Idris2-boot/TypeDD.md

Type Driven Development with Idris

The code in the book "Type Driven Development with Idris" by Edwin Brady, published by 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).

Chapter 1

No changes necessary

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.Strings -- for `words`
import Data.List -- for `length` on lists

In AveMain.idr and Reverse.idr add:

import System.REPL -- for 'repl'

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)

Chapter 4

For the reasons described above:

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

• In SumInputs.idr, add import System.REPL

• In TryIndex.idr, add an implicit argument:

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

Chapter 5

There is no longer a Cast instance from String to Nat, because its behaviour of returing Z if the String wasn't numeric was thought to be confusing. Instead, there is stringToNatOrZ in Data.Strings which at least has a clearer name. So:

In Loops.idr and ReadNum.idr add import Data.Strings and change cast to stringToNatOrZ

Chapter 6

In DataStore.idr and DataStoreHoles.idr, add import Data.Strings 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.Strings

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.

Chapter 9

• In ElemType.idr, add import Decidable.Equality

In Hangman.idr:

• Add import Decidable.Equality and import Data.Strings

• 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

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 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 checker, 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!

isSuffix : Eq a => List a -> List a -> Bool
isSuffix input1 input2 with (snocList input1, snocList input2)
  isSuffix [] input2 | (Empty, s) = True
  isSuffix input1 [] | (s, Empty) = False
  isSuffix (xs ++ [x]) (ys ++ [y]) | (Snoc xsrec, Snoc ysrec)
     = if x == y 
          then isSuffix xs ys | (xsrec, ysrec)
          else False

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

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 scheme 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

Remove %default total throughout - it's not yet implemented.

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 ArithCmd.idr, update DivBy as above. Also add import Data.Strings for Strings.toLower.

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

Chapter 12

TODO

Chapter 13

TODO

Chapter 14

TODO

Chapter 15

TODO