syntax.org

Syntax

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Syntax of our language

This language will be a domain specific language specialising in the manipulation of tiles.

Language specification in Backus-Naur form

<Program> ::= <Program> <Statement> | ε
<Statement> ::= <VariableAssignment> | <ForLoop> | <IfStatement> | "print" <Expression> | <Expression>
<VariableAssignment> ::= "let" <id> "=" <Expression> | <id> "=" <Expression>
<ForLoop> ::= "for" <id> "in" <Expression> ".." <Expression> <Block>
<IfStatement> ::= "if" <Expression> <Block> | "if" <Expression> <Block> "else" <Block>
<Block> ::= "{" <Program> "}"
<Expression> ::= <Expression> <BinaryOp> <Expression> | <UnaryOp> <Expression> | <Primary>
<BinaryOp> ::= "&&" | "||" | "==" | "!=" | ">" | "<" | ">=" | "<=" | "+" | "-" | "*" | "/" | "%" | "++" | "::" | "~" | "**"
<UnaryOp> ::= "!"
<Primary> ::= <id> | <int> | "true" | "false" | <TileDefinition> | "(" <Expression> ")"
<TileDefinition> ::= "[" <RowDefinitions> "]"
<RowDefinitions> ::= <RowDefinitions> <Expression> | ε

Examples (may be outdated)

Defining tiles

tile T1 [
  [1, 0],
  [0, 1]
]

Variables

let myTile = T1

Types

There are two variations of the types of tiles you can use. You can use the type that was defined above, or you can use a fixed size tile:

let myTile : Tile2x2 = T1

This represents the size of the tile, so this one is 2 by 2.

Operations (rotation, vertical and horizontal joining)

let rotatedTile = rotate(T1, 90)
let combinedTile = hjoin(T1, rotatedTile)
let stackedTile = vjoin(T1, rotatedTile)

Iteration

for i in 1..4 {
  let newTile = rotate(myTile, i * 90)
  // Do something with newTile
}

Example dummy program

// Define a 2x2 tile
tile T1 [
  [1, 0],
  [0, 1]
]

// Define another 2x2 tile
tile T2 [
  [0, 1],
  [1, 0]
]

// Declare a variable and store T1 in it
let myTile: Tile2x2 = T1

// Rotate T1 by 90 degrees
let rotatedTile = rotate(T1, 90)

// Join T1 and rotatedTile horizontally
let combinedTile = hjoin(T1, rotatedTile)

// Join T1 and rotatedTile vertically
let stackedTile = vjoin(T1, rotatedTile)

// Iterate over rotations of T2 and join them horizontally
let finalTile = T2
for i in 1..3 {
  let newTile = rotate(T2, i * 90)
  finalTile = hjoin(finalTile, newTile)
}

// Print the final result
print(finalTile)

Problems Solutions

Problem 1

// Declare A and B tiles
tile A [ [1] ]
tile B [ [0] ]

// Declare variable to store the checkerboard
let checkerboard: Tile64x64 = []

// Create the 64x64 checkerboard
for i in 1..32 {
    let tempRow: Tile64x1 = []
    for j in 1..32 {
        if (i % 2 == j % 2) {
            tempRow = hjoin(tempRow, A)
        } else {
            tempRow = hjoin(tempRow, B)
        }
    }
    checkerboard = vjoin(checkerboard, tempRow)
}
    // Done

Problem 2

Part 1

// Declare the input tile (tile1)
tile tile1 [
    [0, 0, 0, 1],
    [0, 0, 1, 1],
    [0, 1, 1, 1],
    [1, 1, 1, 1]
]

// Rotate tile1 in different directions
let tile1_90: Tile4x4 = rotate(tile1, 90)
let tile1_180: Tile4x4 = rotate(tile1, 180)
let tile1_270: Tile4x4 = rotate(tile1, 270)

// Create the output pattern
let topRow: Tile8x4 = hjoin(tile1, tile1_90)
let bottomRow: Tile8x4 = hjoin(tile1_270, tile1_180)

let output: Tile8x8 = vjoin(topRow, bottomRow)
    // Done