Parse a Boolean region expression into bitmasks

Translates an expression like `"A & B + !C"` into a sorted integer vector of region bitmasks (each `1..2^n_sets - 1`). The output is intended for composition with [render_venn_svg()] (`highlight = ...`) and with the region-accessor family in user code.

Usage

parse_region_expression(expr, n_sets)

Arguments

expr

Character scalar; a Boolean expression in the grammar above.

n_sets

Integer; number of sets in the diagram (2..9).

Value

Sorted integer vector of region bitmasks. Empty integer vector when the expression is satisfiable by no region (e.g. `"A & ~A"`).

Details

Grammar:

• `A`, `B`, ..., `I` — set atoms (uppercase ASCII).

• `&` — intersection.

• `|` or `+` — union.

• `~` or `!` — complement (unary, against `1..2^n_sets - 1`).

• `(`, `)` — grouping.

Precedence (highest first): `~ !`, `&`, `| +`. Binary operators are left-associative.

Examples

parse_region_expression("A & B", n_sets = 3L)        # c(3L, 7L)
#> [1] 3 7
parse_region_expression("A + B", n_sets = 3L)        # c(1, 2, 3, 5, 6, 7)
#> [1] 1 2 3 5 6 7
parse_region_expression("A & ~B", n_sets = 3L)       # c(1L, 5L)
#> [1] 1 5
parse_region_expression("(A | B) & C", n_sets = 3L)  # c(5L, 6L, 7L)
#> [1] 5 6 7