lemma | Language Ecosystem for Modeling Microservice Architecture | Microservice library
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kandi X-RAY | lemma Summary
A Language Ecosystem for Modeling Microservice Architecture.
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lemma Key Features
lemma Examples and Code Snippets
Lines of Code : 39License : Permissive (MIT License)
Copydef diophantine_all_soln(a: int, b: int, c: int, n: int = 2) -> None:
"""
Lemma : if n|ab and gcd(a,n) = 1, then n|b.
Finding All solutions of Diophantine Equations:
Theorem : Let gcd(a,b) = d, a = d*p, b = d*q. If (x0,y0) is a s def greatest_common_divisor(a: int, b: int) -> int:
"""
Euclid's Lemma : d divides a and b, if and only if d divides a-b and b
Euclid's Algorithm
>>> greatest_common_divisor(7,5)
1
Note : In number theory, two def greatest_common_divisor(a: int, b: int) -> int:
"""
Euclid's Lemma : d divides a and b, if and only if d divides a-b and b
Euclid's Algorithm
>>> greatest_common_divisor(7,5)
1
Note : In number theory, two i Community Discussions
Trending Discussions on lemma
QUESTION
In the simple example below I get the error Tactic failure: Cannot find witness. The lemma seems rather trivial so I guess, I'm not using the quantification properly.
...ANSWER
Answered 2021-Jun-15 at 11:55Looking at the documentation, it does not seem that the decision procedure for lia handles existential quantifiers, so you have to instantiate the existential by yourself, e.g.
QUESTION
So I'm trying to perform a simple proof using cardinalities. It looks like:
...ANSWER
Answered 2021-Jun-11 at 08:54I believe that the lemma you are trying to prove does not appropriately consider the case of infinite sets.
In Isabelle/HOL, infinite cardinalities are represented by zero. As we can see by the following lemma.
QUESTION
I have been working on an algorithm (Dafny cannot prove function-method equivalence, with High-Order-Polymorphic Recursive vs Linear Iterative) to count the number of subsequences of a sequence that hold a property P. For instance, how many subsequences hold that 'the number of positives on its left part are more that on its right part'.
But this was just to offer some context.
The important function is this CountAux function below. Given a proposition P (like, x is positive), a sequ sequence of sequences, an index i to move through the sequences, and an upper bound j:
ANSWER
Answered 2021-Jun-07 at 13:03You can prove your lemma in recursive manner. You can refer https://www.rise4fun.com/Dafny/tutorialcontent/Lemmas#h25 for detailed explanation. It also has an example which happens to be very similar to your problem.
QUESTION
I've been working with Isabelle/HOL for a few months now, but I've been unable to figure out the exact intention of the use of _tac.
Specifically, I'm talking about cases vs case_tac and induct vs indut_tac (although it would be nice to know the meaning of tac in general, since I'm also using other methods such as cut_tac).
I've noticed I can't use cases or induct using apply with ⋀-bound variables, but I can if it's an structured proof. Why?
An example of this:
...ANSWER
Answered 2021-Jun-06 at 01:13*_tac are built-in tactics used in apply-scripts. In particular, case_tac and induct_tac have been basically superseded by the cases and induction proof methods in Isabelle/Isar. As you mentioned, case_tac and induct_tac can handle ⋀-bound variables. However, this is quite fragile, since their names are often generated automatically and may change when Isabelle changes (of course, you could use rename_tac to choose fixed names). That's one of the reasons why nowadays structured proof methods are preferred to unstructured tactic scripts. Now, back to your example: In order to be able to use cases, you can introduce a structured block as follows:
QUESTION
The input word is standalone and not part of a sentence but I would like to get all of its possible lemmas as if the input word were in different sentences with all possible POS tags. I would also like to get the lookup version of the word's lemma.
Why am I doing this?
I have extracted lemmas from all the documents and I have also calculated the number of dependency links between lemmas. Both of which I have done using en_core_web_sm. Now, given an input word, I would like to return the lemmas that are linked most frequently to all the possible lemmas of the input word.
So in short, I would like to replicate the behaviour of token._lemma for the input word with all possible POS tags to maintain consistency with the lemma links I have counted.
ANSWER
Answered 2021-Jun-01 at 22:11I found it difficult to get lemmas and inflections directly out of spaCy without first constructing an example sentence to give it context. This wasn't ideal, so I looked further and found LemmaInflect did this very well.
QUESTION
In a large corpus of text, I am interested in extracting every sentence which has a specific list of (Verb-Noun) or (Adjective-Noun) somewhere in the sentence. I have a long list but here is a sample. In my MWE I am trying to extract sentences with "write/wrote/writing/writes" and "book/s". I have around 30 such pairs of words.
Here is what I have tried but it's not catching most of the sentences:
...ANSWER
Answered 2021-May-29 at 08:53The issue is that in the Matcher, by default each dictionary in the pattern corresponds to exactly one token. So your regex doesn't match any number of characters, it matches any one token, which isn't what you want.
To get what you want, you can use the OP value to specify that you want to match any number of tokens. See the operators or quantifiers section in the docs.
However, given your problem, you probably want to actually use the Dependency Matcher instead, so I rewrote your code to use that as well. Try this:
QUESTION
I have following simple Isabelle/HOL theory:
...ANSWER
Answered 2021-May-28 at 06:13nat set is interpreted as a function (that does not type correctly). The set of natural numbers can be expressed as UNIV :: nat set. Then, spec_2 reads
QUESTION
I have found the same problem when proving several lemmas: rules with an equality sometimes only work in one direction.
For instance, I'd like to use append_assoc to get from xs @ ys @ zs to (xs @ ys) @ zs, but since append_assoc is defined as (xs @ ys) @ zs = xs @ ys @ zs, I can't.
Is there any way to indicate I want to use some rule backwards?
Thanks in advance.
...ANSWER
Answered 2021-May-27 at 07:36The rule with swapped left- and right-hand sides is obtained by applying an attribute symmetric to the original rule:
QUESTION
I'm having a bit of trouble understanding the difference between strong and weak specification in Coq. For instance, if I wanted to write the replicate function (given a number n and a value x, it creates a list of length n, with all elements equal to x) using the strong specification way, how would I be able to do that? Apparently I have to write an Inductive "version" of the function but how?
Definition in Haskell:
...ANSWER
Answered 2021-May-24 at 17:03Just for fun, here's what it would look like in Haskell, where everything dependent-ish is much more annoying. This code uses some very new GHC features, mostly to make the types more explicit, but it could be modified quite easily to work with older GHC versions.
QUESTION
Here's a minimal example of my problem
Lemma arith: forall T (G: seq T), (size G + 1 + 1).+1 = (size G + 3).
I would like to be able to reduce this to
forall T (G: seq T), (size G + 2).+1 = (size G + 3).
by the simplest possible means. Trying simpl or auto immediately does nothing.
If I rewrite with associativity first, that is,
intros. rewrite - addnA. simpl. auto.,
simpl and auto still do nothing. I am left with a goal of
(size G + (1 + 1)).+1 = size G + 3
I guess the .+1 is "in the way" of simpl and auto working on the (1+1) somehow. It seems like I must first remove the .+1 before I can simplify the 1+1.
However, in my actual proof, there is a lot more stuff than the .+1 "in the way" and I would really like to simplify my copious amount of +1s first. As a hack, I'm using 'replace' on individual occurrences but this feels very clumsy (and there are a lot of different arithmetic expressions to replace). Is there any better way to do this?
I am using the ssrnat library.
Thanks.
...ANSWER
Answered 2021-May-24 at 02:58There are many lemmas in ssrnat to reason about addition. One possible solution to your problem is the following:
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