─────╷─────────── $𝖒𝖘𝖞𝖚/𝖒𝖆𝖘𝖞𝖚-𝖗𝖚𝖑𝖊𝖘.𝖘𝖆𝖕𝖕𝖍𝖎𝖗𝖊 ─────────────────────────────────────────────────────────

    0┊----------------------------------| Masyu Rules in Sapphire |-----------------------------------

    1┊--|∙‹https://www.nikoli.co.jp/en/puzzles/masyu›∙and∙‹https://en.wikipedia.org/wiki/Masyu›      

    2┊                                                                                               

    3┊Idx={0⋯n⨫1}×{0⋯m⨫1}∙--|∙0∙based∙indexing∙by∙pairs                                              

    4┊                                                                                               

    5┊x0∈{0⋯n⨫2}∙∧∙y0∈{0⋯m⨫2}∙∧∙⦗id∙x0∙y0⦘=0                                                         

    6┊                                                                                               

    7┊∀⟨x∙y⟩∈Idx                                                                                     

    8┊∙∙⦗sol∙x∙y⦘∈{0⋯4}                                                                              

    9┊∙∙⦗id∙x∙y⦘∈{0⋯n·m}                                                                             

   10┊∙∙⦗id∙x∙y⦘=0∙⇐⇒∙x=x0∙∧∙y=y0                                                                    

   11┊∙∙⦗sol∙x∙y⦘∈{0⋯3}∙⇒∙y0<=y∙∧∙(y0=y∙⇒∙x0<=x)                                                     

   12┊∙∙⦗sol∙x∙y⦘=4∙⇐⇒∙⦗id∙x∙y⦘=n·m                                                                  

   13┊                                                                                               

   14┊∙∙x=0∙∙∙⇒∙⦗sol∙x∙y⦘∈{1∙3∙4}                                                                    

   15┊∙∙x=n⨫1∙⇒∙⦗sol∙x∙y⦘∈{0∙2∙4}                                                                    

   16┊∙∙y=0∙∙∙⇒∙⦗sol∙x∙y⦘∈{0∙3∙4}                                                                    

   17┊∙∙y=m⨫1∙⇒∙⦗sol∙x∙y⦘∈{1∙2∙4}                                                                    

   18┊                                                                                               

   19┊∙∙--|∙if∙on∙path,∙here∙points∙somewhere∙else∙on∙the∙path                                       

   20┊∙∙⦗sol∙x∙y⦘=0∙⇒∙y<m⨫1∙∧∙⦗sol∙x∙y+1⦘∈{0∙2∙3}∙∧∙⦗id∙x∙y+1⦘=⦗id∙x∙y⦘+1                            

   21┊∙∙⦗sol∙x∙y⦘=1∙⇒∙y>0∙∙∙∧∙⦗sol∙x∙y⨫1⦘∈{1∙2∙3}∙∧∙(⦗id∙x∙y⨫1⦘=⦗id∙x∙y⦘+1∙∨∙⦗id∙x∙y⨫1⦘=0)           

   22┊∙∙⦗sol∙x∙y⦘=2∙⇒∙x>0∙∙∙∧∙⦗sol∙x⨫1∙y⦘∈{0∙1∙2}∙∧∙⦗id∙x⨫1∙y⦘=⦗id∙x∙y⦘+1                            

   23┊∙∙⦗sol∙x∙y⦘=3∙⇒∙x<n⨫1∙∧∙⦗sol∙x+1∙y⦘∈{0∙1∙3}∙∧∙⦗id∙x+1∙y⦘=⦗id∙x∙y⦘+1                            

   24┊                                                                                               

   25┊∙∙--|∙if∙on∙path,∙something∙points∙here                                                        

   26┊∙∙⦗sol∙x∙y⦘¬=4∙⇒                                                                               

   27┊∙∙∙∙∙∙y<m⨫1∙∧∙⦗sol∙x∙y+1⦘=1∙∧∙∙⦗id∙x∙y⦘=⦗id∙x∙y+1⦘+1∙∨                                         

   28┊∙∙∙∙∙∙y>0∙∙∙∧∙⦗sol∙x∙y⨫1⦘=0∙∧∙∙⦗id∙x∙y⦘=⦗id∙x∙y⨫1⦘+1∙∨                                         

   29┊∙∙∙∙∙∙x>0∙∙∙∧∙⦗sol∙x⨫1∙y⦘=3∙∧∙∙⦗id∙x∙y⦘=⦗id∙x⨫1∙y⦘+1∙∨                                         

   30┊∙∙∙∙∙∙x<n⨫1∙∧∙⦗sol∙x+1∙y⦘=2∙∧∙∙⦗id∙x∙y⦘=⦗id∙x+1∙y⦘+1∙∨                                         

   31┊∙∙∙∙∙∙x=x0∙∧∙y=y0∙∧∙y<m⨫1∙∧∙⦗sol∙x∙y⦘=3∙∧∙⦗sol∙x∙y+1⦘=1∙∧∙⦗id∙x∙y⦘=0                           

   32┊                                                                                               

   33┊∙∙--|∙if∙not∙on∙path,∙nothing∙points∙here                                                      

   34┊∙∙⦗sol∙x∙y⦘=4∙⇒                                                                                

   35┊∙∙∙∙y>0∙∙∙⇒∙⦗sol∙x∙y⨫1⦘¬=0                                                                     

   36┊∙∙∙∙y<m⨫1∙⇒∙⦗sol∙x∙y+1⦘¬=1                                                                     

   37┊∙∙∙∙x>0∙∙∙⇒∙⦗sol∙x⨫1∙y⦘¬=3                                                                     

   38┊∙∙∙∙x<n⨫1∙⇒∙⦗sol∙x+1∙y⦘¬=2                                                                     

   39┊                                                                                               

   40┊∙∙⦗dot∙x∙y⦘=1∙⇒                                                                                

   41┊∙∙∙∙⦗sol∙x∙y⦘∈{0⋯3}                                                                            

   42┊∙∙∙∙⦗sol∙x∙y⦘=0∙⇒∙y<m⨫2∙∧∙⦗sol∙x∙y+1⦘=0∙∧                                                      

   43┊∙∙∙∙∙∙∙∙(x>=2∙∧∙⦗sol∙x⨫1∙y⦘=3∙∧∙⦗sol∙x⨫2∙y⦘=3∙∨∙x<n⨫2∙∧∙⦗sol∙x+1∙y⦘=2∙∧∙⦗sol∙x+2∙y⦘=2)         

   44┊∙∙∙∙⦗sol∙x∙y⦘=1∙⇒∙y>=2∙∧∙⦗sol∙x∙y⨫1⦘=1∙∧                                                       

   45┊∙∙∙∙∙∙∙∙(x>=2∙∧∙⦗sol∙x⨫1∙y⦘=3∙∧∙⦗sol∙x⨫2∙y⦘=3∙∨∙x<n⨫2∙∧∙⦗sol∙x+1∙y⦘=2∙∧∙⦗sol∙x+2∙y⦘=2)         

   46┊∙∙∙∙⦗sol∙x∙y⦘=2∙⇒∙x>=2∙∧∙⦗sol∙x⨫1∙y⦘=2∙∧                                                       

   47┊∙∙∙∙∙∙∙∙(y>=2∙∧∙⦗sol∙x∙y⨫1⦘=0∙∧∙⦗sol∙x∙y⨫2⦘=0∙∨∙y<m⨫2∙∧∙⦗sol∙x∙y+1⦘=1∙∧∙⦗sol∙x∙y+2⦘=1)         

   48┊∙∙∙∙⦗sol∙x∙y⦘=3∙⇒∙x<n⨫2∙∧∙⦗sol∙x+1∙y⦘=3∙∧                                                      

   49┊∙∙∙∙∙∙∙∙(y>=2∙∧∙⦗sol∙x∙y⨫1⦘=0∙∧∙⦗sol∙x∙y⨫2⦘=0∙∨∙y<m⨫2∙∧∙⦗sol∙x∙y+1⦘=1∙∧∙⦗sol∙x∙y+2⦘=1)         

   50┊                                                                                               

   51┊∙∙⦗dot∙x∙y⦘=2∙⇒                                                                                

   52┊∙∙∙∙∙∙x>0∙∧∙x<n⨫1∙∧                                                                            

   53┊∙∙∙∙∙∙∙∙(⦗sol∙x∙y⦘=2∙∧∙⦗sol∙x+1∙y⦘=2∙∧                                                         

   54┊∙∙∙∙∙∙∙∙∙∙(⦗sol∙x⨫1∙y⦘∈{0∙1}∙∨∙y>0∙∧∙⦗sol∙x+1∙y⨫1⦘=0∙∨∙y<m⨫1∙∧∙⦗sol∙x+1∙y+1⦘=1)                

   55┊∙∙∙∙∙∙∙∙∨                                                                                      

   56┊∙∙∙∙∙∙∙∙⦗sol∙x∙y⦘=3∙∧∙⦗sol∙x⨫1∙y⦘=3∙∧                                                          

   57┊∙∙∙∙∙∙∙∙∙∙(⦗sol∙x+1∙y⦘∈{0∙1}∙∨∙y>0∙∧∙⦗sol∙x⨫1∙y⨫1⦘=0∙∨∙y<m⨫1∙∧∙⦗sol∙x⨫1∙y+1⦘=1))               

   58┊∙∙∙∙∙∙∨                                                                                        

   59┊∙∙∙∙∙∙y>0∙∧∙y<m⨫1∙∧                                                                            

   60┊∙∙∙∙∙∙∙∙(⦗sol∙x∙y⦘=1∧⦗sol∙x∙y+1⦘=1∙∧                                                           

   61┊∙∙∙∙∙∙∙∙∙∙(⦗sol∙x∙y⨫1⦘∈{2∙3}∙∨∙x>0∙∧∙⦗sol∙x⨫1∙y+1⦘=3∙∨∙x<n⨫1∙∧∙⦗sol∙x+1∙y+1⦘=2)                

   62┊∙∙∙∙∙∙∙∙∨                                                                                      

   63┊∙∙∙∙∙∙∙∙⦗sol∙x∙y⦘=0∧⦗sol∙x∙y⨫1⦘=0∙∧                                                            

   64┊∙∙∙∙∙∙∙∙∙∙(⦗sol∙x∙y+1⦘∈{2∙3}∙∨∙x>0∙∧∙⦗sol∙x⨫1∙y⨫1⦘=3∙∨∙x<n⨫1∙∧∙⦗sol∙x+1∙y⨫1⦘=2))               

   65┊                                                                                               

   66┊                                                                                               

   67┊--|∙add∙to∙help∙solver∙(many∙x∙speedup∙in∙pure∙loop);∙want∙to∙automate∙this∙in∙future          

   68┊∀⟨x∙y⟩∈{0⋯n}×{0⋯m}                                                                             

   69┊∙∙⦗in?∙x∙y⦘∈{0∙1}                                                                              

   70┊∙∙x=0∙∨∙y=0∙∨∙x=n∙∨∙y=m∙⇒∙⦗in?∙x∙y⦘=0                                                          

   71┊∙∙x>0∙∧∙y>0∙∧∙y<m∙⇒∙(⦗in?∙x∙y⦘=⦗in?∙x⨫1∙y⦘∙⇐⇒∙⦗sol∙x⨫1∙y⨫1⦘¬=0∧⦗sol∙x⨫1∙y⦘¬=1)                 

   72┊∙∙x>0∙∧∙x<n∙∧∙y>0∙⇒∙(⦗in?∙x∙y⦘=⦗in?∙x∙y⨫1⦘∙⇐⇒∙⦗sol∙x⨫1∙y⨫1⦘¬=3∧⦗sol∙x∙y⨫1⦘¬=2)                 

   73┊                                                                                               

   74┊∙∙x>0∙∧∙y>0∙∧∙x<n∙∧∙y<m∙⇒                                                                      

   75┊∙∙∙∙⦗sol∙x⨫1∙y⨫1⦘=0∙⇒∙⦗in?∙x∙y⦘=0                                                              

   76┊∙∙∙∙⦗sol∙x∙∙∙y⨫1⦘=0∙⇒∙⦗in?∙x∙y⦘=1                                                              

   77┊∙∙∙∙⦗sol∙x⨫1∙y∙∙⦘=1∙⇒∙⦗in?∙x∙y⦘=1                                                              

   78┊∙∙∙∙⦗sol∙x∙∙∙y∙∙⦘=1∙⇒∙⦗in?∙x∙y⦘=0                                                              

   79┊∙∙∙∙⦗sol∙x∙∙∙y⨫1⦘=2∙⇒∙⦗in?∙x∙y⦘=0                                                              

   80┊∙∙∙∙⦗sol∙x∙∙∙y∙∙⦘=2∙⇒∙⦗in?∙x∙y⦘=1                                                              

   81┊∙∙∙∙⦗sol∙x⨫1∙y⨫1⦘=3∙⇒∙⦗in?∙x∙y⦘=1                                                              

   82┊∙∙∙∙⦗sol∙x⨫1∙y∙∙⦘=3∙⇒∙⦗in?∙x∙y⦘=0                                                              

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