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zAwtW-af-A`0B%1~dp23#=Q}$n3#F?pr1Qqm4$LH(k2Y}Q>M9-BT~fY!8i$NfFO+Ard`7 zHOP2`Yo>hJ8PQfv^_T$J(L_dnm}g6(`AeDL_yo{1tc#%(o-Z&JAbOhUu~{N q) or r) -> ((p and not r) or not q)$ +#let F = _implies( + _or( + _implies( + _not("p"), + "q" + ), + "r" + ), + _or( + _and( + "p", + _not("r") + ), + _not("q") + ) +) +#display(F) +#get-atoms(F) + +#get-components(F) + +#{ + set text(size: 0.8em) + truth-table(F) +} \ No newline at end of file diff --git a/src/logic.typ b/src/logic.typ new file mode 100644 index 0000000..4ea4b82 --- /dev/null +++ b/src/logic.typ @@ -0,0 +1,165 @@ +#let _and(a, b) = ( + type: "and", + a: a, + b: b +) +#let _or(a, b) = ( + type: "or", + a: a, + b: b +) +#let _implies(a, b) = ( + type: "implies", + a: a, + b: b +) +#let _not(a) = ( + type: "not", + a: a +) + +#let display(formula, first: true) = { + let display = display.with(first: false) + if type(formula) == str { + return formula + } + if type(formula) != dictionary { + panic("Invalid type") + } + let res = none + if formula.type == "and" { + res = $#display(formula.a) and #display(formula.b)$ + } else if formula.type == "or" { + res = $#display(formula.a) or #display(formula.b)$ + } else if formula.type == "implies" { + res = $#display(formula.a) -> #display(formula.b)$ + } else if formula.type == "not" { + res = $not #display(formula.a)$ + } else { + panic("Invalid type") + } + if not first and formula.type != "not" { + res = $(#res)$ + } + return res +} + +#let _walk(formula, callback) = { + let result = () + if type(formula) == str { + result += callback(formula, result) + } else if type(formula) == dictionary { + result += callback(formula, result) + if formula.type in ("and", "or", "implies") { + result += _walk(formula.a, callback) + result += _walk(formula.b, callback) + } else if formula.type == "not" { + result += _walk(formula.a, callback) + } + } + return result +} + +#let evaluate(formula, atoms-values) = { + if type(formula) == str { + return atoms-values.at(formula) + } + if type(formula) != dictionary { + panic("Invalid type") + } + if formula.type == "not" { + return 1 - evaluate(formula.a, atoms-values) + } + if not formula.type in ("and", "or", "implies") { + panic("Invalid type") + } + let a = evaluate(formula.a, atoms-values) + let b = evaluate(formula.b, atoms-values) + let cond = false + if formula.type == "and" { + cond = (a == 1 and b == 1) + } else if formula.type == "or" { + cond = (a == 1 or b == 1) + } else if formula.type == "implies" { + cond = (a == 0 or b == 1) + } + return if cond {1} else {0} +} + +#let get-atoms(formula) = { + return _walk(formula, (a, res) => { + if type(a) == str { + res.push(a) + } + return res + }).dedup() +} + +#let get-components(formula) = { + return _walk(formula, (a, res) => { + res.push(a) + return res + }).dedup() +} + +#let get-level(formula) = { + if type(formula) == str { + return 0 + } + if type(formula) != dictionary { + panic("Invalid type") + } + if formula.type in ("and", "or", "implies") { + return calc.max( + get-level(formula.a), + get-level(formula.b) + ) + 1 + } + if formula.type == "not" { + return get-level(formula.a) + 1 + } + panic("Invalid type") +} + +#let truth-table(formula) = { + let atoms = get-atoms(formula).sorted() + let comps = get-components(formula) + let comps-lvls = comps.map(c => (c, get-level(c))) + let sorted = comps-lvls.sorted(key: cl => cl.last()) + + let cells = () + + let cur-lvl = 0 + for (i, (comp, lvl)) in sorted.enumerate() { + if lvl != cur-lvl { + cells.push(table.vline()) + } else if i != 0 { + cells.push(table.vline(stroke: (dash: "dashed"))) + } + cur-lvl = lvl + cells.push(display(comp)) + } + cells.push(table.hline()) + for i in range(calc.pow(2, atoms.len())) { + if calc.rem(i, 4) == 0 and i != 0 { + cells.push(table.hline()) + } + let atoms-values = (:) + for (j, a) in atoms.enumerate() { + let bit = i.bit-rshift(atoms.len() - j - 1).bit-and(1) + atoms-values.insert(a, bit) + } + for (comp, lvl) in sorted { + let value = evaluate(comp, atoms-values) + cells.push($#value$) + } + } + + table( + columns: sorted.len(), + stroke: none, + align: center + horizon, + inset: (left: 0.5em, right: 0.5em, top: 0.4em, bottom: 0.4em), + ..cells + ) +} \ No newline at end of file