a' and 'git help -g' list available subcommands and some
concept guides. See 'git help <command>' or 'git help <concept>' to read
about a specific subcommand or concept. See 'git help git' for an overview
of the system.
-- render width := 40
usage:
    git [--version] [--help]
        [-C <path>] [-c <name>=<value>]
        [--exec-path[=<path>]] [--html-path]
        [--man-path] [--info-path]
        [--p|--paginate|-P|--no-pager]
        [--no-replace-objects] [--bare]
    <command>
    [<args>]
'git help -a' and 'git help -g' list
available subcommands and some concept
guides. See 'git help <command>' or 'git
help <concept>' to read about a specific
subcommand or concept. See 'git help
git' for an overview of the system.
-- render width := 20
usage:
    git [--version]
        [--help]
        [-C <path>]
        [-c <name>=<value>]
        [--exec-path[=<path>]]
        [--html-path]
        [--man-path]
        [--info-path]
        [--p|--paginate|-P|--no-pager]
        [--no-replace-objects]
        [--bare]
    <command>
    [<args>]
'git help
-a' and
'git help
-g' list
available
subcommands
and some
concept
guides. See
'git help
<command>'
or 'git
help
<concept>'
to read
about a
specific
subcommand
or concept.
See 'git
help git'
for an
overview of
the
system.
```
## License
Users are free to copy/distribute/modify this software according to the terms of either the Apache 2.0 license (to match Lean 4), or the GPLv3 (to match Prettiest). Most people will choose Apache 2.0, but licensees who would like to incorporate this in a larger GPL codebase will want to choose the GPLv3 option. Contributions will be accepted under the same dual-license arrangement. 

import Printiest.Tests
def main : IO Unit :=   
  IO.Prim.getStdout >>= bigSexpr2.pretty.renderStream 80

      
inductive Choice
| H : Nat -> Choice
| V : Nat -> Choice
| T : Choice
instance : Inhabited Choice := ⟨Choice.H 0⟩
def Choice.toString (c : Choice) : String :=
  match c with
  | Choice.H n => s!"H({n})"
  | Choice.V n => s!"V({n})"
  | Choice.T   => "T"
instance : ToString Choice := ⟨Choice.toString⟩
/-
Side and Spaces are helper types to keep track of info during rendering; 
we need these to allow for streaming output.
Side keeps track of whether we're on the left or right side of a Concat
so we can determine how linebreaks/flushes should behave.
Spaces determines whether a given indentation is actually supposed to be
rendered or not.
-/
inductive Side
| Left : Side
| Right : Side
instance : Inhabited Side := ⟨Side.Left⟩
inductive Spaces
| Hot : Nat -> Spaces
| Cold : Nat -> Spaces
instance : Inhabited Spaces := ⟨Spaces.Cold 0⟩ 
def Spaces.toHot : Spaces -> Spaces 
| Hot n => Hot n
| Cold n => Hot n
def Spaces.toCold : Spaces -> Spaces 
| Hot n => Cold n
| Cold n => Cold n
def Spaces.toNat : Spaces -> Nat
| Hot n => n
| Cold n => n
def Spaces.isHot : Spaces -> Bool
| Hot _ => true
| Cold _ => false
def Spaces.isCold (s : Spaces) : Bool := !s.isHot
open Spaces Side
structure RenderState (A : Type) where
(sink: A)
(choices: List Choice)
(side: Side)
(spaces: Spaces)
instance {A : Type} : Stream (RenderState A) Choice where
  next? rs :=
  match rs.choices with
  | [] => none
  | hd :: tl => some (hd, { rs with choices := tl })
def RenderState.new {A : Type} (a : A) (choices: List Choice) : RenderState A := 
  ⟨a, choices, Left, Cold 0⟩
instance : Inhabited (RenderState String) := ⟨RenderState.new "" []⟩
structure Options where
(width : Nat)
class HasWrite (σ : Type) (m : Type -> Type v) where
(tell : String -> StateT (RenderState σ) m Unit)
instance : HasWrite String Id := {
  tell := fun s => fun st => return ((), { st with sink := st.sink.append s })
}
instance : HasWrite IO.FS.Stream IO := {
  tell := 
  fun s st => do
  st.sink.write s.toUTF8
  return ((), st)
}

import Printiest.Doc
open Doc
inductive Sexpr
| atom : String -> Sexpr
| list : Array Sexpr -> Sexpr
instance : Inhabited Sexpr := ⟨Sexpr.atom "default"⟩
instance : Coe String Sexpr := ⟨Sexpr.atom⟩
partial def Sexpr.pretty : Sexpr -> Doc
| atom s => Doc.Text s
| list es => 
  let inner := Doc.group (es.map pretty) " "
  "(" <> inner <> ")"
open Sexpr
def abcd : Sexpr := list #["a", "b", "c", "d"]
def abcd4 : Sexpr := list #[abcd, abcd, abcd, abcd]
def anSexpr : Sexpr := list #[
  list #["abcde", abcd4],
  list #["abcdefgh", abcd4]
]
-- The canonical "Prettiest" Sexpr demo
#eval IO.Prim.getStdout >>= anSexpr.pretty.renderStream 15
#eval IO.Prim.getStdout >>= anSexpr.pretty.renderStream 40
#eval IO.Prim.getStdout >>= anSexpr.pretty.renderStream 80
def bigSexpr0 := list #[anSexpr, anSexpr, anSexpr, anSexpr]
def bigSexpr1 := list #[bigSexpr0, bigSexpr0, bigSexpr0, bigSexpr0]
-- Don't bother trying to print these larger ones interactively (use leanpkg build bin)
def bigSexpr2 := list #[bigSexpr1, bigSexpr1, bigSexpr1, bigSexpr1]
def bigSexpr3 := list #[bigSexpr2, bigSexpr2, bigSexpr2, bigSexpr2]
def bigSexpr4 := list #[bigSexpr3, bigSexpr3, bigSexpr3, bigSexpr3]
def bigSexpr5 := list #[bigSexpr4, bigSexpr4, bigSexpr4, bigSexpr4]
def bigSexpr6 := list #[bigSexpr5, bigSexpr5]
def bigSexprTest (w : Nat) := bigSexpr6.pretty.renderString w
#eval IO.print (bigSexpr1.pretty.renderString 40)
-- Demo of the groupText thing.
def lorem := "Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed do eiusmod tempor incididunt ut labore et dolore magna aliqua. Ut enim ad minim veniam, quis nostrud exercitation ullamco laboris nisi ut aliquip ex ea commodo consequat."
#eval IO.Prim.getStdout >>= (groupTextFromString lorem).renderStream 20
#eval IO.Prim.getStdout >>= (groupTextFromString lorem).renderStream 40
#eval IO.Prim.getStdout >>= (groupTextFromString lorem).renderStream 80
namespace test1
def L : Doc := "points:"
def R := Doc.group #["1. first point", "2. second point", "3. third point"] " "
/-
The two hang operators; "alwaysHang" and "hang", where the latter will only
do hanging indentation if the given width can't fit everything on one line.
-/
#eval IO.Prim.getStdout >>= (hang 4 L R).renderStream 80
#eval IO.Prim.getStdout >>= (hang 4 L R).renderStream 20
#eval IO.Prim.getStdout >>= (alwaysHang 4 L R).renderStream 80
#eval IO.Prim.getStdout >>= (alwaysHang 4 L R).renderStream 20
end test1
/-
When there are linebreaks introduced by Flush/vConcat, concatenation
becomes "tetris-style", which is nice for code formatting.
-/
def tetrisDemo1 : Doc := ("xxxxxxxx" <n> "xxxx") <> ("########" <n> "####") <> ("........" <n> "....")
#eval IO.print (tetrisDemo1.renderString 80)
def tetrisDemo2 : Doc := ("abc" <n> "d") <> ("ghi" <n> "jkl") <> ("mno" <n> "pqr")
#eval IO.print (tetrisDemo2.renderString 80)
/-
If you want "normal" in-line concatenation, just don't use the newline operator (or otherwise insert a Flush).
-/
def concatDemo : Doc := ("abc" <> "def") <+> ("ghi" <> "jkl") <+> ("mno" <> "pqr")
#eval IO.print (concatDemo.renderString 80)
def gitOptions : List String :=
[
    "[--version]",
    "[--help]",
    "[-C <path>]",
    "[-c <name>=<value>]",
    "[--exec-path[=<path>]]",
    "[--html-path]",
    "[--man-path]",
    "[--info-path]",
    "[--p|--paginate|-P|--no-pager]",
    "[--no-replace-objects]",
    "[--bare]"
]
def helpText := "'git help -a' and 'git help -g' list available subcommands and some concept guides. See 'git help <command>' or 'git help <concept>' to read about a specific subcommand or concept. See 'git help git' for an overview of the system."
def gitCli := 
  let grp := group #["git" <+> groupText gitOptions, "<command>", "[<args>]"] " "
  --(hang 4 "usage:" ("git" <+> groupText gitOptions)) 
  (hang 4 "usage:" grp)
  <n> Nil 
  <n> groupTextFromString helpText
/-
Recreates a portion of the `git --help` output showing the ability
to render a CLI to best fit a given terminal width (ideally this would be
read from the user's terminal and then printed accordingly).
-/
#eval IO.Prim.getStdout >>= gitCli.renderStream 80
#eval IO.Prim.getStdout >>= gitCli.renderStream 40
#eval IO.Prim.getStdout >>= gitCli.renderStream 20
-- Demo of the helper function for creating a separated and surrounded list of items.
#eval IO.Prim.getStdout >>= (Doc.encloseSep "{" (gitOptions.map (fun x => Doc.Text x)).toArray "," "}" 4).renderStream 40
-- Force a group to be horizontal
def restrict_h := Doc.group (kind := GroupKind.horizontalCode) #["A", "B", "C"] ", "
#eval IO.Prim.getStdout >>= restrict_h.renderStream 1
-- Force a group to be vertical
def restrict_v := Doc.group (kind := GroupKind.vertical) #["A", "B", "C"] " "
#eval IO.Prim.getStdout >>= restrict_v.renderStream 40

import Std.Data.DList
import Printiest.Util
open Std (DList)
/-
Note: all of the comparisons (equality, LE, etc) use ONLY the
measure's dimensions; we're not concerned with the choices.
-/
structure Measure where
(height : Nat)
(maxWidth : Nat)
(lastWidth : Nat)
(choices : DList Choice)
instance Measure.Inhabited : Inhabited Measure where
  default := ⟨0, 0, 0, DList.empty⟩
instance : Ord Measure where
  compare a b :=
  match Ord.compare a.height b.height with
  | Ordering.lt => Ordering.lt
  | Ordering.gt => Ordering.gt
  | Ordering.eq => 
    match Ord.compare a.maxWidth b.maxWidth with
    | Ordering.lt => Ordering.lt
    | Ordering.gt => Ordering.gt
    | Ordering.eq => Ord.compare a.lastWidth b.lastWidth
instance : LE Measure :=
  ⟨fun m1 m2 => 
  match Ord.compare m1 m2 with
  | Ordering.lt => True
  | Ordering.eq => True
  | _ => False⟩
instance : LT Measure := ⟨fun m1 m2 => Ord.compare m1 m2 = Ordering.lt⟩
instance Measure.decLe (m1 m2 : Measure) : Decidable (LE.le m1 m2) := 
  match h:Ord.compare m1 m2 with
  | Ordering.lt => by
    simp only [LE.le, h] 
    exact (isTrue trivial)
  | Ordering.gt => by
    simp only [LE.le, h] 
    exact (isFalse id)
  | Ordering.eq => by
    simp only [LE.le, h]
    exact (isTrue trivial)
def Measure.lt (s1 s2 : Measure) : Bool :=
match Ord.compare s1 s2 with
| Ordering.lt => true
| _ => false
def Measure.dominates (s t : Measure) : Bool := 
  s.height <= t.height
  && s.maxWidth <= t.maxWidth
  && s.lastWidth <= t.lastWidth
def Measure.toString (m : Measure) : String := s!"⟨{m.height}, {m.maxWidth}, {m.lastWidth}, {m.choices.toList}⟩"
instance : ToString Measure := ⟨Measure.toString⟩
def Measure.beq (m1 m2 : Measure) : Bool := 
  match Ord.compare m1 m2 with
  | Ordering.eq => true
  | _ => false
instance : BEq Measure := ⟨Measure.beq⟩
def Measure.text (s : String) : Measure := ⟨0, s.length, s.length, DList.empty⟩
def Measure.concat (l r : Measure) : Measure := 
  ⟨l.height + r.height, 
  l.maxWidth.max (l.lastWidth + r.maxWidth),
  l.lastWidth + r.lastWidth,
  l.choices ++ r.choices⟩
def Measure.flush (m : Measure) : Measure := ⟨m.height.succ, m.maxWidth, 0, m.choices⟩
def Measure.fits (m: Measure) (width : Nat) : Bool := m.maxWidth <= width
def Measure.cons (m : Measure) (c : Choice) : Measure := { m with choices := m.choices.cons c }
def Measure.vConcat (l r : Measure) : Measure := l.flush.concat r
/-
  the end goal is some document that's a combination of a, b, and c.
  [
    possible layotus for a := [a1, a2, .. an]
    possible layouts for b := [b1, b2, .. bn]
    possible layouts for c := [c1, c2, .. cn]
  ]
  For certain horizontal groups, all of the elements have to be zero height.
  If it turns out that (for example) there are no possibilities for `a` that are zero height,
  then we need to detect that and abandon the horizontal grouping altogether, using
  vertical grouping instead.
-/
def zeroHeights (grps : Array (Nat × (Array Measure))) : Option (Array (Array Measure)) :=
  let zeroes_only := grps.map (fun ⟨_, grp⟩ => grp.filterMap (fun s => if s.height = 0 then some s else none))
  if zeroes_only.any (fun grp => grp.size = 0) 
  then none 
  else some zeroes_only
def arrayBind {A B : Type} (xs : Array A) (f : A -> Array B) : Array B :=
  xs.foldl (fun sink next => sink ++ f next) #[]
/--
from [x1, x2, .. xn], [y1, y2, .. yn] make [f x1 y1, f x1 y2, .. f xn yn] 
-/
def flatCartesian {A B C : Type} (f : A -> B -> C) (xs : Array A) (ys : Array B) : Array C :=
arrayBind xs (fun x => ys.map (fun y => f x y))
/--
If there are any measure that fit in the specified width, keep only those.
If there aren't, keep the single least wide (the one that will overflow the least)
-/
partial def discardInvalid (w : Nat) (sils: Array Measure): Array Measure :=
  let fit := sils.filter (fun s => s.fits w)
  if fit.size > 0 then fit else 
  match sils.get? 0 with
  | none => panic "discardInvalid should never get an empty array"
  | some hd => #[sils.foldl (fun least challenger => 
    if challenger.maxWidth < least.maxWidth || (least.maxWidth = challenger.maxWidth && (least <= challenger))
    then challenger
    else least) hd]
/--
Deduplicate a sorted array of measures
-/
partial def dedupSorted (rem: Array Measure) : Array Measure :=
  let rec aux (n : Nat) (out: Array Measure) : Array Measure :=
  match rem.get? n, rem.get? n.succ with
  | none, _ => out
  | some x, none => out.push x
  | some x, some y => if x != y then aux n.succ (out.push x)  else aux n.succ out
  aux 0 #[]
/--
From a list of measures, remove all those that are dominated 
since we know they're not going to give an optimal layout
-/
partial def dominant (rem: Array Measure) : Array Measure :=
  let rec aux (n : Nat) (out : Array Measure) : Array Measure :=
  match rem.get? n with
  | none => out
  | some x => if out.any (fun m => m.dominates x) then aux n.succ out else aux n.succ (out.push x)
  aux 0 #[]
def sort (input : Array Measure) : Array Measure := input.qsort (fun m1 m2 => Measure.lt m1 m2)
def pareto (w : Nat) : Array Measure -> Array Measure := dominant ∘ dedupSorted ∘ sort ∘ (discardInvalid w)
/-
Calculate the measures for different possible horizontal groups.
This is the regular one where the LAST element is the only one 
allowed to be non-zero height
From 
[
  [a1, a2, a3],
  [b1, b2, b3],
  [c1, c2, c3]
]
[(a1, b1, c1), (a1, b1, c2), .., (a3, b3, c3)]
-/
def measureH
  (grps : Array (Nat × (Array Measure))) 
  (width : Nat) 
  (sep : Measure) 
  : Array Measure := 
match grps.back? with
| none => #[]
| some ⟨_, hd⟩ => 
  match zeroHeights (grps.toSubarray 0 (grps.size - 1)) with
  | none => #[]
  | some rest => 
  let concat_sep := fun (s1 s2 : Measure) => (s1.concat sep).concat s2
  let inner := rest.foldr (fun next sink => pareto width $ flatCartesian concat_sep next sink) hd
  inner.map (fun measure => measure.cons (Choice.H measure.lastWidth))
-- The irregular one for text.
-- The FIRST element is the only one allowed to be non-zero height
def measureT
  (grps : Array (Nat × (Array Measure))) 
  (width : Nat) 
  (sep : Measure) 
  : Array Measure := 
match grps.get? 0 with
| none => #[]
| some ⟨_, hd⟩ => 
  match zeroHeights (grps.toSubarray 1 (grps.size)) with
  | none => #[]
  | some rest => 
  let concat_sep := fun m1 m2 => (m1.concat sep).concat m2
  let inner := rest.foldl (fun sink next => pareto width $ flatCartesian concat_sep sink next) hd
  inner.map (fun measure => measure.cons (Choice.T))
  
/-
Calculate the measures for different possible vertical groups.
From 
[
  [a1, a2, a3],
  [b1, b2, b3],
  [c1, c2, c3]
]
[(a1, b1, c1), (a1, b1, c2), .., (a3, b3, c3)]
-/
def measureV
  (grps : Array (Nat × (Array Measure))) 
  (width : Nat) 
  : Array Measure := 
-- for each x in [x1, x2, .. xn], indent it by the proper amount by concatenating
-- some chunk on the left hand side.
let indented := grps.map (fun ⟨amt, grp⟩ => grp.map (fun x => (Measure.mk 0 amt 0 DList.empty).concat x))
match indented.get? 0 with
| none => #[]
| some hd => 
  let rest := indented.toSubarray 1 (grps.size)
  let concat_nl := fun (s1 s2 : Measure) => s1.vConcat s2
  let inner := rest.foldl (fun sink next => pareto width $ flatCartesian concat_nl sink next) hd
  inner.map (fun measure => measure.cons (Choice.V measure.lastWidth))

import Std.Data.DList
import Printiest.Util
import Printiest.Measure
open Std (DList)
open Spaces Side
/-
GroupKind controls how Groups are rendered. Generally the choice is going to be whether
you're formatting code or formatting text. If you don't want to choose, you don't have to,
but this will have some impact performance since we potentially have 3 branches instead of 2 at every
`Group`. Most of the time, one of the choices will dominate the other (have strictly more attractive
dimensions) meaning the alternative won't be considered, but there will be outliers.
The main issue is that the horizontal layout scheme originally implemented in `Prettiest` doesn't
lay out blocks of human-language text well, because it wants all the leading elements to be 
non-zero height, and allows the LAST one to be non-zero, then does a fold right, so we can have 
things that hang/indent nicely, like:
```
a b c d e f
      g h i
      j k l m n o
          p q r s t u
```
But for text, we want to have a block, for which the FIRST element can be non-zero height, but
the rest need to be zero-height, and we want to fold LEFT, so we get things like:
```
Lorem ipsum dolor sit amet, consectetur
adipiscing elit, sed do eiusmod tempor
incididunt ut labore et dolore magna
aliqua. Ut enim ad minim veniam, quis
nostrud exercitation ullamco laboris
nisi ut aliquip ex ea commodo consequat.
```
Here, if we began with a "first" element of 
```
Lorem ipsum dolor sit amet, consectetur
adipiscing elit, 
```
and a second element of `sed`, we want 'sed' to be "tetris'd" into the
rest of the block if we began by wanting the whole thing to be grouped.
For that to happen, we have to allow non-zero height elements on the LHS.
G(G(G(G("", Lorem), ipsum) dolor) sit)...
We allow the first element to be non-zero so we can nicely tetris together blocks of text
without forcing them to be new paragraphs.
GroupKind is supposed to be a bitfield
1 |-> HorizontalCode
2 |-> HorizontalText
4 |-> Vertical
normal is horizontalCode + Vertical
text is horizontalText + Vertical
-/
abbrev GroupKind := UInt8
def GroupKind.horizontalCode : GroupKind := 1
def GroupKind.horizontalText : GroupKind := 2
def GroupKind.vertical : GroupKind := 4
def GroupKind.normal : GroupKind := GroupKind.horizontalCode.lor GroupKind.vertical
def GroupKind.text : GroupKind := GroupKind.horizontalText.lor GroupKind.vertical
def GroupKind.all : GroupKind := (GroupKind.horizontalText.lor GroupKind.vertical).lor GroupKind.horizontalCode
inductive Doc
| Nil : Doc
| Text (s: String) : Doc
| Concat (l: Doc) (r: Doc) : Doc
| Flush (d: Doc) : Doc
| Group (ds: Array (Nat × Doc)) (sep: String) (kind: GroupKind) : Doc
instance : Inhabited Doc := ⟨Doc.Nil⟩
instance : Coe String Doc := ⟨Doc.Text⟩ 
def Doc.vConcat (l r : Doc) : Doc := Doc.Concat (Flush l) r
infixl:65 " <> "  => Doc.Concat
-- Concatenate d1 and d2, putting a single space between them.
infixl:65 " <+> " => fun d1 d2 => d1 <> Doc.Text " " <> d2
/- 
Concatenate d1 and d2 vertically:
d1
d2
-/
infixl:65 " <n> " => fun d1 d2 => Doc.vConcat d1 d2
/-
The default group style is `normal`. Generally if you're grouping a block of text
you want to use groupText to make it look nice, which is different enough that 
it has a slightly different name.
You can limit it to `horizontal` or `vertical` if you KNOW you want to restrict
the rendering to a certain look, or if you're concerned about performance for 
either extremely large or degenerate Docs.
-/
def Doc.group 
  (docs : Array Doc) 
  (sep : String) 
  (kind : GroupKind := GroupKind.normal) : Doc := 
  Group (docs.map $ fun x => (0, x)) sep kind
def Doc.groupIndent 
  (docs : Array (Nat × Doc)) 
  (sep : String) 
  (kind : GroupKind := GroupKind.normal) : Doc := 
  Group docs sep kind
/-
For creating blocks of text.
-/
def Doc.groupText (l: List String) : Doc :=
  match l with
  | [] => Doc.Nil
  | hd :: tl => 
  let base := Doc.Text hd
  tl.foldl (fun sink next => Doc.Group #[(0, sink), (0, Doc.Text next)] " " GroupKind.text) base
/--
For creating blocks of text split on a character identified by `p`.
-/
def Doc.groupTextFromString (s : String) : Doc := Doc.groupText $ s.split (fun c => c = ' ')
def blank (n : Nat): String :=
  let rec aux (n : Nat) (acc : String) : String :=
    match n with
    | 0 => acc
    | (n+1) => aux n (acc ++ " ")
  aux n ""
def Doc.alwaysHang (indent : Nat) (upper : Doc) (lower : Doc) : Doc := 
  let rhs := Doc.Concat (Doc.Text $ blank indent) lower
  Concat (Flush upper) rhs
/-
Given `self` and `ys`, this will print bothon the same line
iff they fit, otherwise it will print `xs`, then hang `ys`.
WARNING: This will probably not look good if the RHS is a group.
```text
  EITHER
  self ys1 ys2
  OR
  self
      ys1
      ys2
```
-/
def Doc.hang (indent : Nat) (upper : Doc) (lower : Doc) (sep : String := " ") : Doc := 
  Doc.groupIndent #[(0, upper), (indent, lower)] sep
/-
Make IE
```
[
  x,
  y,
  z
]
```
-/
def Doc.encloseSep (l : Doc) (docs: Array Doc) (sep: String) (r : Doc) (indent : Nat) : Doc :=
  match docs.get? docs.size.pred with
  | none => Doc.Concat l r
  | some last => 
    let sub := (docs.toSubarray 0 docs.size.pred).toArray
    let middle := sub.map (fun d => Doc.Concat d sep)
    let inner := Doc.group (middle.push last) ""
    Doc.groupIndent #[(0, l), (indent, inner), (0, r)] ""
/-
Calcualte the sizes/shapes of different possible outcomes.
Ideally this would measure strings based on unicode graphemes instead
of length, but for now we're working with what we have.
-/
partial def Doc.measure (w : Nat) : Doc -> Array Measure
| Nil => #[Inhabited.default]
| Text t => #[Measure.text t]
| Concat l r => 
  let ls := l.measure w
  let rs := r.measure w
  pareto w $ flatCartesian Measure.concat ls rs
| Flush d => pareto w $ (d.measure w).map Measure.flush
| Group ds sep kind => 
  let inner := ds.map (fun (indent, d) => (indent, d.measure w))
  let sep := Measure.text sep
  let horizontal := if kind.land GroupKind.horizontalCode != 0 then measureH inner w sep else #[]
  let text := if kind.land GroupKind.horizontalText != 0 then measureT inner w sep else #[]
  let vertical := if kind.land GroupKind.vertical != 0 then measureV inner w else #[]
  pareto w $ horizontal ++ text ++ vertical
partial def Doc.renderAux
  {m : Type -> Type} 
  [inst1: Monad m] 
  [Inhabited (m (RenderState σ))] 
  [HasWrite σ m]
  (w : Nat) 
  : Doc -> StateT (RenderState σ) m Unit
| Nil => return
| Text txt => do
  let blank := match (<- get).spaces with
  | Hot n => blank n
  | _ => ""
  HasWrite.tell blank
  HasWrite.tell txt
  modify $ fun s' => { s' with spaces := Cold (txt.length + s'.spaces.toNat)}
 
| Concat l r => do
  fun s => l.renderAux w { s with side := Left }
  fun s => r.renderAux w { s with side := Right }
  modify $ fun s => { s with spaces := s.spaces.toCold }
| Flush d => do
  let s0 <- get
  d.renderAux w
  HasWrite.tell "\n"
  match s0.side with
  | Left => modify $ fun s' => { s' with spaces := s0.spaces.toHot }
  | Right => modify fun s' => { s' with spaces := Hot 0 }
| Group ds sep kind => do
  let s0 <- get
  let mut diffs_total := 0
  let mut iterations : Nat := 0
  let last <- modifyGet $ fun s => 
    match s.choices with
    | [] => (Choice.V 0, s0)
    | hd :: tl => (hd, { s with choices := tl })
  match last with
  | Choice.H lw =>
      for (_, d) in ds do
        let ind_num := if iterations + 1 = ds.size then s0.spaces.toNat + diffs_total else s0.spaces.toNat
        let ind := if (<- get).spaces.isHot then Hot ind_num else Cold ind_num
        fun s => d.renderAux w { s with side := s0.side, spaces := ind }
        if iterations + 1 != ds.size then 
            diffs_total := (diffs_total + sep.length + (<- get).spaces.toNat) - ind.toNat
            HasWrite.tell sep
        iterations := iterations + 1
      modify $ fun s => { s with spaces := Cold (lw + s0.spaces.toNat) }
  | Choice.V lw => 
        for (local_ind, d) in ds do
          let ind_num := s0.spaces.toNat + local_ind
          let ind := if iterations = 0 && (<- get).spaces.isCold then Cold ind_num else Hot ind_num
          fun s => d.renderAux w { s with side := s0.side, spaces := ind }
          if iterations + 1 != ds.size then HasWrite.tell "\n"
          iterations := iterations + 1
        modify $ fun s => { s with spaces := Cold (lw + s0.spaces.toNat) }
  | Choice.T =>
        for (_, d) in ds do
          let ind_num := s0.spaces.toNat
          let ind := if iterations = 0 && (<- get).spaces.isHot then Hot ind_num else Cold ind_num
          fun s => d.renderAux w { s with side := s0.side, spaces := ind }
          if iterations + 1 != ds.size then HasWrite.tell sep
          iterations := iterations + 1
        modify $ fun state => { state with spaces := s0.spaces.toCold }
/-
Render a Doc with the given width directly to a stream.
I'm not sure how Lean handles writing to a stream internally; I know in Rust there are
performance issues without buffered writers
-/
def Doc.renderStream (doc : Doc) (width: Nat) (stream: IO.FS.Stream) : IO Unit := do 
let sils := doc.measure width
let hd := sils.get! 0
let choices := hd.choices.toList
let _ <- doc.renderAux width (RenderState.new stream choices)
/-
Render a Doc with the given width into a string accumulator.
-/
def Doc.renderString (doc : Doc) (width: Nat) : String := do 
let sils := doc.measure width
let hd := sils.get! 0
let choices := hd.choices.toList
let (_, rs) <- doc.renderAux width (RenderState.new "" choices)
rs.sink

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  11. Patents.
  A "contributor" is a copyright holder who authorizes use under this
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  Notwithstanding any other provision of this License, you have
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                     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
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    (at your option) any later version.
    This program is distributed in the hope that it will be useful,
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    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 <https://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
<https://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
<https://www.gnu.org/licenses/why-not-lgpl.html>.

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