Clines, dexes, merges, and fuses¶
A “cline” is based on a total ordering on values in its domain, or in other words a binary relation that is reflexive, transitive, and antisymmetric. Its antisymmetry is as fine-grained as possible: If any two values in a cline’s domain are related by that cline in both directions, there will be no Cene code at all that can distinguish the two values.
However, a cline does not merely expose this total ordering. Within the cline’s domain, there may be equivalence classes of values for which every two nonequal values will not have their relative order exposed to Cene code. When Cene code uses call-cline to compare two values by a cline, it can get several results:
(nil): The values are not both in the domain.
(yep (yep (nil))): The first value candidly precedes the second.
(yep <encapsulated value>): The first value secretly precedes the second.
(yep <encapsulated value>): The first value secretly follows the second.
(yep (nope (nil))): The first value candidly follows the second.
The “secretly precedes” and “secretly follows” cases are indistinguishable to Cene code.
A “dex” is like a cline, but it never results in the “candidly precedes” and “candidly follows” cases. Thus, a dex is useful as a kind of equality test.
A “merge” is a binary operation that is commutative, associative, and idempotent for values in its domain.
A “fuse” is a binary operation that is commutative and associative for values in its domain.
dex-cline¶
Call with (ignored)
Todo
Document this.
This can distinguish between values that might not have been distinguishable any other way. For instance, it can distinguish between (cline-default (cline-give-up) a) and a.
cline-by-dex¶
Call with dex
Todo
Document this.
cline-give-up¶
Call with (ignored)
Todo
Document this.
cline-default¶
Call with cline-for-trying-first cline-for-trying-second
Given two clines, returns a cline over the union of their domains. The resulting cline’s ascending order consists of the first cline’s ascending order in its domain, followed by the second cline’s ascending order outside the first cline’s domain.
cline-by-own-method¶
Call with dexable-get-method
Given a dexable function, returns a cline that works by invoking that function with each value to get (yep <cline>) or (nil), verifying that the two <cline> values are the same, and then proceeding to invoke that value.
cline-fix¶
Call with dexable-unwrap
Given a dexable function, returns a cline that works by passing itself to the function and then invoking the resulting cline.
call-cline¶
Call with cline a b
Todo
Document this.
in-cline¶
Call with cline x
Todo
Document this.
dexable¶
Construct with dex val
A value tagged with a dex that applies to it.
dex-dex¶
Call with (ignored)
Todo
Document this.
This can distinguish between values that might not have been distinguishable any other way. For instance, it can distinguish between (dex-by-cline (cline-by-dex a)) and a.
dex-by-cline¶
Call with cline
Todo
Document this.
name-of¶
Call with dexable
Todo
Document this.
dex-name¶
Call with (ignored)
Returns a dex that applies to any name. Names are encapsulated values that are good for nothing but comparing using this dex. They are usually obtained by calling procure-name on a namespace.
dex-merge¶
Call with (ignored)
Todo
Document this.
This can distinguish between values that might not have been distinguishable any other way. For instance, it can distinguish between (merge-default a b) and (merge-default b a).
merge-by-dex¶
Call with dex
Todo
Document this.
This only processes the dex operation once, calling it with the two values being merged. It doesn’t sanity-check that the dex is reflexive for either argument.
merge-default¶
Call with merge-for-trying-first merge-for-trying-second
Todo
Document this.
merge-by-own-method¶
Call with dexable-get-method
Given a dexable function, returns a merge that works by invoking that function with each value to get (yep <merge>) or (nil), verifying that the two <merge> values are the same, invoking that value, and invoking the function on the result again to make sure it yields the same <merge>. That final check makes sure this operation is associative.
merge-fix¶
Call with dexable-unwrap
Given a dexable function, returns a merge that works by passing itself to the function and then invoking the resulting merge.
call-merge¶
Call with merge a b
Todo
Document this.
dex-fuse¶
Call with (ignored)
Todo
Document this.
This can distinguish between values that might not have been distinguishable any other way. For instance, it can distinguish between (fuse-default a b) and (fuse-default b a).
fuse-by-merge¶
Call with merge
Todo
Document this.
fuse-default¶
Call with fuse-for-trying-first fuse-for-trying-second
Todo
Document this.
fuse-by-own-method¶
Call with dexable-get-method
Given a dexable function, returns a fuse that works by invoking that function with each value to get (yep <fuse>) or (nil), verifying that the two <fuse> values are the same, invoking that value, and invoking the function on the result again to make sure it yields the same <fuse>. That final check makes sure this operation is associative.
fuse-fix¶
Call with dexable-unwrap
Given a dexable function, returns a fuse that works by passing itself to the function and then invoking the resulting fuse.
call-fuse¶
Call with fuse a b
Todo
Document this.