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Proof by induction in RPN

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Liang Ng

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Mar 11, 2018, 11:08:47 AM3/11/18
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Proof by induction in RPN

I recently implemented the distributive law (5x + 3x = 8x) in reverse polish notation.

I am now wondering if it is possible to implement proof by induction in reverse polish notation as well.

Fundamentally, I believe graph theory is the foundation of mathematics and RPN is a representation of graph.

As such, whatever mathematicians have proven in the past on paper, should be provable using RPN.

Any comments?

Liang Ng

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Mar 11, 2018, 11:12:05 AM3/11/18
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The distributive law in RPN

Infix> 3x + 6x = 9
RPN> 3 x * 6 x * + 9 =
Left hand side> 3 x * 6 x * +
Delete 'x ' '* ' > 3 6 + > 9
Append 'x *' > 9 x *
Append right hand side> 9 x * 9 =
Inverse> x = 1

Unknown

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Mar 19, 2018, 1:00:05 PM3/19/18
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On Sun, 11 Mar 2018 08:12:03 -0700, Liang Ng wrote:
...

> whatever mathematicians have proven in the past on paper, should
> be provable using RPN.

What is provable in "infix notation" is obviously proable in RPM.
Like: VI + IV = X ==> 6 + 4 = 10

But explain how/why "RPN is a representation of graph" ?

Is this related to:
functional languages <are expressions, rather than statements>;
they are representable by a tree/graph;
which is reducable to <the answer> ?


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