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Inequality

Status: Stable

documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

Description

Inequality[v0, op0, v1, op1, v2, ...] is the canonical form for a chained comparison such as a < b <= c. It returns True if every adjacent pair holds, False if any pair fails, and otherwise the residual chain with decidable pairs dropped.

Examples

No verified examples yet for this function.

Implementation notes

Algorithm. builtin_inequality handles the variadic chained-comparison head the parser emits for mixed chains like a < b <= c == d. The argument layout is strict: 2k+1 args, even slots values, odd slots bare operator symbols (Less/LessEqual/Greater/GreaterEqual/Equal); a malformed layout returns NULL. Each adjacent pair (v_i, op_i, v_{i+1}) is resolved by decide_pair, which routes through compare_numeric/expr_eq and returns 1 (True), 0 (False), or -1 (undecidable). Any False pair short-circuits the whole chain to False. If all pairs are True → True. Otherwise the proven-True pairs are dropped and a residual Inequality[...] is rebuilt from the undecided pairs (collapsing to a single binary op[a,b] head when exactly one survives, and de-duplicating a shared boundary value so the residual stays a well-formed 2k+1 chain).

Data structures. A bool* undecided scratch array (one slot per pair) flags which pairs to keep; survivors are deep-copied into a fresh argument array that becomes the residual chain.

  • Adjacent comparisons that evaluate to True are dropped; the result collapses

Attributes: Protected.

Implementation status

Stable — documented, exercised by the test suite and/or worked examples, with no known limitations recorded.

References

Notes & additional examples

Worked examples

In[1]:= 1 < 2 < 3
Out[1]= True

In[2]:= 1 < 5 < 3
Out[2]= False

In[3]:= 2 <= 2 < 5
Out[3]= True

In[1]:= 1 < x < 3 < 5
Out[1]= 1 < x < 3

In[1]:= 2 < 3 < x < 1
Out[1]= 3 < x < 1

Notes

A chained comparison such as a < b <= c parses to the canonical Inequality form and holds only when every adjacent pair holds. Mixed operators (e.g. <= and <) may be combined in a single chain. When some pairs are undecidable (because a value is symbolic), the decidable-and-true pairs are dropped and only the residual chain is returned — 1 < x < 3 < 5 collapses the true 3 < 5 and keeps 1 < x < 3.