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  • Circuits

Boolean-assert-all

Formalization and verification of a circuit for asserting that zero or more field elements are booleans (i.e. 0 or 1).

This is a family of PFCS relations of the form

boolean_assert_all_<n>(x_0, ..., x_<n-1>) := {
     boolean_assert(x_0),
     ...
     boolean_assert(x_<n-1>)
     }

where <n> is a natural number that parameterizes the relation. This relation calls boolean-assert on each parameter.

Currently our PFCS library does not provide a concrete syntax for parameterized PFCS relations. So we construct PFCS abstract syntax, which we lift ``manually'' (not via the lifter). Proofs of correctness are by induction, and cover all the infinitely many members of the family.

Subtopics

Boolean-assert-all-lifting
Lifting of the circuit to a predicate.
Boolean-assert-all-circuit
Construction of the circuit.
Boolean-assert-all-circuit-body
Construct the defining body of the PFCS relation.
Boolean-assert-all-spec
Specification of the circuit.
Boolean-assert-all-correctness
Correctness of the circuit.