General revisions, improve README

README.md

@@ -1,10 +1,25 @@
 # Advent
 
 The goal of this project is to get all 500 currently available stars in the form
-of one single idris application, and thoroughly document the results as literate
+of one single Idris application, and thoroughly document the results as literate
-idris files.
+Idris files.
 
-# Index of non-day modules
+## Authors Note
+
+The solutions contained in this project are intended to be read in sequential
+order, though can reasonably be read in any order if you have a good level of
+familiarity with more advanced functional programming topics.
+
+The solutions will involve progressively more advanced topics as day and year
+number increase, though I try not to introduce too much within the scope of any
+one day.
+
+Suggestions and other feedback are highly welcome, please reach out to me via
+any platform you know me on, or send an email to the
+[~thatonelutenist/public-inbox](https://lists.sr.ht/~thatonelutenist/public-inbox)
+mailing list on source hut.
+
+## Index of non-day modules
 
 - [Runner](src/Runner.md)
 
@@ -26,16 +41,61 @@ solution.
     Extend the functionality of the effects included in the
     [eff](https://github.com/stefan-hoeck/idris2-eff/) library
 
-# Index of years and days
+  - [Util.Digits](src/Util/Digits.md)
+
+    Provide views that enable recursively pattern matching numbers as lists of
+    digits, in both ascending and descending order of significance.
+
+## Index of years and days
 
 - 2015
   - [Day 1](src/Years/Y2015/Day1.md)
+
+    Warm up problem, breaks in our new runner and not much else interesting.
+
   - [Day 2](src/Years/Y2015/Day2.md)
+
+    An early hint of effectful parsing.
+
   - [Day 3](src/Years/Y2015/Day3.md)
+
+    Peculiarities of writing mutually recursive functions in dependently typed
+    languages.
+
   - [Day 4](src/Years/Y2015/Day4.md)
+
+    Basic FFI to openssl to steal its MD5 function for Idris's use.
+
   - [Day 5](src/Years/Y2015/Day5.md)
+
+    First introduction to views and dependent pattern matching[^1].
+
   - [Day 6](src/Years/Y2015/Day6.md)
+
+    Naive approach to handling the first 2d grid problem.
+
   - [Day 7](src/Years/Y2015/Day7.md)
+
+    Introduces dependent maps and indexed type families.
+
   - [Day 8](src/Years/Y2015/Day8.md)
+
+    Proper effectful parsers and non-determinism in effect stacks.
+
   - [Day 9](src/Years/Y2015/Day9.md)
+
+    Naive approach to handling the first graph traversal problem.
+
   - [Day 10](src/Years/Y2015/Day10.md)
+
+    Introduce our `Digits`, dependent pattern matching on integers as lists of
+    digits.
+
+  - [Day 11](src/Years/Y2015/Day11.md)
+
+    Introduces refinement types
+
+## References
+
+[^1]: Idris 2 Manual:
+    [Views and the "with" rule](https://idris2.readthedocs.io/en/latest/tutorial/views.html#views-and-the-with-rule)

advent.ipkg

@@ -21,6 +21,7 @@ depends = base
         , ansi
         , if-unsolved-implicit
         , c-ffi
+        , refined
 
 -- modules to install
 modules = Runner

src/Grid.md

@@ -1,371 +0,0 @@
-# 2D Grid utilities
-
-Types and utilities for dealing with a 2D grid of things
-
-We base our `Grid` type on `Data.Seq.Sized` from `contrib`, a finger tree based
-collection that tracks its size in its type, since it provides somewhat
-efficient random access and updates.
-
-```idris
-module Grid
-  
-import Data.Seq.Sized
-import Data.Fin
-import Data.Fin.Extra
-import Data.List.Lazy
-import Data.Zippable
-import Data.Vect
-import Data.String
-import Decidable.Equality
-
-%default total
-```
-
-## Coordinates
-
-A coordinate is a pair of numbers both less than their respective bounds.
-
-Since `Grid`s will always be non-empty in the contexts we will be using them in,
-this type alias adds one to each of the bounds to ensure non-emptyness
-
-```idris
-public export
-Coord : (rows, cols : Nat) -> Type
-Coord rows cols = (Fin (S rows), Fin (S cols))
-```
-
-### Coordinate utility functions
-
-Lazily generate all the coordinates for a given pair of bounds
-
-Uses an internal helper function to generate a lazy list of all the fins of a
-given bound in ascending order (`all`), and another to convert a lazy list of
-`Fin` into a lazy list of pairs of `Fin`s.
-
-The totality checker likes to go in the descending direction, since then it can
-reason about values getting structurally "smaller", so it has issues with `all'`
-moving in the ascending direction. We know this function is total because the
-`acc < last` check will always eventually be triggered, since `Fin`s only have a
-finite number of values.
-
-We pull out an `assert_smaller` to tell Idris that the argument to the recursive
-call is getting structurally smaller, which while not strictly correct, does
-convey to the compiler that we are getting closer to our recursive base case and
-that the function is thus total.
-
-```idris
-export
-allCords : {rows, cols : Nat} -> LazyList (Coord rows cols)
-allCords = concat . map row $ all
-  where
-    all : {n : Nat} -> LazyList (Fin (S n))
-    all = FZ :: all' FZ
-      where
-        all' : {n : Nat} -> (acc : Fin (S n)) -> LazyList (Fin (S n))
-        all' acc =
-          if acc < last
-            then finS acc :: all' (assert_smaller acc (finS acc))
-            else []
-    row : Fin (S rows) -> LazyList (Coord rows cols)
-    row r = map (\c => (r, c)) all
-```
-
-Add a given vector to a coordinate, returning `Nothing` if we go off the ends of
-the bounds in the process.
-
-To keep this function simple and reasonably efficient, we perform the arithmetic
-in integer space, using `integerToFin` to fallably convert back to `Fin` space,
-making use of the `Maybe` monad to keep the code clean.
-
-```idris
-export
-step : {rows, cols : Nat} -> (input : Coord rows cols) -> (direction : (Integer, Integer))
-     -> Maybe (Coord rows cols)
-step (row, col) (d_row, d_col) = do
-  let (row, col) = (finToInteger row, finToInteger col)
-  row <- integerToFin (row + d_row) (S rows)
-  col <- integerToFin (col + d_col) (S cols)
-  pure (row, col)
-```
-
-## Grid
-
-A grid is a `Seq` of `Seq`s with the given size bounds.
-
-The inner `Seq`s are kept opaque to maintain flexability in the implementation
-
-```idris
-export
-record Grid (rows, cols : Nat) (e : Type) where
-  constructor MkGrid
-  grid : Seq (S rows) (Seq (S cols) e)
-%name Grid grid, grid2, grid3
-```
-
-### Constructors
-
-Construct a `Grid` by filling every slot with identical copies of the provided
-element
-
-```idris
-export
-replicate : {rows, cols : Nat} -> (seed : e) -> Grid rows cols e
-replicate seed = 
-  let row = replicate (S cols) seed
-      grid = replicate (S rows) row
-  in MkGrid grid
-```
-
-Attempt to construct a `Grid` from a Foldable of Foldables. Will return
-`Nothing` if either the rows are of heterogeneous size, or if either the rows or
-columns are empty. Requires that the outer Foldable also be Traversable.
-
-We make heavy use of the `Maybe` monad to keep the code clean here.
-
-```idris
-export
-fromFoldable : Traversable a => Foldable a => Foldable b => a (b e) -> 
-  Maybe (rows : Nat ** cols : Nat ** Grid rows cols e)
-fromFoldable xs = do
-  -- First collect the number of rows from the outer foldable
-  let (S rows) = foldl (\acc, e => acc + 1) 0 xs
-    | _ => Nothing -- Return Nothing if there are no rows
-  -- Get the number of columns in the largest row in the inner foldable
-  let (S cols) = foldl (\acco, eo => max acco (foldl (\acci, ei => acci +1) 0 eo)) 0 xs
-    | _ => Nothing -- Return Nothing if all the rows are empty
-  -- Convert the rows by traversing our foldToSeq function over the outer foldable
-  xs <- traverse (foldToSeq (S cols)) xs
-  -- Reuse our foldToSeq helper function to convert the outer foldable
-  xs <- foldToSeq (S rows) xs
-  -- wrap it up and return
-  pure (rows ** cols ** MkGrid xs)
-  where
-    -- Convert each row to a seq using an intermediate list
-    foldToSeq : Foldable c => (n : Nat) -> c f -> Maybe (Seq n f)
-    foldToSeq n x = 
-      let list = toList x
-      -- Check to see if the list is of the correct length, then rewrite the
-      -- output type to match if that's the case, otherwise return Nothing
-      in case decEq (length list) n of
-        Yes Refl => Just $ fromList list
-        No _ => Nothing
-```
-
-Construct a `Grid` from a non-empty `Vect` of non-empty `Vect`s. To keep the
-function simple, we require that both the row and column dimension are known to
-be non-zero before calling this constructor.
-
-```idris
-export
-fromVect : Vect (S rows) (Vect (S cols) e) -> Grid rows cols e
-fromVect xs = MkGrid . fromVect . map fromVect $ xs
-```
-
-Construct `Grid` containing the coordinate of the location in each location
-
-```idris
-export
-coordinateGrid : {rows, cols : Nat} -> Grid rows cols (Coord rows cols)
-coordinateGrid = 
-  let row = fromVect $ allFins (S cols) 
-      grid = zip (fromVect $ allFins (S rows)) (replicate _ row)
-      grid = map (\(x, xs) => map (x,) xs) grid
-  in MkGrid grid
-```
-
-### Accessors and Mutators
-
-Get the value at a specific index in the grid
-
-```idris
-export
-index : Coord rows cols -> Grid rows cols e -> e
-index (row, col) grid = 
-  index' (index' grid.grid row) col
-```
-
-Replace the value at a specific index in the grid
-
-```idris
-export
-replaceAt : Coord rows cols -> e -> Grid rows cols e -> Grid rows cols e
-replaceAt (row, col) x (MkGrid grid) = 
-  let r = index' grid row
-      r = update (finToNat col) x r @{elemSmallerThanBound col}
-      grid = update (finToNat row) r grid @{elemSmallerThanBound row}
-  in MkGrid grid
-```
-
-Update the value at a specific index in the grid
-
-```idris
-export
-updateAt : Coord rows cols -> (e -> e) -> Grid rows cols e -> Grid rows cols e
-updateAt (row, col) f (MkGrid grid) = 
-  let r = index' grid row
-      r = adjust f (finToNat col) r @{elemSmallerThanBound col}
-      grid = update (finToNat row) r grid @{elemSmallerThanBound row}
-  in MkGrid grid
-```
-
-Lazily provide all the values in the grid as a flat collection
-
-```idris
-export
-flat : {rows, cols : Nat} -> Grid rows cols e -> LazyList e
-flat (MkGrid grid) = 
-  let grid = seqToLazy . map (seqToLazy {n = S cols}) $ grid 
-      grid = grid []
-  in foldrLazy (\a, acc => a acc) [] grid
-  where
-    seqToLazy : {n : Nat} -> (seq : Seq n a) -> (rest : LazyList a) -> LazyList a
-    seqToLazy {n = 0} seq rest = rest
-    seqToLazy {n = (S k)} seq rest = 
-      let (head, tail) = viewl seq
-      in head :: seqToLazy tail rest
-```
-
-### Interface Implementations
-
-#### Show
-
-```idris
-export
-{rows, cols : Nat} -> Show e => Show (Grid rows cols e) where
-  show (MkGrid grid) = 
-    show . toVect . map toVect $ grid
-```
-
-#### Eq/Ord
-
-```idris
-export
-Eq e => Eq (Grid rows cols e) where
-  (MkGrid grid_x) == (MkGrid grid_y) = grid_x == grid_y
-
-export
-Ord e => Ord (Grid rows cols e) where
-  compare (MkGrid grid_x) (MkGrid grid_y) = compare grid_x grid_y
-```
-
-#### Functor
-
-```idris
-export
-Functor (Grid rows cols) where
-  map f (MkGrid grid) = 
-    MkGrid . map (map f) $ grid
-```
-
-#### Foldable
-
-Cheeze it a little and use our `flat` function internally here.
-
-Also, `null` can statically return false, as `Grid` is structurally non-empty
-
-```idris
-export
-{rows, cols : Nat} -> Foldable (Grid rows cols) where
-  foldr f acc grid = foldr f acc (flat grid)
-  foldl f acc grid = foldl f acc (flat grid)
-  null _ = False
-  toList grid = toList (flat grid)
-```
-
-#### Applicative
-
-```idris
-export
-{rows, cols : Nat} -> Applicative (Grid rows cols) where
-  pure a = replicate a
-  (MkGrid f) <*> (MkGrid grid) = 
-    MkGrid . map (\(a,b) => a <*> b) . zip f $ grid
-```
-
-#### Traversable
-
-```idris
-export
-{rows, cols : Nat} -> Traversable (Grid rows cols) where
-  traverse f (MkGrid grid) = 
-    map MkGrid . traverse (traverse f) $ grid 
-```
-
-#### Zippable
-
-```idris
-export
-Zippable (Grid rows cols) where
-  zipWith f (MkGrid grid_x) (MkGrid grid_y) = 
-    let xs = zip grid_x grid_y
-    in MkGrid . map (\(a,b) => zipWith f a b) $ xs
-  unzipWith f (MkGrid grid) = 
-    let (xs, ys) = unzip . map (unzipWith f) $ grid
-    in (MkGrid xs, MkGrid ys)
-  zipWith3 f (MkGrid as) (MkGrid bs) (MkGrid cs) = 
-    let xs = zip3 as bs cs
-    in MkGrid . map (\(a, b, c) => zipWith3 f a b c) $ xs 
-  unzipWith3 f (MkGrid grid) = 
-    let (a, b, c) = unzip3 . map (unzipWith3 f) $ grid
-    in (MkGrid a, MkGrid b, MkGrid c)
-```
-
-### Extra
-
-Extensions of the above functionality
-
-#### Indexing
-
-Convert this grid to one with both the index of the location and the element in
-each location
-
-```idris
-export
-indexed : {rows, cols : Nat} -> Grid rows cols e -> Grid rows cols (Coord rows cols, e)
-indexed grid = zip coordinateGrid grid
-```
-
-Same as `flat` above, but indexed
-
-```idris
-export
-flatIndexed : {rows, cols : Nat} -> Grid rows cols e -> LazyList (Coord rows cols, e)
-flatIndexed = flat . indexed
-```
-
-#### String functionality
-
-Attempts to convert a string, with newline delimited rows, to a grid of
-characters
-
-```idris
-export
-stringToGrid : String -> Maybe (rows : Nat ** cols : Nat ** Grid rows cols Char) 
-stringToGrid = fromFoldable . map (unpack . trim) . lines . trim
-```
-
-Converts a grid of chars to a string, delimiting the rows with newlines
-
-```idris
-export
-gridToString : Grid rows cols Char -> String
-gridToString (MkGrid grid) = unlines . toList . map (pack . toList) $ grid
-```
-
-#### Conversion
-
-Convert a grid to a vect of vects
-
-```idris
-export
-toVects : {rows, cols : Nat} -> Grid rows cols e -> Vect (S rows) (Vect (S cols) e)
-toVects (MkGrid grid) = toVect . map toVect $ grid
-```
-
-Convert a grid to a list of lists
-
-```idris
-export
-toLists : Grid rows cols e -> List (List e)
-toLists (MkGrid grid) = toList . map toList $ grid
-```

src/Main.md

@@ -181,8 +181,8 @@ failures doing so.
 ## Handling the arguments and finding the input
 
 Handle the verbosity flag, if it is set, hook our logger up to stderr, otherwise
-blackhole the logs. Afterwards, use `logHandler` to introduce the logging
+blackhole the logs. Afterwards, use `logHandler` to introduce the `Logger` into
-`Writer` into the effects list.
+the effects list.
 
 ```idris
   -- If the verbose flag is set, hook up the logging writer to stderr
@@ -259,8 +259,8 @@ a `SolveError`, then print out the result, then return, closing out the program.
 
 ### Lower logging into the IO component of the effect
 
-This function uses the provided `String -> IO ()` to remove the `Writer` from
+Makes use of `Logger`'s `handleLoggerIO` function to "lower" logging actions
-the effects list by translating `tell` calls to IO actions within the effect.
+into `IO` within the effect.
 
 ```idris
     -- Lowers logging into IO within the effect using the given IO function

src/Runner.md

@@ -22,16 +22,15 @@ import public Util.Eff
 # Effectful Parts
 
 The solution to each part of a day is run as an effectful computation, and as
-the available effects are meant to be the same across both parts, only varying
+the effect stack is meant to be the same across both parts, only varying in the
-in the type of the error value in the `Except` effect, I construct a type level
+type of the error value for the `Except` effect, we construct a type level
-function to have a single source of truth for this. The `err` type can be any
+function to have a single source of truth. The `err` type can be any type with a
-type with a `Show` implementation, but that constraint will be tacked on in the
+`Show` implementation, but that constraint will be tacked on in the next step.
-next step.
 
-A `Writer` effect is provided for logging, and a `Reader` effect is provided to
+The `Logger` effect is provided for logging, and a `Reader` effect is provided
-pass in the input, just to make the top level API a little bit cleaner. `IO` is
+to pass in the input, to make the top level API a little bit cleaner. `IO` is
 also provided, even though the part solutions themselves shouldn't really be
-doing any IO, this may come in handy if a part needs `IO` for performance
+doing any IO, this will come in handy if a part needs `IO` for performance
 reasons.
 
 ```idris
@@ -46,19 +45,19 @@ PartEff err =
 # The `Day` Record
 
 The `Day` type groups together an effectful `part1` computation, an optional
-effectful `part2` computation, the day number, and does some type wrangling to
+effectful `part2` computation, and the day number, with some type wrangling to
-get the type system out of our way on this one.
+get the type system out of our way.
 
 `part1` and `part2` are allowed independent output and error types, and this
 record captures `Show` implementations for those output and error types so that
-we can display them in `Main` where the `Day` is consumed without having to
+we can display them in `Main`, where the `Day` is consumed, without having to
 actually know what the types are.
 
 It is often useful to pass a bit of context, such as the data structures
-resulting from parsing, between `part1` and `part2`, and this is achieved by the
+resulting from parsing, between `part1` and `part2`. This is achieved through
-erased `ctx` type, which is totally opaque here. The runner code in `Main` will
+the erased `ctx` type, which is totally opaque to the runner. The code in `Main`
-provide the value of the `ctx` type produced as part of the output of `part1` as
+will provide the value of the `ctx` type produced as part of the output of
-the input of `part2`.
+`part1` and as the input of `part2`.
 
 ```idris
 ||| Model solving a single day
@@ -80,9 +79,9 @@ record Day where
 
 The default `MkDay` constructor is slightly cumbersome to use, always requiring
 _something_ for the `part2` slot, even if there isn't a part 2 yet, and
-requiring that `part2` be wrapped in a `Just` when there is one, so we provide a
+requiring that `part2` be wrapped in a `Just` when there is one. We provide a
-pair of constructors for the case where there is only a `part1` and for where
+pair of constructors for the case where there is only a `part1`, as well as one
-there is a `part1` and a `part2` that handle that for us.
+for when there is a `part1` and a `part2`.
 
 ```idris
 namespace Day
@@ -91,8 +90,7 @@ namespace Day
 ### First
 
 The `First` constructor only accepts a `part1`, it does the work of filling in
-`part2` with `Nothing` and setting all of `part2`'s type arguments to `()` for
+`part2` with `Nothing` and setting all of `part2`'s type arguments to `()`.
-us.'
 
 ```idris
   ||| Constructor for a day with only part one ready to run
@@ -106,8 +104,8 @@ us.'
 
 ### Both
 
-The `Both` constructor does a little bit less heavy lifting, the only thing it
+The `Both` constructor does less heavy lifting, the only thing it needs to do is
-needs to do for us is wrap `part2` in a `Just`.
+wrap `part2` in a `Just`.
 
 ```idris
   ||| Constructor for a day with both parts ready to run
@@ -123,16 +121,17 @@ needs to do for us is wrap `part2` in a `Just`.
 ## Freshness
 
 We will be using a _Fresh List_ from the
-[structures](https://git.sr.ht/~thatonelutenist/Structures) package to build
+[structures](https://git.sr.ht/~thatonelutenist/Structures) package to build our
-defensiveness into the API. A Fresh List structurally only allows you to prepend
+API defensively against duplicate days and cosmetically annoying out of order
-an element onto it when it satisfies some _freshness_ criteria relative to the
+day registration. A Fresh List structurally only allows you to prepend/cons an
-elements already in the list.
+element onto it when it satisfies some _freshness criteria_ relative to the
+elements already contained in the list.
 
-Here, we compare the day numbers of the two `Day`s using the less-than
+We compare the day numbers of the two `Day`s using the less-than(`<`)
 relationship. Since we are operating on the start of the list when this
 comparison takes place, this enforces, through type checking, that the resulting
-Fresh List is sorted in ascending order and that no two `Day`s have the same day
+Fresh List of `Day`s is sorted in ascending order and that no two `Day`s have
-number.
+the same day number.
 
 ```idris
 ||| Freshness criteria for days
@@ -150,7 +149,7 @@ FreshDay x y = x.day < y.day
 # The `Year` Record
 
 The `Year` record collects a number of `Day`s into a single Fresh List for the
-year, and is mostly just a simple container.
+year, also containing the year number for this collection.
 
 ```idris
 ||| Collect all the days in a given year
@@ -166,9 +165,10 @@ record Year where
 
 Much like `Day`s are stored in a `FreshList` in `Year`, `Year`s will be stored
 in a `FreshList` in `Advent`, so we need to provide a freshness criteria for
-`Year` as well. We do so by applying the less-than relationship against the year
+`Year` as well.
-number of the two `Years`, for the same reasons and with the same results as
+
-with `FreshDay`.
+We do so by applying the less-than relationship against the year number of the
+two `Years`, for the same reasons and with the same results as with `FreshDay`.
 
 ```idris
 ||| Freshness criteria for years
@@ -186,8 +186,7 @@ FreshYear x y = x.year < y.year
 # The `Advent` Record
 
 The `Advent` record collects a number of `Year`s in much the same way that
-`Year` collects a number of days, sorting the `Year`s in a `FreshList` to
+`Year` collects a number of days.
-provide API defensiveness.
 
 ```idris
 ||| Collect all years

src/Util/Eff.md

@@ -22,9 +22,18 @@ import System.File
 Basic enumeration describing log levels, we define some (hidden) utility
 functions for working with these.
 
+The `Other n` log level is restricted to `n` greater than 4, to prevent
+ambiguity between custom log levels and predefined log levels.
+
 ```idris
 public export
-data Level = Err | Warn | Info | Debug | Trace | Other Nat 
+data Level : Type where
+  Err : Level
+  Warn : Level
+  Info : Level
+  Debug : Level
+  Trace : Level
+  Other : (n : Nat) -> {auto _ : n `GT` 4} -> Level
 ```
 
 <!-- idris
@@ -44,7 +53,7 @@ natToLevel 1 = Warn
 natToLevel 2 = Info
 natToLevel 3 = Debug
 natToLevel 4 = Trace
-natToLevel k = Other k
+natToLevel (S (S (S (S (S k))))) = Other (5 + k)
 
 export
 Eq Level where
@@ -130,10 +139,8 @@ handleLoggerIO max_level x =
     else pure . ignore $ x
 ```
 
-Use the `WriterL "log" String` effect like a logging library. We'll provide a
+Provide a family of effectful actions that emit log messages at the different
-few "log levels" as verbs for the effect, but no filtering is done, when logging
+log levels.
-is enabled, all logs are always displayed, however the log level is indicated
-with a colored tag.
 
 ```idris
 export
@@ -155,6 +162,10 @@ debug x = send $ Log Debug x
 export
 trace : Has Logger fs => Lazy String -> Eff fs ()
 trace x = send $ Log Trace x
+
+export
+logAt : Has Logger fs => Level -> Lazy String -> Eff fs ()
+logAt level x = send $ Log level x
 ```
 
 ## Choose

src/Years/Y2015.md

@@ -17,6 +17,7 @@ import Years.Y2015.Day7
 import Years.Y2015.Day8
 import Years.Y2015.Day9
 import Years.Y2015.Day10
+import Years.Y2015.Day11
 -->
 
 # Days
@@ -87,6 +88,12 @@ y2015 = MkYear 2015 [
   , day10
 ```
 
+## [Day 11](Y2015/Day11.md)
+
+```idris
+  , day11
+```
+
 ```idris
   ]
 ```

src/Years/Y2015/Day1.md

@@ -1,4 +1,4 @@
-# Year 2015 Day 1
+# [Year 2015 Day 1](https://adventofcode.com/2015/day/1)
 
 Pretty simple, basic warmup problem, nothing really novel is on display here
 except the effectful part computations.

src/Years/Y2015/Day10.md

@@ -1,4 +1,4 @@
-# Year 2015 Day 10
+# [Year 2015 Day 10](https://adventofcode.com/2015/day/10)
 
 This day doesn't really add anything new, but we will show off our new views for
 viewing integers as lists of digits.

src/Years/Y2015/Day11.md

@@ -0,0 +1,227 @@
+# [Year 2015 Day 11](https://adventofcode.com/2015/day/11)
+
+This day provides a gentle introduction to refinement types, types which augment
+other types with a predicate that must hold for all the values of the refined
+type, which allow easily defining types as subsets of other types based on some
+property of the acceptable elements.
+
+While refinement types are quite easy to implement in Idris, and we easily could
+implement the one we need for today's task as a throw away data structure just
+for this module, we will be using the `refined`[^1] library's implementation for
+the sake of getting on with it.
+
+<!-- idris 
+module Years.Y2015.Day11
+
+import Control.Eff
+
+import Runner
+-->
+
+```idris
+import Data.Vect
+import Data.String
+import Data.Refined.Char
+
+import Util
+```
+
+## Data Structures and Parsing
+
+Provide a predicate which establishes that a char is a lowercase alphabetic
+character, the only type of character that passwords are allowed to contain. We
+use the `FromTo` predicate from the `refined`[^1] library to restrict chars to
+within the range from `a` to `z`.
+
+This predicate has multiplicity 0, a full discussion of multiplicites and linear
+types is out of scope for today, but put simply this enforces that a value of
+this predicate type can be "used" at most 0 times, having the effect of erasing
+the value at runtime, making this more or less a zero-cost abstraction.
+
+```idris
+0 IsPasswordChar : Char -> Type
+IsPasswordChar = FromTo 'a' 'z'
+```
+
+Combine a `Char` with its corresponding `IsPasswordChar` predicate into a
+combined "refined" type, whose elements are the subset of `Char`s that are
+lowercase alphabetic characters.
+
+```idris
+record PasswordChar where
+  constructor MkPC
+  char : Char
+  {auto 0 prf : IsPasswordChar char}
+%name PasswordChar pc
+```
+
+<!-- idris
+Show PasswordChar where
+  show (MkPC char) = singleton char
+
+Eq PasswordChar where
+  x == y = x.char == y.char
+-->
+
+A function to fallible convert `Char`s into refined `PasswordChar`s, this will
+return `Just` if the `Char` satisfies the predicate, and `Nothing` otherwise,
+aligning with the type-level guarantees of the `PasswordChar` type.
+
+```idris
+refineChar : Char -> Maybe PasswordChar
+refineChar c = map fromSubset $ refine0 c
+  where
+    fromSubset : Subset Char IsPasswordChar -> PasswordChar
+    fromSubset (Element char prf) = MkPC char
+```
+
+Convenience function returning `a` as a `PasswordChar`
+
+```idris
+lowest : PasswordChar
+lowest = MkPC 'a'
+```
+
+"Increment" a `PasswordChar`, changing it to the next letter (`a` becomes `b`,
+`b` becomes `c`, so on), returning nothing if we go past `z`, corresponding to a
+carry.
+
+We do this by converting the internal `Char` to an integer, adding one to it,
+then converting back to a `Char`. This low-level conversion loses the refinement
+context, forcing us to call `refineChar` on the new value to bring it back into
+the refined type, providing us type-level assurance that this function will
+return `Nothing` if an overflow occurs.
+
+```idris
+incriment : PasswordChar -> Maybe PasswordChar
+incriment (MkPC char) = 
+  let next = chr $ ord char + 1
+  in refineChar next
+```
+
+A `Password` is a `Vect` of 8 `PasswordChar`s. This `Vect` is sorted in reverse
+order compared to the `String` it corresponds to, with the right-most letter
+first, to make implementing the `incrimentPassword` function a little easier and
+cleaner.
+
+We also provide conversion to/from a `String`
+
+```idris
+Password : Type
+Password = Vect 8 PasswordChar
+  
+parsePassword : Has (Except String) fs => String -> Eff fs Password
+parsePassword str = do
+  cs <- note "Password has incorrect number of characters: \{str}" 
+        . toVect 8 . reverse . unpack $ str
+  cs <- note "Password contained invalid characters: \{str}" 
+        $ traverse refineChar cs
+  pure cs
+
+passwordToString : Password -> String
+passwordToString = pack . toList . reverse . map char
+```
+
+Define a function to increment a `Password`, this function will "roll over",
+producing `aaaaaaaa` if provided `zzzzzzzz`.
+
+```idris
+incrimentPassword : Vect n PasswordChar -> Vect n PasswordChar
+incrimentPassword [] = []
+incrimentPassword (x :: xs) = 
+  case incriment x of
+    Nothing => lowest :: incrimentPassword xs
+    Just x => x :: xs
+```
+
+### Password validity
+
+A password must contain a run of at least 3 incrementing characters, check this
+by converting the `PasswordChar`s to their integer representations. Remember
+that our `Password` `Vect` is backwards compared to the string representation.
+
+```idris
+incrimentingChars : Vect n PasswordChar -> Bool
+incrimentingChars (z :: next@(y :: (x :: xs))) = 
+  let [x, y, z] : Vect _ Int = map (ord . char) [x, y, z]
+  in if y == x + 1 && z == y + 1
+    then True
+    else incrimentingChars next
+incrimentingChars _ = False
+```
+
+A password may not contain `i`, `o`, or `l`
+
+```idris
+noInvalidChars : Vect n PasswordChar -> Bool
+noInvalidChars = not . (any (flip contains $ ['i', 'o', 'l'])) . map char
+```
+
+A password contains at least two different non-overlapping pairs.
+
+We check this by pattern matching our password two characters at a time,
+consuming both characters if a matched pair is found, and tacking on the `Char`
+the list is composed of to an accumulator list as we go. This list is then
+reduced to only its unique elements (it's `nub`), and checking to see if it's
+length is at least 2.
+
+```idris
+containsPairs : Vect n PasswordChar -> Bool
+containsPairs xs = length (nub $ pairs (reverse xs) []) >= 2
+  where
+    pairs : Vect m PasswordChar -> (acc : List Char) -> List Char
+    pairs [] acc = acc
+    pairs (x :: []) acc = acc
+    pairs (x :: (y :: xs)) acc = 
+      if x == y 
+        -- If there is a pair, consume it to prevent detecting overlapping pairs
+        then pairs xs (x.char :: acc)
+        -- If there isn't a pair, only consume one character
+        else pairs (y :: xs) acc
+```
+
+Combine our password criteria into one function
+
+```idris
+part1Critera : Vect n PasswordChar -> Bool
+part1Critera xs = incrimentingChars xs && noInvalidChars xs && containsPairs xs
+```
+
+### Find the next password
+
+Find the next password based on a criteria function
+
+```idris
+findNextPassword : 
+  (f : Vect n PasswordChar -> Bool) -> (password : Vect n PasswordChar)
+  -> Vect n PasswordChar
+findNextPassword f password = 
+  let next = incrimentPassword password
+  in if f next
+    then next
+    else findNextPassword f next
+```
+
+## Part Functions
+
+### Part 1
+
+```idris
+part1 : Eff (PartEff String) (String, ())
+part1 = do
+  input <- map trim $ askAt "input"
+  password <- parsePassword input
+  info "Starting password: \{show password} -> \{passwordToString password}"
+  let next_password = findNextPassword part1Critera password
+  pure (passwordToString next_password, ())
+```
+
+<!-- idris
+public export
+day11 : Day
+day11 = First 11 part1
+-->
+
+## References
+
+[^1]: https://github.com/stefan-hoeck/idris2-refined/

src/Years/Y2015/Day2.md

@@ -1,4 +1,4 @@
-# Year 2015 Day 2
+# [Year 2015 Day 2](https://adventofcode.com/2015/day/2)
 
 This day provides us our first little taste of effectful parsing
 

src/Years/Y2015/Day3.md

@@ -1,4 +1,4 @@
-# Year 2015 Day 3
+# [Year 2015 Day 3](https://adventofcode.com/2015/day/3)
 
 This day provides a gentle introduction to `mutual` blocks and mutually
 recursive functions.

src/Years/Y2015/Day4.md

@@ -1,4 +1,4 @@
-# Year 2015 Day 4
+# [Year 2015 Day 4](https://adventofcode.com/2015/day/4)
 
 This day introduces us to a little bit of FFI, linking to openssl to use it's
 `MD5` functionality.

src/Years/Y2015/Day5.md

@@ -1,4 +1,4 @@
-# Year 2015 Day 5
+# [Year 2015 Day 5](https://adventofcode.com/2015/day/5)
 
 This day provides a nice chance to introduce
 [views](https://idris2.readthedocs.io/en/latest/tutorial/views.html),

src/Years/Y2015/Day6.md

@@ -1,4 +1,8 @@
-# Year 2015 Day 6
+# \[Year 2015 Day 6\](https://adventofcode.com/2015/day/
+
+6.
+
+Introduction to the advent of code classic 2d grid problem.
 
 <!-- idris
 module Years.Y2015.Day6

src/Years/Y2015/Day7.md

@@ -1,4 +1,6 @@
-# Year 2015 Day 7
+# \[Year 2015 Day 7\](https://adventofcode.com/2015/day/
+
+7.
 
 This day provides us a gentle introduction to dependent maps.
 
@@ -53,7 +55,10 @@ Input : Type
 Input = Either Literal Wire
 ```
 
-Description of a Gate, tagged in the type with the name of the output wire
+Description of a Gate, tagged in the type with the name of the output wire.
+
+This creates what is referred to as an "indexed type family", in this case a
+family of `Gate` types indexed by values of type `Wire`.
 
 ```idris
 data Gate : Wire -> Type where

src/Years/Y2015/Day8.md

@@ -1,4 +1,4 @@
-# Year 2015 Day 8
+# [Year 2015 Day 8](https://adventofcode.com/2015/day/8)
 
 This day provides a more in depth introduction to writing effectful parsers,
 making use of state and non-determinism in our parsers.

src/Years/Y2015/Day9.md

@@ -1,4 +1,4 @@
-# Year 2015 Day 9
+# [Year 2015 Day 9](https://adventofcode.com/2015/day/9)
 
 This day provides our first example of a graph traversal problem. We'll use a
 `Choose` based effectful breath first search to identify all the possible paths