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On page 18 "Logic as Algebra" Halmos&Givant wrote the distributive law in Polish notation as $$ = \times a + bc + \times ab \times ac $$ I fail to see anything remarkable here, is there a combinatorial pattern that I'm missing?

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    What exactly do me mean when you say 'remarkable'? Are you asking how to interpret Polish notation? Or the reason why one might represent things in this way?2011-11-22
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    After rereading the passage it seems that I should lower my expectations. The authors indicated that they can write distributive law without parenthesis, and that's probably all to it. On a related note, is there any algebraic identity which is syntactically much clearer in PN?2011-11-22
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    I think you are right, the main advantage of Polish notation is omission of parentheses. Some formulas in symbolic logic become impenetrable masses of parentheses, so there was a need to do something about it if mere humans were to read it. Another attempt was a system of dots to replace parentheses.2011-11-22
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    I've had a Hewlett Packard 48G (graphing calculator) for years. It uses a stack (and thus reverse polish notation). I have to say it wasn't easy to use at first, but there are some tasks it really speeds up and makes incredibly efficient. However, given we're "all" trained to regularly use infix notation, mental gymnastics are needed to more over into the world of prefix/postfix notation. And programming in the world of prefix or postfix notation, ouch, my head hurts. :(2011-11-22
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    Programming field suggested several insights how to handle expression complexity, and PN is not one of them. Nested expressions are just parse trees which structure can be emphasized with generous use of carriage return and proper identation.2011-11-23

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