I'd like to create a function with type constrained by an interface. My intention is to build a simple monoid solver using VerifiedMonoid defined inClasses.Verified module from contrib package.
Idris gives me the following error:
Monoid-prover.idr line 29 col 5:
When checking type of MonoidProver.eval:
Can't find implementation for VerifiedMonoid a
for the type signature of eval:
eval : VerifiedMonoid a => Expr n -> Env a n -> a
Am I doing something silly or missing something? Such constrained types (like eval's type) can be interpreted like Haskell's types?
The complete code is shown below.
module MonoidProver
import Classes.Verified
import Data.Fin
import Data.Vect
%default total
infixl 5 :+:
data Expr : Nat -> Type where
Var : Fin n -> Expr n
Id : Expr n
(:+:) : Expr n -> Expr n -> Expr n
Env : VerifiedMonoid a => (a : Type) -> Nat -> Type
Env a n = Vect n a
eval : VerifiedMonoid a => Expr n -> Env a n -> a
eval (Var i) env = index i env
eval Id env = neutral
eval (e :+: e') env = eval e env <+> eval e' env
As #Cactus mentioned in a comment, the problem here is that the type signature for Env is not correct. Specifically, since the constraint is on the value of the argument, it is a dependent (pi) type, and Idris enforces that dependent types go left-to-right (be introduced before they are used). My understanding is that basically the compiler will see the argument x : a as being shorthand for , where is the part of the type signature to the right of the quantifier. This means that (a : Type) actually binds a fresh a, which is not the same a that was used in the VerifiedMonoid a constraint (which is implicitly universally bound).
Luckily, since Idris isn't Haskell (where all type class constraints must be at the head of the type signature), this is easy to fix: just change your type signature to Env : (a : Type) -> VerifiedMonoid a => Nat -> Type, so that a is bound before it is used!
Related
Going at the root of Agda standard library, and issuing the following command:
grep -r "module _" . | wc -l
Yields the following result:
843
Whenever I encounter such anonymous modules (I assume that's what they are called), I quite cannot figure out what their purpose is, despite of their apparent ubiquity, nor how to use them because, by definition, I can't access their content using their name, although I assume this should be possible, otherwise their would be no point in even allowing them to be defined.
The wiki page:
https://agda.readthedocs.io/en/v2.6.1/language/module-system.html#anonymous-modules
has a section called "anonymous modules" which is in fact empty.
Could somebody explain what the purpose of anonymous modules is ?
If possible, any example to emphasize the relevance of the definition of such modules, as well as how to use their content would be very much appreciated.
Here are the possible ideas I've come up with, but none of them seems completely satisfying:
They are a way to regroup thematically identical definitions inside an Agda file.
Their name is somehow infered by Agda when using the functions they provide.
Their content is only meant to be visible / used inside their englobing module (a bit like a private block).
Anonymous modules can be used to simplify a group of definitions which share some arguments. Example:
open import Data.Empty
open import Data.Nat
<⇒¬≥ : ∀ {n m} → n < m → n ≥ m → ⊥
<⇒¬≥ = {!!}
<⇒> : ∀ {n m} → n < m → m > n
<⇒> = {!!}
module _ {n m} (p : n < m) where
<⇒¬≥′ : n ≥ m → ⊥
<⇒¬≥′ = {!!}
<⇒>′ : m > n
<⇒>′ = {!!}
Afaik this is the only use of anonymous modules. When the module _ scope is closed, you can't refer to the module anymore, but you can refer to its definitions as if they hadn't been defined in a module at all (but with extra arguments instead).
I would like to write a module that exports a predicate where the user should be able to access a predicate p/1 as a prefix operator. I have defined the following module:
:- module(lala, [p/1]).
:- op(500, fy, [p]).
p(comment).
p(ca).
p(va).
and load it now via:
?- use_module(lala).
true.
Unfortunately, a query fails:
?- p X.
ERROR: Syntax error: Operator expected
ERROR: p
ERROR: ** here **
ERROR: X .
After setting the operator precedence properly, everything works:
?- op(500, fy, [p]).
true.
?- p X.
X = comment ;
X = ca ;
X = va.
I used SWI Prolog for my output but the same problem occurs in YAP as well (GNU Prolog does not support modules). Is there a way the user does not need to set the precedence themselves?
You can export the operator with the module/2 directive.
For example:
:- module(lala, [p/1,
op(500, fy, p)]).
Since the operator is then also available in the module, you can write for example:
p comment.
p ça.
p va.
where p is used as a prefix operator.
I am trying to get generic type-bound operators to work using
gfortran 4.9, however I get errors. I have tried using Type(Vector)
and Class (Vector) without success.
Type :: Vector
Real :: x, y, z
Contains
Procedure :: set => vector_set
Procedure :: write => vector_write
generic :: Operator (+) => vector_add
End Type Vector
Function vector_add &
( &
u, v &
) &
Result (w)
!!$ Input
Type (Vector), Intent(in) :: u, v
!!$ Output
Type (Vector) :: w
w% x = u% x + v% x
w% y = u% y + v% y
w% z = u% z + v% z
End Function vector_add
I am getting the following error:
gfortran -o build/lib/foul.o -c -ffree-form -g -J./build/lib lib/foul.f
gfortran -o build/lib/vectors.o -c -ffree-form -g -J./build/lib lib/vectors.f
lib/vectors.f:194.28:
generic :: Operator (+) => vector_add
1
Error: Undefined specific binding 'vector_add' as target of GENERIC '+' at (1)
scons: *** [build/lib/vectors.o] Error 1
scons: building terminated because of errors.
Inserting the line
procedure :: vector_add
into the contains section of the type definition. As #IanH explains in his comment
Generic bindings resolve to specific bindings (analogous to how
generic procedures resolve to specific procedures). If you don't have
the line that you recommend inserting, then there is no specific
binding (listing a specific binding in the generic statement doesn't
define the specific binding - you need an explicit separate type bound
procedure statement to do that). The ordering isn't important.
I've promoted his explanation for ease of reading and to make this a better answer than my own now-expunged witchcraft-based explanation.
I figured that I can do it on the command line REPL like so:
java -jar frege-repl-1.0.3-SNAPSHOT.jar -hints -warnings
But how can I do the same in http://try.frege-lang.org
Hints and warnings are already enabled by default. For example,
frege> f x = f x
function f :: α -> β
3: application of f will diverge.
Perhaps we can make it better by explicitly saying it as warning or hint (instead of colors distinguishing them) something like:
[Warning] 3: application of f will diverge.
and providing an option to turn them on/off.
Update:
There was indeed an issue (Thanks Ingo for pointing that out!) with showing warnings that are generated in a later phase during the compilation. This issue has been fixed and the following examples now correctly display warnings in the REPL:
frege> h x = 0; h false = 42
function h :: Bool -> Int
4: equation or case alternative cannot be reached.
frege> f false = 6
function f :: Bool -> Int
5: function pattern is refutable, consider
adding a case for true
So, I have read from
setq and defvar in lisp,
http://www.cs.ucf.edu/courses/cop4020/spr2006/plsetup.html, and
In Lisp, how do I fix "Warning: Assumed Special?"
among other places about the difference between setf and defvar. So I decided to play around with the idea a bit:
CL-USER> (defun foo ()
(setf x 10)
(print x))
; in: DEFUN FOO
; (SETF X 10)
; ==>
; (SETQ X 10)
;
; caught WARNING:
; undefined variable: X
;
; compilation unit finished
; Undefined variable:
; X
; caught 1 WARNING condition
FOO
CL-USER> x
; Evaluation aborted on #<UNBOUND-VARIABLE X {10040F1543}>.
CL-USER> (foo)
10
10
CL-USER> x
10
Okay, I know that setf should be used to change the value of an existing variable, but the undefined variable warning seems to be handled pretty well in SBCL (though I have read that different CL implementations may handle this differently, thus it isn't the best thing to do).
Enter the second test:
CL-USER> (defun bar ()
(defvar y 15)
(print y))
; in: DEFUN BAR
; (PRINT Y)
;
; caught WARNING:
; undefined variable: Y
;
; compilation unit finished
; Undefined variable:
; Y
; caught 1 WARNING condition
BAR
CL-USER> y
; Evaluation aborted on #<UNBOUND-VARIABLE Y {10045033D3}>.
CL-USER> (bar)
15
15
CL-USER> y
15
As per the links, I changed the setf to defvar which I think should create and bind the variable all at once. Now my undefined variable warning gets pushed into the (print y) line ... what is going on here?
As a secondary question, I am expecting the values of any variables assinged within a funciton to be inaccessible outside of the function, as is the case in Python:
>>> def foo():
... x = 10
... print x
...
>>> foo()
10
>>> x
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
NameError: name 'x' is not defined
I am guessing this has something to do with the way common lisp deals with scope, ie defvar creates a "global special variabe" ... So I tried one last time with (let ...)
CL-USER> (defun baz ()
(let ((z 10)) (print z))
(incf z 10)
(print z))
; in: DEFUN BAZ
; (INCF Z 10)
; --> LET*
; ==>
; (SETQ Z #:NEW0)
;
; caught WARNING:
; undefined variable: Z
;
; compilation unit finished
; Undefined variable:
; Z
; caught 1 WARNING condition
And after reading What's difference between defvar, defparameter, setf and setq, this one seems to work right:
CL-USER> (defun apple ()
(defparameter x 10)
(print 10))
APPLE
CL-USER> x
; Evaluation aborted on #<UNBOUND-VARIABLE X {1004436993}>.
CL-USER> (apple)
10
10
CL-USER> x
10
Just to reiterate my questions:
1) what is really going on with setf, defvar and let?
2) is there a way to get common lisp to scope the variables inside a function as in the python example?
answering 2) DEFVAR defines a variable. But it has not been executed. So the compiler does not know about the variable in the print form - when compiling the DEFUN form.. It's also inside a DEFUN. Thus it is not on the top-level. As a top-level form the compiler would recognize the DEFVAR and would notice that y is a global special variable.
Just to reiterate my questions: 1) what is really going on with setf, defvar and let?
2) is there a way to get common lisp to scope the variables inside a function as in the python example?
1) SETF sets a variable value, but does not define it. If that variable is undefined, then the Common Lisp standard does not really say what happens. Most Common Lisp implementations will do something useful. Typically it gets executed as if the variable would have been declared special (thus you also get a warning).
DEFVAR is used as a top-level form (usually not inside functions) to define global special variables. Since DEFVAR declares the variable name to be special, it is a very useful convention to write a variable with stars around it: *y* instead of just y.
LET defines a scope for local variables.
2) Common Lisp functions have the parameter list to introduce variables. Other than that they don't define a variable scope. If you want to introduce a local variable inside a function, use LET.
>>> def foo():
... x = 10
... print x
Is
(defun foo ()
(let ((x 10))
(print x)))
Again: a function does not provide a scope for variables, such that assigning a variable inside a function will automagically define it to be function-local. Use LET instead.
Note also that LET is syntactic sugar, mostly: (let ((a 1) (b 2)) (+ a b)) is basically doing the same as ((lambda (a b) (+ a b)) 1 2). It's just a simple function application written differently to improve it for the human reader.
There is also support in Common Lisp for an older syntax:
(defun foo (&aux (x 10))
(print x))
Above defines a local variable X, just like a LET would do.
I'll keep it short and simple:
1) what is really going on with setf, defvar and let?
defvar and defparameter are used to declare and set globally special variables. They only differ when the name is already bound.
setf is used for assignment (to special variables, lexical variables, and other – possibly custom – setfable places.)
let (and let*) creates new variable bindings that are visible inside its body. It may create either lexical or special bindings, depending on (global or local) declarations. If there are no special declarations, lexical bindings will be created.
2) is there a way to get common lisp to scope the variables inside a
function as in the python example?
Put the code inside let's body, where the binding is visible:
CL-USER> (defun baz ()
(let ((z 10))
(print z)
(incf z 10) ; i.e. (setf z (+ z 10))
(print z)))
BAZ
CL-USER> (baz)
10
20
20
CL-USER> z
; Evaluation aborted on #<UNBOUND-VARIABLE #x186C611E>.