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Estimated hours taken: 2 The following change was made by Peter Moulder <pmoulder@csse.monash.edu.au>. extras/quickcheck/tutes/*.html: Many HTML fixes. (Previously there were enough problems that it made more sense to read them as plain text files than with a web browser.) The files now pass through weblint (cleanly) and tidy (only `table lacks "summary" attribute' warnings remain). A small number of textual changes, and also a couple of <!-- XXX ... --> comments where I suspect the text should be changed.
214 lines
6.5 KiB
HTML
214 lines
6.5 KiB
HTML
<!DOCTYPE html PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN">
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<html>
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<head>
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<title>QuickCheck</title>
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</head>
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<body>
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<p>
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Files :
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<a href="use51.m">use51.m</a>
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<br>
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<a href="index.html">Back to main</a>
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<H1> QuickCheck Tutorial 5 </H1>
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<h2> Generators - Basic </h2>
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<p>
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The invariant function is of the form
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<pre>
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:- func Invariant_Function_X(T, T1, T2 ...) = property
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:- mode Invariant_Function_X(in, in, in ...) = out.
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</pre>
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Quickcheck generates random values for each input argument at run time.
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The following types have default generators:
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<ul>
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<li> int
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<li> char
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<li> float
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<li> string
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<li> some functions (more detail in Tutorial 8)
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<li> any type defined as a discriminated union, provided
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that all types in the body of the definition have
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default/custom generators
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<li> any type defined as being equivalent to a type with a
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default/custom generator
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</ul>
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<p>
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There is no code written to handle equivalent types. But it works
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as if the compiler replaced all the equivalent types with their real type
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before compiling.
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<p>
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The default generator for int is rand_int/2, which has distribution:
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<table>
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<tr>
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<td> 50%
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<td> even distribution in the range [-100, 100]
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<tr>
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<td> 50%
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<td> even distribution in the range (-2^31, 2^31)
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<br>(This will probably change to [int__min_int, int__max_int] in
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a future version.)
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</table>
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<table border=0 width="100%" bgcolor="#eeeee0"><tr><td><pre>
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:- func rand_int(rnd, rnd) = int.
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:- mode rand_int(in, out) = out is det.
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rand_int(BS0, BS) = Int :-
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Temp = rand_allint(BS0, BS1) rem 2,
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(if Temp = 0
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then
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irange(-100, 100, Int, BS1, BS)
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else
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Int = rand_allint(BS1, BS)
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).
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:- func rand_allint(rnd, rnd) = int.
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:- mode rand_allint(in, out) = out is det.
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rand_allint(BS0, BS) = Int :-
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next(1, Sign, BS0, BS1),
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next(31, TempInt, BS1, BS),
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( Sign > 0 ->
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Int = TempInt
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;
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Int = -TempInt
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).
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</pre></tr></table>
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Default for char is rand_char/2, with even spread over
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char__to_int(Char, X) where X is (-1000, 1000).
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<!-- Maybe insert `∩ {I : some[C] char__to_int(C, I)}' or English comment. -->
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<table border=0 width="100%" bgcolor="#eeeee0"><tr><td><pre>
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:- func rand_char(rnd, rnd) = char.
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:- mode rand_char(in, out) = out is det.
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rand_char(RS0, RS) = Char :-
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Int = rand_allint(RS0, RS1) rem 1000,
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(if char__to_int(Char0, Int)
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then
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Char = Char0,
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RS = RS1
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else
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Char = rand_char(RS1, RS)
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).
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</pre></tr></table>
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Default for float is rand_float/2, which has roughly even
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distribution over all discrete values for a 32-bit float.
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If machine is less then 32bits, overfloat occurs. It should still
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cover all possible values, but may alter distribution.
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If machine is more than 32bits, rand_float/2 will miss some values
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but retains even distribution.
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<table border=0 width="100%" bgcolor="#eeeee0"><tr><td><pre>
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:- func rand_float(rnd, rnd) = float.
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:- mode rand_float(in, out) = out is det.
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rand_float(BS0, BS) = Flt :-
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next(31, Mant0, BS0, BS1),
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next(1, Sign, BS1, BS2),
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( Sign > 0 ->
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Mant = Mant0
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;
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Mant = -Mant0
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),
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next(7, Exp, BS2, BS3),
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next(1, ExpSign, BS3, BS),
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Flt0 = float(Mant) * pow(2.0, Exp),
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( ExpSign > 0, Flt0 \= 0.0 ->
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Flt = 1.0/Flt0
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;
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Flt = Flt0
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).
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</pre></tr></table>
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Default for string is rand_string/2, each element is generated by
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rand_char/2.
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<table summary="The probability of the string having length i is 0.9^i * 0.1.">
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<tr>
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<td>0.9^0 * 0.1
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<td>chance being string length == 0
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<tr>
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<td>0.9^1 * 0.1
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<td>chance being string length == 1
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<tr>
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<td>0.9^2 * 0.1
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<td>chance being string length == 2
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<tr>
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<td>...etc...
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</table>
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So the mean string length is Sum(0.1* 0.9^N * N) where N ← {0, infinity},
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which converges to 9.
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<table border=0 width="100%" bgcolor="#eeeee0"><tr><td><pre>
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:- func rand_string(rnd, rnd) = string.
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:- mode rand_string(in, out) = out is det.
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rand_string(RS0, RS) = X :-
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gen(Charlist, [], [ {type_of(['A']), [{10,[]},{90,[]}]} ],
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[], RS0, RS),
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string__from_char_list(Charlist,X).
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</pre></tr></table>
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Note that the default generator for stirng actually uses the default generator
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for discriminated union (indirectly).
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<p>
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use51.m gives an illustration of generating int, char, float, string.
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<table border=0 width="100%" bgcolor="#eeeee0"><tr><td><pre>
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:- module use51.
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:- interface.
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:- type marks == int.
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:- use_module io.
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:- pred main(io__state, io__state).
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:- mode main(di, uo) is det.
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%---------------------------------------------------------------------------%
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:- implementation.
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:- import_module int, char, float, string, list.
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:- import_module qcheck.
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%---------------------------------------------------------------------------%
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main -->
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qcheck(qcheck__f(junk), "just to show the inputs", 5, [], []).
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:- func junk(marks, char, float, string) = property.
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junk(A, B, C, D) =
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{A,B,C,D} `>>>` [yes].
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</pre></tr></table>
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There are a few thing to note about use51.m :
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<pre>
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qcheck(qcheck__f(junk), "just to show the inputs", 5, [], []).
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</pre>
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The 3rd argument is an int, which specifies how many times to run. In this
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example 5 tests are run , but the default is 100. The other auguments will
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be described later.
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<pre>
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junk(A, B, C, D) =
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{A,B,C,D} `>>>` [yes].
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</pre>
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the invariant function doesn't do any testing, it always succeeds. But
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`>>>` collects all the inputs.
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A Sample output
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<pre>
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Test Description : just to show the inputs
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Number of test cases that succeeded : 5
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Number of trivial tests : 0
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Number of tests cases which failed the pre-condition : 0
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Distributions of selected argument(s) :
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1 {-50, '4', -3.55475907854864e+25, "\241r\371~~\316\002LJ~\204\246"}
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1 {27, '\342', -311727734390784., "\377g.\001"}
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1 {1389908257, '8', 2.63071847153664e+15, "\342"}
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1 {-90973704, '<', -2.10559053720692e-22, ""}
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1 {-896549770, 's', 7.72155851221736e+30, "[\230m\304\2561\254Q"}
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</pre>
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The char and string output doesn't look pretty, since most are not printable,
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eg: \342, \254
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</body>
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</html>
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