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39 votes

Why colon to denote that a value belongs to a type?

The main reason to prefer the colon notation $t : T$ to the membership relation $t \in T$ is that the membership relation can be misleading because types are not (just) collections. [Supplemental: I ...
Andrej Bauer's user avatar
  • 29.2k
14 votes
Accepted

Why colon to denote that a value belongs to a type?

Because what's on the right of the colon isn't necessarily a set and what's on the left of the colon isn't necessarily a member of that set. Type theory started out in the early 20th century as an ...
Gilles 'SO- stop being evil''s user avatar
5 votes

Why colon to denote that a value belongs to a type?

Björn, There's probably an earlier reference but for one thing, the colon was used in the Pascal programming language:
Bjørn Kjos-Hanssen's user avatar
4 votes

What are the widely used notations for quickly referring to a single component of a multi-component object?

Papers I've seen that have this issue often present 1 as the initial definition and then also define 2 (or 3 with subscripts) as an additional definition that is used when necessary for clarity. A ...
Aaron Rotenberg's user avatar
4 votes

notation in graph theory

By ChatGPT: In the notation E[|S|], the expression |S| denotes the cardinality or the number of elements in the set S. So, E[|S|] means the expected value of the number of elements in the set S. On ...
domotorp's user avatar
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3 votes
Accepted

What does x.y notation mean?

This is the notation for Harper's "abstract binding structures": x.t represents the binding site of a variable x and ...
gasche's user avatar
  • 2,040

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