dsh-boolean
Boolean algebra toolbox for DeepSeek Harness (dsh).
Parse propositional-logic expressions and get full truth tables with minterm/maxterm summaries,
canonical DNF/CNF, NNF, and NAND-only / NOR-only gate networks — no hand-drawn 16-row tables,
no De Morgan slips.
Zero runtime dependencies, pure local math.
Why
Modeled reasoning often derails on small logic chores: expanding ¬(a∧b), listing the satisfying
rows of a 3-variable expression, or checking whether two formulas say the same thing. These tools do
the bookkeeping exactly, one expression at a time.
Install
dsh plugin --profile web add github:TYEclipse/dsh-boolean
Restart the profile session (or start a new one) and the four tools are registered
under tools for every agent. Requires pnpm on PATH (the plugin host resolves it).
Tools
| Tool | What it does |
|---|
truth_table | Enumerates every assignment row (up to 8 variables / 256 rows) with the result, minterm & maxterm indices, tautology / contradiction / satisfiability flags, and canonical DNF and CNF strings. |
logic_eval | Evaluates an expression under one complete assignment (trueVars / falseVars); missing variables are reported, never silently defaulted. |
logic_equiv | Compares two expressions over all rows of the combined table; reports how many rows differ and one concrete counterexample when they are not equivalent. |
logic_convert | Converts an expression to nnf, dnf, cnf, nand, or nor canonical form. DNF/CNF come from the truth table (8-variable cap); nnf/nand/nor are structural rewrites without a cap. |
Expression syntax
| Meaning | Symbols | Words | Unicode |
|---|
| NOT (prefix) | ! | not | ¬ |
| AND | & | and | ∧ |
| XOR | ^ | xor | ⊕ |
| OR | | | or | ∨ |
| IMPLIES | -> => | implies | → |
| IFF | <-> <=> | iff | ↔ |
- Variables are single letters
a–z (upper case is normalized); parentheses () group.
- Precedence, high to low:
NOT → AND → XOR → OR → IMPLIES → IFF.
- Binary operators are left-associative; parenthesize chains of
-> / <-> when in doubt.
- XOR, IMPLIES and IFF are desugared at parse time to NOT/AND/OR with the textbook identities
(
a^b ≡ (a&!b)|(!a&b), a->b ≡ !a|b, a<->b ≡ (a&b)|(!a&!b)).
- Expressions are limited to 512 characters; truth-table enumeration to 8 variables.
Examples
All outputs below are real tool output (v0.1.0).
Truth table of XOR — every row plus the canonical forms:
truth_table { expr: "a ^ b" }
→ rows: m0(00)=0, m1(01)=1, m2(10)=1, m3(11)=0
minterms [1,2] DNF = (!a & b) | (a & !b)
maxterms [0,3] CNF = (a | b) & (!a | !b)
Check one row instead of the whole table:
logic_eval { expr: "a -> (b | c)", trueVars: ["a"], falseVars: ["b","c"] }
→ a -> (b | c) with a=true, b=false, c=false = false
Verify a rewrite identity (De Morgan):
logic_equiv { exprA: "!(a | b)", exprB: "!a & !b" }
→ equivalent: !(a | b) == !a & !b (all 4 rows agree)
Push negations down or build single-gate networks:
logic_convert { expr: "!(a & b)", operation: "nnf" } → !a | !b
logic_convert { expr: "a & b", operation: "nand" } → NAND(NAND(a,b),NAND(a,b))
logic_convert { expr: "a | b", operation: "nor" } → NOR(NOR(a,b),NOR(a,b))
logic_convert { expr: "a -> b", operation: "dnf" } → (!a & !b) | (!a & b) | (a & b)
Invalid input is reported with a position and a reason instead of a wrong answer:
a & → unexpected end of expression (at position 3); foo & a → variables must be single
letters a–z.
Notes & limits
- Truth-table tools cap at 8 variables (256 rows);
nnf/nand/nor conversions are
structural and unlimited.
logic_eval needs every expression variable in exactly one of trueVars / falseVars;
listing a variable in both, or a variable name outside a–z, is an error.- Gate outputs use function-call syntax:
NAND(a,b) / NOR(a,b), with NOT(x) written as
NAND(x,x) or NOR(x,x). Input grammar does not accept gate names — convert, don't write gates.
- Canonical DNF of a contradiction and canonical CNF of a tautology are the empty string, with an
explanatory
note.
Development
pnpm install
pnpm build # tsc -> dist/ (committed: git installs do not build)
pnpm test # 99 tests: parser semantics, oracle-anchored tables (independent Python
# enumeration), gate networks, schema guards, lossless-JSON discipline
pnpm lint # oxlint src test
Test anchors are generated by an independent Python oracle (itertools brute-force truth
enumeration + textbook canonical-form construction); every DNF/CNF string and every truth row in
the fixture is cross-checked against the TypeScript implementation.
License
MIT — see LICENSE.
