12.2 Constructor Functions of DataStream
A stream is created by functions stream which come with different argument
types.
There is, however, also a constructor called new which creates an uninitialized
stream. A new() stream should never be asked for elements. That function is mainly
provided to allow recursive definitions of structures like in the following code.
-
-
T ==> Integer;
S ==> DataStream T;
import from T, S;
(x: S) + (y: S): S == stream(a+b for a in x for b in y);
(x: S) * (y: S): S == {
local times(n: I): T == {
t: T := 0;
for k in 0..n | not zero?(xk := x.k) repeat {
t := t + xk * y.(n-k);
}
t;
}
stream(times n for n: I in 0..);
}
s: DataStream T := new();
1: S := stream(generator [1, 0]);
x: S := stream(generator [0, 1, 0]);
set!(s, generator(1 + x * s * s));
l1: List Integer := [1,1,2*2,5*6,14*24,42*120];
l2: List Integer := [i for i in l1 for t in s];
Note that the the two lists at the end appear to be equal. See also test case
testStream10.
Export of DataStream
stream: T -> %
Usage
T == Integer;
t: T := 7;
s: DataStream T := stream(t);
a: MachineInteger := #s;
s.1 := 0;
b: MachineInteger := #s;
Description
Construct a constant stream.
This function constructs a stream that for each i gives si = t. In the example code
above we get (7,7,7,7,…) which would become (7,0,7,7,…) after the last
assignment.
The values of a and b are 1 and 3 respectively.
392b⟨implementation: DataStream 392b⟩≡ (386) 394b ⊳
stream(t: T): % == {
g: Generator T == generate yield t;
per [g, [t], 1, 1, true];
}
Uses Generator 617.
Export of DataStream
stream: Generator T -> %
Usage
T == Integer;
g: Generator T := generator [2,4,6,7];
s: DataStream T := stream g;
Parameters
-
g: Generator Integer
-
A (finite or infinite) generator that computes the next values of the
stream.
Description
Construct a stream.
The function constructs the stream
 |
(169)
|
or (informally) the infinite array
where
gi is the
i-th element generated by the generator
g.
In case the generator g is finite and generates n elements then the result is
 |
(170)
|
Remarks
It is allowed to call stream with a generator that does not generate any element,
but the resulting stream may not be ask to reveal any of its entries, since
there are none. It is basically the same to say stream(generate) and
new().
Export of DataStream
stream: (Generator T, T) -> %
Usage
g: Generator Integer := generator [2,4,6,7];
c: Integer := 3;
s: DataStream Integer := stream(g, c);
Description
Construct a stream.
stream(g, c) is an abbreviation for
-
-
stream(generate {for t in g repeat yield t; yield c});
395b⟨implementation: DataStream 392b⟩+
≡ (386) ⊲394b 397 ⊳
stream(g: Generator T, c: T): % == {
stream(generate {for t in g repeat yield t; yield c});
}
Uses Generator 617.
Export of DataStream
stream: ((MachineInteger, %) -> T) -> %
Usage
macro T == Integer;
h(n: I, s: DataStream T): T == {
n < 2 => 1;
s(n-1) + s(n-2);
}
s: DataStream Integer := stream(h);
Description
Construct a stream.
The function h that is given as a parameter is assumed to compute the n-th value of
the stream depending on some or all previous entries of the stream. Thus,
s:=stream(h) can be seen as encoding for every n
 |
(171)
|
Remarks
If h(n,s) is called, it is only assured that the stream is initialized for the values
s0,…,sn−1. h(n,s) may not access sk for k ≥ n.
397⟨implementation: DataStream 392b⟩+
≡ (386) ⊲395b 398b ⊳
stream(f: (I, %) -> T): % == {
s: % := new();
set!(s, generate for n in 0.. repeat yield f(n, s));
s;
}
Uses I 47.
Export of DataStream
new: () -> %
Usage
Give an recursion example!
Description
Construct an uninitialized stream.
new() is an abbreviation for stream(generator empty$List(T)).
398b⟨implementation: DataStream 392b⟩+
≡ (386) ⊲397 401b ⊳
--local emptyList: List T == [];
new(): % == {import from List T; stream generator empty}