Glossary of primitives

Types

typically specified via the collection of values of the type; for instance, the type natural is introduced in terms of the collection {naturals}. This exploits the special handling I give to types in my specification for denotations of formulaic collections delimited with { and }.

{relations}

A relation is a formal description of a predicate involving two unresolved names (i.e. a two-name relationship), canonically left and right. If (denotations for) values x and y are substituted in place of the two names, x in place of left and y in place of right, the predicate becomes a statement: if this statement is true, we say that the relation (describing the predicate) relates x to y, otherwise not.

In so far as a relation, r, relates some value, x, to some value, y, I describe x as a left value of r and y as a right value of r.

Example: left is an ancestor of right is a predicate of the canonical form; if I am substituted for right and one of my (living) ancestors is substituted for left, the statement is true; so the associated relation relates each of my (living) ancestors to me. Everyone (except Adam and Eve) is a right value of this relation: every parent is a left value of it.

{collections}

= {relation r: r relates x to y implies x = y}

A collection is a relation subsumed by the universal identity (: x←x :), i.e. a relation which relates x to y only if x and y are the same value (and typically subject to some further restriction on this value). A collection is synonymous with (and encodes, as a relation) a predicate involving only one unresolved name (a one-name relationship). If C is a collection and relates x to x, then x is said to be in C (as a special case of a general reading of fixed points) and x is described as a member of C.

{mappings}

= {relation r: r relates x to z and y to z implies x = y}

Verbs

see also the bestiary, since quite a few of the names I've used for specific entities are, in fact, verbs.

relates

See {relations}, above. The template relation relates left to right matches a great many sub-texts of what I've written: in each, relation denotes a relation describing some two-name relationship, of which left and right denote a left value and a right value, respectively.

maps

See {mappings} above.

Other