Type Driven Development with Idris: Updates Required

Type Driven Development with Idris: Updates Required#

The code in the book Type-Driven Development with Idris by Edwin Brady, available from Manning, will mostly work in Idris 2, with some small changes as detailed in this document. The updated code is also [going to be] part of the test suite (see tests/typedd-book in the Idris 2 source).

If you are new to Idris, and learning from the book, we recommend working through the first 3-4 chapters with Idris 1, to avoid the need to worry about the changes described here. After that, refer to this document for any necessary changes.

Chapter 1#

Instead of entering 2.1 * 20, enter the Double (2.1 * 20).

Instead of entering :exec to run Hello.idr in the REPL, enter :exec main.

Chapter 2#

The Prelude is smaller than Idris 1, and many functions have been moved to the base libraries instead. So:

In Average.idr, add:

import Data.String -- for `words`
import Data.List -- for `length` on lists
import System.REPL -- for `repl`

Instead of entering 6.0 + 3 * 12, enter the Double (6.0 + 3 * 12).

In AveMain.idr and Reverse.idr add:

import System.REPL -- for 'repl'

Instead of entering :exec to run main from AveMain.idr, enter :exec main.

Chapter 3#

Unbound implicits have multiplicity 0, so we can’t match on them at run-time. Therefore, in Matrix.idr, we need to change the type of createEmpties and transposeMat so that the length of the inner vector is available to match on:

createEmpties : {n : _} -> Vect n (Vect 0 elem)
transposeMat : {n : _} -> Vect m (Vect n elem) -> Vect n (Vect m elem)

For the same reason, we also need to change the type of length to:

length : {n : _} -> Vect n elem -> Nat

Chapter 4#

For the reasons described above:

  • In DataStore.idr, add import System.REPL and import Data.String

  • In SumInputs.idr, add import System.REPL

  • In TryIndex.idr, add an implicit argument:

tryIndex : {n : _} -> Integer -> Vect n a -> Maybe a

  • In exercise 5 of 4.2, add an implicit argument:

sumEntries : Num a => {n : _} -> (pos : Integer) -> Vect n a -> Vect n a -> Maybe a

Chapter 5#

Although there is a Cast instance from String to Nat, its behaviour of returning Z if the String is not numeric is now thought to be confusing and potentially error prone. Instead, there is stringToNatOrZ in Data.String which at least has a clearer name. So:

In Loops.idr and ReadNum.idr it’s preferable to add import Data.String and change cast to stringToNatOrZ.

In ReadNum.idr, since functions must now be covering by default, add a partial annotation to readNumbers_v2. (This is the version of readNumbers on page 135.)

The file-handling functions for the exercises in section 5.3.4 are no longer in the Prelude. Import System.File.Handle and System.File.ReadWrite to use them.

Chapter 6#

In DataStore.idr and DataStoreHoles.idr, add import Data.String and import System.REPL. Also in DataStore.idr, the schema argument to display is required for matching, so change the type to:

display : {schema : _} -> SchemaType schema -> String

In TypeFuns.idr add import Data.String

Listing 6.9 says that data Schema declares a type that hasn’t been defined yet. In Idris2, a colon and a type are required:

data Schema : Type

Chapter 7#

Abs is now a separate interface from Neg. So, change the type of eval to include Abs specifically:

eval : (Abs num, Neg num, Integral num) => Expr num -> num

Also, take abs out of the Neg implementation for Expr and add an implementation of Abs as follows:

Abs ty => Abs (Expr ty) where
    abs = Abs

Chapter 8#

In AppendVec.idr, add import Data.Nat for the Nat proofs

cong now takes an explicit argument for the function to apply. So, in CheckEqMaybe.idr change the last case to:

checkEqNat (S k) (S j) = case checkEqNat k j of
                              Nothing => Nothing
                              Just prf => Just (cong S prf)

A similar change is necessary in CheckEqDec.idr.

In ExactLength.idr, the m argument to exactLength is needed at run time, so change its type to:

exactLength : {m : _} ->
              (len : Nat) -> (input : Vect m a) -> Maybe (Vect len a)

A similar change is necessary in ExactLengthDec.idr. Also, DecEq is no longer part of the prelude, so add import Decidable.Equality.

In ReverseVec.idr, add import Data.Nat for the Nat proofs.

In Void.idr, since functions must now be covering by default, add a partial annotation to nohead and its helper function getHead.

In Exercise 2 of 8.2.5, the definition of reverse' should be changed to reverse' : Vect k a -> Vect m a -> Vect (k + m) a, because the n in reverse' is otherwise bound to the same value as the n in the signature of myReverse.

Chapter 9#

  • In ElemType.idr, add import Decidable.Equality

  • In Elem.idr, add import Data.Vect.Elem

In Hangman.idr:

  • Add import Data.String, import Data.Vect.Elem and import Decidable.Equality

  • removeElem pattern matches on n, so it needs to be written in its type:

removeElem : {n : _} ->
             (value : a) -> (xs : Vect (S n) a) ->
             {auto prf : Elem value xs} ->
             Vect n a

  • letters is used by processGuess, because it’s passed to removeElem:

processGuess : {letters : _} ->
               (letter : Char) -> WordState (S guesses) (S letters) ->
               Either (WordState guesses (S letters))
                      (WordState (S guesses) letters)

  • guesses and letters are implicit arguments to game, but are used by the definition, so add them to its type:

game : {guesses : _} -> {letters : _} ->
       WordState (S guesses) (S letters) -> IO Finished

In RemoveElem.idr

  • Add import Data.Vect.Elem

  • removeElem needs to be updated as above.

Chapter 10#

Lots of changes necessary here, at least when constructing views, due to Idris 2 having a better (that is, more precise and correct!) implementation of unification, and the rules for recursive with application being tightened up.

In MergeSort.idr, add import Data.List

In MergeSortView.idr, add import Data.List, and make the arguments to the views explicit:

mergeSort : Ord a => List a -> List a
mergeSort input with (splitRec input)
  mergeSort [] | SplitRecNil = []
  mergeSort [x] | SplitRecOne x = [x]
  mergeSort (lefts ++ rights) | (SplitRecPair lefts rights lrec rrec)
       = merge (mergeSort lefts | lrec)
               (mergeSort rights | rrec)

In the problem 1 of exercise 10-1, the rest argument of the data constructor Exact of TakeN must be made explicit.

data TakeN : List a -> Type where
  Fewer : TakeN xs
  Exact : (n_xs : List a) -> {rest : _} -> TakeN (n_xs ++ rest)

In SnocList.idr, in my_reverse, the link between Snoc rec and xs ++ [x] needs to be made explicit. Idris 1 would happily decide that xs and x were the relevant implicit arguments to Snoc but this was little more than a guess based on what would make it type check, whereas Idris 2 is more precise in what it allows to unify. So, x and xs need to be explicit arguments to Snoc:

data SnocList : List a -> Type where
     Empty : SnocList []
     Snoc : (x, xs : _) -> (rec : SnocList xs) -> SnocList (xs ++ [x])

Correspondingly, they need to be explicit when matching. For example:

my_reverse : List a -> List a
my_reverse input with (snocList input)
  my_reverse [] | Empty = []
  my_reverse (xs ++ [x]) | (Snoc x xs rec) = x :: my_reverse xs | rec

Similar changes are necessary in snocListHelp and my_reverse_help. See tests/typedd-book/chapter10/SnocList.idr for the full details.

Also, in snocListHelp, input is used at run time so needs to be bound in the type:

snocListHelp : {input : _} ->
               (snoc : SnocList input) -> (rest : List a) -> SnocList (input +

It’s no longer necessary to give {input} explicitly in the patterns for snocListHelp, although it’s harmless to do so.

In IsSuffix.idr, the matching has to be written slightly differently. The recursive with application in Idris 1 probably shouldn’t have allowed this! Note that the Snoc - Snoc case has to be written first otherwise Idris generates a case tree splitting on input1 and input2 instead of the SnocList objects and this leads to a lot of cases being detected as missing.

isSuffix : Eq a => List a -> List a -> Bool
isSuffix input1 input2 with (snocList input1, snocList input2)
  isSuffix _ _ | (Snoc x xs xsrec, Snoc y ys ysrec)
     = (x == y) && (isSuffix _ _ | (xsrec, ysrec))
  isSuffix _ _ | (Empty, s) = True
  isSuffix _ _ | (s, Empty) = False

This doesn’t yet get past the totality checker, however, because it doesn’t know about looking inside pairs.

For the VList view in the exercise 4 after Chapter 10-2 import Data.List.Views.Extra from contrib library.

In DataStore.idr: Well this is embarrassing - I’ve no idea how Idris 1 lets this through! I think perhaps it’s too “helpful” when solving unification problems. To fix it, add an extra parameter schema to StoreView, and change the type of SNil to be explicit that the empty is the function defined in DataStore. Also add entry and store as explicit arguments to SAdd:

data StoreView : (schema : _) -> DataStore schema -> Type where
     SNil : StoreView schema DataStore.empty
     SAdd : (entry, store : _) -> (rec : StoreView schema store) ->
            StoreView schema (addToStore entry store)

Since size is as explicit argument in the DataStore record, it also needs to be relevant in the type of storeViewHelp:

storeViewHelp : {size : _} ->
                (items : Vect size (SchemaType schema)) ->
                StoreView schema (MkData size items)

In TestStore.idr:

  • In listItems, empty needs to be DataStore.empty to be explicit that you mean the function

  • In filterKeys, there is an error in the SNil case, which wasn’t caught because of the type of SNil above. It should be:

filterKeys test DataStore.empty | SNil = []

Chapter 11#

In Streams.idr add import Data.Stream for iterate.

In Arith.idr and ArithTotal.idr, the Divides view now has explicit arguments for the dividend and remainder, so they need to be explicit in bound:

bound : Int -> Int
bound x with (divides x 12)
  bound ((12 * div) + rem) | (DivBy div rem prf) = rem + 1

In addition, import Data.Bits has to be added for shiftR, which now uses a safer type for the number of shifts:

randoms : Int -> Stream Int
randoms seed = let seed' = 1664525 * seed + 1013904223 in
                   (seed' `shiftR` 2) :: randoms seed'

In ArithCmd.idr, update DivBy, randoms, and import Data.Bits as above. Also add import Data.String for String.toLower.

In ArithCmd.idr, update DivBy, randoms, import Data.Bits and import Data.String as above. Also, since export rules are per-namespace now, rather than per-file, you need to export (>>=) from the namespaces CommandDo and ConsoleDo.

In ArithCmdDo.idr, since (>>=) is export, Command and ConsoleIO also have to be export. Also, update randoms and import Data.Bits as above.

In StreamFail.idr, add a partial annotation to labelWith.

In order to support do notation for custom types (like RunIO), you need to implement (>>=) for binding values in a do block and (>>) for sequencing computations without binding values. See tests for complete implementations.

For instance, the following do block is desugared to foo >>= (\x => bar >>= (\y => baz x y)):

do
  x <- foo
  y <- bar
  baz x y

while the following is converted to foo >> bar >> baz:

do
  foo
  bar
  baz

Chapter 12#

For reasons described above: In ArithState.idr, add import Data.String and import Data.Bits and update randoms. Also the (>>=) operators need to be set as export since they are in their own namespaces, and in getRandom, DivBy needs to take additional arguments div and rem.

In ArithState.idr, since (>>=) is export, Command and ConsoleIO also have to be export.

evalState from Control.Monad.State now takes the stateType argument first.

Chapter 13#

In StackIO.idr:

  • tryAdd pattern matches on height, so it needs to be written in its type:

tryAdd : {height : _} -> StackIO height

  • height is also an implicit argument to stackCalc, but is used by the definition, so add it to its type:

stackCalc : {height : _} -> StackIO height

  • In StackDo namespace, export (>>=):

namespace StackDo
  export
  (>>=) : StackCmd a height1 height2 ->
          (a -> Inf (StackIO height2)) -> StackIO height1
          (>>=) = Do

In Vending.idr:

  • Add import Data.String and change cast to stringToNatOrZ in strToInput

  • In MachineCmd type, add an implicit argument to (>>=) data constructor:

(>>=) : {state2 : _} ->
        MachineCmd a state1 state2 ->
        (a -> MachineCmd b state2 state3) ->
        MachineCmd b state1 state3

  • In MachineIO type, add an implicit argument to Do data constructor:

data MachineIO : VendState -> Type where
  Do : {state1 : _} ->
       MachineCmd a state1 state2 ->
       (a -> Inf (MachineIO state2)) -> MachineIO state1

  • runMachine pattern matches on inState, so it needs to be written in its type:

runMachine : {inState : _} -> MachineCmd ty inState outState -> IO ty

  • In MachineDo namespace, add an implicit argument to (>>=) and export it:

namespace MachineDo
  export
  (>>=) : {state1 : _} ->
          MachineCmd a state1 state2 ->
          (a -> Inf (MachineIO state2)) -> MachineIO state1
  (>>=) = Do

  • vend and refill pattern match on pounds and chocs, so they need to be written in their type:

vend : {pounds : _} -> {chocs : _} -> MachineIO (pounds, chocs)
refill: {pounds : _} -> {chocs : _} -> (num : Nat) -> MachineIO (pounds, chocs)

  • pounds and chocs are implicit arguments to machineLoop, but are used by the definition, so add them to its type:

machineLoop : {pounds : _} -> {chocs : _} -> MachineIO (pounds, chocs)

Chapter 14#

In ATM.idr:

  • Add import Data.String and change cast to stringToNatOrZ in runATM

In Hangman.idr, add:

import Data.Vect.Elem -- `Elem` now has its own submodule
import Data.String -- for `toUpper`
import Data.List -- for `nub`

  • In Loop namespace, export GameLoop type and its data constructors:

namespace Loop
  public export
  data GameLoop : (ty : Type) -> GameState -> (ty -> GameState) -> Type where
    (>>=) : GameCmd a state1 state2_fn ->
            ((res : a) -> Inf (GameLoop b (state2_fn res) state3_fn)) ->
            GameLoop b state1 state3_fn
    Exit : GameLoop () NotRunning (const NotRunning)

  • letters and guesses are used by gameLoop, so they need to be written in its type:

gameLoop : {letters : _} -> {guesses : _} ->
           GameLoop () (Running (S guesses) (S letters)) (const NotRunning)

  • In Game type, add an implicit argument letters to InProgress data constructor:

data Game : GameState -> Type where
  GameStart : Game NotRunning
  GameWon : (word : String) -> Game NotRunning
  GameLost : (word : String) -> Game NotRunning
  InProgress : {letters : _} -> (word : String) -> (guesses : Nat) ->
               (missing : Vect letters Char) -> Game (Running guesses letters)

  • removeElem pattern matches on n, so it needs to be written in its type:

removeElem : {n : _} ->
             (value : a) -> (xs : Vect (S n) a) ->
             {auto prf : Elem value xs} ->
             Vect n a

Chapter 15#

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