Content deleted Content added
Basic examples |
m uncategorized |
||
Line 3:
==Definition==
A ''partial applicative structure''{{r|van-oosten|p=1}} is simply a set <math>A</math> equipped with a [[partial function|partial]] binary operation <math>A \times A \rightharpoonup A</math>. In the context of realizability, this operation is usually denoted by simple juxtaposition, i.e., <math>(a, b) \mapsto a b</math>. It is usually ''not'' associative; by convention, the notation <math>a b c</math> associates to the left as <math>(a b) c</math>, matching the standard convention in [[λ-calculus]].
The ''terms''{{r|van-oosten|p=2}} (or ''expressions'') over a partial applicative structure <math>A</math> are defined inductively:
Line 68:
<ref name=van-oosten>{{ cite book | title = Realizability: an introduction to its categorical side | author = Jaap van Oosten | isbn = 9780444515841 | year = 2008 | publisher = Elsevier Science | pages = 328 }}</ref>
</references>
{{mathlogic-stub}}
{{uncategorized|date=February 2025}}
| |||