# Substitutions¶

With the notion of Substitutions,
the Model Exchange Format [MEF] provides a general way to express
Delete Terms, Recovery Rules, and Exchange Events.
As noted in the MEF specification,
*non-declarative* substitutions (e.g., Exchange Events) should be avoided
or replaced with event-tree instructions if possible.
Moreover, the *non-declarative* substitutions come with extra performance penalty
since this approach forces set manipulations at post-analysis
and may require analysis re-evaluation
(e.g., the application of truncations at analysis time may become corrupted).

Note

Non-declarative substitutions are applied only to minimal cut sets (i.e., no exact-probability BDD or prime implicants).

## Validation¶

Hypothesis and source events must be unique (no duplicates allowed).

Hypothesis formulas must be built-over basic events only (e.g., no gates or nested formulas).

Hypothesis formulas must be coherent.

If a substitution is non-declarative (i.e., the source is not empty), its hypothesis can only be defined with OR/AND/NULL connectives.

The optional “traditional” type is helpful and declared for validation purposes only. The validity error is detected if the declared type does not match the deduced one.

If a declarative substitution (i.e., empty source) has constant target

`true`

, the substitution has no effect and is considered invalid.If a non-declarative substitution has constant target

`false`

, the substitution is malformed since the source set is irrelevant (it should have been declarative delete-terms).Non-declarative substitution hypothesis, source, and target events cannot be in CCF groups.

Since the order of

*non-declarative*substitutions is unspecified, the application of*all*substitutions must be idempotent regardless of their order (i.e., the composition of substitutions must be commutative). The following requirements apply only to*non-declarative*substitutions:- No target event can be a source event of any substitution.
- No target or source event can be an argument of another substitution hypothesis.