# 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:

1. No target event can be a source event of any substitution.
2. No target or source event can be an argument of another substitution hypothesis.