Using the Consequence Rule - proof

I have the following example that I have to prove
{a>7 ^ b>=0} n=a-b {n<a ^ a+b>=0}
Using the Consequence Rule I assumed that the P is true
{true} n=a-b {n<a ^ a+b>=0}
so logically, the Q should be true, but I'm not sure if that'd be enough.

Related

Treesitter precedence not taking effect

I'm learning how to use tree sitter and making a grammar for parsing simple predicate logic. I'll clearly need precedence to make negation, ~, bind more tightly than conjunction and dis-junction, (/\ and \/). I think I've applied precedence correctly, practically copying the example in the documentation.
Here is the grammar:
module.exports = grammar({
name: 'Predicate_Calculus',
rules: {
// TODO: add the actual grammar rules
source_file: $ => repeat($._expression),
_expression: $ => choice($.identifier,
$._unary_expression,
$._binary_expression,
seq('(', $._expression, ')')),
_binary_expression: $ => choice(
$.and,
$.or
),
_unary_expression: $ => prec(2, choice(
$.not
)),
not: $ => seq('~', $._expression),
and: $ => prec.left(seq($._expression, "/\\", $._expression)),
or: $ => prec.left(seq($._expression, "\\/", $._expression)),
identifier: $ => /[a-z_]+/
}
});
However, when I run tree-sitter generate I get this error:
╰─➤ tree-sitter generate
Unresolved conflict for symbol sequence:
'~' _expression • '/\' …
Possible interpretations:
1: '~' (and _expression • '/\' _expression) (precedence: 0, associativity: Left)
2: (not '~' _expression) • '/\' …
Possible resolutions:
1: Specify a higher precedence in `and` than in the other rules.
2: Specify a higher precedence in `not` than in the other rules.
3: Specify a left or right associativity in `not`
4: Add a conflict for these rules: `not`, `and`
I believe what I've done with the prec(2 choice($.not)) is option 2 but it doesn't seem to be in effect in the grammar. I'm using tree-sitter 0.20.7 installed via cargo.
Okay, after experimenting with some more permutations I found that moving the precedence directive into the not definition fixes this issue.
_unary_expression: $ => choice(
$.not
),
not: $ => prec(2, seq('~', $._expression)),
Removing the precedence from _unary_expression and moving it to inside not.

Match-zero-or-more operator in nextflow glob

I am trying to create a robust glob pattern that will match most of the different naming conventions used for fastq files we receive. However, the version of nextflow I am using (20.10.0) on the HPC doesn't seem to accept what I've written.
Here are some examples of file names:
19_S8_R1_001.fastq.gz 19_S8_R2_001.fastq.gz
F1HD1_S28_R1.fastq.gz F1HD1_S28_R2.fastq.gz
SRR3137747_1.fastq SRR3137747_2.fastq
The pattern I originally wrote to go with the fromFilePairs operator was *_?(R){1,2}?(_001).f?(ast)q?(.gz). Which I tested in a bash environment. Here is the output from testing in the directory with the top two example files:
-bash-4.2$ shopt -s extglob
-bash-4.2$ ls -1 *_?(R){1,2}?(_001).f?(ast)q?(.gz)
19_S8_R1_001.fastq.gz
19_S8_R2_001.fastq.gz
But when I tried to run this with nextflow, it just gave me the error message I put into the ifEmpty operator.
I've eventually got it working, but using this pattern: *_{R1,R2,1,2}{.fastq.gz,.fq.gz,.fastq,.fq,_001.fastq.gz,_001.fq.gz,_001.fastq,_001.fq}, which isn't particularly robust.
Unless I've missed it in the nextflow documentation (and the information I've found about glob), I don't see alternatives to match-zero-or-more operators in nextflow. Any alternative solutions?
Thanks in advance.
The following glob pattern seems to match some of the more common FASTQ filenames:
Channel
.fromFilePairs( '*_{,R}{1,2}{,_001}.{fq,fastq}{,.gz}' )
.view()
Or with a parameterized directory prefix:
Channel
.fromFilePairs( "${params.input_dir}/*_{,R}{1,2}{,_001}.{fq,fastq}{,.gz}" )
.view()
Results:
N E X T F L O W ~ version 21.04.3
Launching `script.nf` [serene_austin] - revision: 5527b9b3c0
[SRR3137747, [/path/to/fasta/SRR3137747_1.fastq, /path/to/fasta/SRR3137747_2.fastq]]
[19_S8, [/path/to/fasta/19_S8_R1_001.fastq.gz, /path/to/fasta/19_S8_R2_001.fastq.gz]]
[F1HD1_S28, [/path/to/fasta/F1HD1_S28_R1.fastq.gz, /path/to/fasta/F1HD1_S28_R2.fastq.gz]]
Another option, which might be more robust (and readable), is to make use of the fact that you can specify more than one glob pattern using a list as argument, and build your list of glob patterns dynamically:
nextflow.enable.dsl=2
params.input_dir = '/path/to/fasta'
def cartesian_product(A, B) {
A.collectMany{ a -> B.collect { b -> [a, b] } }
}
def extensions = [
'.fastq.gz',
'.fastq',
'.fq.gz',
'.fq',
]
def suffixes = [
'*_R{1,2}_001',
'*_R{1,2}',
'*_{1,2}',
]
workflow {
def patterns = cartesian_product(suffixes, extensions).collect {
"${params.input_dir}/${it.join()}"
}
Channel.fromFilePairs( patterns ).view()
}
Results:
N E X T F L O W ~ version 21.04.3
Launching `script.nf` [deadly_payne] - revision: 6d2472ef23
[19_S8, [/path/to/fasta/19_S8_R1_001.fastq.gz, /path/to/fasta/19_S8_R2_001.fastq.gz]]
[F1HD1_S28, [/path/to/fasta/F1HD1_S28_R1.fastq.gz, /path/to/fasta/F1HD1_S28_R2.fastq.gz]]
[SRR3137747, [/path/to/fasta/SRR3137747_1.fastq, /path/to/fasta/SRR3137747_2.fastq]]

regex pattern starting with "=" and exceptions

I'm trying to write an expression which will be used with json files for a vscode extension. My expression should start with "=\s*" and then I want it to select everything after the equal except for the following cases:
TRUE or FALSE after the equality
starting with digit
starting with ' or "
I have tried many things and separately each case I manage to make it work but when I try to put it all together, it doesn't work
Example of doc strings:
abc = test
abc = TRUE
abc = FALSE
abc = "test"
abc = 'test'
abc = 123
Out of these examples my regex should only keep the very first one and "test" can be anything.
What was the closest to the solution was this one /(=\s*)^(((?!TRUE|FALSE|[0-9]|\"|\').)*)$/gm
You can use
Find what: ^(.*?=)(?!\s*(?:TRUE|FALSE|[0-9"'])).*
Replace With: $1
Details:
^ - start of a line
(.*?=) - Group 1: any zero or more chars other than line break chars, as few as possible and then a = char
(?!\s*(?:TRUE|FALSE|[0-9"'])) - a negative lookahead that fails the match if, immediately to the right of the current location, there are
\s* - zero or more whitespace
(?:TRUE|FALSE|[0-9"']) - TRUE, FALSE, digit or " or '
.* - the rest of the line.
See the regex demo and the demo screenshot:

Parse a MySQL insert statement with multiple rows [duplicate]

I need a regular expression to select all the text between two outer brackets.
Example:
START_TEXT(text here(possible text)text(possible text(more text)))END_TXT
^ ^
Result:
(text here(possible text)text(possible text(more text)))
I want to add this answer for quickreference. Feel free to update.
.NET Regex using balancing groups:
\((?>\((?<c>)|[^()]+|\)(?<-c>))*(?(c)(?!))\)
Where c is used as the depth counter.
Demo at Regexstorm.com
Stack Overflow: Using RegEx to balance match parenthesis
Wes' Puzzling Blog: Matching Balanced Constructs with .NET Regular Expressions
Greg Reinacker's Weblog: Nested Constructs in Regular Expressions
PCRE using a recursive pattern:
\((?:[^)(]+|(?R))*+\)
Demo at regex101; Or without alternation:
\((?:[^)(]*(?R)?)*+\)
Demo at regex101; Or unrolled for performance:
\([^)(]*+(?:(?R)[^)(]*)*+\)
Demo at regex101; The pattern is pasted at (?R) which represents (?0).
Perl, PHP, Notepad++, R: perl=TRUE, Python: PyPI regex module with (?V1) for Perl behaviour.
(the new version of PyPI regex package already defaults to this → DEFAULT_VERSION = VERSION1)
Ruby using subexpression calls:
With Ruby 2.0 \g<0> can be used to call full pattern.
\((?>[^)(]+|\g<0>)*\)
Demo at Rubular; Ruby 1.9 only supports capturing group recursion:
(\((?>[^)(]+|\g<1>)*\))
Demo at Rubular  (atomic grouping since Ruby 1.9.3)
JavaScript  API :: XRegExp.matchRecursive
XRegExp.matchRecursive(str, '\\(', '\\)', 'g');
Java: An interesting idea using forward references by #jaytea.
Without recursion up to 3 levels of nesting:
(JS, Java and other regex flavors)
To prevent runaway if unbalanced, with * on innermost [)(] only.
\((?:[^)(]|\((?:[^)(]|\((?:[^)(]|\([^)(]*\))*\))*\))*\)
Demo at regex101; Or unrolled for better performance (preferred).
\([^)(]*(?:\([^)(]*(?:\([^)(]*(?:\([^)(]*\)[^)(]*)*\)[^)(]*)*\)[^)(]*)*\)
Demo at regex101; Deeper nesting needs to be added as required.
Reference - What does this regex mean?
RexEgg.com - Recursive Regular Expressions
Regular-Expressions.info - Regular Expression Recursion
Mastering Regular Expressions - Jeffrey E.F. Friedl 1 2 3 4
Regular expressions are the wrong tool for the job because you are dealing with nested structures, i.e. recursion.
But there is a simple algorithm to do this, which I described in more detail in this answer to a previous question. The gist is to write code which scans through the string keeping a counter of the open parentheses which have not yet been matched by a closing parenthesis. When that counter returns to zero, then you know you've reached the final closing parenthesis.
You can use regex recursion:
\(([^()]|(?R))*\)
[^\(]*(\(.*\))[^\)]*
[^\(]* matches everything that isn't an opening bracket at the beginning of the string, (\(.*\)) captures the required substring enclosed in brackets, and [^\)]* matches everything that isn't a closing bracket at the end of the string. Note that this expression does not attempt to match brackets; a simple parser (see dehmann's answer) would be more suitable for that.
This answer explains the theoretical limitation of why regular expressions are not the right tool for this task.
Regular expressions can not do this.
Regular expressions are based on a computing model known as Finite State Automata (FSA). As the name indicates, a FSA can remember only the current state, it has no information about the previous states.
In the above diagram, S1 and S2 are two states where S1 is the starting and final step. So if we try with the string 0110 , the transition goes as follows:
0 1 1 0
-> S1 -> S2 -> S2 -> S2 ->S1
In the above steps, when we are at second S2 i.e. after parsing 01 of 0110, the FSA has no information about the previous 0 in 01 as it can only remember the current state and the next input symbol.
In the above problem, we need to know the no of opening parenthesis; this means it has to be stored at some place. But since FSAs can not do that, a regular expression can not be written.
However, an algorithm can be written to do this task. Algorithms are generally falls under Pushdown Automata (PDA). PDA is one level above of FSA. PDA has an additional stack to store some additional information. PDAs can be used to solve the above problem, because we can 'push' the opening parenthesis in the stack and 'pop' them once we encounter a closing parenthesis. If at the end, stack is empty, then opening parenthesis and closing parenthesis matches. Otherwise not.
(?<=\().*(?=\))
If you want to select text between two matching parentheses, you are out of luck with regular expressions. This is impossible(*).
This regex just returns the text between the first opening and the last closing parentheses in your string.
(*) Unless your regex engine has features like balancing groups or recursion. The number of engines that support such features is slowly growing, but they are still not a commonly available.
It is actually possible to do it using .NET regular expressions, but it is not trivial, so read carefully.
You can read a nice article here. You also may need to read up on .NET regular expressions. You can start reading here.
Angle brackets <> were used because they do not require escaping.
The regular expression looks like this:
<
[^<>]*
(
(
(?<Open><)
[^<>]*
)+
(
(?<Close-Open>>)
[^<>]*
)+
)*
(?(Open)(?!))
>
I was also stuck in this situation when dealing with nested patterns and regular-expressions is the right tool to solve such problems.
/(\((?>[^()]+|(?1))*\))/
This is the definitive regex:
\(
(?<arguments>
(
([^\(\)']*) |
(\([^\(\)']*\)) |
'(.*?)'
)*
)
\)
Example:
input: ( arg1, arg2, arg3, (arg4), '(pip' )
output: arg1, arg2, arg3, (arg4), '(pip'
note that the '(pip' is correctly managed as string.
(tried in regulator: http://sourceforge.net/projects/regulator/)
I have written a little JavaScript library called balanced to help with this task. You can accomplish this by doing
balanced.matches({
source: source,
open: '(',
close: ')'
});
You can even do replacements:
balanced.replacements({
source: source,
open: '(',
close: ')',
replace: function (source, head, tail) {
return head + source + tail;
}
});
Here's a more complex and interactive example JSFiddle.
Adding to bobble bubble's answer, there are other regex flavors where recursive constructs are supported.
Lua
Use %b() (%b{} / %b[] for curly braces / square brackets):
for s in string.gmatch("Extract (a(b)c) and ((d)f(g))", "%b()") do print(s) end (see demo)
Raku (former Perl6):
Non-overlapping multiple balanced parentheses matches:
my regex paren_any { '(' ~ ')' [ <-[()]>+ || <&paren_any> ]* }
say "Extract (a(b)c) and ((d)f(g))" ~~ m:g/<&paren_any>/;
# => (「(a(b)c)」 「((d)f(g))」)
Overlapping multiple balanced parentheses matches:
say "Extract (a(b)c) and ((d)f(g))" ~~ m:ov:g/<&paren_any>/;
# => (「(a(b)c)」 「(b)」 「((d)f(g))」 「(d)」 「(g)」)
See demo.
Python re non-regex solution
See poke's answer for How to get an expression between balanced parentheses.
Java customizable non-regex solution
Here is a customizable solution allowing single character literal delimiters in Java:
public static List<String> getBalancedSubstrings(String s, Character markStart,
Character markEnd, Boolean includeMarkers)
{
List<String> subTreeList = new ArrayList<String>();
int level = 0;
int lastOpenDelimiter = -1;
for (int i = 0; i < s.length(); i++) {
char c = s.charAt(i);
if (c == markStart) {
level++;
if (level == 1) {
lastOpenDelimiter = (includeMarkers ? i : i + 1);
}
}
else if (c == markEnd) {
if (level == 1) {
subTreeList.add(s.substring(lastOpenDelimiter, (includeMarkers ? i + 1 : i)));
}
if (level > 0) level--;
}
}
return subTreeList;
}
}
Sample usage:
String s = "some text(text here(possible text)text(possible text(more text)))end text";
List<String> balanced = getBalancedSubstrings(s, '(', ')', true);
System.out.println("Balanced substrings:\n" + balanced);
// => [(text here(possible text)text(possible text(more text)))]
The regular expression using Ruby (version 1.9.3 or above):
/(?<match>\((?:\g<match>|[^()]++)*\))/
Demo on rubular
The answer depends on whether you need to match matching sets of brackets, or merely the first open to the last close in the input text.
If you need to match matching nested brackets, then you need something more than regular expressions. - see #dehmann
If it's just first open to last close see #Zach
Decide what you want to happen with:
abc ( 123 ( foobar ) def ) xyz ) ghij
You need to decide what your code needs to match in this case.
"""
Here is a simple python program showing how to use regular
expressions to write a paren-matching recursive parser.
This parser recognises items enclosed by parens, brackets,
braces and <> symbols, but is adaptable to any set of
open/close patterns. This is where the re package greatly
assists in parsing.
"""
import re
# The pattern below recognises a sequence consisting of:
# 1. Any characters not in the set of open/close strings.
# 2. One of the open/close strings.
# 3. The remainder of the string.
#
# There is no reason the opening pattern can't be the
# same as the closing pattern, so quoted strings can
# be included. However quotes are not ignored inside
# quotes. More logic is needed for that....
pat = re.compile("""
( .*? )
( \( | \) | \[ | \] | \{ | \} | \< | \> |
\' | \" | BEGIN | END | $ )
( .* )
""", re.X)
# The keys to the dictionary below are the opening strings,
# and the values are the corresponding closing strings.
# For example "(" is an opening string and ")" is its
# closing string.
matching = { "(" : ")",
"[" : "]",
"{" : "}",
"<" : ">",
'"' : '"',
"'" : "'",
"BEGIN" : "END" }
# The procedure below matches string s and returns a
# recursive list matching the nesting of the open/close
# patterns in s.
def matchnested(s, term=""):
lst = []
while True:
m = pat.match(s)
if m.group(1) != "":
lst.append(m.group(1))
if m.group(2) == term:
return lst, m.group(3)
if m.group(2) in matching:
item, s = matchnested(m.group(3), matching[m.group(2)])
lst.append(m.group(2))
lst.append(item)
lst.append(matching[m.group(2)])
else:
raise ValueError("After <<%s %s>> expected %s not %s" %
(lst, s, term, m.group(2)))
# Unit test.
if __name__ == "__main__":
for s in ("simple string",
""" "double quote" """,
""" 'single quote' """,
"one'two'three'four'five'six'seven",
"one(two(three(four)five)six)seven",
"one(two(three)four)five(six(seven)eight)nine",
"one(two)three[four]five{six}seven<eight>nine",
"one(two[three{four<five>six}seven]eight)nine",
"oneBEGINtwo(threeBEGINfourENDfive)sixENDseven",
"ERROR testing ((( mismatched ))] parens"):
print "\ninput", s
try:
lst, s = matchnested(s)
print "output", lst
except ValueError as e:
print str(e)
print "done"
You need the first and last parentheses. Use something like this:
str.indexOf('('); - it will give you first occurrence
str.lastIndexOf(')'); - last one
So you need a string between,
String searchedString = str.substring(str1.indexOf('('),str1.lastIndexOf(')');
because js regex doesn't support recursive match, i can't make balanced parentheses matching work.
so this is a simple javascript for loop version that make "method(arg)" string into array
push(number) map(test(a(a()))) bass(wow, abc)
$$(groups) filter({ type: 'ORGANIZATION', isDisabled: { $ne: true } }) pickBy(_id, type) map(test()) as(groups)
const parser = str => {
let ops = []
let method, arg
let isMethod = true
let open = []
for (const char of str) {
// skip whitespace
if (char === ' ') continue
// append method or arg string
if (char !== '(' && char !== ')') {
if (isMethod) {
(method ? (method += char) : (method = char))
} else {
(arg ? (arg += char) : (arg = char))
}
}
if (char === '(') {
// nested parenthesis should be a part of arg
if (!isMethod) arg += char
isMethod = false
open.push(char)
} else if (char === ')') {
open.pop()
// check end of arg
if (open.length < 1) {
isMethod = true
ops.push({ method, arg })
method = arg = undefined
} else {
arg += char
}
}
}
return ops
}
// const test = parser(`$$(groups) filter({ type: 'ORGANIZATION', isDisabled: { $ne: true } }) pickBy(_id, type) map(test()) as(groups)`)
const test = parser(`push(number) map(test(a(a()))) bass(wow, abc)`)
console.log(test)
the result is like
[ { method: 'push', arg: 'number' },
{ method: 'map', arg: 'test(a(a()))' },
{ method: 'bass', arg: 'wow,abc' } ]
[ { method: '$$', arg: 'groups' },
{ method: 'filter',
arg: '{type:\'ORGANIZATION\',isDisabled:{$ne:true}}' },
{ method: 'pickBy', arg: '_id,type' },
{ method: 'map', arg: 'test()' },
{ method: 'as', arg: 'groups' } ]
While so many answers mention this in some form by saying that regex does not support recursive matching and so on, the primary reason for this lies in the roots of the Theory of Computation.
Language of the form {a^nb^n | n>=0} is not regular. Regex can only match things that form part of the regular set of languages.
Read more # here
I didn't use regex since it is difficult to deal with nested code. So this snippet should be able to allow you to grab sections of code with balanced brackets:
def extract_code(data):
""" returns an array of code snippets from a string (data)"""
start_pos = None
end_pos = None
count_open = 0
count_close = 0
code_snippets = []
for i,v in enumerate(data):
if v =='{':
count_open+=1
if not start_pos:
start_pos= i
if v=='}':
count_close +=1
if count_open == count_close and not end_pos:
end_pos = i+1
if start_pos and end_pos:
code_snippets.append((start_pos,end_pos))
start_pos = None
end_pos = None
return code_snippets
I used this to extract code snippets from a text file.
This do not fully address the OP question but I though it may be useful to some coming here to search for nested structure regexp:
Parse parmeters from function string (with nested structures) in javascript
Match structures like:
matches brackets, square brackets, parentheses, single and double quotes
Here you can see generated regexp in action
/**
* get param content of function string.
* only params string should be provided without parentheses
* WORK even if some/all params are not set
* #return [param1, param2, param3]
*/
exports.getParamsSAFE = (str, nbParams = 3) => {
const nextParamReg = /^\s*((?:(?:['"([{](?:[^'"()[\]{}]*?|['"([{](?:[^'"()[\]{}]*?|['"([{][^'"()[\]{}]*?['")}\]])*?['")}\]])*?['")}\]])|[^,])*?)\s*(?:,|$)/;
const params = [];
while (str.length) { // this is to avoid a BIG performance issue in javascript regexp engine
str = str.replace(nextParamReg, (full, p1) => {
params.push(p1);
return '';
});
}
return params;
};
This might help to match balanced parenthesis.
\s*\w+[(][^+]*[)]\s*
This one also worked
re.findall(r'\(.+\)', s)

R parse HTML document and use xpath to get all matches of two patterns

So, I parsed HTML code from FIFA worldcup website, and want to get all the matches:
wcup <- htmlTreeParse("http://www.fifa.com/worldcup/matches/", useInternalNodes=T)
However, the field for one country is 't-nText kern' and for the rest of countries is 't-nText '.
<span class="t-nText kern">Bosnia and Herzegovina</span>
Therefore, if I use this command, I will miss 'Bosnia and Herzegovina', like this command:
xpathSApply(wcup, "//span[#class='t-nText ']", xmlValue)
So, is there any way that I can search for both attributes 't-nText ' and 't-nText kern' at the same time? Or do you have any other solution? I want to keep the order of the matches as is.
xpath doesn't support logical OR:
xpathSApply(wcup, "//span[#class='t-nText ' || 't-nText kern']", xmlValue)
XPath error : Invalid expression
//span[#class='t-nText ' || 't-nText kern']
^
XPath error : Invalid expression
//span[#class='t-nText ' || 't-nText kern']
^
Error in xpathApply.XMLInternalDocument(doc, path, fun, ..., namespaces = namespaces, :
error evaluating xpath expression //span[#class='t-nText ' || 't-nText kern']
Use 'or' or perhaps 'starts-with()',
wcup["//span[#class='t-nText kern' or #class='t-nText ']"]
wcup["//span[starts-with(#class, 't-nText ')]"]
I originally posted this ,, then noticed order was needed, so I searched SO for "XPath OR"
Why not just append the results of the two searches together:
c( xpathSApply(wcup, "//span[#class='t-nText kern']", xmlValue),
xpathSApply(wcup, "//span[#class='t-nText ']", xmlValue)
)
Lo and behold I came up with:
xpathSApply(wcup, "//*[starts-with(#class,'t-nText')]", xmlValue)
Which appears mighty similar to Martin Morgan's solution. I had not realized that XPath was it's own language. Guess I'm at least 10 years behind the times.