# Progletariat

## Fabled F# Maze

My son likes mazes. He asked me for a webpage that does mazes... Trouble is, maze generation is way too complicated for my javascript skills. But I was sure I could do better in a more idiot-proof language like F#... Fortunately, now that F# can be compiled to javascript by the wonderful Fable, maze building in the browser is (just about) achievable for my simple mind. The demo above has been built entirely from the F# code in this webpage, using Fable. Graphics are courtesy of Fable's bindings to ThreeJs. (You can also view the complete code on my GitHub repo if you prefer). As a disclaimer, nicer and shorter maze generation algorithms are available than the one described here, but this is what I ended up with and it does illustrate quite a few F# concepts...

### Building blocks

So we're going to need to generate a maze, and then render it graphically. My 3D graphics skills are pretty much limited to drawing cubes, so we'll base our representation of a maze around single cells, that either do or don't get drawn as a cube. If a Cell is drawn as a cube, it's part of a wall in the maze. If a Cell is not drawn, then it's a gap or passage in the maze. So a Cell is effectively a thing that can exist as one of several possible forms (but an individual Cell can only ever be one of these possible forms). In F#, a discriminated union type fits the bill when we need to encompass several independent possibilities within the same type. I'll use X to represent a Cell that is part of a maze-wall and O to represent a Cell that is open-space in the maze. I'll also throw in I to represent a Cell who's type is either as yet indeterminate or not important (more on that later when we generate mazes).

 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: #r "../../../packages/Fable.Core/lib/netstandard1.6/Fable.Core.dll" #load "../../../node_modules/fable-import-three/Fable.Import.Three.fs" open System open Fable.Core open Fable.Core.JsInterop open Fable.Import open Fable.Import.Three // Here's our union-type for representing a maze. type Cell = | X // X is going to represent a wall. | O // O is going to represent open space / gap / a passage. | I // I represents intederminate / unknown / don't care. let o = O // Sneaky trick to get syntax-highlighting to show the difference let x = X // betweeen different cell categories more noticably sometimes.

#### Bigger bits and pieces

Now that we have established the Cell union type for representing the lowest level building blocks of our maze, we need to move up a level. The simpest possible maze is a 3 x 3 grid of Cells. We'll call this a SmallSquare. I've used a tuple with 9 members to represent a SmallSquare. Arguably I could have attempted to represent the 3x3-ness better using a 2d array or a 3-tuple of 3-tuples etc, but they would generally introduce more syntactic noise (which F# does a pretty good job of minimizing) in the form of additional brackets etc, so I'll stick with a tuple. Although the syntax for creating a tuple is pretty minimal, the code will be clearer (in our case of needing to represent 2-dimensional mazes) if we can omit tuple-syntax (brackets and commas) from the source. What we can do is create ss which is a curried function that requires no commas or brackets around its arguments for creating a SmallSquare. When we are generating mazes, we will want to replace a 3 x 3 SmallSquare with an equivalent (but more complex) 5 x 5 grid of Cells, which we'll call LargeSquare. I've also added ls for creating a LargeSquare in a syntactically-minimal way (like ss).

 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: // SmallSquare is a 3x3 grid of Cells type SmallSquare = Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell // ss gives us a nice-looking way to create a small square // without needing to type lots, of, commas. let ss a b c d e f g h i : SmallSquare = a, b, c, d, e, f, g, h, i // LargeSquare is a 5x5 grid of Cells type LargeSquare = Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell // ls creates LargeSquares in a visually pleasing (i.e. comma-free) way. let ls a b c d e f g h i j k l m n o p q r s t u v w x y : LargeSquare = a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y

### Flipping functions

When we're generating mazes, we'll want to be able to come up with new squares, based on existing ones. One of the ways we can derive a new square from an existing one is to flip or rotate the existing square. We can achieve this pretty easily by taking each Cell from a LargeSquare and rearranging the cells as required. It's reasonably easy to see just by looking at the code how the flip or rotation transforms the input square's cells. Whilst we're writing utility functions, we'll also include one to convert the cells from a large square into F# list form, which will be useful later. As you can see, the F# syntax for creating a list is pretty neat.

 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: // Flip a large square horizontally let flip a b c d e f g h i j k l m n o p q r s t u v w x y = ls e d c b a j i h g f o n m l k t s r q p y x w v u // Rotate a large square clockwise by 90 degrees let rotate a b c d e f g h i j k l m n o p q r s t u v w x y = ls u p k f a v q l g b w r m h c x s n i d y t o j e // Convert a large square to list representation let toList a b c d e f g h i j k l m n o p q r s t u v w x y = [a; b; c; d; e; f; g; h; i; j; k; l; m; n; o; p; q; r; s; t; u; v; w; x; y]

Although the above functions are (in my eyes) quite elegant, we can't actually use them at the moment, as they take each cell individually from a square as input, but we have defined SmallSquare and LargeSquare as tuples, which group up 9 or 25 Cells into singular entities. To be able to rotate or flip a square, we will need adapter function that takes a nice-syntax function and an ugly-tuple-syntax square then extracts each Cell from the square and then passes each Cell individually to the nice-syntax function. As we will need to use these adapter functions an aweful lot, we'll make them custom infix operators so that we can use them in an intuitive way (well, intuitive if you like that kind of thing).

 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: // Adapt a 'nice-syntax' function (sf) to work with an actual SmallSquare. let (|>>|) sf (a, b, c, d, e, f, g, h, i) = sf a b c d e f g h i // Adapt a 'nice-syntax' function (sf) to work with an actual LargeSquare. let (||>>||) sf (a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y) = sf a b c d e f g h i j k l m n o p q r s t u v w x y

### All things being equal

We need to be able to work out if a Cell is the same as another Cell. F# helps us out here by implementing structural-equality by default on tuple, union and record types. However, if you remember back to the initial definition of the Cell type, we included I type cells to represent cases where the type of a cell can be indeterminate (i.e. when it doesn't matter if the Cell finally becomes an X or an O). So, we need to define equals (|=|) and not-equals (|<>|) operators for Cell type that take the unimportance of I cells into account. We can also scale equals and not-equals up to work on LargeSqaures. To do this we convert the squares in question to Lists (via our ||>>|| adapter function / operator) and use the List.fold2 function to compare cells from corresponding positions in each square's list and combine the results into a single bool.

 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: // Equals operator for Cells let (|=|) (a:Cell) (b:Cell) = match a, b with | X, I -> true | O, I -> true | I, X -> true | I, O -> true | _, _ -> a = b // Not-Equals operator for Cells let (|<>|) (a:Cell) (b:Cell) = match a, b with | I, _ -> false | _, I -> false | _, _ -> a <> b // Equals operator for LargeSquares let (||=||) (a:LargeSquare) (b:LargeSquare) = let al = toList ||>>|| a let bl = toList ||>>|| b List.fold2 (fun s x y -> s && (x |=| y)) true al bl // Not-Equals operator for LargeSquares let (||<>||) (a:LargeSquare) (b:LargeSquare) = let al = toList ||>>|| a let bl = toList ||>>|| b List.fold2 (fun s x y -> s || (x |<>| y)) false al bl

#### I'll tell you what I don't want

To generate mazes, we need a collection of all possible maze squares. We'll approach this by generating all possible combinations of cells and then filtering out ones which aren't valid for some reason (such as ones that contain loops or don't have entry/exit points). To avoid having to manually specify hundreds of invalid squares, we can write an allRotationsAndFlips function that takes an square and generates all possible rotated and flipped versions of it (the idea being that if a square is invalid in one orientation then it is invalid in all orientations). Our allRotationsAndFlips function accepts a LargeSquare to work on, but it would also be nice if it accepted individual cells that would form a square, so all is an adapter function for that. We can use all to help build up a neverValid list of squares that are not valid in any maze that we generate.

 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: 41: 42: 43: 44: 45: 46: 47: 48: 49: 50: 51: 52: 53: 54: 55: 56: 57: 58: 59: 60: 61: 62: 63: let allRotationsAndFlips (s:LargeSquare) = let r0 = s let r90 = rotate ||>>|| r0 let r180 = rotate ||>>|| r90 let r270 = rotate ||>>|| r180 let f0 = flip ||>>|| s let f90 = rotate ||>>|| f0 let f180 = rotate ||>>|| f90 let f270 = rotate ||>>|| f180 [r0; r90; r180; r270; f0; f90; f180; f270] // adapter function for allRotationsAndFlips let all a b c d e f g h i j k l m n o p q r s t u v w x y = allRotationsAndFlips <| ls a b c d e f g h i j k l m n o p q r s t u v w x y // Using the ampersand operator for list.append is a problem // for my blogging framework (this is a work-around). let (|.|) x y = List.append x y // Specifies characteristics that make squares invalid let neverValid = [ls I I I I I I o o o I I o I o I I o o o I I I I I I ] // A loop isn't valid |.| all I I x I I I I x I I x x x I I I I I I I I I I I I // Small closed section isn't valid |.| all I I I I I I I I I I x x x x x I I I I I I I I I I // Medium closed section isn't valid |.| [ls x x x x x x I I I x x I I I x x I I I x x x x x x ] // Full closed square isn't valid |.| all X o X o X I I I I I I I I I I I I I I I I I I I I // Two entry points on any side aren't valid // In a 5x5 cell - corners and certain dividing cells are always required. let alwaysRequired = ls X I X I X I o I o I X I X I X I o I o I X I X I X // Standard structure boundary walls

### Give me everything

To actually generate all valid squares, we can write a recursive function (als) that builds all possible squares (in list form) by starting with an empty list and adding both an X and O to the empty list and then (recursively) to each list that has already been generated. Rather than generate (5x5)^2 candidate squares, we note that in a valid (orthodox) square certain wall-cells must always be present in each corner, in the center and in the mid-point of each side. Similarly, certain cells always have to be open. This means that we only need to generate 12^2 candidates as less than half the cells are actually variable within a large square. The orthodoxLS function enforces this principal - when given the variable parts of a square as inputs. We build allLargeSquares by filtering 12^2 possible candidates and filtering out ones matching neverValid squares with undesirable characteristics. We also put the squares into a set to eliminate any duplicates, again this is helped by F# implementing structural-equality by default (rather than using reference equality by default - which is one of the inherent flaws in C#, Java, Javascript... Kotlin looks better on that but not totally great either!).

 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: let orthodoxLS [b; d; f; h; j; l; n; p; r; t; v; x] = ls X b X d X f O h O j X l X n X p O r O t X v X x X let allLargeSquares = let rec als n b = match n with | 0 -> b | n -> als (n-1) <| ((List.map (fun a -> X :: a) b) |.| (List.map (fun a -> O :: a) b)) let allInputs = als 12 [[]] List.map (fun l -> orthodoxLS l) allInputs |> List.filter (fun x -> List.fold (fun a y -> a && x ||<>|| y) true neverValid) |> List.filter (fun x -> x ||=|| alwaysRequired) |> Set.ofList |> Set.toArray

#### Mixing and matching

When we generate a maze, we will start off with a simple 3x3 Cell maze and generate an equivalent (in terms of ways in and out of it) 5x5 Cell maze. Then, after that, we'll break the 5x5 maze down into 4 overlapping 3x3 mazes and then generate equivalent 5x5 mazes for each 3x3 maze (and so on...). This means that we need to be able to judge if a 5x5 Cell maze is equivalent to a 3x3 Cell maze, which is what isMatch does for us. The other factor that comes into play is that in larger mazes, if we do the 3x3 to 5x5 replacement from left to right and from top to bottom, then we must take into account that the edges of preceeding squares place requirements on the edges of squares that come after them (i.e. squares must match where they meet each other). For example, the left side of a square must match the right side of the preceeding square. I've called these constraints a SideReq, which come in two varieties; TopReq and LeftReq. Additionally, if a square is on the top row or the left column of a maze, it doesn't have any constraints on it's sides from neighbouring squares, so requirements are an option (see Scott Wlaschin's excellent page on the F# option type for more details. Whilst you're looking you could also check out his notes on F# record types which I've used to wrap up a TopReq and a LeftReq as a pair of Reqs).

 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: 41: 42: 43: 44: 45: 46: 47: 48: 49: 50: 51: 52: 53: 54: 55: type SideReq = | TopReq of (Cell * Cell * Cell * Cell * Cell) option | LeftReq of (Cell * Cell * Cell * Cell * Cell) option type Reqs = { Top : SideReq; Left : SideReq} // Is a more-complex 5x5 Cell LargeSquare equivalent (in terms of // ways in and ways out) to a simpler 3x3 Cell SmallSquare (and // does the larger square meet additional requirements imposed by // its neighbours) let isMatch a b c d e f g h i j k l m n o p q r s t u v w x y a' b' c' d' e' f' g' h' i' (topReq : SideReq) (leftReq : SideReq) = let l = ls a b c d e f g h i j k l m n o p q r s t u v w x y // Nested function, used to decide if a Cell from a side // of the small square is equivalent to 2 cells from the // same side of the larger square let sideOK ssCell lsCellA lsCellB = if ssCell = X then lsCellA = X && lsCellB = X else lsCellA <> lsCellB let topOK = sideOK b' b d let bottomOK = sideOK h' v x let leftOK = sideOK d' f p let rightOK = sideOK f' j t // Do the cells on the side of a large square meet the // requirements imposed by its neighbour let reqOK (req:SideReq) a'' b'' c'' d'' e'' = match req with | TopReq None | LeftReq None -> true | TopReq (Some (a''', b''', c''', d''', e''')) | LeftReq (Some (a''', b''', c''', d''', e''')) -> a'' = a''' && b'' = b''' && c'' = c''' && d'' = d''' && e'' = e''' let topReqOK = reqOK topReq a b c d e let leftReqOK = reqOK leftReq a f k p u topOK && bottomOK && leftOK && rightOK && topReqOK && leftReqOK

### Making a random selection

Each time a maze needs growing a 3x3 SmallSquare needs replacing with an equivalent 5x5 LargeSquare. To do this, we can take our collection of all known large squares - allLargeSquares and filter is to eliminate ones that don't match (i.e. aren't equivalent to) the small 3x3 square (also checking that the replacement meets any requirements imposed by its neighbours). It's likely that there will be more than one candidate replacement square, so replace makes a random choice to ensure that we generate different mazes each time. The last function in this section, decompose does the work of breaking a 5x5 Cell LargeSquare into a 2x2 arrangement of (partially overlapping) 3x3 Cell SmallSquares.

 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: 41: 42: 43: 44: 45: 46: 47: 48: 49: 50: 51: let random = new System.Random (); // Get a (randomly selected) LargeSquare that is a valid replacement for // the given small square, and that also meets the given neighbour requirements. let replace a b c d e f g h i topReq leftReq = let possibles = allLargeSquares |> Array.filter (fun s -> (isMatch ||>>|| s) a b c d e f g h i topReq leftReq) let n = Array.length possibles let choice = int (double n * random.NextDouble ()) Array.item choice possibles // Utility to take the bottom row of a square and turn it into // 'top' requirements for a prospective neighbour below it. let getBottomAsTopReq a b c d e f g h i j k l m n o p q r s t u v w x y = TopReq (Some (u, v, w, x, y)) // Utility to take the right column of a square and turn it into // 'left' requirements for a prospective neighbour to its right. let getRightAsLeftReq a b c d e f g h i j k l m n o p q r s t u v w x y = TopReq (Some (e, j, o, t, y)) // Break a 5x5 LargeSquare down into 4 overlapping 3x3 SmallSquares. let decompose a b c d e f g h i j k l m n o p q r s t u v w x y = (ss a b c f g h k l m, ss c d e h i j m n o, ss k l m p q r u v w, ss m n o r s t w x y)

### Growing mazes

The below section has the final steps in this implementation of maze growing. The replaceSquare function takes a 5x5 LargeSquare, decomposes it into 4 overlapping 3x3 small squares, and then replaces each of those with 5x5 squares. A Maze is defined as a list (rows) of lists of LargeSquares (each individual row also being a list of squares). This means that each time growMaze is called, it takes each row list of squares and replaces it with two rows, each of which is twice as long as the input row. Most of growMaze is concerned with extracting neighbour requirements from rows of squares and passing these requirements into the next row of squares to be generated. Quite a few list functions are needed, including my personal favourite; pairwise. The starting point for generating mazes in this demo is the randomMaze function. It starts with the simplest possible 3x3 Cell (SmallSquare) maze, replaces it with a random 5x5 (LargeSquare) equivalent and then grows that maze randomly as many times as requested.

 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: 41: 42: 43: 44: 45: 46: 47: 48: 49: 50: 51: 52: 53: 54: 55: 56: 57: 58: 59: 60: 61: // Replace a large square with 4 equivalent large squares, taking into account // edge requirements from neighbours that have already been similarly replaced. let replaceSquare sq topReqL topReqR leftReqT leftReqB = let (tl, tr, bl, br) = decompose ||>>|| sq let ntl = (replace |>>| tl) topReqL leftReqT let ntr = (replace |>>| tr) topReqR (getRightAsLeftReq ||>>|| ntl) let nbl = (replace |>>| bl) (getBottomAsTopReq ||>>|| ntl) leftReqB let nbr = (replace |>>| br) (getBottomAsTopReq ||>>|| ntr) (getRightAsLeftReq ||>>|| nbl) (ntl, ntr, nbl, nbr) // Mazes are list of rows. Each row is a list of the LargeSquares in it. type Maze = LargeSquare list list // Grow a maze by one increment, i.e. replacing each LargeSquare in it with a // 2x2 arrangement of LargeSquares (i.e. growth is quadratic) let growMaze (lsll : Maze) = let rec grl output (lsll : LargeSquare list list) = // Get intra-row requirements so that the new row matches the preceeding new row let prevRowReqs = match output with | [] -> List.init (List.length <| List.item 0 lsll) (fun x -> (TopReq None, TopReq None)) | _ -> List.last output |> List.mapi (fun i b -> i, getBottomAsTopReq ||>>|| b) |> List.pairwise |> List.filter (fun ((i, r), (j, s)) -> i % 2 = 0) // Only need half of them |> List.map (fun ((i, r), (j, s)) -> (r, s)) // Keep reqs, lose numbering match lsll with | [] -> output | row::tail -> // Take one row from input // Replace each square in the row with 4 replacements, which means // we replace each row with an new upper row and a new lower row. let folder ((upper, lower), leftReqT, leftReqB) s (topReqL, topReqR) = let (ntl, ntr, nbl, nbr) = replaceSquare s topReqL topReqR leftReqT leftReqB let newUpperRow, newLowerRow = upper |.| [ntl; ntr], lower |.| [nbl; nbr] let lReqForNextUpperSquare = getRightAsLeftReq ||>>|| ntr let lReqForNextLowerSquare = getRightAsLeftReq ||>>|| nbr ((newUpperRow, newLowerRow), lReqForNextUpperSquare, lReqForNextLowerSquare) // Replace current row with two rows, using above folder func to take account // of the current input row and the requirements placed on it by the preceeding // new row, generating two new longer rows to replace the one current input row. let (newTop, newBottom), _, _ = List.fold2 folder (([],[]), LeftReq None, LeftReq None) row prevRowReqs // Input row has been processed, move it to the output let newOutput = output |.| [newTop; newBottom] grl newOutput tail // Process next input row (tail) grl [] lsll // Take the simplest possible 3x3 Cell (SmallSquare) maze, replace it with // a random 5x5 (LargeSquare) equivalent (as a single LargeSquare maze) and then // grow that maze randomly as many times as requested. let rec randomMaze n = match n with | n when n > 1 -> growMaze (randomMaze (n - 1)) | _ -> [[replace X X X o o o X X X (TopReq None) (LeftReq None)]]

#### Drawing mazes

I'm not going to go into detail of how the rendering code works, as it's secondary to how the maze is generated. The approach is basically hierarchical, breaking a Maze back down into rows, the each row into a list of LargeSquares, and then then breaking each LargeSquare down into rows of Cells. If a Cell is an X then it is rendered individually as a cube, if it is an O (open space in the maze) then it is not rendered. The available width and height of the canvas is broken down and allocated to each row, then square and then cell during rendering to position the elements correctly on screen.

 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: 41: 42: 43: 44: 45: 46: let renderCube (scene:Scene) xs xe ys ye = let size = xe - xs let cube = Three.BoxBufferGeometry(size, size, 0.3 * size) let matProps = createEmpty matProps.color <- Some (U2.Case2 "#9430B3") let mesh = Three.Mesh(cube, Three.MeshLambertMaterial(matProps)) mesh.translateX (xs - size / 2.0) |> ignore mesh.translateY (ys - size / 2.0) |> ignore mesh.translateZ 0.0 |> ignore scene.add(mesh) let renderSquareRow (gs:Scene) xs xe ys ye a b c d e = let widthStep = (xe - xs) / 5.0 if a = X then renderCube gs (xs + 0.0 * widthStep) (xs + 1.0 * widthStep) ys ye if b = X then renderCube gs (xs + 1.0 * widthStep) (xs + 2.0 * widthStep) ys ye if c = X then renderCube gs (xs + 2.0 * widthStep) (xs + 3.0 * widthStep) ys ye if d = X then renderCube gs (xs + 3.0 * widthStep) (xs + 4.0 * widthStep) ys ye if e = X then renderCube gs (xs + 4.0 * widthStep) (xs + 5.0 * widthStep) ys ye let rec renderSquare (gs:Scene) tlx tly brx bry a b c d e f g h i j k l m n o p q r s t u v w x y = let heightStep = (bry - tly) / 5.0 renderSquareRow gs tlx brx (tly + 0.0 * heightStep) (tly + 1.0 * heightStep) a b c d e renderSquareRow gs tlx brx (tly + 1.0 * heightStep) (tly + 2.0 * heightStep) f g h i j renderSquareRow gs tlx brx (tly + 2.0 * heightStep) (tly + 3.0 * heightStep) k l m n o renderSquareRow gs tlx brx (tly + 3.0 * heightStep) (tly + 4.0 * heightStep) p q r s t renderSquareRow gs tlx brx (tly + 4.0 * heightStep) (tly + 5.0 * heightStep) u v w x y let rec renderMazeRow (scene:Scene) tlx tly brx bry row = let step = (brx - tlx) / (float <| List.length row) row |> List.iteri (fun i sq -> let fi = float i (renderSquare scene (tlx + fi * step) tly (tlx + (fi + 1.0) * step) bry) ||>>|| sq) let rec renderMaze(scene:Scene) tlx tly brx bry maze = let step = (bry - tly) / (float <| List.length maze) maze |> List.iteri (fun i r -> let fi = float i renderMazeRow scene tlx (tly + fi * step) brx (tly + (fi + 1.0) * step) r)

### Graphics time

Again I won't dwell on how the graphics setup is done (see my earlier post here for general details of how to initialise ThreeJs). Probably worth pointing out that as this involves interacting with a javascript graphics library so we see lots of mutable properties being accessed (with the <- operator). Mutable state is generally avoided where possible when writing functional programs, however, when needed F# can handle (mutability)[https://en.wikibooks.org/wiki/F_Sharp_Programming/Mutable_Data], to our benefit here. We also create the Easy, Medium, Hard buttons in this block and attach event handlers to them so that a new maze will be generated when they are clicked. We use the mutibility of the camera object's properties to implement a zoom-out effect to add some visual interest when the maze is regenerated.

 1: 2: 3: 4: 5: 6: 7: 8: 9: 10: 11: 12: 13: 14: 15: 16: 17: 18: 19: 20: 21: 22: 23: 24: 25: 26: 27: 28: 29: 30: 31: 32: 33: 34: 35: 36: 37: 38: 39: 40: 41: 42: 43: 44: 45: 46: 47: 48: 49: 50: 51: 52: 53: 54: 55: 56: 57: 58: 59: 60: 61: 62: 63: 64: 65: 66: 67: 68: 69: 70: 71: 72: 73: 74: 75: 76: 77: 78: 79: let initGraphics() = let width () = Browser.window.innerWidth * 0.75; let height () = Browser.window.innerHeight * 0.5 let scene = Three.Scene() scene.autoUpdate <- true let camera = Three.PerspectiveCamera(75.0, width() / height(), 0.01, 1000.0) camera.matrixAutoUpdate <- true camera.rotationAutoUpdate <- true let initLights () = scene.add(Three.AmbientLight(U2.Case2 "#3C3C3C", 1.0)) let spotLight = Three.SpotLight(U2.Case2 "#FFFFFF") spotLight.position.set(-30., 60., 60.) |> ignore scene.add(spotLight) initLights () let renderer = Three.WebGLRenderer() renderer.setClearColor("#0A1D2D") (renderer :> Three.Renderer).setSize(width(), height()) let container = if Browser.document.getElementById("graphicsContainer") <> null then Browser.document.getElementById("graphicsContainer") else Browser.document.body container.innerHTML <- "" container.appendChild((renderer :> Three.Renderer).domElement) |> ignore let makeButton text difficulty cssClass = let button = Browser.document.createElement("button") button.innerText <- text button.className <- cssClass let buttonClick (b : Browser.MouseEvent) = let maze = randomMaze difficulty // Create new random maze on button click while(scene.children.Count > 0) do scene.remove(scene.children.Item(0)) initLights () camera.position.z <- 0.0 renderMaze scene -1.025 1.15 1.275 -1.15 maze (Boolean() :> obj) button.onclick <- Func<_,_> buttonClick button let buttonContainer = Browser.document.createElement("div") buttonContainer.className <- "buttonContainer" container.appendChild(buttonContainer) |> ignore buttonContainer.appendChild(makeButton "Easy" 2 "yellowGreen") |> ignore buttonContainer.appendChild(makeButton "Medium" 3 "yellowOrange") |> ignore buttonContainer.appendChild(makeButton "Hard" 4 "blueViolet") |> ignore renderMaze scene -1.025 1.15 1.275 -1.15 (randomMaze 3) // New random maze on start-up renderer, scene, camera let renderer, scene, camera = initGraphics() let cameraPositionZ = 2.0 let rec reqFrame (dt:float) = Browser.window.requestAnimationFrame(Func<_,_> animate) |> ignore if camera.position.z < cameraPositionZ then camera.position.z <- camera.position.z + 0.25 else camera.position.z <- cameraPositionZ renderer.render(scene, camera) and animate (dt:float) = Browser.window.setTimeout(Func<_,_> reqFrame, 1000.0 / 20.0) |> ignore // aim for 20 fps animate(0.0) // Start! Browser.console.log "maze v22"

#### In conclusion

So, the image above shows what you should have seen (if anything went wrong with the actual demo at the top of the page). You might have noticed that the maze generation algorithm could be better; there's only ever one path between each quadrant (and sub-quadrant etc...). This makes the maze easier to solve that it might otherwise be, it's a drawback of the kind of algorithm that I used. Don't worry, many different approaches to maze generation are available - if you can take some of the above but implement a different kind of maze then I'd be really interested to see the results.

namespace System
namespace Microsoft.FSharp.Core
type Cell =
| X
| O
| I

Full name: 07-03-fsharp-fable-three-maze_.Cell
union case Cell.X: Cell
union case Cell.O: Cell
union case Cell.I: Cell
val o : Cell

Full name: 07-03-fsharp-fable-three-maze_.o
val x : Cell

Full name: 07-03-fsharp-fable-three-maze_.x
type SmallSquare = Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell

Full name: 07-03-fsharp-fable-three-maze_.SmallSquare
val ss : a:Cell -> b:Cell -> c:Cell -> d:Cell -> e:Cell -> f:Cell -> g:Cell -> h:Cell -> i:Cell -> SmallSquare

Full name: 07-03-fsharp-fable-three-maze_.ss
val a : Cell
val b : Cell
val c : Cell
val d : Cell
val e : Cell
val f : Cell
val g : Cell
val h : Cell
val i : Cell
type LargeSquare = Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell

Full name: 07-03-fsharp-fable-three-maze_.LargeSquare
val ls : a:Cell -> b:Cell -> c:Cell -> d:Cell -> e:Cell -> f:Cell -> g:Cell -> h:Cell -> i:Cell -> j:Cell -> k:Cell -> l:Cell -> m:Cell -> n:Cell -> o:Cell -> p:Cell -> q:Cell -> r:Cell -> s:Cell -> t:Cell -> u:Cell -> v:Cell -> w:Cell -> x:Cell -> y:Cell -> LargeSquare

Full name: 07-03-fsharp-fable-three-maze_.ls
val j : Cell
val k : Cell
val l : Cell
val m : Cell
val n : Cell
val o : Cell
val p : Cell
val q : Cell
val r : Cell
val s : Cell
val t : Cell
val u : Cell
val v : Cell
val w : Cell
val x : Cell
val y : Cell
val flip : a:Cell -> b:Cell -> c:Cell -> d:Cell -> e:Cell -> f:Cell -> g:Cell -> h:Cell -> i:Cell -> j:Cell -> k:Cell -> l:Cell -> m:Cell -> n:Cell -> o:Cell -> p:Cell -> q:Cell -> r:Cell -> s:Cell -> t:Cell -> u:Cell -> v:Cell -> w:Cell -> x:Cell -> y:Cell -> LargeSquare

Full name: 07-03-fsharp-fable-three-maze_.flip
val rotate : a:Cell -> b:Cell -> c:Cell -> d:Cell -> e:Cell -> f:Cell -> g:Cell -> h:Cell -> i:Cell -> j:Cell -> k:Cell -> l:Cell -> m:Cell -> n:Cell -> o:Cell -> p:Cell -> q:Cell -> r:Cell -> s:Cell -> t:Cell -> u:Cell -> v:Cell -> w:Cell -> x:Cell -> y:Cell -> LargeSquare

Full name: 07-03-fsharp-fable-three-maze_.rotate
val toList : a:'a -> b:'a -> c:'a -> d:'a -> e:'a -> f:'a -> g:'a -> h:'a -> i:'a -> j:'a -> k:'a -> l:'a -> m:'a -> n:'a -> o:'a -> p:'a -> q:'a -> r:'a -> s:'a -> t:'a -> u:'a -> v:'a -> w:'a -> x:'a -> y:'a -> 'a list

Full name: 07-03-fsharp-fable-three-maze_.toList
val a : 'a
val b : 'a
val c : 'a
val d : 'a
val e : 'a
val f : 'a
val g : 'a
val h : 'a
val i : 'a
val j : 'a
val k : 'a
val l : 'a
val m : 'a
val n : 'a
val o : 'a
val p : 'a
val q : 'a
val r : 'a
val s : 'a
val t : 'a
val u : 'a
val v : 'a
val w : 'a
val x : 'a
val y : 'a
val sf : ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i -> 'j)
val b : 'b
val c : 'c
val d : 'd
val e : 'e
val f : 'f
val g : 'g
val h : 'h
val i : 'i
val sf : ('a -> 'b -> 'c -> 'd -> 'e -> 'f -> 'g -> 'h -> 'i -> 'j -> 'k -> 'l -> 'm -> 'n -> 'o -> 'p -> 'q -> 'r -> 's -> 't -> 'a1 -> 'a2 -> 'a3 -> 'a4 -> 'a5 -> 'a6)
val j : 'j
val k : 'k
val l : 'l
val m : 'm
val n : 'n
val o : 'o
val p : 'p
val q : 'q
val r : 'r
val s : 's
val t : 't
val u : 'a1
val v : 'a2
val w : 'a3
val x : 'a4
val y : 'a5
val a : LargeSquare
val b : LargeSquare
val al : Cell list
val bl : Cell list
Multiple items
module List

from Microsoft.FSharp.Collections

--------------------
type List<'T> =
| ( [] )
| ( :: ) of Head: 'T * Tail: 'T list
interface IEnumerable
interface IEnumerable<'T>
member GetSlice : startIndex:int option * endIndex:int option -> 'T list
member IsEmpty : bool
member Item : index:int -> 'T with get
member Length : int
member Tail : 'T list
static member Cons : head:'T * tail:'T list -> 'T list
static member Empty : 'T list

Full name: Microsoft.FSharp.Collections.List<_>
val fold2 : folder:('State -> 'T1 -> 'T2 -> 'State) -> state:'State -> list1:'T1 list -> list2:'T2 list -> 'State

Full name: Microsoft.FSharp.Collections.List.fold2
val s : bool
val allRotationsAndFlips : Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell -> LargeSquare list

Full name: 07-03-fsharp-fable-three-maze_.allRotationsAndFlips
val s : LargeSquare
val r0 : LargeSquare
val r90 : LargeSquare
val r180 : LargeSquare
val r270 : LargeSquare
val f0 : LargeSquare
val f90 : LargeSquare
val f180 : LargeSquare
val f270 : LargeSquare
val all : a:Cell -> b:Cell -> c:Cell -> d:Cell -> e:Cell -> f:Cell -> g:Cell -> h:Cell -> i:Cell -> j:Cell -> k:Cell -> l:Cell -> m:Cell -> n:Cell -> o:Cell -> p:Cell -> q:Cell -> r:Cell -> s:Cell -> t:Cell -> u:Cell -> v:Cell -> w:Cell -> x:Cell -> y:Cell -> LargeSquare list

Full name: 07-03-fsharp-fable-three-maze_.all
val x : 'a list
val y : 'a list
val append : list1:'T list -> list2:'T list -> 'T list

Full name: Microsoft.FSharp.Collections.List.append
val neverValid : LargeSquare list

Full name: 07-03-fsharp-fable-three-maze_.neverValid
val alwaysRequired : LargeSquare

Full name: 07-03-fsharp-fable-three-maze_.alwaysRequired
val orthodoxLS : Cell list -> LargeSquare

Full name: 07-03-fsharp-fable-three-maze_.orthodoxLS
val allLargeSquares : LargeSquare []

Full name: 07-03-fsharp-fable-three-maze_.allLargeSquares
val als : (int -> Cell list list -> Cell list list)
val n : int
val b : Cell list list
val map : mapping:('T -> 'U) -> list:'T list -> 'U list

Full name: Microsoft.FSharp.Collections.List.map
val a : Cell list
val allInputs : Cell list list
val l : Cell list
val filter : predicate:('T -> bool) -> list:'T list -> 'T list

Full name: Microsoft.FSharp.Collections.List.filter
val x : LargeSquare
val fold : folder:('State -> 'T -> 'State) -> state:'State -> list:'T list -> 'State

Full name: Microsoft.FSharp.Collections.List.fold
val a : bool
val y : LargeSquare
Multiple items
module Set

from Microsoft.FSharp.Collections

--------------------
type Set<'T (requires comparison)> =
interface IComparable
interface IEnumerable
interface IEnumerable<'T>
interface ICollection<'T>
new : elements:seq<'T> -> Set<'T>
member Add : value:'T -> Set<'T>
member Contains : value:'T -> bool
override Equals : obj -> bool
member IsProperSubsetOf : otherSet:Set<'T> -> bool
member IsProperSupersetOf : otherSet:Set<'T> -> bool
...

Full name: Microsoft.FSharp.Collections.Set<_>

--------------------
new : elements:seq<'T> -> Set<'T>
val ofList : elements:'T list -> Set<'T> (requires comparison)

Full name: Microsoft.FSharp.Collections.Set.ofList
val toArray : set:Set<'T> -> 'T [] (requires comparison)

Full name: Microsoft.FSharp.Collections.Set.toArray
type SideReq =
| TopReq of (Cell * Cell * Cell * Cell * Cell) option
| LeftReq of (Cell * Cell * Cell * Cell * Cell) option

Full name: 07-03-fsharp-fable-three-maze_.SideReq
union case SideReq.TopReq: (Cell * Cell * Cell * Cell * Cell) option -> SideReq
type 'T option = Option<'T>

Full name: Microsoft.FSharp.Core.option<_>
union case SideReq.LeftReq: (Cell * Cell * Cell * Cell * Cell) option -> SideReq
type Reqs =
{Top: SideReq;
Left: SideReq;}

Full name: 07-03-fsharp-fable-three-maze_.Reqs
Reqs.Top: SideReq
Reqs.Left: SideReq
val isMatch : a:Cell -> b:Cell -> c:Cell -> d:Cell -> e:Cell -> f:Cell -> g:Cell -> h:Cell -> i:Cell -> j:Cell -> k:Cell -> l:Cell -> m:Cell -> n:Cell -> o:Cell -> p:Cell -> q:Cell -> r:Cell -> s:Cell -> t:Cell -> u:Cell -> v:Cell -> w:Cell -> x:Cell -> y:Cell -> a':'a -> b':Cell -> c':'b -> d':Cell -> e':'c -> f':Cell -> g':'d -> h':Cell -> i':'e -> topReq:SideReq -> leftReq:SideReq -> bool

Full name: 07-03-fsharp-fable-three-maze_.isMatch
val a' : 'a
val b' : Cell
val c' : 'b
val d' : Cell
val e' : 'c
val f' : Cell
val g' : 'd
val h' : Cell
val i' : 'e
val topReq : SideReq
val leftReq : SideReq
val l : LargeSquare
val sideOK : (Cell -> Cell -> Cell -> bool)
val ssCell : Cell
val lsCellA : Cell
val lsCellB : Cell
val topOK : bool
val bottomOK : bool
val leftOK : bool
val rightOK : bool
val reqOK : (SideReq -> Cell -> Cell -> Cell -> Cell -> Cell -> bool)
val req : SideReq
val a'' : Cell
val b'' : Cell
val c'' : Cell
val d'' : Cell
val e'' : Cell
union case Option.None: Option<'T>
union case Option.Some: Value: 'T -> Option<'T>
val a''' : Cell
val b''' : Cell
val c''' : Cell
val d''' : Cell
val e''' : Cell
val topReqOK : bool
val leftReqOK : bool
val random : Random

Full name: 07-03-fsharp-fable-three-maze_.random
Multiple items
type Random =
new : unit -> Random + 1 overload
member Next : unit -> int + 2 overloads
member NextBytes : buffer:byte[] -> unit
member NextDouble : unit -> float

Full name: System.Random

--------------------
Random() : unit
Random(Seed: int) : unit
val replace : a:'a -> b:Cell -> c:'b -> d:Cell -> e:'c -> f:Cell -> g:'d -> h:Cell -> i:'e -> topReq:SideReq -> leftReq:SideReq -> LargeSquare

Full name: 07-03-fsharp-fable-three-maze_.replace
val c : 'b
val e : 'c
val g : 'd
val i : 'e
val possibles : LargeSquare []
type Array =
member Clone : unit -> obj
member CopyTo : array:Array * index:int -> unit + 1 overload
member GetEnumerator : unit -> IEnumerator
member GetLength : dimension:int -> int
member GetLongLength : dimension:int -> int64
member GetLowerBound : dimension:int -> int
member GetUpperBound : dimension:int -> int
member GetValue : index:int64 -> obj + 7 overloads
member Initialize : unit -> unit
member IsFixedSize : bool
...

Full name: System.Array
val filter : predicate:('T -> bool) -> array:'T [] -> 'T []

Full name: Microsoft.FSharp.Collections.Array.filter
val length : array:'T [] -> int

Full name: Microsoft.FSharp.Collections.Array.length
val choice : int
Multiple items
val int : value:'T -> int (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.int

--------------------
type int = int32

Full name: Microsoft.FSharp.Core.int

--------------------
type int<'Measure> = int

Full name: Microsoft.FSharp.Core.int<_>
Multiple items
val double : value:'T -> double (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.double

--------------------
type double = Double

Full name: Microsoft.FSharp.Core.double
Random.NextDouble() : float
val item : index:int -> array:'T [] -> 'T

Full name: Microsoft.FSharp.Collections.Array.item
val getBottomAsTopReq : a:'a -> b:'b -> c:'c -> d:'d -> e:'e -> f:'f -> g:'g -> h:'h -> i:'i -> j:'j -> k:'k -> l:'l -> m:'m -> n:'n -> o:'o -> p:'p -> q:'q -> r:'r -> s:'s -> t:'t -> u:Cell -> v:Cell -> w:Cell -> x:Cell -> y:Cell -> SideReq

Full name: 07-03-fsharp-fable-three-maze_.getBottomAsTopReq
val getRightAsLeftReq : a:'a -> b:'b -> c:'c -> d:'d -> e:Cell -> f:'e -> g:'f -> h:'g -> i:'h -> j:Cell -> k:'i -> l:'j -> m:'k -> n:'l -> o:Cell -> p:'m -> q:'n -> r:'o -> s:'p -> t:Cell -> u:'q -> v:'r -> w:'s -> x:'t -> y:Cell -> SideReq

Full name: 07-03-fsharp-fable-three-maze_.getRightAsLeftReq
val f : 'e
val g : 'f
val h : 'g
val i : 'h
val k : 'i
val l : 'j
val m : 'k
val n : 'l
val p : 'm
val q : 'n
val r : 'o
val s : 'p
val u : 'q
val v : 'r
val w : 's
val x : 't
val decompose : a:Cell -> b:Cell -> c:Cell -> d:Cell -> e:Cell -> f:Cell -> g:Cell -> h:Cell -> i:Cell -> j:Cell -> k:Cell -> l:Cell -> m:Cell -> n:Cell -> o:Cell -> p:Cell -> q:Cell -> r:Cell -> s:Cell -> t:Cell -> u:Cell -> v:Cell -> w:Cell -> x:Cell -> y:Cell -> SmallSquare * SmallSquare * SmallSquare * SmallSquare

Full name: 07-03-fsharp-fable-three-maze_.decompose
val replaceSquare : Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell -> topReqL:SideReq -> topReqR:SideReq -> leftReqT:SideReq -> leftReqB:SideReq -> LargeSquare * LargeSquare * LargeSquare * LargeSquare

Full name: 07-03-fsharp-fable-three-maze_.replaceSquare
val sq : Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell
val topReqL : SideReq
val topReqR : SideReq
val leftReqT : SideReq
val leftReqB : SideReq
val tl : SmallSquare
val tr : SmallSquare
val bl : SmallSquare
val br : SmallSquare
val ntl : LargeSquare
val ntr : LargeSquare
val nbl : LargeSquare
val nbr : LargeSquare
type Maze = LargeSquare list list

Full name: 07-03-fsharp-fable-three-maze_.Maze
type 'T list = List<'T>

Full name: Microsoft.FSharp.Collections.list<_>
val growMaze : lsll:Maze -> (Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell) list list

Full name: 07-03-fsharp-fable-three-maze_.growMaze
val lsll : Maze
val grl : ((Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell) list list -> LargeSquare list list -> (Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell) list list)
val output : (Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell) list list
val lsll : LargeSquare list list
val prevRowReqs : (SideReq * SideReq) list
val init : length:int -> initializer:(int -> 'T) -> 'T list

Full name: Microsoft.FSharp.Collections.List.init
val length : list:'T list -> int

Full name: Microsoft.FSharp.Collections.List.length
val item : index:int -> list:'T list -> 'T

Full name: Microsoft.FSharp.Collections.List.item
val x : int
val last : list:'T list -> 'T

Full name: Microsoft.FSharp.Collections.List.last
val mapi : mapping:(int -> 'T -> 'U) -> list:'T list -> 'U list

Full name: Microsoft.FSharp.Collections.List.mapi
val i : int
val b : Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell
val pairwise : list:'T list -> ('T * 'T) list

Full name: Microsoft.FSharp.Collections.List.pairwise
val r : SideReq
val j : int
val s : SideReq
val row : LargeSquare list
val tail : LargeSquare list list
val folder : ((LargeSquare list * LargeSquare list) * SideReq * SideReq -> Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell -> SideReq * SideReq -> (LargeSquare list * LargeSquare list) * SideReq * SideReq)
val upper : LargeSquare list
val lower : LargeSquare list
val s : Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell
val newUpperRow : LargeSquare list
val newLowerRow : LargeSquare list
val lReqForNextUpperSquare : SideReq
val lReqForNextLowerSquare : SideReq
val newTop : LargeSquare list
val newBottom : LargeSquare list
val newOutput : (Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell) list list
val randomMaze : n:int -> (Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell) list list

Full name: 07-03-fsharp-fable-three-maze_.randomMaze
val renderCube : scene:'a -> xs:float -> xe:float -> ys:'b -> ye:'c -> 'd

Full name: 07-03-fsharp-fable-three-maze_.renderCube
val scene : 'a
val xs : float
val xe : float
val ys : 'b
val ye : 'c
val size : float
val cube : obj
val matProps : obj
val mesh : obj
val ignore : value:'T -> unit

Full name: Microsoft.FSharp.Core.Operators.ignore
val renderSquareRow : gs:'a -> xs:float -> xe:float -> ys:'b -> ye:'c -> a:Cell -> b:Cell -> c:Cell -> d:Cell -> e:Cell -> unit

Full name: 07-03-fsharp-fable-three-maze_.renderSquareRow
val gs : 'a
val widthStep : float
val renderSquare : gs:'a -> tlx:float -> tly:float -> brx:float -> bry:float -> a:Cell -> b:Cell -> c:Cell -> d:Cell -> e:Cell -> f:Cell -> g:Cell -> h:Cell -> i:Cell -> j:Cell -> k:Cell -> l:Cell -> m:Cell -> n:Cell -> o:Cell -> p:Cell -> q:Cell -> r:Cell -> s:Cell -> t:Cell -> u:Cell -> v:Cell -> w:Cell -> x:Cell -> y:Cell -> unit

Full name: 07-03-fsharp-fable-three-maze_.renderSquare
val tlx : float
val tly : float
val brx : float
val bry : float
val heightStep : float
val renderMazeRow : scene:'a -> tlx:float -> tly:float -> brx:float -> bry:float -> row:(Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell) list -> unit

Full name: 07-03-fsharp-fable-three-maze_.renderMazeRow
val row : (Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell) list
val step : float
Multiple items
val float : value:'T -> float (requires member op_Explicit)

Full name: Microsoft.FSharp.Core.Operators.float

--------------------
type float = Double

Full name: Microsoft.FSharp.Core.float

--------------------
type float<'Measure> = float

Full name: Microsoft.FSharp.Core.float<_>
val iteri : action:(int -> 'T -> unit) -> list:'T list -> unit

Full name: Microsoft.FSharp.Collections.List.iteri
val fi : float
val renderMaze : scene:'a -> tlx:float -> tly:float -> brx:float -> bry:float -> maze:(Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell) list list -> unit

Full name: 07-03-fsharp-fable-three-maze_.renderMaze
val maze : (Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell) list list
val r : (Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell * Cell) list
val initGraphics : unit -> 'a * 'b * 'c

Full name: 07-03-fsharp-fable-three-maze_.initGraphics
val width : (unit -> float)
val height : (unit -> float)
val scene : 'b
val camera : 'c
val initLights : (unit -> 'd)
val spotLight : obj
val set : elements:seq<'T> -> Set<'T> (requires comparison)

Full name: Microsoft.FSharp.Core.ExtraTopLevelOperators.set
val renderer : 'a
val container : obj
val makeButton : ('d -> int -> 'e -> 'f)
val text : 'd
val difficulty : int
val cssClass : 'e
val button : 'f
val buttonClick : ('g -> obj)
val b : 'g
type Boolean =
struct
member CompareTo : obj:obj -> int + 1 overload
member Equals : obj:obj -> bool + 1 overload
member GetHashCode : unit -> int
member GetTypeCode : unit -> TypeCode
member ToString : unit -> string + 1 overload
static val TrueString : string
static val FalseString : string
static member Parse : value:string -> bool
static member TryParse : value:string * result:bool -> bool
end

Full name: System.Boolean
type obj = Object

Full name: Microsoft.FSharp.Core.obj
Multiple items
type Func<'TResult> =
delegate of unit -> 'TResult

Full name: System.Func<_>

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type Func<'T,'TResult> =
delegate of 'T -> 'TResult

Full name: System.Func<_,_>

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type Func<'T1,'T2,'TResult> =
delegate of 'T1 * 'T2 -> 'TResult

Full name: System.Func<_,_,_>

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type Func<'T1,'T2,'T3,'TResult> =
delegate of 'T1 * 'T2 * 'T3 -> 'TResult

Full name: System.Func<_,_,_,_>

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type Func<'T1,'T2,'T3,'T4,'TResult> =
delegate of 'T1 * 'T2 * 'T3 * 'T4 -> 'TResult

Full name: System.Func<_,_,_,_,_>

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type Func<'T1,'T2,'T3,'T4,'T5,'TResult> =
delegate of 'T1 * 'T2 * 'T3 * 'T4 * 'T5 -> 'TResult

Full name: System.Func<_,_,_,_,_,_>

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type Func<'T1,'T2,'T3,'T4,'T5,'T6,'TResult> =
delegate of 'T1 * 'T2 * 'T3 * 'T4 * 'T5 * 'T6 -> 'TResult

Full name: System.Func<_,_,_,_,_,_,_>

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type Func<'T1,'T2,'T3,'T4,'T5,'T6,'T7,'TResult> =
delegate of 'T1 * 'T2 * 'T3 * 'T4 * 'T5 * 'T6 * 'T7 -> 'TResult

Full name: System.Func<_,_,_,_,_,_,_,_>

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type Func<'T1,'T2,'T3,'T4,'T5,'T6,'T7,'T8,'TResult> =
delegate of 'T1 * 'T2 * 'T3 * 'T4 * 'T5 * 'T6 * 'T7 * 'T8 -> 'TResult

Full name: System.Func<_,_,_,_,_,_,_,_,_>

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type Func<'T1,'T2,'T3,'T4,'T5,'T6,'T7,'T8,'T9,'TResult> =
delegate of 'T1 * 'T2 * 'T3 * 'T4 * 'T5 * 'T6 * 'T7 * 'T8 * 'T9 -> 'TResult

Full name: System.Func<_,_,_,_,_,_,_,_,_,_>

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type Func<'T1,'T2,'T3,'T4,'T5,'T6,'T7,'T8,'T9,'T10,'TResult> =
delegate of 'T1 * 'T2 * 'T3 * 'T4 * 'T5 * 'T6 * 'T7 * 'T8 * 'T9 * 'T10 -> 'TResult

Full name: System.Func<_,_,_,_,_,_,_,_,_,_,_>

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type Func<'T1,'T2,'T3,'T4,'T5,'T6,'T7,'T8,'T9,'T10,'T11,'TResult> =
delegate of 'T1 * 'T2 * 'T3 * 'T4 * 'T5 * 'T6 * 'T7 * 'T8 * 'T9 * 'T10 * 'T11 -> 'TResult

Full name: System.Func<_,_,_,_,_,_,_,_,_,_,_,_>

--------------------
type Func<'T1,'T2,'T3,'T4,'T5,'T6,'T7,'T8,'T9,'T10,'T11,'T12,'TResult> =
delegate of 'T1 * 'T2 * 'T3 * 'T4 * 'T5 * 'T6 * 'T7 * 'T8 * 'T9 * 'T10 * 'T11 * 'T12 -> 'TResult

Full name: System.Func<_,_,_,_,_,_,_,_,_,_,_,_,_>

--------------------
type Func<'T1,'T2,'T3,'T4,'T5,'T6,'T7,'T8,'T9,'T10,'T11,'T12,'T13,'TResult> =
delegate of 'T1 * 'T2 * 'T3 * 'T4 * 'T5 * 'T6 * 'T7 * 'T8 * 'T9 * 'T10 * 'T11 * 'T12 * 'T13 -> 'TResult

Full name: System.Func<_,_,_,_,_,_,_,_,_,_,_,_,_,_>

--------------------
type Func<'T1,'T2,'T3,'T4,'T5,'T6,'T7,'T8,'T9,'T10,'T11,'T12,'T13,'T14,'TResult> =
delegate of 'T1 * 'T2 * 'T3 * 'T4 * 'T5 * 'T6 * 'T7 * 'T8 * 'T9 * 'T10 * 'T11 * 'T12 * 'T13 * 'T14 -> 'TResult

Full name: System.Func<_,_,_,_,_,_,_,_,_,_,_,_,_,_,_>

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type Func<'T1,'T2,'T3,'T4,'T5,'T6,'T7,'T8,'T9,'T10,'T11,'T12,'T13,'T14,'T15,'TResult> =
delegate of 'T1 * 'T2 * 'T3 * 'T4 * 'T5 * 'T6 * 'T7 * 'T8 * 'T9 * 'T10 * 'T11 * 'T12 * 'T13 * 'T14 * 'T15 -> 'TResult

Full name: System.Func<_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_>

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type Func<'T1,'T2,'T3,'T4,'T5,'T6,'T7,'T8,'T9,'T10,'T11,'T12,'T13,'T14,'T15,'T16,'TResult> =
delegate of 'T1 * 'T2 * 'T3 * 'T4 * 'T5 * 'T6 * 'T7 * 'T8 * 'T9 * 'T10 * 'T11 * 'T12 * 'T13 * 'T14 * 'T15 * 'T16 -> 'TResult

Full name: System.Func<_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_,_>
val buttonContainer : obj
val renderer : obj

Full name: 07-03-fsharp-fable-three-maze_.renderer
val scene : obj

Full name: 07-03-fsharp-fable-three-maze_.scene
val camera : obj

Full name: 07-03-fsharp-fable-three-maze_.camera
val cameraPositionZ : float

Full name: 07-03-fsharp-fable-three-maze_.cameraPositionZ
val reqFrame : dt:float -> 'a

Full name: 07-03-fsharp-fable-three-maze_.reqFrame
val dt : float
val animate : dt:float -> unit

Full name: 07-03-fsharp-fable-three-maze_.animate
val log : value:'T -> 'T (requires member Log)

Full name: Microsoft.FSharp.Core.Operators.log