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6 changed files (+462/-0)

• .gitignore (new)
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    + /target
• Cargo.lock (new)
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    + # This file is automatically @generated by Cargo. + # It is not intended for manual editing. + version = 4 + + [[package]] + name = "bitflags" + version = "2.9.0" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "5c8214115b7bf84099f1309324e63141d4c5d7cc26862f97a0a857dbefe165bd" + + [[package]] + name = "cfg-if" + version = "1.0.0" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "baf1de4339761588bc0619e3cbc0120ee582ebb74b53b4efbf79117bd2da40fd" + + [[package]] + name = "getrandom" + version = "0.3.2" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "73fea8450eea4bac3940448fb7ae50d91f034f941199fcd9d909a5a07aa455f0" + dependencies = [ + "cfg-if", + "libc", + "r-efi", + "wasi", + ] + + [[package]] + name = "lambda" + version = "0.1.0" + dependencies = [ + "rand", + ] + + [[package]] + name = "libc" + version = "0.2.171" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "c19937216e9d3aa9956d9bb8dfc0b0c8beb6058fc4f7a4dc4d850edf86a237d6" + + [[package]] + name = "ppv-lite86" + version = "0.2.21" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "85eae3c4ed2f50dcfe72643da4befc30deadb458a9b590d720cde2f2b1e97da9" + dependencies = [ + "zerocopy", + ] + + [[package]] + name = "proc-macro2" + version = "1.0.94" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "a31971752e70b8b2686d7e46ec17fb38dad4051d94024c88df49b667caea9c84" + dependencies = [ + "unicode-ident", + ] + + [[package]] + name = "quote" + version = "1.0.40" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "1885c039570dc00dcb4ff087a89e185fd56bae234ddc7f056a945bf36467248d" + dependencies = [ + "proc-macro2", + ] + + [[package]] + name = "r-efi" + version = "5.2.0" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "74765f6d916ee2faa39bc8e68e4f3ed8949b48cccdac59983d287a7cb71ce9c5" + + [[package]] + name = "rand" + version = "0.9.0" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "3779b94aeb87e8bd4e834cee3650289ee9e0d5677f976ecdb6d219e5f4f6cd94" + dependencies = [ + "rand_chacha", + "rand_core", + "zerocopy", + ] + + [[package]] + name = "rand_chacha" + version = "0.9.0" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "d3022b5f1df60f26e1ffddd6c66e8aa15de382ae63b3a0c1bfc0e4d3e3f325cb" + dependencies = [ + "ppv-lite86", + "rand_core", + ] + + [[package]] + name = "rand_core" + version = "0.9.3" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "99d9a13982dcf210057a8a78572b2217b667c3beacbf3a0d8b454f6f82837d38" + dependencies = [ + "getrandom", + ] + + [[package]] + name = "syn" + version = "2.0.100" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "b09a44accad81e1ba1cd74a32461ba89dee89095ba17b32f5d03683b1b1fc2a0" + dependencies = [ + "proc-macro2", + "quote", + "unicode-ident", + ] + + [[package]] + name = "unicode-ident" + version = "1.0.18" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "5a5f39404a5da50712a4c1eecf25e90dd62b613502b7e925fd4e4d19b5c96512" + + [[package]] + name = "wasi" + version = "0.14.2+wasi-0.2.4" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "9683f9a5a998d873c0d21fcbe3c083009670149a8fab228644b8bd36b2c48cb3" + dependencies = [ + "wit-bindgen-rt", + ] + + [[package]] + name = "wit-bindgen-rt" + version = "0.39.0" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "6f42320e61fe2cfd34354ecb597f86f413484a798ba44a8ca1165c58d42da6c1" + dependencies = [ + "bitflags", + ] + + [[package]] + name = "zerocopy" + version = "0.8.24" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "2586fea28e186957ef732a5f8b3be2da217d65c5969d4b1e17f973ebbe876879" + dependencies = [ + "zerocopy-derive", + ] + + [[package]] + name = "zerocopy-derive" + version = "0.8.24" + source = "registry+https://github.com/rust-lang/crates.io-index" + checksum = "a996a8f63c5c4448cd959ac1bab0aaa3306ccfd060472f85943ee0750f0169be" + dependencies = [ + "proc-macro2", + "quote", + "syn", + ]
• Cargo.toml (new)
  • @@ -0,0 +1,7 @@
    + [package] + name = "lambda" + version = "0.1.0" + edition = "2024" + + [dependencies] + rand = "0.9.0"
• src/main.hs (new)
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    + data Term = L Int Term + | A Term Term + | I Int + deriving (Eq, Show) + + sub (L var body) bvar rep = L var (sub body bvar rep) + sub (A fn arg) bvar rep = A (sub fn bvar rep) (sub arg bvar rep) + sub x bvar rep = if x == I bvar then rep else x + + red (L var body) = L var (red body) + red (A fn arg) = case rfn of (L var body) -> red (sub body var arg) + _ -> A rfn (red arg) + where rfn = red fn + red x = x
• src/main.py (new)
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    + # Don't use any features above Python 3.9! + # Since that's what Ren'Py uses + # So no pattern matching sadly + # Format with ruff format lambcalc.py + # Must specify file or it'll mess with the vendored deps too + + import sys + from random import randrange + from typing import Any, NamedTuple + + + ## Lambda term + class L(NamedTuple): + var: int + body: Any + + + # Application term + class A(NamedTuple): + fn: Any + arg: Any + + + # Recursively substitute var with rep in term + def sub(term, var, rep): + if type(term) is L: + # assert term.var != var + if term.var == var: + # Shadowing + return term + return L(term.var, sub(term.body, var, rep)) + if type(term) is A: + return A(sub(term.fn, var, rep), sub(term.arg, var, rep)) + if term == var: + return rep + return term + + + # Add offset to all bound vars + def alpha(term, offset, bound): + if type(term) is L: + return L(term.var + offset, alpha(term.body, offset, bound | {term.var})) + if type(term) is A: + return A(alpha(term.fn, offset, bound), alpha(term.arg, offset, bound)) + # if term in bound: + return term + offset + return term + + + # Simplify term using beta reduction + def red(term): + if type(term) is L: + return L(term.var, red(term.body)) + if type(term) is A: + fn = red(term.fn) + if type(fn) is L: + # Rename bound vars in fn.body to avoid name collisions + return red(sub(fn.body, fn.var, alpha(term.arg, randrange(10**8), set()))) + return A(fn, red(term.arg)) + return term + + + # Simplify term using beta reduction without var renaming + def red_dumb(term): + if type(term) is L: + return L(term.var, red_dumb(term.body)) + if type(term) is A: + fn = red_dumb(term.fn) + if type(fn) is L: + return red_dumb(sub(fn.body, fn.var, term.arg)) + return A(fn, red_dumb(term.arg)) + return term + + + # Rename vars using first available int + # Input term must be reduced first + def canonicalize(term, bound, free): + if type(term) is L: + # Shadowing should never happen + assert not term.var in bound + if len(bound) == 0 and len(free) == 0: + var2 = 1 + else: + var2 = max((bound | free).values()) + 1 + return L(var2, canonicalize(term.body, bound | {term.var: var2}, free)) + if type(term) is A: + return A( + canonicalize(term.fn, bound, free), canonicalize(term.arg, bound, free) + ) + if term in bound: + return bound[term] + if len(bound) == 0 and len(free) == 0: + free[term] = 1 + elif not term in free: + free[term] = max((bound | free).values()) + 1 + return free[term] + + + # Get size of term + def size(term): + if type(term) is L: + return 1 + size(term.body) + if type(term) is A: + return size(term.fn) + size(term.arg) + return 1 + + + # Check equality + def eq(term1, term2): + return canonicalize(term1, {}, {}) == canonicalize(term2, {}, {}) + + + animals = " 🦊🐱🐸🐷🐼🐶🐭🐻🐨🐯🐺🦁🐮🐹🐰🐵🦝🤔😱" + + + # Get friendly uncurried repr of canon term + def animal_repr_canon(term): + if type(term) is str: + return term + if type(term) is L: + if type(term.body) is L: + return f"{animal_repr_canon(term.var)}{animal_repr_canon(term.body)}" + return f"{animal_repr_canon(term.var)}->{animal_repr_canon(term.body)}|" + if type(term) is A: + return f"{animal_repr_canon(term.fn)}({animal_repr_canon(term.arg)})" + return animals[term] + + + # Wrapper func + def animal_repr(term): + return animal_repr_canon(canonicalize(term, {}, {})) + + + # https://en.wikipedia.org/wiki/SKI_combinator_calculus + I = L(1, 1) + K = L(1, L(2, 1)) + S = L(1, L(2, L(3, A(A(1, 3), A(2, 3))))) + # https://en.wikipedia.org/wiki/Fixed-point_combinator + # red(Y) doesn't terminate though... + Y = L(1, A(L(2, A(1, A(2, 2))), L(2, A(1, A(2, 2))))) + Z = L(1, A(L(2, A(1, L(3, A(A(2, 2), 3)))), L(2, A(1, L(3, A(A(2, 2), 3)))))) + + # From https://lambster.dev/ + # Same as K + ltrue = L(1, L(2, 1)) + lfalse = L(1, L(2, 2)) + land = L(1, L(2, A(A(1, 2), 1))) + lor = L(1, L(2, A(A(1, 1), 2))) + lnot = L(1, A(A(1, lfalse), ltrue)) + lif = L(1, L(2, L(3, A(A(1, 2), 3)))) + # Can also use pair/first/second for lists + lpair = L(1, L(2, L(3, A(A(3, 1), 2)))) + lfirst = L(1, A(1, ltrue)) + lsecond = L(1, A(1, lfalse)) + lnil = L(1, ltrue) + lnull = L(1, A(1, L(2, L(3, lfalse)))) + ltree = L(1, L(2, L(3, A(A(1, 2), 3)))) + ldatum = L(1, A(1, lfirst)) + lleft = L(1, A(A(1, lsecond), lfirst)) + lright = L(1, A(1, lsecond)) + lincr = L(1, L(2, L(3, A(2, A(A(1, 2), 3))))) + lplus = L(1, L(2, A(1, lincr))) + ltimes = L(1, L(2, A(1, A(lplus, 2)))) + liszero = L(1, A(A(1, L(2, lfalse)), ltrue)) + # Church numerals + lzero = lfalse + lone = L(1, L(2, A(1, 2))) + ltwo = L(1, L(2, A(1, A(1, 2)))) + lthree = L(1, L(2, A(1, A(1, A(1, 2))))) + lfour = L(1, L(2, A(1, A(1, A(1, A(1, 2)))))) + lfive = L(1, L(2, A(1, A(1, A(1, A(1, A(1, 2))))))) + lsix = L(1, L(2, A(1, A(1, A(1, A(1, A(1, A(1, 2)))))))) + lseven = L(1, L(2, A(1, A(1, A(1, A(1, A(1, A(1, A(1, 2))))))))) + leight = L(1, L(2, A(1, A(1, A(1, A(1, A(1, A(1, A(1, A(1, 2)))))))))) + lnine = L(1, L(2, A(1, A(1, A(1, A(1, A(1, A(1, A(1, A(1, A(1, 2))))))))))) + + + # Tests + assert eq(red(A(A(A(S, K), I), A(A(K, I), S))), I) + assert eq(red(A(A(A(S, K), S), K)), K) + assert eq(red(A(A(A(S, K), I), K)), K) + assert eq(red(A(A(K, S), A(I, A(A(A(S, K), S), I)))), S) + # eta reduction + assert eq(red(L(1, A(L(2, A(2, 2)), 1))), L(1, A(1, 1))) + # Rename bound variable in lambda after name collision + assert eq(red(A(K, K)), L(1, L(2, L(3, 2)))) + # Avoid name capture of bound variables + # https://www.cs.yale.edu/homes/hudak/CS201S08/lambda.pdf + assert eq(red(A(L(1, L(2, 1)), 2)), L(2, 3)) + # Should two free vars refer to the same var?? + # Like maybe we should just assume all vars are bound above us somewhere + # I think that massively simplifies the code, since then red doesn't need to track currently bound vars + # I should choose the one that makes for better puzzles + assert eq(red(A(L(1, A(2, 1)), 2)), A(2, 2)) + + + # Brute force!! + def solve(terms, moves, depth): + cnt = sum(type(term) is int for term in terms) + if cnt == len(terms): + print(moves) + return + if len(terms) - cnt > depth: + # Can only increase cnt by one per turn anyways + return + for i in range(len(terms)): + for j in range(len(terms)): + newterms = terms.copy() + try: + newterms[j] = red_dumb(A(terms[i], terms[j])) + # if size(newterms[j]) > 50: + # Heuristic: stop if term is blowing up + # continue + except: + continue + solve(newterms, moves + [i, j], depth - 1) + + + if __name__ == "__main__": + sys.setrecursionlimit(50) + # solve([A(1, 3), L(5, L(2, 5)), L(1, L(2, 2))], [], 9)
• src/main.rs (new)
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    + use std::collections::HashSet; + + #[derive(PartialEq, Clone, Debug)] + enum E { + L(i64, Box<E>), + A(Box<E>, Box<E>), + I(i64), + } + + fn sub(term: E, var: i64, rep: &E, offset: i64, bound: &mut HashSet<i64>) -> E { + match term { + E::L(var, body) => { + bound.insert(var); + let x = E::L(var + offset, Box::new(sub(*body, var, rep, offset, bound))); + bound.remove(&var); + x + } + E::A(func, arg) => E::A( + Box::new(sub(*func, var, rep, offset, bound)), + Box::new(sub(*arg, var, rep, offset, bound)), + ), + x => { + if x == E::I(var) { + rep.clone() + } else { + x + } + } + } + } + + fn red(term: E) -> E { + match term { + E::L(var, body) => E::L(var, Box::new(red(*body))), + E::A(func, arg) => { + let rfunc = red(*func); + match rfunc { + E::L(var, body) => red(sub( + *body, + var, + &arg, + rand::random_range(0..1 << 32), + &mut HashSet::<i64>::new(), + )), + x => x, + } + } + x => x, + } + } + + fn main() { + // Prints nothing? + println!( + "{:?}", + red(E::A( + Box::new(E::L(1, Box::new(E::L(2, Box::new(E::I(1)))))), + Box::new(E::I(2)) + )) + ); + }