Logic, windows and occurrences

Logical, not bitwise operators#

P4:D(I<T&T)
P4:D(I<T|S<Z)
P4:D(!T)
P4:D(!(I<T))
P4:D((I<T|S<Z)&T)

Precedence is grouped/atomic conditions, NOT, AND, OR. Validate the entire syntax, features and windows first; then short-circuit valid conditions left to right. T|IN(1,5,I) is a window error on P4 even when T is present.

Commas, grouping and chains#

P4:D(I|T&S)
P4:D(I|T,S)
P4:D((I|T)&S)

A comma separates outer condition-list items. Use & and | inside a Boolean grouping. Commas in IN and advanced calls delimit their arguments. Do not conflate these contexts by textual replacement.

Per-kind counts and bare presence#

P4:D(T=1&S=0)
P4:D(T!=0)
P4:D(T<=0)
P4:D(T>=1)

= tests equality, never assignment. Counts are integers from 0 to 256 for one kind. TS=1 is not a group total and is rejected; T[2]=1 is also rejected because an occurrence is not a kind count. One standard 7-bag has no repeated kind; counts are also useful across bags and in custom multisets.

IN: inspect positions without resampling#

P7:D(IN(1,3,T))
P7:D(IN(2,5,I<T&T))
P7:D(IN(1,3,T)&IN(4,7,I))

IN(start,end,condition) uses inclusive one-based bounds. IN(2,2,T) tests position two. It does not change supply length, bags or correlations. Resampling P7:D(IN(1,3,T)) as P3:D(T)P4 produces a different set.

Bounds must fit the current scope. Zero, reversed bounds or positions beyond a known length produce INVALID_FILTER_WINDOW; no silent clipping. Nested IN bounds are relative to their immediate window, and absence is local to that window.

kind[n]: occurrence, not token identity#

{P7P7}:D(I[2]<T[2])
{P7P7}:D(I[2]<T[2],T[2])
{P7P7}:D(IN(5,12,T[2]<I))

kind[n] selects the nth occurrence inside the current inspection scope (n=1..256). I equals I[1]; repeated II remains a kind group, not I[2]. Inside IN, count again from that window.

The ordinal is not a global token-origin or hold ID. U rejects n>1 selectors; n=1 remains ordinary first-occurrence semantics.

Unsupported spellings and outcomes#

Distinguish invalid syntax, unsupported features, proven UNSAT, NOT_CHECKED and budget-limited INCOMPLETE. One impossible OR branch must not delete surviving branches; NOT and different windows must not leak into one positive cycle graph.