### Maps
[ Type maps Funcon map Funcon map-elements Funcon map-lookup Alias lookup Funcon map-domain Alias dom Funcon map-override Funcon map-unite Funcon map-delete ] Meta-variables GT <: ground-values T? <: values? Built-in Type maps(GT, T?)
*/ Built-in Funcon map(_:(tuples(GT, T?))*) : =>(maps(GT, T?))?
/* `map(tuple(K1, V1?), ..., tuple(Kn, Vn?))` constructs a map from
`K1` to `V1?`, ..., `Kn` to `Vn?`, provided that `K1`, ..., `Kn`
are distinct, otherwise the result is `( )`.
Note that `map(...)` is not a constructor operation.
The built-in notation `{K1|->V1?, ..., Kn|->Vn?}` is equivalent to
`map(tuple(K1, V1?), ..., tuple(Kn, Vn?))`. Note however that in general,
maps cannot be identified with sets of tuples, since the values `Vi?` are
not restricted to `ground-values`.
When ``T? <: types``, ``maps(GT, T?) <: types``. The type `MT:maps(GT, T?)`
represents the set of value-maps `MV:maps(GT, values?)` such that
`dom(MV)` is a subset of `dom(MT)` and for all `K` in `dom(MV)`,
``map-lookup(MV, K) : map-lookup(MT, K)``.
*/ Built-in Funcon map-elements(_:maps(GT, T?)) : =>(tuples(GT, T?))*
/* The sequence of tuples `(tuple(K1, V1?), ..., tuple(Kn, Vn?))` given by
`map-elements(M)` contains each mapped value `Ki` just once. The order of
the elements is unspecified, and may vary between maps.
*/
Assertmap(map-elements(M)) == M
Built-in Funcon map-lookup(_:maps(GT, T?), K:GT) : =>(T?)? Alias lookup = map-lookup
/* `map-lookup(M,K)` gives the optional value to which `K` is mapped by `M`,
if any, and otherwise `( )`.
*/ Built-in Funcon map-domain(_:maps(GT, T?)) : =>sets(GT) Alias dom = map-domain
/* `map-domain(M)` gives the set of values mapped by `M`.
`map-lookup(M, K)` is always `( )` when `K` is not in `map-domain(M)`.
*/ Built-in Funcon map-override(_:(maps(GT, T?))*) : =>maps(GT,T?)
/* `map-override(...)` takes a sequence of maps. It returns the map whose
domain is the union of their domains, and which maps each of those values
to the same optional value as the first map in the sequence in whose domain
it occurs
.
When the domains of the `M*` are disjoint, `map-override(M*)` is equivalent
to `map-unite(M*)`.
*/ Built-in Funcon map-unite(_:(maps(GT, T?))*) : =>(maps(GT, T?))?
/* `map-unite(...)` takes a sequence of maps. It returns the map whose
domain is the union of their domains, and which maps each of those values
to the same optional value as the map in the sequence in whose domain it occurs,
provided that those domains are disjoint - otherwise the result is `( )`.
*/ Built-in Funcon map-delete(_:maps(GT, T?), _:sets(GT)) : =>maps(GT, T?)
/* `map-delete(M, S)` takes a map `M` and a set of values `S`, and returns the
map obtained from `M` by removing `S` from its domain.
*/
Assertmap-domain(map-delete(M, S)) == set-difference(map-domain(M), S)
/*`maps(GT, T?)` is the type of possibly-empty finite maps from values of type `GT` to optional values of type `T?`.