Does anyone have a small working snippet of code to read strings from a file in Coq (the ynot library seems to do this, but I can't figure it out)?
Ynot can be found here: http://ynot.cs.harvard.edu/
The distribution contains an IO directory in the examples, which includes FS.v which defines things like:
Fixpoint ReadFile (fm : fd_model) (ms : list mode) (fd : File fm ms) (str : string) {struct str} : Trace :=
match str with
| EmptyString => Read fd None :: nil
| String a b => (ReadFile fd b) ++ (Read fd (Some a) :: nil)
end.
But I can't figure out how to invoke it.
I've tried things like:
Eval compute in ReadFile (File (FileModel "demo.txt") [R]).
^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Error: The term "File (FileModel "demo.txt") [R]" has type "Set" while it is expected to have type "File ?16 ?17".
Similarly, the Quark project (http://goto.ucsd.edu/quark/) defines VCRIO.v with alternative mechanisms.
Any help would be much appreciated!
In general, you will not be able to perform file I/O directly inside Coq for the very simple reason that the underlying language Gallina is pure and total.
In particular, the function ReadFile you are looking at is not a function that reads a file, but a function that computes the trace generated by the action of reading a file.
The way we get around that in Quark (and its successor project Reflex http://goto.ucsd.edu/reflex ) is to axiomatize these effectful actions, see for instance https://github.com/UCSD-PL/kraken/blob/master/reflex/coq/ReflexIO.v from line 323 for the axiomatized type of our primitives.
So, on the Coq side, we reason using this monadic effectful type, and then once the code gets extracted, these axioms are realized with OCaml functions of the proper type, see here
https://github.com/UCSD-PL/kraken/blob/master/reflex/ml/primitives/ReflexImpl.ml line 111.
This obviously increases your trusted computing base, as you need to make sure your primitives do exactly what you axiomatized and no more.
To recap, there is no way we can execute effectful operations in Gallina itself, so we axiomatize these actions and can only really perform them with the extracted OCaml code.
I am unaware of any technique that would let you do these with rich types inside Gallina.
Modelling IO (by axiomatizing it) and setting it up for extraction (by realizing it) is similar to using Haskell's FFI. You won't be able to run the code in proofs or using the interpreter though. You will only be able to run it by extracting it and compiling it. But this is just a mere inconvenience. Imagine if you defined plus like this:
Axiom plus : nat -> nat -> nat.
Infix "+" := plus.
Axiom plus_0 : forall n1, n1 + 0 = n1.
Axiom plus_S : forall n1 n2, n1 + (S n2) = S (n1 + n2).
This wouldn't be executable, but you would still be able to prove everything you needed to prove about plus. The proof terms would be larger though. For example, eq_refl would no longer be a proof of 2 + 2 = 4. Also, Coq would no longer be doing any sanity checking.
For the "realizing" part, if you are extracting to Haskell, you do something like this:
Extract Constant plus => "(\ n1 n2 -> case n2 of
O -> n1
S n3 -> S (plus n1 n3))".
And then you extract it.
Extraction Language Haskell.
Recursive Extraction plus.
Now, try extracting without realizing.
Related
I have a 'QuasiQuoter' which is useful in source code in Haskell, but also as a standalone application. So, I need to be able to run QuasiQuoter
During the compile time in Haskell - [myGrammar|someCommand|]
In runtime (runtime compilation) in shell - mygrammar 'someCommand'
The first part is easy but the second part might be a little clumsy if solved as calling the compiler with some generated code from the runtime.
I would like to solve a second part of the problem using some nice method in Haskell which doesn't accept only the source code, but accepts QuasyQuoter datatype instead so the code is less clumsy. But I can't find any compilation method like that.
Do you know any? Thanks.
Example of usage
Haskell
The function takes tuple [(a,b,c,d,e)] and returns a list of the strings with the products.
function = [lsql| {1..5}, r=[ a.* |> (*) ], "Product of a.1 * a.2 * ... * a.5 is &a.r"|]
Bash
The command reads from stdin csv with at least 5 numerical columns and returns a list of their products (one per line).
lsql-csv '-, r=[ a.* |> (*) ], "Product of a.1 * a.2 * ... * a.5 is &a.r"'
I think the question is how to parse and process a string in a uniform way between a quasiquoter and some other chunk of code. If this interpretation is right, then you just... do that. For example:
-- implementation of these is left to the reader, but can use standard Haskell
-- programming techniques and libraries, like parsec and ADTs and stuff
command :: Parser Command
interpret :: Command -> IO ()
jit :: Command -> Exp -- or Q Exp
Then, in your lsql-csv.hs, you would write something like
main = do
[s] <- getArgs
case parse command s of
Left err -> die (show err)
Right com -> interpret com
and in your LSql/CSV/QQ.hs, you would write something like
lsql = QuasiQuoter { quoteExp = \s -> case parse command s of
Left err -> qReport True (show err) >> fail ""
Right com -> return (jit com) -- or just jit com if that's already a Q Exp
}
As the title states, I see pieces of code online where the variables/functions have ' next to it, what does this do/mean?
ex:
function :: [a] -> [a]
function ...
function' :: ....
The notation comes from mathematics. It is read x prime. In pretty much any math manual you can find something like let x be a number and x' be the projection of ... (math stuff).
Why not using another convention? well, in mathematics It makes a lot of sense because It can be very pedagogical... In programming we aren't used to this convention so I don't see the point of using it, but I am not against it neither.
Just to give you an example of its use in mathematics so you can understand why It is used in Haskell. Below, the same triangle concept but one using prime convention and other not using it. It is pretty clear in the first picture that pairs (A, A'), (B, B'), ... are related by one being the vertex and the prime version being the midpoint of the oposite edge. Whereas in the second example, you just have to remember that A is the midpoint of the oposite edge of vertex P. First is easier and more pedagogical:
As the other answers said, function' is just another variable name. So,
don'tUse :: Int -> IO ()
don'tUse won'tBe''used'' = return ()
is just like
dontUse :: Int -> IO ()
dontUse wontBeUsed = return ()
with slightly different names. The only requirement is that the name starts with a lowercase-letter or underscore, after that you can have as many single-quote characters as you want.
Prelude> let _' = 1
Prelude> let _'' = 2
Prelude> let _''''''''' = 9
Prelude> _' + _'' * _'''''''''
19
...Of course it's not necessarily a good idea to name variables like that; normally such prime-names are used when making a slightly different version of an already named thing. For example, foldl and foldl' are functions with the same signature that do essentially the same thing, only with different strictness (which often affects performance memory usage and whether infinite inputs are allowed, but not the actual results).
That said, to the question
Haskell what does the ' symbol do?
– the ' symbol does in fact do various other things as well, but only when it appears not as a non-leading character in a name.
'a' is a character literal.
'Foo is a constructor used on the type level. See DataKinds.
'bar and ''Baz are quoted names. See TemplateHaskell.
Consider the following fragment:
data File
= NoFile
| FileInfo {
path :: FilePath,
modTime :: Data.Time.Clock.UTCTime
}
| FileFull {
path :: FilePath,
modTime :: Data.Time.Clock.UTCTime,
content :: String
}
deriving Eq
That duplication is a bit of a "wart", though in this one-off instance not particularly painful. In order to further improve my understanding of Haskell's rich type system, what might be preferred "clean"/"idiomatic" approaches for refactoring other than either simply creating a separate data record type for the 2 duplicate fields (then replacing them with single fields of that new data type) or replacing the FileFull record notation with something like | FileFull File String, which wouldn't be quite clean either (as here one would only want FileInfo in there for example, not NoFile)?
(Both these "naive" approaches would be somewhat intrusive/annoying with respect to having to then fix up many modules manually throughout the rest of the code-base here.)
One thing I considered would be parameterizing like so:
data File a
= NoFile
| FileMaybeWithContent {
path :: FilePath,
modTime :: Data.Time.Clock.UTCTime
content :: a
}
deriving Eq
Then for those "just info, not loaded" contexts a would be (), otherwise String. Seems too general anyway, we want either String or nothing, leading us to Maybe, doing once again away with the a parameter.
Of course we've been there before: content could just be done with Maybe String of course, then "refactor any compile errors away" and "done". That'll probably be the order of the day, but knowing Haskell and the many funky GHC extensions.. who knows just what exotic theoretic trick/axiom/law I've been missing, right?! See, the differently-named "semantic insta-differentiator" between a "just meta-data info" value and a "file content with meta info" value does work well throughout the rest of the code-base as far as eased comprehension.
(And yes, I perhaps should have removed NoFile and used Maybe Files throughout, but then... not sure whether there's really a solid reason to do so and a different question altogether anyway..)
All of the following are equivalent/isomorphic, as I think you've discovered:
data F = U | X A B | Y A B C
data F = U | X AB | Y AB C
data AB = AB A B
data F = U | X A B (Maybe C)
So the color of the bike shed really depends on the context (e.g. do you have use for an AB elsewhere?) and your own aesthetic preferences.
It might clarify things and help you understand what you're doing to have some sense of the algebra of algebraic data types
We call types like Either "sum types" and types like (,) "product types" and they are subject to the same kinds of transformations you're familiar with like factoring
f = 1 + (a * b) + (a * b * c)
= 1 + ((a * b) * ( 1 + c))
As others have noted, the NoFile constructor is probably not necessary, but you can keep it if you want. If you feel your code is more readable and/or better understood with it, then I say keep it.
Now the trick with combining the other two constructors is by hiding the content field. You were on the right track by parameterizing File, but that alone isn't enough since then we can have File Foo, File Bar, etc. Fortunately, GHC has some nifty ways to help us.
I'll write out the code here and then explain how it works.
{-# LANGUAGE TypeFamilies #-}
{-# LANGUAGE DataKinds #-}
import Data.Void
data Desc = Info | Full
type family Content (a :: Desc) where
Content Full = String
Content _ = Void
data File a = File
{ path :: FilePath
, modTime :: UTCTime
, content :: Content a
}
There are a few things going on here.
First, note that in the File record, the content field now has type Content a instead of just a. Content is a type family, which is (in my opinion) a confusing name for type-level function. That is, the compiler replaces Content a with some other type based on what a is and how we've defined Content.
We defined Content Full to be String, so that when we have a value f1 :: File Full, its content field will have a String value. On the other hand, f2 :: File Info will have a content field with type Void which has no values.
Cool right? But what's preventing us from having File Foo now?
That's where DataKinds comes to the rescue. It "promotes" the data type Desc to a kind (the type of types in Haskell) and type constructors ,Info and Full, to types of kind Desc instead of merely values of type Desc.
Notice in the declaration of Content that I have annotated a. It looks like a type annotation, but a is already a type. This is a kind annotation. It forces a to be something of kind Desc and the only types of kind Desc are Info and Full.
By now you're probably totally sold on how awesome this is, but I should warn you there's no free lunch. In particular, this is a compile-time construction. Your single File type becomes two different types. This can cause other related logic (producers and consumers of File records) to become complicated. If your use case doesn't mix File Info records with File Full records, then this is the way to go. On the other hand, if you want to do something like have a list of File records which can be a mixture of both types, then you're better off just making the type of your content field Maybe String.
Another thing is, how exactly do you make a File Info since there's no value of Void to use for the content field? Well, technically it should be ok to use undefined or error "this should never happen" since it is (morally) impossible to have a function of type Void -> a, but if that makes you feel uneasy (and it probably should), then just replace Void with (). Unit is almost as useless and doesn't require 'values' of bottom.
I'm currently reading Implementing functional languages: a tutorial by SPJ and the (sub)chapter I'll be referring to in this question is 3.8.7 (page 136).
The first remark there is that a reader following the tutorial has not yet implemented C scheme compilation (that is, of expressions appearing in non-strict contexts) of ECase expressions.
The solution proposed is to transform a Core program so that ECase expressions simply never appear in non-strict contexts. Specifically, each such occurrence creates a new supercombinator with exactly one variable which body corresponds to the original ECase expression, and the occurrence itself is replaced with a call to that supercombinator.
Below I present a (slightly modified) example of such transformation from 1
t a b = Pack{2,1} ;
f x = Pack{2,2} (case t x 7 6 of
<1> -> 1;
<2> -> 2) Pack{1,0} ;
main = f 3
== transformed into ==>
t a b = Pack{2,1} ;
f x = Pack{2,2} ($Case1 (t x 7 6)) Pack{1,0} ;
$Case1 x = case x of
<1> -> 1;
<2> -> 2 ;
main = f 3
I implemented this solution and it works like charm, that is, the output is Pack{2,2} 2 Pack{1,0}.
However, what I don't understand is - why all that trouble? I hope it's not just me, but the first thought I had of solving the problem was to just implement compilation of ECase expressions in C scheme. And I did it by mimicking the rule for compilation in E scheme (page 134 in 1 but I present that rule here for completeness): so I used
E[[case e of alts]] p = E[[e]] p ++ [Casejump D[[alts]] p]
and wrote
C[[case e of alts]] p = C[[e]] p ++ [Eval] ++ [Casejump D[[alts]] p]
I added [Eval] because Casejump needs an argument on top of the stack in weak head normal form (WHNF) and C scheme doesn't guarantee that, as opposed to E scheme.
But then the output changes to enigmatic: Pack{2,2} 2 6.
The same applies when I use the same rule as for E scheme, i.e.
C[[case e of alts]] p = E[[e]] p ++ [Casejump D[[alts]] p]
So I guess that my "obvious" solution is inherently wrong - and I can see that from outputs. But I'm having trouble stating formal arguments as to why that approach was bound to fail.
Can someone provide me with such argument/proof or some intuition as to why the naive approach doesn't work?
The purpose of the C scheme is to not perform any computation, but just delay everything until an EVAL happens (which it might or might not). What are you doing in your proposed code generation for case? You're calling EVAL! And the whole purpose of C is to not call EVAL on anything, so you've now evaluated something prematurely.
The only way you could generate code directly for case in the C scheme would be to add some new instruction to perform the case analysis once it's evaluated.
But we (Thomas Johnsson and I) decided it was simpler to just lift out such expressions. The exact historical details are lost in time though. :)
Consider the following problem: given a list of length three of tuples (String,Int), is there a pair of elements having the same "Int" part? (For example, [("bob",5),("gertrude",3),("al",5)] contains such a pair, but [("bob",5),("gertrude",3),("al",1)] does not.)
This is how I would implement such a function:
import Data.List (sortBy)
import Data.Function (on)
hasPair::[(String,Int)]->Bool
hasPair = napkin . sortBy (compare `on` snd)
where napkin [(_, a),(_, b),(_, c)] | a == b = True
| b == c = True
| otherwise = False
I've used pattern matching to bind names to the "Int" part of the tuples, but I want to sort first (in order to group like members), so I've put the pattern-matching function inside a where clause. But this brings me to my question: what's a good strategy for picking names for functions that live inside where clauses? I want to be able to think of such names quickly. For this example, "hasPair" seems like a good choice, but it's already taken! I find that pattern comes up a lot - the natural-seeming name for a helper function is already taken by the outer function that calls it. So I have, at times, called such helper functions things like "op", "foo", and even "helper" - here I have chosen "napkin" to emphasize its use-it-once, throw-it-away nature.
So, dear Stackoverflow readers, what would you have called "napkin"? And more importantly, how do you approach this issue in general?
General rules for locally-scoped variable naming.
f , k, g, h for super simple local, semi-anonymous things
go for (tail) recursive helpers (precedent)
n , m, i, j for length and size and other numeric values
v for results of map lookups and other dictionary types
s and t for strings.
a:as and x:xs and y:ys for lists.
(a,b,c,_) for tuple fields.
These generally only apply for arguments to HOFs. For your case, I'd go with something like k or eq3.
Use apostrophes sparingly, for derived values.
I tend to call boolean valued functions p for predicate. pred, unfortunately, is already taken.
In cases like this, where the inner function is basically the same as the outer function, but with different preconditions (requiring that the list is sorted), I sometimes use the same name with a prime, e.g. hasPairs'.
However, in this case, I would rather try to break down the problem into parts that are useful by themselves at the top level. That usually also makes naming them easier.
hasPair :: [(String, Int)] -> Bool
hasPair = hasDuplicate . map snd
hasDuplicate :: Ord a => [a] -> Bool
hasDuplicate = not . isStrictlySorted . sort
isStrictlySorted :: Ord a => [a] -> Bool
isStrictlySorted xs = and $ zipWith (<) xs (tail xs)
My strategy follows Don's suggestions fairly closely:
If there is an obvious name for it, use that.
Use go if it is the "worker" or otherwise very similar in purpose to the original function.
Follow personal conventions based on context, e.g. step and start for args to a fold.
If all else fails, just go with a generic name, like f
There are two techniques that I personally avoid. One is using the apostrophe version of the original function, e.g. hasPair' in the where clause of hasPair. It's too easy to accidentally write one when you meant the other; I prefer to use go in such cases. But this isn't a huge deal as long as the functions have different types. The other is using names that might connote something, but not anything that has to do with what the function actually does. napkin would fall into this category. When you revisit this code, this naming choice will probably baffle you, as you will have forgotten the original reason that you named it napkin. (Because napkins have 4 corners? Because they are easily folded? Because they clean up messes? They're found at restaurants?) Other offenders are things like bob and myCoolFunc.
If you have given a function a name that is more descriptive than go or h, then you should be able to look at either the context in which it is used, or the body of the function, and in both situations get a pretty good idea of why that name was chosen. This is where my point #3 comes in: personal conventions. Much of Don's advice applies. If you are using Haskell in a collaborative situation, then coordinate with your team and decide on certain conventions for common situations.