Related
I would like to have an N long tuple as an optional argument of a function but I do not know how to provide a N long default value:
function create_grid(d::Int64, n::Tuple{Vararg{Int64, N}}; xmin::Tuple{Vararg{Float64, N}}) where N
I understand xmin should be declared with a default value such as xmin::Tuple{Vararg{Float64, N}}::0., but this is evidently wrong as it is defaulting to a Float instead of Tuple. How can I state I want a N long tuple as optional argument defaulting to (eg.) 0. for all the elements if the argument is not provided explicitly?
Here it is - you just provide the default as a one element tuple:
function somefun(d::Int64, n::Tuple{Vararg{Int64, N}}; xmin::Tuple{Vararg{Float64, N}}=(0.0,)) where N
println("d=$d n=$n xmin=$xmin")
end
To understand how it works just note that:
Tuple{Vararg{Int, 2}} == typeof((2,2))
#and
Tuple{Vararg{Int, 1}} == typeof((2,))
so you needed 1-element tuple as a default.
Let's test it:
julia> somefun(4,(4,))
d=4 n=(4,) xmin=(0.0,)
This works as expected.
Finally, note that providing a 2-element tuple as the second argument without the third one will throw an error because the sizes do not match:
julia> somefun(4,(4,5))
ERROR: MethodError: no method matching #somefun#1(::Tuple{Float64}, ::typeof(somefun), ::Int64, ::Tuple{Int64,Int64})
If you want to workaround this you need another constructor:
function somefun(d::Int64, n::Tuple{Vararg{Int64, N}}; xmin::Tuple{Vararg{Float64, N}}= tuple(zeros(length(n))...)) where N
println("d=$d n=$n xmin=$xmin")
end
Testing:
julia> somefun(4,(4,5))
d=4 n=(4, 5) xmin=(0.0, 0.0)
I'm studying Standard ML and one of the exercices I have to do is to write a function called opPairs that receives a list of tuples of type int, and returns a list with the sum of each pair.
Example:
input: opPairs [(1, 2), (3, 4)]
output: val it = [3, 7]
These were my attempts, which are not compiling:
ATTEMPT 1
type T0 = int * int;
fun opPairs ((h:TO)::t) = let val aux =(#1 h + #2 h) in
aux::(opPairs(t))
end;
The error message is:
Error: unbound type constructor: TO
Error: operator and operand don't agree [type mismatch]
operator domain: {1:'Y; 'Z}
operand: [E]
in expression:
(fn {1=1,...} => 1) h
ATTEMPT 2
fun opPairs2 l = map (fn x => #1 x + #2 x ) l;
The error message is: Error: unresolved flex record (need to know the names of ALL the fields
in this context)
type: {1:[+ ty], 2:[+ ty]; 'Z}
The first attempt has a typo: type T0 is defined, where 0 is zero, but then type TO is referenced in the pattern, where O is the letter O. This gets rid of the "operand and operator do not agree" error, but there is a further problem. The pattern ((h:T0)::t) does not match an empty list, so there is a "match nonexhaustive" warning with the corrected type identifier. This manifests as an exception when the function is used, because the code needs to match an empty list when it reaches the end of the input.
The second attempt needs to use a type for the tuples. This is because the tuple accessor #n needs to know the type of the tuple it accesses. To fix this problem, provide the type of the tuple argument to the anonymous function:
fun opPairs2 l = map (fn x:T0 => #1 x + #2 x) l;
But, really it is bad practice to use #1, #2, etc. to access tuple fields; use pattern matching instead. Here is a cleaner approach, more like the first attempt, but taking full advantage of pattern matching:
fun opPairs nil = nil
| opPairs ((a, b)::cs) = (a + b)::(opPairs cs);
Here, opPairs returns an empty list when the input is an empty list, otherwise pattern matching provides the field values a and b to be added and consed recursively onto the output. When the last tuple is reached, cs is the empty list, and opPairs cs is then also the empty list: the individual tuple sums are then consed onto this empty list to create the output list.
To extend on exnihilo's answer, once you have achieved familiarity with the type of solution that uses explicit recursion and pattern matching (opPairs ((a, b)::cs) = ...), you can begin to generalise the solution using list combinators:
val opPairs = map op+
I'm writing a genetic program in order to test the fitness of randomly generated expressions. Shown here is the function to generate the expression as well a the main function. DIV and GT are defined elsewhere in the code:
function create_single_full_tree(depth, fs, ts)
"""
Creates a single AST with full depth
Inputs
depth Current depth of tree. Initially called from main() with max depth
fs Function Set - Array of allowed functions
ts Terminal Set - Array of allowed terminal values
Output
Full AST of typeof()==Expr
"""
# If we are at the bottom
if depth == 1
# End of tree, return function with two terminal nodes
return Expr(:call, fs[rand(1:length(fs))], ts[rand(1:length(ts))], ts[rand(1:length(ts))])
else
# Not end of expression, recurively go back through and create functions for each new node
return Expr(:call, fs[rand(1:length(fs))], create_single_full_tree(depth-1, fs, ts), create_single_full_tree(depth-1, fs, ts))
end
end
function main()
"""
Main function
"""
# Define functional and terminal sets
fs = [:+, :-, :DIV, :GT]
ts = [:x, :v, -1]
# Create the tree
ast = create_single_full_tree(4, fs, ts)
#println(typeof(ast))
#println(ast)
#println(dump(ast))
x = 1
v = 1
eval(ast) # Error out unless x and v are globals
end
main()
I am generating a random expression based on certain allowed functions and variables. As seen in the code, the expression can only have symbols x and v, as well as the value -1. I will need to test the expression with a variety of x and v values; here I am just using x=1 and v=1 to test the code.
The expression is being returned correctly, however, eval() can only be used with global variables, so it will error out when run unless I declare x and v to be global (ERROR: LoadError: UndefVarError: x not defined). I would like to avoid globals if possible. Is there a better way to generate and evaluate these generated expressions with locally defined variables?
Here is an example for generating an (anonymous) function. The result of eval can be called as a function and your variable can be passed as parameters:
myfun = eval(Expr(:->,:x, Expr(:block, Expr(:call,:*,3,:x) )))
myfun(14)
# returns 42
The dump function is very useful to inspect the expression that the parsers has created. For two input arguments you would use a tuple for example as args[1]:
julia> dump(parse("(x,y) -> 3x + y"))
Expr
head: Symbol ->
args: Array{Any}((2,))
1: Expr
head: Symbol tuple
args: Array{Any}((2,))
1: Symbol x
2: Symbol y
typ: Any
2: Expr
[...]
Does this help?
In the Metaprogramming part of the Julia documentation, there is a sentence under the eval() and effects section which says
Every module has its own eval() function that evaluates expressions in its global scope.
Similarly, the REPL help ?eval will give you, on Julia 0.6.2, the following help:
Evaluate an expression in the given module and return the result. Every Module (except those defined with baremodule) has its own 1-argument definition of eval, which evaluates expressions in that module.
I assume, you are working in the Main module in your example. That's why you need to have the globals defined there. For your problem, you can use macros and interpolate the values of x and y directly inside the macro.
A minimal working example would be:
macro eval_line(a, b, x)
isa(a, Real) || (warn("$a is not a real number."); return :(throw(DomainError())))
isa(b, Real) || (warn("$b is not a real number."); return :(throw(DomainError())))
return :($a * $x + $b) # interpolate the variables
end
Here, #eval_line macro does the following:
Main> #macroexpand #eval_line(5, 6, 2)
:(5 * 2 + 6)
As you can see, the values of macro's arguments are interpolated inside the macro and the expression is given to the user accordingly. When the user does not behave,
Main> #macroexpand #eval_line([1,2,3], 7, 8)
WARNING: [1, 2, 3] is not a real number.
:((Main.throw)((Main.DomainError)()))
a user-friendly warning message is provided to the user at parse-time, and a DomainError is thrown at run-time.
Of course, you can do these things within your functions, again by interpolating the variables --- you do not need to use macros. However, what you would like to achieve in the end is to combine eval with the output of a function that returns Expr. This is what the macro functionality is for. Finally, you would simply call your macros with an # sign preceding the macro name:
Main> #eval_line(5, 6, 2)
16
Main> #eval_line([1,2,3], 7, 8)
WARNING: [1, 2, 3] is not a real number.
ERROR: DomainError:
Stacktrace:
[1] eval(::Module, ::Any) at ./boot.jl:235
EDIT 1. You can take this one step further, and create functions accordingly:
macro define_lines(linedefs)
for (name, a, b) in eval(linedefs)
ex = quote
function $(Symbol(name))(x) # interpolate name
return $a * x + $b # interpolate a and b here
end
end
eval(ex) # evaluate the function definition expression in the module
end
end
Then, you can call this macro to create different line definitions in the form of functions to be called later on:
#define_lines([
("identity_line", 1, 0);
("null_line", 0, 0);
("unit_shift", 0, 1)
])
identity_line(5) # returns 5
null_line(5) # returns 0
unit_shift(5) # returns 1
EDIT 2. You can, I guess, achieve what you would like to achieve by using a macro similar to that below:
macro random_oper(depth, fs, ts)
operations = eval(fs)
oper = operations[rand(1:length(operations))]
terminals = eval(ts)
ts = terminals[rand(1:length(terminals), 2)]
ex = :($oper($ts...))
for d in 2:depth
oper = operations[rand(1:length(operations))]
t = terminals[rand(1:length(terminals))]
ex = :($oper($ex, $t))
end
return ex
end
which will give the following, for instance:
Main> #macroexpand #random_oper(1, [+, -, /], [1,2,3])
:((-)([3, 3]...))
Main> #macroexpand #random_oper(2, [+, -, /], [1,2,3])
:((+)((-)([2, 3]...), 3))
Thanks Arda for the thorough response! This helped, but part of me thinks there may be a better way to do this as it seems too roundabout. Since I am writing a genetic program, I will need to create 500 of these ASTs, all with random functions and terminals from a set of allowed functions and terminals (fs and ts in the code). I will also need to test each function with 20 different values of x and v.
In order to accomplish this with the information you have given, I have come up with the following macro:
macro create_function(defs)
for name in eval(defs)
ex = quote
function $(Symbol(name))(x,v)
fs = [:+, :-, :DIV, :GT]
ts = [x,v,-1]
return create_single_full_tree(4, fs, ts)
end
end
eval(ex)
end
end
I can then supply a list of 500 random function names in my main() function, such as ["func1, func2, func3,.....". Which I can eval with any x and v values in my main function. This has solved my issue, however, this seems to be a very roundabout way of doing this, and may make it difficult to evolve each AST with each iteration.
I'm trying to convert the following to pointfree style: a function that partially applies a value to the transformer function add before passing in the collection to be iterated over. (Using Ramda.js)
R.compose(
R.map,
R.add
)(1, [1,2,3])
The problem is that R.add is arity 2, as is R.map. I want the application order to be as follows:
add(1)
map(add(1))
map(add(1), [1,2,3])
[add(1,1), add(1,2), add(1,3)]
But what happens instead is this:
add(1, [1,2,3])
map(add(1, [1,2,3]))
<partially applied map, waiting for collection>
Anyone know of a way to specify this behavior?
A plain compose or pipe won't do this because either will absorb all the arguments supplied into the first function. Ramda includes two additional functions that help with this, converge and useWith. In this case useWith is the one that will help:
useWith(map, [add, identity])(1, [1, 2, 3]); //=> [2, 3, 4]
While identity is not absolutely required here, it gives the generated function the correct arity.
Figured it out. If anyone's curious, here's the gist. (You can try it in the console on RamdaJS.com.)
0) For a baseline, here's the pointed version.
func0 = x => R.map(R.add(x))
addOne = func0(1)
addOne([1,2,3]) // [2,3,4]
1) Here's the pointfree core, but it has the ordering problem from the question above.
func1 = R.compose(R.map, R.add)
addOne = func1(1)
addOne([1,2,3]) // [2,3,4])
func1(1, [1,2,3]) // function
2) If the composition is unary (arity 1) 2 invocations are needed apply all params.
func2 = R.unary(R.compose(R.map, R.add))
addOne = func2(1)
addOne([1,2,3]) // [2,3,4])
3) We want one invocation to apply both params, so we uncurry 2.
func3 = R.uncurryN(2, func2)
func3(1, [1,2,3]) // [2,3,4])
4) To prove func2 is composable, let's double the results.
func4 = R.compose(
R.map(R.multiply(2)),
R.uncurryN(2, func2)
)
func4(1, [1,2,3]) // [4,6,8])
5) Substitution gives us a completely pointfree function.
func5 = R.compose(
R.map(R.multiply(2)),
R.uncurryN(2, R.unary(R.compose(
R.map,
R.add
)))
)
func5(1, [1,2,3]) // [4,6,8])
I find functools.partial to be extremely useful, but I would like to be able to freeze arguments out of order (the argument you want to freeze is not always the first one) and I'd like to be able to apply it to several methods on a class at once, to make a proxy object that has the same methods as the underlying object except with some of its methods parameters being frozen (think of it as generalizing partial to apply to classes). And I'd prefer to do this without editing the original object, just like partial doesn't change its original function.
I've managed to scrap together a version of functools.partial called 'bind' that lets me specify parameters out of order by passing them by keyword argument. That part works:
>>> def foo(x, y):
... print x, y
...
>>> bar = bind(foo, y=3)
>>> bar(2)
2 3
But my proxy class does not work, and I'm not sure why:
>>> class Foo(object):
... def bar(self, x, y):
... print x, y
...
>>> a = Foo()
>>> b = PureProxy(a, bar=bind(Foo.bar, y=3))
>>> b.bar(2)
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: bar() takes exactly 3 arguments (2 given)
I'm probably doing this all sorts of wrong because I'm just going by what I've pieced together from random documentation, blogs, and running dir() on all the pieces. Suggestions both on how to make this work and better ways to implement it would be appreciated ;) One detail I'm unsure about is how this should all interact with descriptors. Code follows.
from types import MethodType
class PureProxy(object):
def __init__(self, underlying, **substitutions):
self.underlying = underlying
for name in substitutions:
subst_attr = substitutions[name]
if hasattr(subst_attr, "underlying"):
setattr(self, name, MethodType(subst_attr, self, PureProxy))
def __getattribute__(self, name):
return getattr(object.__getattribute__(self, "underlying"), name)
def bind(f, *args, **kwargs):
""" Lets you freeze arguments of a function be certain values. Unlike
functools.partial, you can freeze arguments by name, which has the bonus
of letting you freeze them out of order. args will be treated just like
partial, but kwargs will properly take into account if you are specifying
a regular argument by name. """
argspec = inspect.getargspec(f)
argdict = copy(kwargs)
if hasattr(f, "im_func"):
f = f.im_func
args_idx = 0
for arg in argspec.args:
if args_idx >= len(args):
break
argdict[arg] = args[args_idx]
args_idx += 1
num_plugged = args_idx
def new_func(*inner_args, **inner_kwargs):
args_idx = 0
for arg in argspec.args[num_plugged:]:
if arg in argdict:
continue
if args_idx >= len(inner_args):
# We can't raise an error here because some remaining arguments
# may have been passed in by keyword.
break
argdict[arg] = inner_args[args_idx]
args_idx += 1
f(**dict(argdict, **inner_kwargs))
new_func.underlying = f
return new_func
Update: In case anyone can benefit, here's the final implementation I went with:
from types import MethodType
class PureProxy(object):
""" Intended usage:
>>> class Foo(object):
... def bar(self, x, y):
... print x, y
...
>>> a = Foo()
>>> b = PureProxy(a, bar=FreezeArgs(y=3))
>>> b.bar(1)
1 3
"""
def __init__(self, underlying, **substitutions):
self.underlying = underlying
for name in substitutions:
subst_attr = substitutions[name]
if isinstance(subst_attr, FreezeArgs):
underlying_func = getattr(underlying, name)
new_method_func = bind(underlying_func, *subst_attr.args, **subst_attr.kwargs)
setattr(self, name, MethodType(new_method_func, self, PureProxy))
def __getattr__(self, name):
return getattr(self.underlying, name)
class FreezeArgs(object):
def __init__(self, *args, **kwargs):
self.args = args
self.kwargs = kwargs
def bind(f, *args, **kwargs):
""" Lets you freeze arguments of a function be certain values. Unlike
functools.partial, you can freeze arguments by name, which has the bonus
of letting you freeze them out of order. args will be treated just like
partial, but kwargs will properly take into account if you are specifying
a regular argument by name. """
argspec = inspect.getargspec(f)
argdict = copy(kwargs)
if hasattr(f, "im_func"):
f = f.im_func
args_idx = 0
for arg in argspec.args:
if args_idx >= len(args):
break
argdict[arg] = args[args_idx]
args_idx += 1
num_plugged = args_idx
def new_func(*inner_args, **inner_kwargs):
args_idx = 0
for arg in argspec.args[num_plugged:]:
if arg in argdict:
continue
if args_idx >= len(inner_args):
# We can't raise an error here because some remaining arguments
# may have been passed in by keyword.
break
argdict[arg] = inner_args[args_idx]
args_idx += 1
f(**dict(argdict, **inner_kwargs))
return new_func
You're "binding too deep": change def __getattribute__(self, name): to def __getattr__(self, name): in class PureProxy. __getattribute__ intercepts every attribute access and so bypasses everything that you've set with setattr(self, name, ... making those setattr bereft of any effect, which obviously's not what you want; __getattr__ is called only for access to attributes not otherwise defined so those setattr calls become "operative" & useful.
In the body of that override, you can and should also change object.__getattribute__(self, "underlying") to self.underlying (since you're not overriding __getattribute__ any more). There are other changes I'd suggest (enumerate in lieu of the low-level logic you're using for counters, etc) but they wouldn't change the semantics.
With the change I suggest, your sample code works (you'll have to keep testing with more subtle cases of course). BTW, the way I debugged this was simply to stick in print statements in the appropriate places (a jurassic=era approach but still my favorite;-).