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Document some predicates in reif #2981

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Document some predicates in reif #2981

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b172413
Document some predicates in reif
rotu Jun 16, 2025
cddec6f
Maybe less operationalizing language?
rotu Jun 16, 2025
bb8171d
Better wording?
rotu Jun 16, 2025
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32 changes: 32 additions & 0 deletions src/lib/reif.pl
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Original file line number Diff line number Diff line change
@@ -1,5 +1,12 @@
/** Predicates from [*Indexing dif/2*](https://arxiv.org/abs/1607.01590).

The core trick that, unlike the traditional conditional `A -> B ; C`,
the branching condition is *not* provided as a complete goal.

Rather, the branching condition is a "reified goal",
i.e. a term which is completed with an additional argument `T`,
representing its satisfaction (`T = true`) and refutation (`T = false`).

Example:

```
Expand All @@ -19,6 +26,15 @@

:- meta_predicate(if_(1, 0, 0)).

%% if_(Cond_1, IfTrue, IfFalse).
% Monotonic if-then-else construct.
%
% Unlike `Cond_0 -> IfTrue; IfFalse`, this is nondeterministic in the condition.
% `Cond` is expected to be a reified goal.
% e.g. `if_((A=1), _, _)`
% where the `=` above is NOT the `(=)/2` predicate, but rather the `(=)/3` predicate
% defined in this module.

if_(If_1, Then_0, Else_0) :-
call(If_1, T),
( T == true -> call(Then_0)
Expand All @@ -27,13 +43,29 @@
; throw(error(instantiation_error, _))
).

%% =(X, Y, T).
% Reified equality predicate.
%
% `=(X,Y,true)` succeeds if X, Y *could* unify
% `=(X,Y,false)` succeeds if X, Y *could* fail to unify
% Partially call as a branching condition in `if_/3`:
% `if_(A=B, IfTrue, IfFalse)`

=(X, Y, T) :-
( X == Y -> T = true
; X \= Y -> T = false
; T = true, X = Y
; T = false, dif(X, Y)
).

%% dif(X, Y, T).
% Reified disequality predicate.
%
% `dif(X,Y,true)` succeeds if X, Y *could* fail to unify
% `dif(X,Y,false)` succeeds if X, Y *could* unify
% Partially call as a branching condition in `if_/3`:
% `if_(dif(A,B), IfTrue, IfFalse)`

dif(X, Y, T) :-
=(X, Y, NT),
non(NT, T).
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