[Haskell-beginners] Simple function comparison

[MJ Williams]

All right, how about this for a proof:

Let f x = x + 1
let g x = x + 2

if f ( g a )
then f ( a + 2 ) .............. (g)
then ( a + 2 ) + 1 ............ (f)
...
then a + 3 .................... (+)
therefore f ( g a ) <-> a + 3

if g ( f a )
then g ( a + 1 ) .............. (f)
then ( a + 1 ) + 2 ............ (g)
...
then a + 3 .................... (+)
therefore g ( f a ) <-> a + 3

therefore f ( g a ) = g ( f a ) (transitivity)

Feel free to take it apart and smash it to bits. Seriously, any
feedback welcome.

Cheers, Matthew


On 25/11/2015, Henk-Jan van Tuyl <hjgtuyl at chello.nl> wrote:
> On Wed, 25 Nov 2015 12:39:15 +0100, Stephen Renehan <d11124067 at mydit.ie>
> wrote:
>
>> Hi,
>>
>> I'm looking to do a comparison between 2 simple functions to see if
>> they are equivalent but I appear to be running into some problems if
>> anyone can help.
>>
>> The two functions I want to compare are f (g a) and g (f a).
>>
>> I have f defined and g defined as
>>  f :: a -> a
>>  f = undefined
>>
>> g :: a -> a.
>> g =  undefined
>
> As you can not say anything about the type of input or output (except that
>
> they are equal), the only normally terminating function possible is 'id'.
> So, if you don't want to use 'undefined' or 'error', f and g are equal.
>
> Regards,
> Henk-Jan van Tuyl
>
>
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