I'm interested in knowing the possibilities of this. I'm working on a project that validates the skills of a software engineer, currently we validate skills based on code reviews by credentialed developers.
I know the answer if far more completed that the question, I couldn't imagine how complex the program would have to be able to analyse complex code but I am starting with basic programming interview questions.
For example, the classic FizzBuzz question:
Write a program that prints the numbers from 1 to 20. But for multiples of three print “Fizz” instead of the number and for the multiples of five print “Buzz”. For numbers which are multiples of both three and five print “FizzBuzz”.
and below is the solution in python:
for num in range(1,21):
string = ""
if num % 3 == 0:
string = string + "Fizz"
if num % 5 == 0:
string = string + "Buzz"
if num % 5 != 0 and num % 3 != 0:
string = string + str(num)
print(string)
Question is, can we programatically analyse the validity of this solution?
I would like to know if anyone has attempted this, and if there are current implementations I can take a look at. Also if anyone has used z3, and if it is something I can use to solve this problem.
As Vilx- mentioned, correctness of programs (including whether or not they terminate) is in general known to be undecidable. However, tools such as Z3 show that relevant concrete cases can still be reasoned about, despite the general undecidability of the problem.
Static analysers typically look for "simple" problems (e.g. null dereferences, out-of-bounds accesses, numerical overflows), but are comparably fast and require little user guidance (think of guidance in the spirit of adding type annotations to your code).
A non-exhaustive (and biased) list of keywords to search for: "static analysers", "abstract interpretation"; "facebook infer", "airbus absint", "juliasoft".
Verifiers attempt to prove much richer properties, in particular functional correctness, e.g. "does this sort-implementation really sort my array (and not do anything else, e.g. deallocate some global memory or update an element reachable from the array)?" or "does that crypto-implementation really implement the crypto protocol it promises to implement?". This is a much harder task and tools from that line of research are typically rather slow, require expert users with a background in formal verification and significant user guidance.
A non-exhaustive (and biased) list of keywords to search for: "verification", "hoare logic", "separation logic"; "eth viper", "microsoft dafny", "kuleuven verifast", "microsoft f*".
Other formal methods exist, e.g. refinement (or correct-by-construction), but with even less tool support and, as far as I know, industry acceptance.
Let's put it this way: it's been mathematically proven that you CANNOT determine if a program will ever terminate. So if you want a mathematically perfect answer of if the target program is correct, you're doomed.
That said, you can still do unit tests and "linting" which will give you plenty of intetesting insights.
But for simple pieces of code like the FizzBuzz, I think that eyeballing by an experienced dev will probably bring the best results.
What good naming conventions do you use for PLC?
I've seen hundreds of projects from different programmers, dozens of companies standards, RA, Beckhoff posted in some documents their naming... dozens of different ideas.
For years, naming tags was one of the most difficult task for me. You can't imagine discussion when I ask a student to create a bit. It's like being the hardest thing on Earth :) (usually, after creating a_bit and another_bit, inspiration is gone).
I asked for RSLogix 5000 because I found it most flexible, having tags, alias, scope tags, descriptions(stored in CPU for latest versions).
Have some tips to share that you find suitable for your use?
Naming tags should have a refrence to the real world. A recent example I did was this:
PTK3KOS1
Pressure Transmitter Kettle 3 Kettle Overhead Solvent #1
This is the tag used in the CMMS system (Maintenance system), and the P&ID
I use UDT's in RSL5K, so that becomes the following in RSLogix:
PTK3KOS1.VAL (Current value)
PTK3KOS1.MIN (I use this especially when I use flex I/O for scaling)
PTK3KOS1.MAX (And I also use it to pass min/max values to some HMI's like WW)
PTK3KOS1.LFF (Signal fault)
PTK3KOS1.LLA (Low alarm bit)
PTK3KOS1.LLL (Low Low bit)
PTK3KOS1.LHA (Hi Alarm bit)
PTK3KOS1.LHH (Hi Hi Bit)
PTK3KOS1.SLA (Setpoint low alarm)
PTK3KOS1.SLL
PTK3KOS1.SHA
PTK3KOS1.SHH
The most common system is the ISA system, see
http://www.engineeringtoolbox.com/isa-intrumentation-codes-d_415.html for an example.
There is also the KKS system, which I personally believe was designed by masochists, and will only use it when forced to do so.
http://www.vgb.org/en/db_kks_eng.html
I like to use some thing like this:
aabccdd_eeee_human-readable-name_wirenumber
aa
DO=Digital Output
DI=Digital Input
AO=Analog Output
AI=Analog Input
gl=Global variable
co=constant
pt=produced Tag
ct=consumed Tag
b
Rack Number
cc
Slot
dd
address 0-64
eeeee
panel/drawing tag
DO10606_MA949_WshLoaderAdvance_9491
I have created a game, (4 in a row), in prolog. My heuristic function requires me to know how many Player's and Opponent's chips are in each possible 4-row combination on the board. The method I am using is as follows (in psuedocodish):
I have 1 list of all possible fours of the board (ComboList) =of the form==> [[A,B,C,D]|Rest].
I have 1 list of all the moves of the 1st player (List1) =of the form==> [[1],[7],[14]]
And 1 for opponent's moves (List2).
Step 1: obtain the first combo from ComboList, 2:
Check all of List1 to see how many are in this combo, 3:
Check all of List2 to see how many are in this combo,
Move onto the next combo from ComboList and start over...
This PROCESS takes waay too much runtime for what is required.
Please can someone suggest something better and more efficient! Much thanks in advance!
The following code uses member/3, which has also to become
known as nth1/3. See here:
http://storage.developerzen.com/fourrow.pro.txt
The predicate is nowadays found in library(lists) and has
possibly native support or a fast implementation:
http://www.swi-prolog.org/pldoc/man?predicate=nth1/3
But I guess asserting some facts and relying on argument
indexing might get you an even better result. See for
example here:
http://www.mxro.de/applications/four-in-a-row
Hope this helps.
Bye
So I'm trying to teach myself Haskell. I am currently on the 11th chapter of Learn You a Haskell for Great Good and am doing the 99 Haskell Problems as well as the Project Euler Problems.
Things are going alright, but I find myself constantly doing something whenever I need to keep track of "variables". I just create another function that accepts those "variables" as parameters and recursively feed it different values depending on the situation. To illustrate with an example, here's my solution to Problem 7 of Project Euler, Find the 10001st prime:
answer :: Integer
answer = nthPrime 10001
nthPrime :: Integer -> Integer
nthPrime n
| n < 1 = -1
| otherwise = nthPrime' n 1 2 []
nthPrime' :: Integer -> Integer -> Integer -> [Integer] -> Integer
nthPrime' n currentIndex possiblePrime previousPrimes
| isFactorOfAnyInThisList possiblePrime previousPrimes = nthPrime' n currentIndex theNextPossiblePrime previousPrimes
| otherwise =
if currentIndex == n
then possiblePrime
else nthPrime' n currentIndexPlusOne theNextPossiblePrime previousPrimesPlusCurrentPrime
where currentIndexPlusOne = currentIndex + 1
theNextPossiblePrime = nextPossiblePrime possiblePrime
previousPrimesPlusCurrentPrime = possiblePrime : previousPrimes
I think you get the idea. Let's also just ignore the fact that this solution can be made to be more efficient, I'm aware of this.
So my question is kind of a two-part question. First, am I going about Haskell all wrong? Am I stuck in the imperative programming mindset and not embracing Haskell as I should? And if so, as I feel I am, how do avoid this? Is there a book or source you can point me to that might help me think more Haskell-like?
Your help is much appreciated,
-Asaf
Am I stuck in the imperative programming mindset and not embracing
Haskell as I should?
You are not stuck, at least I don't hope so. What you experience is absolutely normal. While you were working with imperative languages you learned (maybe without knowing) to see programming problems from a very specific perspective - namely in terms of the van Neumann machine.
If you have the problem of, say, making a list that contains some sequence of numbers (lets say we want the first 1000 even numbers), you immediately think of: a linked list implementation (perhaps from the standard library of your programming language), a loop and a variable that you'd set to a starting value and then you would loop for a while, updating the variable by adding 2 and putting it to the end of the list.
See how you mostly think to serve the machine? Memory locations, loops, etc.!
In imperative programming, one thinks about how to manipulate certain memory cells in a certain order to arrive at the solution all the time. (This is, btw, one reason why beginners find learning (imperative) programming hard. Non programmers are simply not used to solve problems by reducing it to a sequence of memory operations. Why should they? But once you've learned that, you have the power - in the imperative world. For functional programming you need to unlearn that.)
In functional programming, and especially in Haskell, you merely state the construction law of the list. Because a list is a recursive data structure, this law is of course also recursive. In our case, we could, for example say the following:
constructStartingWith n = n : constructStartingWith (n+2)
And almost done! To arrive at our final list we only have to say where to start and how many we want:
result = take 1000 (constructStartingWith 0)
Note that a more general version of constructStartingWith is available in the library, it is called iterate and it takes not only the starting value but also the function that makes the next list element from the current one:
iterate f n = n : iterate f (f n)
constructStartingWith = iterate (2+) -- defined in terms of iterate
Another approach is to assume that we had another list our list could be made from easily. For example, if we had the list of the first n integers we could make it easily into the list of even integers by multiplying each element with 2. Now, the list of the first 1000 (non-negative) integers in Haskell is simply
[0..999]
And there is a function map that transforms lists by applying a given function to each argument. The function we want is to double the elements:
double n = 2*n
Hence:
result = map double [0..999]
Later you'll learn more shortcuts. For example, we don't need to define double, but can use a section: (2*) or we could write our list directly as a sequence [0,2..1998]
But not knowing these tricks yet should not make you feel bad! The main challenge you are facing now is to develop a mentality where you see that the problem of constructing the list of the first 1000 even numbers is a two staged one: a) define how the list of all even numbers looks like and b) take a certain portion of that list. Once you start thinking that way you're done even if you still use hand written versions of iterate and take.
Back to the Euler problem: Here we can use the top down method (and a few basic list manipulation functions one should indeed know about: head, drop, filter, any). First, if we had the list of primes already, we can just drop the first 1000 and take the head of the rest to get the 1001th one:
result = head (drop 1000 primes)
We know that after dropping any number of elements form an infinite list, there will still remain a nonempty list to pick the head from, hence, the use of head is justified here. When you're unsure if there are more than 1000 primes, you should write something like:
result = case drop 1000 primes of
[] -> error "The ancient greeks were wrong! There are less than 1001 primes!"
(r:_) -> r
Now for the hard part. Not knowing how to proceed, we could write some pseudo code:
primes = 2 : {-an infinite list of numbers that are prime-}
We know for sure that 2 is the first prime, the base case, so to speak, thus we can write it down. The unfilled part gives us something to think about. For example, the list should start at some value that is greater 2 for obvious reason. Hence, refined:
primes = 2 : {- something like [3..] but only the ones that are prime -}
Now, this is the point where there emerges a pattern that one needs to learn to recognize. This is surely a list filtered by a predicate, namely prime-ness (it does not matter that we don't know yet how to check prime-ness, the logical structure is the important point. (And, we can be sure that a test for prime-ness is possible!)). This allows us to write more code:
primes = 2 : filter isPrime [3..]
See? We are almost done. In 3 steps, we have reduced a fairly complex problem in such a way that all that is left to write is a quite simple predicate.
Again, we can write in pseudocode:
isPrime n = {- false if any number in 2..n-1 divides n, otherwise true -}
and can refine that. Since this is almost haskell already, it is too easy:
isPrime n = not (any (divides n) [2..n-1])
divides n p = n `rem` p == 0
Note that we did not do optimization yet. For example we can construct the list to be filtered right away to contain only odd numbers, since we know that even ones are not prime. More important, we want to reduce the number of candidates we have to try in isPrime. And here, some mathematical knowledge is needed (the same would be true if you programmed this in C++ or Java, of course), that tells us that it suffices to check if the n we are testing is divisible by any prime number, and that we do not need to check divisibility by prime numbers whose square is greater than n. Fortunately, we have already defined the list of prime numbers and can pick the set of candidates from there! I leave this as exercise.
You'll learn later how to use the standard library and the syntactic sugar like sections, list comprehensions, etc. and you will gradually give up to write your own basic functions.
Even later, when you have to do something in an imperative programming language again, you'll find it very hard to live without infinte lists, higher order functions, immutable data etc.
This will be as hard as going back from C to Assembler.
Have fun!
It's ok to have an imperative mindset at first. With time you will get more used to things and start seeing the places where you can have more functional programs. Practice makes perfect.
As for working with mutable variables you can kind of keep them for now if you follow the rule of thumb of converting variables into function parameters and iteration into tail recursion.
Off the top of my head:
Typeclassopedia. The official v1 of the document is a pdf, but the author has moved his v2 efforts to the Haskell wiki.
What is a monad? This SO Q&A is the best reference I can find.
What is a Monad Transformer? Monad Transformers Step by Step.
Learn from masters: Good Haskell source to read and learn from.
More advanced topics such as GADTs. There's a video, which does a great job explaining it.
And last but not least, #haskell IRC channel. Nothing can even come close to talk to real people.
I think the big change from your code to more haskell like code is using higher order functions, pattern matching and laziness better. For example, you could write the nthPrime function like this (using a similar algorithm to what you did, again ignoring efficiency):
nthPrime n = primes !! (n - 1) where
primes = filter isPrime [2..]
isPrime p = isPrime' p [2..p - 1]
isPrime' p [] = True
isPrime' p (x:xs)
| (p `mod` x == 0) = False
| otherwise = isPrime' p xs
Eg nthPrime 4 returns 7. A few things to note:
The isPrime' function uses pattern matching to implement the function, rather than relying on if statements.
the primes value is an infinite list of all primes. Since haskell is lazy, this is perfectly acceptable.
filter is used rather than reimplemented that behaviour using recursion.
With more experience you will find you will write more idiomatic haskell code - it sortof happens automatically with experience. So don't worry about it, just keep practicing, and reading other people's code.
Another approach, just for variety! Strong use of laziness...
module Main where
nonmults :: Int -> Int -> [Int] -> [Int]
nonmults n next [] = []
nonmults n next l#(x:xs)
| x < next = x : nonmults n next xs
| x == next = nonmults n (next + n) xs
| otherwise = nonmults n (next + n) l
select_primes :: [Int] -> [Int]
select_primes [] = []
select_primes (x:xs) =
x : (select_primes $ nonmults x (x + x) xs)
main :: IO ()
main = do
let primes = select_primes [2 ..]
putStrLn $ show $ primes !! 10000 -- the first prime is index 0 ...
I want to try to answer your question without using ANY functional programming or math, not because I don't think you will understand it, but because your question is very common and maybe others will benefit from the mindset I will try to describe. I'll preface this by saying I an not a Haskell expert by any means, but I have gotten past the mental block you have described by realizing the following:
1. Haskell is simple
Haskell, and other functional languages that I'm not so familiar with, are certainly very different from your 'normal' languages, like C, Java, Python, etc. Unfortunately, the way our psyche works, humans prematurely conclude that if something is different, then A) they don't understand it, and B) it's more complicated than what they already know. If we look at Haskell very objectively, we will see that these two conjectures are totally false:
"But I don't understand it :("
Actually you do. Everything in Haskell and other functional languages is defined in terms of logic and patterns. If you can answer a question as simple as "If all Meeps are Moops, and all Moops are Moors, are all Meeps Moors?", then you could probably write the Haskell Prelude yourself. To further support this point, consider that Haskell lists are defined in Haskell terms, and are not special voodoo magic.
"But it's complicated"
It's actually the opposite. It's simplicity is so naked and bare that our brains have trouble figuring out what to do with it at first. Compared to other languages, Haskell actually has considerably fewer "features" and much less syntax. When you read through Haskell code, you'll notice that almost all the function definitions look the same stylistically. This is very different than say Java for example, which has constructs like Classes, Interfaces, for loops, try/catch blocks, anonymous functions, etc... each with their own syntax and idioms.
You mentioned $ and ., again, just remember they are defined just like any other Haskell function and don't necessarily ever need to be used. However, if you didn't have these available to you, over time, you would likely implement these functions yourself when you notice how convenient they can be.
2. There is no Haskell version of anything
This is actually a great thing, because in Haskell, we have the freedom to define things exactly how we want them. Most other languages provide building blocks that people string together into a program. Haskell leaves it up to you to first define what a building block is, before building with it.
Many beginners ask questions like "How do I do a For loop in Haskell?" and innocent people who are just trying to help will give an unfortunate answer, probably involving a helper function, and extra Int parameter, and tail recursing until you get to 0. Sure, this construct can compute something like a for loop, but in no way is it a for loop, it's not a replacement for a for loop, and in no way is it really even similar to a for loop if you consider the flow of execution. Similar is the State monad for simulating state. It can be used to accomplish similar things as static variables do in other languages, but in no way is it the same thing. Most people leave off the last tidbit about it not being the same when they answer these kinds of questions and I think that only confuses people more until they realize it on their own.
3. Haskell is a logic engine, not a programming language
This is probably least true point I'm trying to make, but hear me out. In imperative programming languages, we are concerned with making our machines do stuff, perform actions, change state, and so on. In Haskell, we try to define what things are, and how are they supposed to behave. We are usually not concerned with what something is doing at any particular time. This certainly has benefits and drawbacks, but that's just how it is. This is very different than what most people think of when you say "programming language".
So that's my take how how to leave an imperative mindset and move to a more functional mindset. Realizing how sensible Haskell is will help you not look at your own code funny anymore. Hopefully thinking about Haskell in these ways will help you become a more productive Haskeller.
Since many of the Project Euler problems require you to do a divisibility check for quite a number of times, I've been trying to figure out the fastest way to perform this task in ZX81 BASIC.
So far I've compared (N/D) to INT(N/D) to check, whether N is dividable by D or not.
I have been thinking about doing the test in Z80 machine code, I haven't yet figured out how to use the variables in the BASIC in the machine code.
How can it be achieved?
You can do this very fast in machine code by subtracting repeatedly. Basically you have a procedure like:
set accumulator to N
subtract D
if carry flag is set then it is not divisible
if zero flag is set then it is divisible
otherwise repeat subtraction until one of the above occurs
The 8 bit version would be something like:
DIVISIBLE_TEST:
LD B,10
LD A,100
DIVISIBLE_TEST_LOOP:
SUB B
JR C, $END_DIVISIBLE_TEST
JR Z, $END_DIVISIBLE_TEST
JR $DIVISIBLE_TEST_LOOP
END_DIVISIBLE_TEST:
LD B,A
LD C,0
RET
Now, you can call from basic using USR. What USR returns is whatever's in the BC register pair, so you would probably want to do something like:
REM poke the memory addresses with the operands to load the registers
POKE X+1, D
POKE X+3, N
LET r = USR X
IF r = 0 THEN GOTO isdivisible
IF r <> 0 THEN GOTO isnotdivisible
This is an introduction I wrote to Z80 which should help you figure this out. This will explain the flags if you're not familiar with them.
There's a load more links to good Z80 stuff from the main site although it is Spectrum rather than ZX81 focused.
A 16 bit version would be quite similar but using register pair operations. If you need to go beyond 16 bits it would get a bit more convoluted.
How you load this is up to you - but the traditional method is using DATA statements and POKEs. You may prefer to have an assembler figure out the machine code for you though!
Your existing solution may be good enough. Only replace it with something faster if you find it to be a bottleneck in profiling.
(Said with a straight face, of course.)
And anyway, on the ZX81 you can just switch to FAST mode.
Don't know if RANDOMIZE USR is available in ZX81 but I think it can be used to call routines in assembly. To pass arguments you might need to use POKE to set some fixed memory locations before executing RANDOMIZE USR.
I remember to find a list of routines implemented in the ROM to support the ZX Basic. I'm sure there are a few to perform floating operation.
An alternative to floating point is to use fixed point math. It's a lot faster in these kind of situations where there is no math coprocessor.
You also might find more information in Sinclair User issues. They published some articles related to programming in the ZX Spectrum
You should place the values in some pre-known memory locations, first. Then use the same locations from within Z80 assembler. There is no parameter passing between the two.
This is based on what I (still) remember of ZX Spectrum 48. Good luck, but you might consider upgrading your hw. ;/
The problem with Z80 machine code is that it has no floating point ops (and no integer divide or multiply, for that matter). Implementing your own FP library in Z80 assembler is not trivial. Of course, you can use the built-in BASIC routines, but then you may as well just stick with BASIC.