Re: Understanding Boolean Expressions
On Tue, 16 Apr 2013 15:19:25 -0700, Bruce McGoveran wrote: Hello. I am new to this group. I've done a search for the topic about which I'm posting, and while I have found some threads that are relevant, I haven't found anything exactly on point that I can understand. So, I'm taking the liberty of asking about something that may be obvious to many readers of this group. The relevant Python documentation reference is: http://docs.python.org/2/reference/expressions.html#boolean-operations. I'm trying to make sense of the rules of or_test, and_test, and not_test that appear in this section. While I understand the substance of the text in this section, it is the grammar definitions themselves that confuse me. For example, I am not clear how an or_test can be an and_test. In this case, you could have saved us some time by copying and pasting the relevant three lines: or_test ::= and_test | or_test or and_test and_test ::= not_test | and_test and not_test not_test ::= comparison | not not_test I agree that this is not entirely the most obvious wording, but it makes a sort of sense if you follow it through carefully. Unfortunately, to really understand the grammar, you have to follow through the entire thing. But translated into English, the above three rules might read like this: An expression which we call an or_test can be either: 1) an and_test; or 2) another or_test, followed by the literal string or, followed by an and_test. An expression which we call an and_test can be either: 3) a not_test; or 4) another and_test, followed by the literal string and, followed by another not_test. An expression which we call a not_test can be either: 5) a comparison; or 6) the literal string not, followed by another not_test. An expression which we call a comparison can be: ... a bunch more different alternatives, going through bitwise comparisons, then arithmetic operators, then other expressions, and so on, until finally you reach the simplest expressions possible, names and constant literals. So in a sense, an or_test does not JUST mean it's a test with an or in it. The thing called an or_test is an and_test *or* a test with an or in it; an and_test is a not_test *or* a test with an and in it; a not_test is a comparison *or* a test with a not in it; a comparison is ... and so forth, until you run out of expressions and end up with a simple atom like a name or a constant. So paradoxically, that means that x or y counts as an and_test (obviously!) but also as an or_test, since every and_test also counts as an or_test. Here's some crappy ASCII art of a Venn diagram with a couple of examples shown: (best viewed in a fixed-width font): +-+ | or_tests | | x or y | |+--+ | || and_tests | | ||x and y | | ||+-+ | | ||| not_tests | | | ||| | | | ||| not x | | | ||+-+ | | |+--+ | +-+ Inside the not_test box, not shown, are other boxes relating to other expressions, and ending deep down with boxes labelled names and literals. (Or so I expect, since I haven't followed the maze of twisty grammar rules, all alike, to the very end.) Of course, in practice we wouldn't normally call an expression such as x and y as an or_test, even though strictly speaking the grammar says it is. We would call it by the smallest box it is contained within, namely and_test. An analogy: normally, we would refer to Python's creator Guido van Rossum as a man, not a mammal, but since all men are mammals, it wouldn't be wrong to call him such. But not all mammals are men, and not all or_tests are and_tests. x or y is an or_test, obviously, but not an and_test. Does this help explain it? Perhaps an example will help put my confusion into more concrete terms. Suppose I write the expression if x or y in my code. I presume this is an example of an or_test. Beyond that, though, I'm not sure whether this maps to an and_test (the first option on the right-hand side of the rule) or to the or_test or and_test option (the second on the right-hand side of the rule). x or y maps to the second option. The x matches and_test, which then matches not_test, which then matches comparison, which ... blah blah blah ... which finally matches a plain name. The or matches the literal string or in the grammar rule. Then the y matches and_test, which ... finally matches a plain name. Of course, this is NOT necessarily what Python does every time it parses a piece of code! It's just a description of the grammar. -- Steven -- http://mail.python.org/mailman/listinfo/python-list
Re: Understanding Boolean Expressions
Steven D'Aprano writes: So paradoxically, that means that x or y counts as an and_test (obviously!) but also as an or_test, since every and_test also counts as an or_test. Here's some crappy ASCII art of a Venn diagram I think you mean to say that x and y counts as an and_test and also as an or_test. -- http://mail.python.org/mailman/listinfo/python-list
Re: Understanding Boolean Expressions
On Wed, 17 Apr 2013 11:47:49 +0300, Jussi Piitulainen wrote: Steven D'Aprano writes: So paradoxically, that means that x or y counts as an and_test (obviously!) but also as an or_test, since every and_test also counts as an or_test. Here's some crappy ASCII art of a Venn diagram I think you mean to say that x and y counts as an and_test and also as an or_test. You may very well be right, but I'll be damned if I go back and read through my post trying to work out what I intended to say instead of what I actually said! :-) And-or-or-and-or-or-or-and-and-or-ly y'rs, -- Steven -- http://mail.python.org/mailman/listinfo/python-list
Re: Understanding Boolean Expressions
Steven D'Aprano steve+comp.lang.pyt...@pearwood.info writes: On Wed, 17 Apr 2013 11:47:49 +0300, Jussi Piitulainen wrote: Steven D'Aprano writes: So paradoxically, that means that x or y counts as an and_test (obviously!) but also as an or_test, since every and_test also counts as an or_test. Here's some crappy ASCII art of a Venn diagram I think you mean to say that x and y counts as an and_test and also as an or_test. You may very well be right, but I'll be damned if I go back and read through my post trying to work out what I intended to say instead of what I actually said! :-) The quote above is sufficient context for one who knows that x or y is not an and_test. I'm hoping that pointing this little thing out will help some potentially confused reader of your otherwise excellent explanation see more quickly that this is really just a harmless typo. (Unless it's me who's confused :) The quote appeared just before your ASCII art. -- http://mail.python.org/mailman/listinfo/python-list
Understanding Boolean Expressions
Hello. I am new to this group. I've done a search for the topic about which I'm posting, and while I have found some threads that are relevant, I haven't found anything exactly on point that I can understand. So, I'm taking the liberty of asking about something that may be obvious to many readers of this group. The relevant Python documentation reference is: http://docs.python.org/2/reference/expressions.html#boolean-operations. I'm trying to make sense of the rules of or_test, and_test, and not_test that appear in this section. While I understand the substance of the text in this section, it is the grammar definitions themselves that confuse me. For example, I am not clear how an or_test can be an and_test. Moreover, if I follow the chain of non-terminal references, I move from or_test, to and_test, to not_test, to comparison. And when I look at the definition for comparison, I seem to be into bitwise comparisons. I cannot explain this. Perhaps an example will help put my confusion into more concrete terms. Suppose I write the expression if x or y in my code. I presume this is an example of an or_test. Beyond that, though, I'm not sure whether this maps to an and_test (the first option on the right-hand side of the rule) or to the or_test or and_test option (the second on the right-hand side of the rule). If people can offer some thoughts to put me in the right direction (or out of my misery), I would appreciate it. Thank you in advance. -- http://mail.python.org/mailman/listinfo/python-list
Re: Understanding Boolean Expressions
On Tue, 16 Apr 2013 15:19:25 -0700, Bruce McGoveran wrote: Hello. I am new to this group. I've done a search for the topic about which I'm posting, and while I have found some threads that are relevant, I haven't found anything exactly on point that I can understand. So, I'm taking the liberty of asking about something that may be obvious to many readers of this group. The relevant Python documentation reference is: http://docs.python.org/2/reference/expressions.html#boolean-operations. I'm trying to make sense of the rules of or_test, and_test, and not_test that appear in this section. While I understand the substance of the text in this section, it is the grammar definitions themselves that confuse me. For example, I am not clear how an or_test can be an and_test. Moreover, if I follow the chain of non-terminal references, I move from or_test, to and_test, to not_test, to comparison. And when I look at the definition for comparison, I seem to be into bitwise comparisons. I cannot explain this. Perhaps an example will help put my confusion into more concrete terms. Suppose I write the expression if x or y in my code. I presume this is an example of an or_test. Beyond that, though, I'm not sure whether this maps to an and_test (the first option on the right-hand side of the rule) or to the or_test or and_test option (the second on the right-hand side of the rule). If people can offer some thoughts to put me in the right direction (or out of my misery), I would appreciate it. $ python Python 2.7.3 (default, Jan 15 2013, 02:26:36) [GCC 4.2.1 20070831 patched [FreeBSD]] on freebsd9 Type help, copyright, credits or license for more information. not True False not False True True or False True True and False False x = 2 not (x == 2) False not (x == 3) True x == 2 True x == 3 False -- http://mail.python.org/mailman/listinfo/python-list
Re: Understanding Boolean Expressions
On 04/16/2013 06:19 PM, Bruce McGoveran wrote: Hello. I am new to this group. I've done a search for the topic about which I'm posting, and while I have found some threads that are relevant, I haven't found anything exactly on point that I can understand. So, I'm taking the liberty of asking about something that may be obvious to many readers of this group. The relevant Python documentation reference is: http://docs.python.org/2/reference/expressions.html#boolean-operations. I'm trying to make sense of the rules of or_test, and_test, and not_test that appear in this section. While I understand the substance of the text in this section, it is the grammar definitions themselves that confuse me. For example, I am not clear how an or_test can be an and_test. Moreover, if I follow the chain of non-terminal references, I move from or_test, to and_test, to not_test, to comparison. And when I look at the definition for comparison, I seem to be into bitwise comparisons. I cannot explain this. Perhaps an example will help put my confusion into more concrete terms. Suppose I write the expression if x or y in my code. I presume this is an example of an or_test. Beyond that, though, I'm not sure whether this maps to an and_test (the first option on the right-hand side of the rule) or to the or_test or and_test option (the second on the right-hand side of the rule). If people can offer some thoughts to put me in the right direction (or out of my misery), I would appreciate it. It's been decades since I really had to understand a complete grammar. But in some ways, a fragment like you're referencing is even harder. The trick is to take those names and_test as rather arbitrary. There's no token meaning an expression containing 4 or's, 2 and's, and 1 not So sometimes the terms used are rather silly looking. The point is you can combine 'not', 'and', 'or', and comparison operators like ==, = etc. in some complex ways. The grammar just says which of these is legal, and doesn't help you figure out the semantics, which is usually much more important to you and me. First, nearly all objects have a 'truth' value, for which I use the terms 'true' and 'false'. For numbers, nonzero values are true, and zero values are false. For collections, nonempty collections are true and empty ones are false. And so on. So if x is an int, and if you say: if x: You're checking the 'truth' of x, and it'll execute the if clause for nonzero integers, for example. If you have an arbitrary object 'x', it is not necessarily of type bool. But if you compare it to another one, x==y the result is a bool, either True or False. Likewise if you apply the unary 'not' to an object; the result will be either True or False. But if you combine two expressions with 'or' the result is NOT necessarily of type bool. If the first expression is true, then the second expression isn't even examined. If the first expression is false, the second expression is the result. 'and' has the reverse meaning. And more complex expressions can be understood by breaking them into steps, according to operator precedence and parentheses. -- DaveA -- http://mail.python.org/mailman/listinfo/python-list
Re: Understanding Boolean Expressions
On Tue, 16 Apr 2013 23:19:25 +0100, Bruce McGoveran bruce.mcgove...@gmail.com wrote: Hello. I am new to this group. I've done a search for the topic about which I'm posting, and while I have found some threads that are relevant, I haven't found anything exactly on point that I can understand. So, I'm taking the liberty of asking about something that may be obvious to many readers of this group. The relevant Python documentation reference is: http://docs.python.org/2/reference/expressions.html#boolean-operations. I'm trying to make sense of the rules of or_test, and_test, and not_test that appear in this section. While I understand the substance of the text in this section, it is the grammar definitions themselves that confuse me. For example, I am not clear how an or_test can be an and_test. Moreover, if I follow the chain of non-terminal references, I move from or_test, to and_test, to not_test, to comparison. And when I look at the definition for comparison, I seem to be into bitwise comparisons. I cannot explain this. Perhaps an example will help put my confusion into more concrete terms. Suppose I write the expression if x or y in my code. I presume this is an example of an or_test. Beyond that, though, I'm not sure whether this maps to an and_test (the first option on the right-hand side of the rule) or to the or_test or and_test option (the second on the right-hand side of the rule). If people can offer some thoughts to put me in the right direction (or out of my misery), I would appreciate it. What the grammar rules are giving you is operator precedence -- not has higher precedence than and, which is higher than or. As you follow the non-terminals back you go further through precedence chain: comparisons, then bitwise operators (*not* bitwise comparisons!), then shifts, then arithmetic operators, the unary operators, the power operator, and finally primaries. -- Rhodri James *-* Wildebeest Herder to the Masses -- http://mail.python.org/mailman/listinfo/python-list
Re: Understanding Boolean Expressions
[2nd try, quotation a bit messed up] On 4/16/2013 6:19 PM, Bruce McGoveran wrote: Hello. I am new to this group. I've done a search for the topic about which I'm posting, and while I have found some threads that are relevant, I haven't found anything exactly on point that I can understand. So, I'm taking the liberty of asking about something that may be obvious to many readers of this group. The relevant Python documentation reference is: http://docs.python.org/2/reference/expressions.html#boolean-operations. I'm trying to make sense of the rules of or_test, and_test, and not_test that appear in this section. While I understand the substance of the text in this section, The substance is that 1) 'not' binds tighter than 'and' binds tigher than 'or' and 2) 'and' and 'or' both associate left to right in the normal manner so that 'a op b op c' == '(a op b) op c'. it is the grammar definitions themselves that confuse me. The techinical details reflect the fact that Python's grammar is ll(1) (top-down, parsed by recursive descent) rather than lr(1) (bottom-up). The latter (in lalr(1) form) is what yacc, etc use and might be more familiar to you. For example, I am not clear how an or_test can be an and_test. or_test ::= and_test | or_test or and_test The second option expresses the associativity rule, but more is needed to get out of infinite regress. Substituting the second rule into second rule gives or_test = (or_test 'or' and_test) 'or' and_test and so on. At some point, one must replace or_test with and_test to get an 'or' of ands. Similarly, an and_test must resolve to an 'and' of nots. Moreover, if I follow the chain of non-terminal references, I move from or_test, to and_test, to nt_test, to comparison. And when I look at the definition for comparison, I seem to be into bitwise comparisons. I cannot explain this. Eventually the chain takes one to primaries, which include things like literals and identifiers. Perhaps an example will help put my confusion into more concrete terms. Suppose I write the expression if x or y in my code. I presume this is an example of an or_test. Yes. Beyond that, though, I'm not sure whether this maps to an and_test (the first option on the right-hand side of the rule) or to the or_test or and_test option (the second on the right-hand side of the rule). The second. Then the or_test on the left also maps to an and_test. Each and_test eventually resolves to 'identifier', specifically 'x' and 'y'. -- Terry Jan Reedy -- http://mail.python.org/mailman/listinfo/python-list
Re: Understanding Boolean Expressions
Thank you all for thoughts. I'm just about to post another question about atoms and primaries. If you have a moment to look it over, I would appreciate your thoughts. Many thanks in advance. On Tuesday, April 16, 2013 6:19:25 PM UTC-4, Bruce McGoveran wrote: Hello. I am new to this group. I've done a search for the topic about which I'm posting, and while I have found some threads that are relevant, I haven't found anything exactly on point that I can understand. So, I'm taking the liberty of asking about something that may be obvious to many readers of this group. The relevant Python documentation reference is: http://docs.python.org/2/reference/expressions.html#boolean-operations. I'm trying to make sense of the rules of or_test, and_test, and not_test that appear in this section. While I understand the substance of the text in this section, it is the grammar definitions themselves that confuse me. For example, I am not clear how an or_test can be an and_test. Moreover, if I follow the chain of non-terminal references, I move from or_test, to and_test, to not_test, to comparison. And when I look at the definition for comparison, I seem to be into bitwise comparisons. I cannot explain this. Perhaps an example will help put my confusion into more concrete terms. Suppose I write the expression if x or y in my code. I presume this is an example of an or_test. Beyond that, though, I'm not sure whether this maps to an and_test (the first option on the right-hand side of the rule) or to the or_test or and_test option (the second on the right-hand side of the rule). If people can offer some thoughts to put me in the right direction (or out of my misery), I would appreciate it. Thank you in advance. -- http://mail.python.org/mailman/listinfo/python-list
