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This overview explains the distinction between an explicit
dense CM and the shared computation graph stored by CM-IR.

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Building a program and materializing all its outputs
incur different costs and satisfy different requests.

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The program for A and B, then or C, stores operations that can be applied to a request.

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Calling the first result S makes the dependency explicit.

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The program is like a recipe: it explains how to obtain an output

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from the current ingredients.

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For input one one zero, evaluate S first and then combine it with C.

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Both operations yield one.

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This execution produces one answer for one request; the other seven assignments have not

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been delivered simply because the program exists.

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A complete explicit representation stores all eight answers in a declared layout.

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In zero-first order, the outputs are zero, one, zero, one, zero, one, one, one.

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This is the filled answer sheet, whereas the program is a reusable way

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to calculate those entries.

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to calculate those entries.

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An explicit CM stores a dense row-column truth layout.

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CM-IR stores a canonicalized shared computation graph.

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Building that graph and materializing all outputs are separate operations.

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F takes the exclusive-or of two results: A AND B, and C OR D.

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The AND node and the OR node feed their
results into the final exclusive-or node.

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Trace 1011 through them: zero and one give one.

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Separately declare ascending AB rows and CD columns.

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That output of one belongs at row index two, column index three.

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Evaluating the other assignments fills the remaining cells.

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The grid is 0111 in each of its first three rows, and 1000 in its last row.

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The graph and grid describe the same function but store different artifacts.

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A graph evaluation path may produce packed
or reduced output under its API contract.

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A kernel measurement does not automatically include graph
construction, dense materialization or the public wrapper.

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Return to the opening three-input recipe: S equals A and B, and F equals S or C.

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This is separate from the intervening larger program.

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A, B and C are Boolean inputs.

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Set them to zero, one and zero respectively.

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The first and combines zero with one and returns zero.

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The final or combines that zero with C zero and also returns zero.

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The program structure is unchanged from the earlier input that returned one.

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Reusing a recipe therefore does not imply reusing its previous answer.

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This case establishes a specific contrast.

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Same compiled recipe.

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Different input and different output.

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Keep the input, intermediate values, and conclusion together when comparing it with the previous case.

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The calculated answer belongs to this complete assignment under the stated rule.

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The calculated answer belongs to this complete assignment under the stated rule.

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If the caller needs only input one zero zero, the required answer is zero.

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Constructing a full table may do work the caller did not request.

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Whether that construction later pays off depends on the actual reuse and costs.

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If the caller requests the full vector, every output must be supplied.

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A compact intermediate program does not discharge that obligation by itself.

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It must be executed or otherwise used to obtain all required answers.

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For repeated requests, the two representations save different work.

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Reusing a program can avoid rebuilding its structure; retaining a full

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table can support lookup.

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The useful comparison specifies residency, input changes, and delivery rather than

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assuming that either form is universally better.

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Keep the program representation distinct from the filled grid.

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Charge materialization when the caller requires every output.