Question 4735: Outer and Lexically Shadowed Values

Original question and givens

All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=-3, locally shadowing inner x=-8, c=-1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.

• G001 — All operations and evaluations are exact in Q, not truncated natural-number arithmetic. Outer x=-3, locally shadowing inner x=-8, c=-1. Give (outer x+c, inner x+c) as integers; the inner binding does not mutate the outer one.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-variable-expression

Step-by-step derivation

typed rational expression and explicitly given environment

evaluation,not solving an equation

outer x+c := sum(-3, -1)

outer x+c = -4

inner x+c := sum(-8, -1)

inner x+c = -9

outer x=-3;local inner x=-8

outer x after inner evaluation=-3

Reverse checks

• S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S003 · premise_and_result_audit — Recompute inner x+c with exact rational arithmetic, not rounded decimals.
• S002 · premise_and_result_audit — Recompute outer x+c with exact rational arithmetic, not rounded decimals.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(-4, -9)

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.