WEBVTT

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Why keep both a graph and a matrix?

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The repository can represent the same Boolean rule as a written expression, a compiled graph,

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or an explicit grid of answers. Our example takes exclusive-or between A AND B and C OR D.

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We will compare what these objects contain and learn
which questions each representation can answer.

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The root operation is exclusive-or.

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Its left child computes A and B; its right child computes C or D.

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At the leaves are four variables. This tree describes how to compute a result.

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It does not yet contain a separate output cell for every possible assignment.

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The public compile expression function builds a compiled

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object containing a node graph and an expression hash.

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The builder normalizes supported operations and can share repeated structure.

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Compilation prepares a representation that later evaluators or materializers can use;

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it is not itself a dense output matrix.

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To make a dense CM, declare row variables A B and column variables C D.

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The repository uses false-first binary order, zero-zero through one-one.

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That differs from the paper’s true-first examples. Each output
cell is now the rule evaluated at one complete assignment.

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Choose A one, B one, C zero, D zero.

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AND produces one, OR produces zero, and the root exclusive-or produces one.

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This assignment selects row three and column zero in the repository layout.

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The same answer appears in that matrix cell.

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An expression hash helps identify a stored expression structure.

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It is not a proof that all logically equivalent formulas have the same key. For example,

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distributivity gives two equivalent formulas with different
expression structures. Their truth tables agree,

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but the repository’s expression hashes differ in our checked example.

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Suppose you receive a sixteen-entry array together with the row and column variable lists.

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Is that an expression graph, an explicit CM, or merely a hash key?

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Identify the artifact by what it contains and what you can do with it.

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The array with its axis lists is an explicit CM. It lets you address stored results.

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A graph stores operations and dependencies; a hash is an identity key.

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Next we will build this exact example using the actual public API, then validate every lookup.