[Haskell-cafe] Propositions in Haskell

[Alberto G. Corona]

Not exactly what you ask, but it is noteworthy that the mind has different
logic processors. The fastest one work with IF THEN ELSE rules applied
specifically to deals. This is why your example (and most examples of
logic) involves a kind of deal expressed in the first person. This trigger
a fast mental evaluation, while an equivalent but more general case is
harder to process and need some paper work.  (That special treatment of
first person deals logic respond to the need to detect breaks of deals as
fast as possible)

http://en.wikipedia.org/wiki/Wason_selection_task

That's why higher level languages have redundant logical structures and do
not follow a general abstract and short mathematical notation. Therefore
"higher level", in programming languages, does not mean higher
mathematical abstraction, but to be closer to the way the mind works.


2013/5/15 Patrick Browne <patrick.browne at dit.ie>

> -- Hi
> -- I am trying to show that a set of propositions and a conclusion the
> form a valid argument.
> -- I used two approaches; 1) using if-then-else, 2) using pattern matching.
> -- The version using if-then-else seems to be consistent with my knowledge
> of Haskell and logic (either of which could be wrong).
> -- Can the second approach be improved to better reflect the propositions
> and conclusion? Maybe type level reasoning could be used?
> --
> -- Valid argument?
> -- 1. I work hard or I play piano
> -- 2. If I work hard then I will get a bonus
> -- 3. But I did not get a bonus
> --     Therefore I played piano
> -- Variables: p = Piano, w = worked hard, b = got a bonus
> --    (w \/ p) /\ (w => b) /\ ¬(b)
> --   ---------------------------
> --                p
>
> -- First approach using language control structure if-then-else
> w, p, b::Bool
> -- Two equivalences for (w \/ p) as an implication.
> -- 1. (w \/ p) =equivalent-to=> (not p) => w
> -- 2. (w \/ p) =equivalent-to=> (not w) => p
> -- Picked 2
> p = if (not w) then True else False
> -- Contrapositive:  (w => b)  =equivalent-to=>  ~b => ~w
> w = if (not b) then False else True
> b = False
> -- gives p is true and w is false
>
> -- Second approach using pattern matching
> -- I think the rewriting goes from left to right but the logical inference
> goes in the opposite direction.
> w1, p1, b1::Bool
> p1 = (not w1)
> w1 = b1 -- Not consistent with statements, but I do not know how to write
> ~b1 => ~w1 in Haskell
> b1 = False
> -- Again gives p1 is true and w1 is false
>
>
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-- 
Alberto.
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