------------------------------------------------------------------------
-- The Agda standard library
--
-- Pretty Printing
-- This module is based on Jean-Philippe Bernardy's functional pearl
-- "A Pretty But Not Greedy Printer"
------------------------------------------------------------------------

{-# OPTIONS --with-K #-}

module Text.Pretty.Core where

import Level

open import Data.Bool.Base using (Bool)
open import Data.Irrelevant as Irrelevant using (Irrelevant) hiding (module Irrelevant)
open import Data.List.Base as List   using (List; []; _∷_)
open import Data.Nat.Base            using (; zero; suc; _+_; _⊔_; _≤_; z≤n)
open import Data.Nat.Properties
open import Data.Product.Base as Prod using (_×_; _,_; uncurry; proj₁; proj₂)
import Data.Product.Relation.Unary.All as Allᴾ

open import Data.Tree.Binary as Tree using (Tree; leaf; node; #nodes; mapₙ)
open import Data.Tree.Binary.Relation.Unary.All as Allᵀ using (leaf; node)
open import Data.Unit using (; tt)
import Data.Tree.Binary.Relation.Unary.All.Properties as Allᵀₚ
import Data.Tree.Binary.Properties as Treeₚ

open import Data.Maybe.Base as Maybe using (Maybe; nothing; just; maybe′)
open import Data.Maybe.Relation.Unary.All as Allᴹ using (nothing; just)

open import Data.String.Base as String
  using (String; length; replicate; _++_; unlines)
open import Data.String.Unsafe as Stringₚ
open import Function.Base
open import Relation.Nullary.Decidable using (Dec)
open import Relation.Unary using (IUniversal; _⇒_; U)
open import Relation.Binary.PropositionalEquality

open import Data.Refinement hiding (map)
import Data.Refinement.Relation.Unary.All as Allᴿ

------------------------------------------------------------------------
-- Block of text

-- Content is a representation of the first line and the middle of the
-- block. We use a tree rather than a list for the middle of the block
-- so that we can extend it with lines on the left and on the line for
-- free. We will ultimately render the block by traversing the tree left
-- to right in a depth-first manner.

Content : Set
Content = Maybe (String × Tree String )

size : Content  
size = maybe′ (suc  #nodes  proj₂) 0

All :  {p} (P : String  Set p)  (Content  Set p)
All P = Allᴹ.All (Allᴾ.All P (Allᵀ.All P U))

All≤ :   Content  Set
All≤ n = All  s  length s  n)

record Block : Set where
  field
    height    : 
    block     : [ xs  Content  size xs  height ]
  -- last line
    lastWidth : 
    last      : [ s  String  length s  lastWidth ]
  -- max of all the widths
    maxWidth  : [ n    lastWidth  n × All≤ n (block .value) ]

------------------------------------------------------------------------
-- Raw string

text : String  Block
text s = record
  { height    = 0
  ; block     = nothing ,  refl 
  ; lastWidth = width
  ; last      = s ,  refl 
  ; maxWidth  = width ,  (≤-refl , nothing) 
  } where width = length s; open Irrelevant

------------------------------------------------------------------------
-- Empty

empty : Block
empty = text ""

------------------------------------------------------------------------
-- Helper functions

node? : Content  String  Tree String   Content
node? (just (x , xs)) y ys = just (x , node xs y ys)
node? nothing         y ys = just (y , ys)

∣node?∣ :  b y ys  size (node? b y ys)
                    size b + suc (#nodes ys)
∣node?∣ (just (x , xs)) y ys = refl
∣node?∣ nothing         y ys = refl

≤-Content :  {m n} {b : Content}  m  n  All≤ m b  All≤ n b
≤-Content {m} {n} m≤n = Allᴹ.map (Prod.map step (Allᵀ.mapₙ step))

  where

  step :  {p}  p  m  p  n
  step = flip ≤-trans m≤n

All≤-node? :  {l m r n} 
             All≤ n l  length m  n  Allᵀ.All  s  length s  n) U r 
             All≤ n (node? l m r)
All≤-node? nothing           py pys = just (py , pys)
All≤-node? (just (px , pxs)) py pys = just (px , node pxs py pys)

------------------------------------------------------------------------
-- Appending two documents

private
  module append (x y : Block) where

    module x = Block x
    module y = Block y

    blockx = x.block .value
    blocky = y.block .value

    widthx = x.maxWidth .value
    widthy = y.maxWidth .value

    lastx = x.last .value
    lasty = y.last .value

    height : 
    height = (_+_ on Block.height) x y

    lastWidth : 
    lastWidth = (_+_ on Block.lastWidth) x y

    pad : Maybe String
    pad with x.lastWidth
    ... | 0 = nothing
    ... | l = just (replicate l ' ')

    size-pad : maybe′ length 0 pad  x.lastWidth
    size-pad with x.lastWidth
    ... | 0         = refl
    ... | l@(suc _) = length-replicate l

    indent : Maybe String  String  String
    indent = maybe′ _++_ id

    size-indent :  ma str  length (indent ma str)
                 maybe′ length 0 ma + length str
    size-indent nothing    str = refl
    size-indent (just pad) str = length-++ pad str

    indents : Maybe String  Tree String   Tree String 
    indents = maybe′ (mapₙ  _++_) id

    size-indents :  ma t  #nodes (indents ma t)  #nodes t
    size-indents nothing    t = refl
    size-indents (just pad) t = Treeₚ.#nodes-mapₙ (pad ++_) t

    unfold-indents :  ma t  indents ma t  mapₙ (indent ma) t
    unfold-indents nothing    t = sym (Treeₚ.map-id t)
    unfold-indents (just pad) t = refl

    vContent : Content × String
    vContent with blocky
    ... | nothing        = blockx
                         , lastx ++ lasty
    ... | just (hd , tl) = node?
      {-,--------------,-}
      {-|-} blockx   {-|-}
      {-|-}          {-'---,-}    {-,------------------,-}
      {-|-} (lastx       {-|-} ++ {-|-}  hd)         {-|-}
      {-'------------------'-}    {-|-}              {-|-}
      (indents pad                {-|-}  tl)    {-,----'-}
      , indent pad                {-|-} lasty   {-|-}
                                  {-'-------------'-}

    vBlock = proj₁ vContent
    vLast  = proj₂ vContent

    isBlock : size blockx  x.height  size blocky  y.height 
              size vBlock  height
    isBlock ∣x∣ ∣y∣ with blocky
    ... | nothing        = begin
      size blockx         ≡⟨ ∣x∣ 
      x.height            ≡⟨ +-identityʳ x.height 
      x.height + 0        ≡⟨ cong (_ +_) ∣y∣ 
      x.height + y.height  where open ≡-Reasoning
    ... | just (hd , tl) = begin
      ∣node∣                            ≡⟨ ∣node?∣ blockx middle rest 
      ∣blockx∣ + suc (#nodes rest) ≡⟨ cong ((size blockx +_) ∘′ suc) ∣rest∣ 
      ∣blockx∣ + suc (#nodes tl)   ≡⟨ cong₂ _+_ ∣x∣ ∣y∣ 
      x.height + y.height                where

      open ≡-Reasoning
      ∣blockx∣ = size blockx
      middle   = lastx ++ hd
      rest     = indents pad tl
      ∣rest∣   = size-indents pad tl
      ∣node∣   = size (node? blockx middle rest)

    block : [ xs  Content  size xs  height ]
    block .value = vBlock
    block .proof =  isBlock (Block.block x .proof) (Block.block y .proof) 
      where open Irrelevant

    isLastLine : length lastx  x.lastWidth 
                 length lasty  y.lastWidth 
                 length vLast  lastWidth
    isLastLine ∣x∣ ∣y∣ with blocky
    ... | nothing        = begin
      length (lastx ++ lasty)       ≡⟨ length-++ lastx lasty 
      length lastx + length lasty   ≡⟨ cong₂ _+_ ∣x∣ ∣y∣ 
      x.lastWidth + y.lastWidth      where open ≡-Reasoning
    ... | just (hd , tl) = begin
      length (indent pad lasty)          ≡⟨ size-indent pad lasty 
      maybe′ length 0 pad + length lasty ≡⟨ cong₂ _+_ size-pad ∣y∣ 
      x.lastWidth + y.lastWidth           where open ≡-Reasoning

    last : [ s  String  length s  lastWidth ]
    last .value = vLast
    last .proof =  isLastLine (Block.last x .proof) (Block.last y .proof) 
      where open Irrelevant

    vMaxWidth : 
    vMaxWidth = widthx  (x.lastWidth + widthy)

    isMaxWidth₁ : y.lastWidth  widthy  lastWidth  vMaxWidth
    isMaxWidth₁ p = begin
      lastWidth            ≤⟨ +-monoʳ-≤ x.lastWidth p 
      x.lastWidth + widthy ≤⟨ m≤n⊔m _ _ 
      vMaxWidth             where open ≤-Reasoning

    isMaxWidth₂ : length lastx  x.lastWidth 
                  x.lastWidth  widthx 
                  All≤ widthx blockx 
                  All≤ widthy blocky 
                  All≤ vMaxWidth vBlock
    isMaxWidth₂ ∣x∣≡ ∣x∣≤ ∣xs∣ ∣ys∣ with blocky
    ... | nothing        = ≤-Content (m≤m⊔n _ _) ∣xs∣
    isMaxWidth₂ ∣x∣≡ ∣x∣≤ ∣xs∣ (just (∣hd∣ , ∣tl∣))
        | just (hd , tl) =
      All≤-node? (≤-Content (m≤m⊔n _ _) ∣xs∣)
                 middle
                 (subst (Allᵀ.All _ U) (sym $ unfold-indents pad tl)
                 $ Allᵀₚ.mapₙ⁺ (indent pad) (Allᵀ.mapₙ (indented _) ∣tl∣))
      where

      middle : length (lastx ++ hd)  vMaxWidth
      middle = begin
        length (lastx ++ hd)     ≡⟨ length-++ lastx hd 
        length lastx + length hd ≡⟨ cong (_+ _) ∣x∣≡ 
        x.lastWidth + length hd  ≤⟨ +-monoʳ-≤ x.lastWidth ∣hd∣ 
        x.lastWidth + widthy     ≤⟨ m≤n⊔m _ _ 
        vMaxWidth                 where open ≤-Reasoning

      indented :  s  length s  widthy 
                 length (indent pad s)  vMaxWidth
      indented s ∣s∣ = begin
        length (indent pad s)          ≡⟨ size-indent pad s 
        maybe′ length 0 pad + length s ≡⟨ cong (_+ _) size-pad 
        x.lastWidth + length s         ≤⟨ +-monoʳ-≤ x.lastWidth ∣s∣ 
        x.lastWidth + widthy           ≤⟨ m≤n⊔m (widthx) _ 
        vMaxWidth                       where open ≤-Reasoning

    maxWidth : [ n    lastWidth  n × All≤ n vBlock ]
    maxWidth .value = vMaxWidth
    maxWidth .proof =
       _,_  isMaxWidth₁ (map proj₁ (Block.maxWidth y .proof)) 
             isMaxWidth₂ (Block.last x .proof)
                          (map proj₁ (Block.maxWidth x .proof))
                          (map proj₂ (Block.maxWidth x .proof))
                          (map proj₂ (Block.maxWidth y .proof))
            
       where open Irrelevant

infixl 4 _<>_
_<>_ : Block  Block  Block
x <> y = record { append x y }

------------------------------------------------------------------------
-- Flush (introduces a new line)

private
  module flush (x : Block) where

    module x = Block x
    blockx  = x.block .value
    lastx   = x.last .value
    widthx  = x.maxWidth .value
    heightx = x.height

    height    = suc heightx
    lastWidth = 0
    vMaxWidth = widthx

    last : [ s  String  length s  lastWidth ]
    last = "" ,  refl  where open Irrelevant

    vContent = node? blockx lastx (leaf tt)

    isBlock : size blockx  heightx  size vContent  height
    isBlock ∣x∣ = begin
      size vContent   ≡⟨ ∣node?∣ blockx lastx (leaf tt) 
      size blockx + 1 ≡⟨ cong (_+ 1) ∣x∣ 
      heightx + 1     ≡⟨ +-comm heightx 1 
      height           where open ≡-Reasoning

    block : [ xs  Content  size xs  height ]
    block .value = vContent
    block .proof = Irrelevant.map isBlock $ Block.block x .proof

    maxWidth : [ n    lastWidth  n × All≤ n vContent ]
    maxWidth .value = widthx
    maxWidth .proof = map (z≤n ,_)
       All≤-node?  proj₂ (Block.maxWidth x .proof) 
                    middle (Block.last x .proof)  proj₁ (Block.maxWidth x .proof)  
                   (pure (leaf tt))
       where

      open Irrelevant

      middle : length lastx  x.lastWidth  x.lastWidth  vMaxWidth 
               length lastx  vMaxWidth
      middle p q = begin
        length lastx ≡⟨ p 
        x.lastWidth  ≤⟨ q 
        vMaxWidth     where open ≤-Reasoning

flush : Block  Block
flush x = record { flush x }

------------------------------------------------------------------------
-- Other functions

render : Block  String
render x = unlines
  $ maybe′ (uncurry  hd tl  hd  Tree.Infix.toList tl)) []
  $ node? (Block.block x .value) (Block.last x .value) (leaf tt)

valid : (width : ) (b : Block)  Dec (Block.maxWidth b .value  width)
valid width b = Block.maxWidth b .value ≤? width