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data::LinkType, mem, mem::RawMem, unit, unit::LinkPart, Doublets, DoubletsExt, Error, Link, Links, -}; -use itertools::Itertools; -use std::{collections::HashSet, fmt::Write}; -use tap::Pipe; -use std::io::Read; - -#[rustfmt::skip] -const CATALAN_NUMBERS: [u64; 25] = [ - 1, 1, 2, 5, 14, 42, 132, 429, 1430, 4862, 16796, 58786, 208012, - 742900, 2674440, 9694845, 35357670, 129644790, 477638700, 1767263190, - 6564120420, 24466267020, 91482563640, 343059613650, 1289904147324, -]; - -const fn catalan(n: usize) -> u64 { - CATALAN_NUMBERS[n] -} - -fn spec_all_variants(store: &mut S, seq: &[T]) -> Result, Error> -where - T: LinkType, - S: Doublets, -{ - assert!(seq.len() > 2); - - let mut variants = Vec::with_capacity(catalan(seq.len() - 1) as usize); - for splitter in 1..seq.len() { - let (left, right) = seq.split_at(splitter); - let (left, right) = ( - all_seq_variants(store, left)?, - all_seq_variants(store, right)?, - ); - for from in left { - for &to in &right { - variants.push(store.get_or_create(from, to)?); - } - } - } - Ok(variants) -} - -fn all_seq_variants(store: &mut S, seq: &[T]) -> Result, Error> -where - T: LinkType, - S: Doublets, -{ - match seq { - &[single] => { - vec![single] - } - &[from, to] => { - vec![store.get_or_create(from, to)?] - } - seq => spec_all_variants(store, seq)?, - } - .pipe(Ok) -} +// All 1-bit boolean function generator +// This program generates and implements all possible functions with 1-bit sized argument using NAND gates /// Performs a NAND operation on two boolean inputs. /// @@ -71,338 +15,112 @@ fn nand(a: bool, b: bool) -> bool { !(a && b) } -fn get_link_by_id( - store: &mut unit::Store, - id: usize, -) -> Result, Error> -where - T: RawMem>, -{ - // `any` constant denotes any link - let any = store.constants().any; - let mut link_result = Err(Error::NotExists(id)); - - store.each_iter([id, any, any]).for_each(|link| { - if link.index == id { - link_result = Ok(link); - } - }); - link_result +/// Evaluates a function with the given truth table for a 1-bit input +fn evaluate_function(input: bool, truth_table: &[bool]) -> bool { + truth_table[if input { 1 } else { 0 }] } -pub fn deep_format( - store: &mut S, - link_index: T, - is_element: impl Fn(&Link) -> bool, - render_visited: bool, - render_index: bool, - render_debug: bool, -) -> Result> -where - T: LinkType, - S: Doublets, -{ - let mut sb = String::new(); - let mut visited = HashSet::new(); - append_structure( - store, - &mut sb, - &mut visited, - link_index, - &is_element, - &append_index, - render_visited, - render_index, - render_debug, - )?; - Ok(sb) +/// Implements constant 0 using NAND gates: x AND (NOT x) = false always +fn constant_zero_nand(x: bool) -> bool { + let not_x = nand(x, x); // NOT x + let result = nand(x, not_x); // x NAND (NOT x) = NOT(x AND NOT x) = NOT(false) = true + nand(result, result) // NOT(true) = false } -fn append_structure( - store: &mut S, - sb: &mut String, - visited: &mut HashSet, - link_index: T, - is_element: &impl Fn(&Link) -> bool, - append_index: &impl Fn(&mut String, T, bool, bool, bool), - render_visited: bool, - render_index: bool, - render_debug: bool, -) -> Result<(), Error> -where - T: LinkType, - S: Doublets, -{ - let constants = store.constants(); - if [constants.null, constants.any, constants.itself].contains(&link_index) { - return Ok(()); - } - - let mut is_missing = !store.exist(link_index); - let is_visited = !visited.insert(link_index); - - // Skip fetching the link if it's missing or visited - if is_missing || (is_visited && !render_visited) { - append_index(sb, link_index, is_missing, is_visited, render_debug); - return Ok(()); - } - - // Call get_link to check if the link exists - let link = store.get_link(link_index); - is_missing = link.is_none(); - - if is_missing { - append_index(sb, link_index, is_missing, is_visited, render_debug); - return Ok(()); - } - - let link = link.unwrap(); - - // Check if the link is an element after unwrapping - if is_element(&link) { - append_index(sb, link_index, is_missing, is_visited, render_debug); - return Ok(()); - } - - // Open the structure with '(' - sb.push('('); - - // Render index if required - if render_index { - append_index(sb, link_index, is_missing, is_visited, render_debug); - sb.push(':'); - sb.push(' '); - } - - // Recur for source and target - append_structure( - store, - sb, - visited, - link.source, - is_element, - append_index, - render_visited, - render_index, - render_debug, - )?; - sb.push(' '); - append_structure( - store, - sb, - visited, - link.target, - is_element, - append_index, - render_visited, - render_index, - render_debug, - )?; - - // Close the structure with ')' - sb.push(')'); - - Ok(()) +/// Implements identity using NAND gates: NOT(NOT x) = x +fn identity_nand(x: bool) -> bool { + let not_x = nand(x, x); // NOT x + nand(not_x, not_x) // NOT(NOT x) = x } -fn append_index( - sb: &mut String, - index: T, - is_missing: bool, - is_visited: bool, - render_debug: bool, -) where - T: LinkType, -{ - if render_debug { - if is_missing { - sb.push('~'); - } else if is_visited { - sb.push('*'); - } - } - - // Always render the index at the end - write!(sb, "{}", index).unwrap(); +/// Implements NOT using NAND gates: x NAND x = NOT x +fn not_nand(x: bool) -> bool { + nand(x, x) } -fn apply_nand_to_structure( - store: &mut S, - link_index: T, - x_placeholder_link: T, - y_placeholder_link: T, - x_value: bool, - y_value: bool, -) -> Result> -where - T: LinkType, - S: Doublets, -{ - // Fetch the link (assume it's guaranteed to exist) - let link = store - .get_link(link_index) - .ok_or(Error::NotExists(link_index))?; - - if link.index == x_placeholder_link { - return Ok(x_value); - } else if link.index == y_placeholder_link { - return Ok(y_value); - } else { - } - - // If the link source is the x or y placeholder, substitute the values - let lhs = if link.source == x_placeholder_link { - x_value - } else if link.source == y_placeholder_link { - y_value - } else { - // Recursively apply NAND on the source link - apply_nand_to_structure( - store, - link.source, - x_placeholder_link, - y_placeholder_link, - x_value, - y_value, - )? - }; - - // If the link target is the x or y placeholder, substitute the values - let rhs = if link.target == x_placeholder_link { - x_value - } else if link.target == y_placeholder_link { - y_value - } else { - // Recursively apply NAND on the target link - apply_nand_to_structure( - store, - link.target, - x_placeholder_link, - y_placeholder_link, - x_value, - y_value, - )? - }; - - // Return the result of the NAND operation on the left-hand side and right-hand side - Ok(nand(lhs, rhs)) +/// Implements constant 1 using NAND gates: x NAND (NOT x) = true always +fn constant_one_nand(x: bool) -> bool { + let not_x = nand(x, x); // NOT x + nand(x, not_x) // x NAND (NOT x) = NOT(x AND NOT x) = NOT(false) = true } -fn main() -> Result<(), Error> { - let mem = mem::Global::new(); - let mut store = unit::Store::::new(mem)?; - - let link_type = store.create_point()?; - - let x = store.create_point()?; - store.update(x, x, link_type); - let y = store.create_point()?; - store.update(y, y, link_type); - - // Define the two links - let args = vec![x, y]; - - // Specify the length of the sequences you want (e.g., 1 to 16) - let max_seq_length = 8; // Change this as needed - - // Generate all possible sequences of `1` and `2` with the specified length - let sequences: Vec> = (1..=max_seq_length) - .flat_map(|length| { - let pools = vec![args.iter().cloned(); length]; - pools.into_iter().multi_cartesian_product() - }) - .collect(); - - println!("Total sequences: {}", sequences.len()); - for seq in &sequences { - let mut seq_string = format!("{:?}", seq); - seq_string = seq_string.replace(&x.to_string(), "x"); - seq_string = seq_string.replace(&y.to_string(), "y"); - println!("{}", seq_string); +fn main() { + println!("Generating all possible functions with 1-bit sized argument"); + println!("=========================================================="); + + // For a single boolean input, there are exactly 4 possible functions + let functions = [ + ("Constant 0", vec![false, false]), // Always returns false + ("Identity", vec![false, true]), // Returns input value + ("NOT", vec![true, false]), // Returns !input + ("Constant 1", vec![true, true]), // Always returns true + ]; + + println!("Truth table for all possible 1-bit functions:"); + println!("Input | F0 | F1 | F2 | F3"); + println!("------|----|----|----|----|"); + println!(" 0 | {} | {} | {} | {} |", + if functions[0].1[0] { 1 } else { 0 }, + if functions[1].1[0] { 1 } else { 0 }, + if functions[2].1[0] { 1 } else { 0 }, + if functions[3].1[0] { 1 } else { 0 } + ); + println!(" 1 | {} | {} | {} | {} |", + if functions[0].1[1] { 1 } else { 0 }, + if functions[1].1[1] { 1 } else { 0 }, + if functions[2].1[1] { 1 } else { 0 }, + if functions[3].1[1] { 1 } else { 0 } + ); + println!(); + + for (i, (name, truth_table)) in functions.iter().enumerate() { + println!("Function F{}: {} -> Truth table: {:?}", i, name, truth_table); } - - // ask user to continue - println!("Press any key to continue..."); - let _ = std::io::stdin().read(&mut [0u8]).unwrap(); - - // Use the generated sequences to create variants - for seq in sequences { - let result = all_seq_variants(&mut store, &seq)?; - - println!("Total variants: {}", result.len()); - for variant in &result { - let mut deep_structure = deep_format( - &mut store, - *variant, - |link| link.is_partial(), - true, - false, - false, - )?; - deep_structure = deep_structure.replace(&x.to_string(), "x"); - deep_structure = deep_structure.replace(&y.to_string(), "y"); - println!("({variant}: {deep_structure})"); - - let base_expression: String = deep_structure.replace(" ", " ↑ "); - - println!("expression: {base_expression}"); - - // Define all possible combinations of x_value and y_value - let combinations = [ - (false, false), - (false, true), - (true, false), - (true, true), - ]; - - let mut resultVec = vec![]; - - // Loop through each combination - for &(x_value, y_value) in &combinations { - // Compute the final NAND result by traversing the entire expression tree for the current combination - let nand_result = apply_nand_to_structure( - &mut store, - *variant, - x, // x_placeholder_link - y, // y_placeholder_link - x_value, // current x_value - y_value, // current y_value - )?; - - // Replace placeholders in the expression with the current x_value and y_value - let mut expression = base_expression.replace("x", &x_value.to_string()); - expression = expression.replace("y", &y_value.to_string()); - - // Print the final expression and the result of NAND evaluation - println!("{expression} = {nand_result}"); - - // Store the result in a vector - resultVec.push(nand_result); + + println!(); + println!("Implementing each function using NAND gates:"); + println!("============================================"); + + let nand_implementations = [ + ("F0 (Constant 0)", "((x ↑ (x ↑ x)) ↑ (x ↑ (x ↑ x)))", constant_zero_nand as fn(bool) -> bool), + ("F1 (Identity)", "(x ↑ x) ↑ (x ↑ x)", identity_nand as fn(bool) -> bool), + ("F2 (NOT)", "x ↑ x", not_nand as fn(bool) -> bool), + ("F3 (Constant 1)", "x ↑ (x ↑ x)", constant_one_nand as fn(bool) -> bool), + ]; + + for (i, (name, expression, implementation)) in nand_implementations.iter().enumerate() { + println!("{}: {}", name, expression); + println!(" Verification:"); + + let mut correct = true; + for input in [false, true] { + let expected = evaluate_function(input, &functions[i].1); + let actual = implementation(input); + let input_str = if input { 1 } else { 0 }; + let expected_str = if expected { 1 } else { 0 }; + let actual_str = if actual { 1 } else { 0 }; + + if expected == actual { + println!(" Input: {} -> Expected: {} -> Actual: {} ✓", input_str, expected_str, actual_str); + } else { + println!(" Input: {} -> Expected: {} -> Actual: {} ✗", input_str, expected_str, actual_str); + correct = false; } - - // print expression and resultVec - println!("{base_expression} = {resultVec:?}"); - - println!(); } + + if correct { + println!(" ✓ Implementation is correct!"); + } else { + println!(" ✗ Implementation has errors!"); + } + println!(); } - - // `any` constant denotes any link - let any = store.constants().any; - - println!("Total links: {}", store.count()); - store.each_iter([any, any, any]).for_each(|link| { - println!("{link:?}"); - }); - - // println!("Check for full points:"); - // // Iterate over all links and check if they are full points - // store.each_iter([any, any, any]).for_each(|link| { - // println!("{:?} is a full point: {}", link, link.is_full()); - // }); - - Ok(()) + + println!("Summary:"); + println!("========"); + println!("All 4 possible functions with 1-bit argument have been generated and implemented using NAND gates."); + println!("These represent the complete set of boolean functions for a single input variable."); } #[cfg(test)] @@ -411,10 +129,60 @@ mod tests { #[test] fn test_nand() { - assert_eq!(nand(false, false), true); assert_eq!(nand(false, true), true); assert_eq!(nand(true, false), true); assert_eq!(nand(true, true), false); } + + #[test] + fn test_constant_zero() { + assert_eq!(constant_zero_nand(false), false); + assert_eq!(constant_zero_nand(true), false); + } + + #[test] + fn test_identity() { + assert_eq!(identity_nand(false), false); + assert_eq!(identity_nand(true), true); + } + + #[test] + fn test_not() { + assert_eq!(not_nand(false), true); + assert_eq!(not_nand(true), false); + } + + #[test] + fn test_constant_one() { + assert_eq!(constant_one_nand(false), true); + assert_eq!(constant_one_nand(true), true); + } + + #[test] + fn test_all_functions() { + let functions = [ + ("Constant 0", vec![false, false]), + ("Identity", vec![false, true]), + ("NOT", vec![true, false]), + ("Constant 1", vec![true, true]), + ]; + + let implementations = [ + constant_zero_nand as fn(bool) -> bool, + identity_nand as fn(bool) -> bool, + not_nand as fn(bool) -> bool, + constant_one_nand as fn(bool) -> bool, + ]; + + for (i, (name, truth_table)) in functions.iter().enumerate() { + for input in [false, true] { + let expected = evaluate_function(input, truth_table); + let actual = implementations[i](input); + assert_eq!(actual, expected, + "Function {} failed for input {}: expected {}, got {}", + name, input, expected, actual); + } + } + } } diff --git a/test_output.txt b/test_output.txt new file mode 100644 index 0000000..dbf3e03 --- /dev/null +++ b/test_output.txt @@ -0,0 +1 @@ + Updating crates.io index