Section 5.4: Wrong simplification for checkCompany

[h-bex]

Please quote the text that is incorrect:

One more simplification is possible. For every Applicative, pure f <*> E is equivalent to f <$> E. In other words, using seq to apply a function that was placed into the Applicative type using pure is overkill, and the function could have just been applied using Functor.map. This simplification yields:
def checkCompany (input : RawInput) :
Validate (Field × String) LegacyCheckedInput :=
checkThat (input.birthYear == "FIRM")
"birth year" "FIRM if a company" *>
.company <$> checkName input.name

In what way is this incorrect?

This simplification is technically incorrect, because:

The second definition of checkCompany yields to the following expansion:

Seq.seq
  (SeqRight.seqRight (checkThat (BEq.beq myInput.birthYear "FIRM") "birth year" "FIRM is a company") fun x ↦
    pure LegacyCheckedInput.company)
  fun x ↦ checkName myInput.name : Validate (Prod Field String) LegacyCheckedInput

and the third one using map yields to:

SeqRight.seqRight (checkThat (BEq.beq myInput.birthYear "FIRM") "birth year" "FIRM is a company") fun x ↦
  Functor.map LegacyCheckedInput.company (checkName myInput.name) : Validate (Prod Field String) LegacyCheckedInput

Proposed Correction

Add necessary parenthesis to the second checkCompany implementation:

def checkCompany (input : RawInput) : Validate (Field × String) LegacyCheckedInput :=
    checkThat (input.birthYear == "FIRM") "birth year" "FIRM is a company" *>
    (pure .company <*> checkName input.name)

this yields to the following expansion:

SeqRight.seqRight (checkThat (BEq.beq myInput.birthYear "FIRM") "birth year" "FIRM is a company") fun x ↦
  Seq.seq (pure LegacyCheckedInput.company) fun x ↦
    checkName myInput.name : Validate (Prod Field String) LegacyCheckedInput

which is consistent tho the third implementation.