├── gleam.toml ├── .gitignore ├── rebar.config ├── src ├── gleam_logic.app.src ├── gleam_logic │ └── stream.gleam └── gleam_logic.gleam ├── README.md ├── .github └── workflows │ └── test.yml ├── rebar.lock ├── test └── gleam_logic_test.gleam └── LICENSE /gleam.toml: -------------------------------------------------------------------------------- 1 | name = "gleam_logic" 2 | 3 | # [docs] 4 | # links = [ 5 | # { title = 'GitHub', href = 'https://github.com/username/project_name' } 6 | # ] 7 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | *.beam 2 | *.iml 3 | *.o 4 | *.plt 5 | *.swo 6 | *.swp 7 | *~ 8 | .erlang.cookie 9 | .eunit 10 | .idea 11 | .rebar 12 | .rebar3 13 | _* 14 | _build 15 | docs 16 | ebin 17 | erl_crash.dump 18 | gen 19 | log 20 | logs 21 | rebar3.crashdump 22 | -------------------------------------------------------------------------------- /rebar.config: -------------------------------------------------------------------------------- 1 | {erl_opts, [debug_info]}. 2 | {src_dirs, ["src", "gen/src"]}. 3 | 4 | {profiles, [ 5 | {test, [{src_dirs, ["src", "test", "gen/src", "gen/test"]}]} 6 | ]}. 7 | 8 | {project_plugins, [rebar_gleam]}. 9 | 10 | {deps, [ 11 | {gleam_stdlib, "0.11.0"}, 12 | {gleam_otp, "0.1.0"} 13 | ]}. 14 | -------------------------------------------------------------------------------- /src/gleam_logic.app.src: -------------------------------------------------------------------------------- 1 | {application, gleam_logic, 2 | [{description, "A Gleam program"}, 3 | {vsn, "1.0.0"}, 4 | {registered, []}, 5 | {applications, 6 | [kernel, 7 | stdlib, 8 | gleam_stdlib 9 | ]}, 10 | {env,[]}, 11 | {modules, []}, 12 | 13 | {include_files, ["gleam.toml", "gen"]}, 14 | {licenses, ["Apache 2.0"]}, 15 | {links, []} 16 | ]}. 17 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # gleam_logic 2 | 3 | A Gleam program 4 | 5 | 6 | ## Quick start 7 | 8 | ```sh 9 | # Build the project 10 | rebar3 compile 11 | 12 | # Run the eunit tests 13 | rebar3 eunit 14 | 15 | # Run the Erlang REPL 16 | rebar3 shell 17 | ``` 18 | 19 | 20 | ## Installation 21 | 22 | If [available in Hex](https://www.rebar3.org/docs/dependencies#section-declaring-dependencies) 23 | this package can be installed by adding `gleam_logic` to your `rebar.config` dependencies: 24 | 25 | ```erlang 26 | {deps, [ 27 | gleam_logic 28 | ]}. 29 | ``` 30 | -------------------------------------------------------------------------------- /.github/workflows/test.yml: -------------------------------------------------------------------------------- 1 | name: test 2 | 3 | on: 4 | push: 5 | branches: 6 | - master 7 | - main 8 | pull_request: 9 | 10 | jobs: 11 | test: 12 | runs-on: ubuntu-latest 13 | steps: 14 | - uses: actions/checkout@v2.0.0 15 | - uses: gleam-lang/setup-erlang@v1.1.0 16 | with: 17 | otp-version: 22.1 18 | - uses: gleam-lang/setup-gleam@v1.0.2 19 | with: 20 | gleam-version: 0.12.1 21 | - run: rebar3 install_deps 22 | - run: rebar3 eunit 23 | - run: gleam format --check src test 24 | -------------------------------------------------------------------------------- /rebar.lock: -------------------------------------------------------------------------------- 1 | {"1.2.0", 2 | [{<<"gleam_otp">>,{pkg,<<"gleam_otp">>,<<"0.1.0">>},0}, 3 | {<<"gleam_stdlib">>,{pkg,<<"gleam_stdlib">>,<<"0.11.0">>},0}]}. 4 | [ 5 | {pkg_hash,[ 6 | {<<"gleam_otp">>, <<"6E2CC2C379AADBC94DCA77D7381ABB6005D6E34E26F5228B178C07BB4515DC2B">>}, 7 | {<<"gleam_stdlib">>, <<"9B1089739574CDF78A1C25A463D770A98F59E63A92324D17095AD67E867EE549">>}]}, 8 | {pkg_hash_ext,[ 9 | {<<"gleam_otp">>, <<"115B50FB701AB417C05963A148ABA8E2EADC9B6178FD7E0B5F29483A2513C7BE">>}, 10 | {<<"gleam_stdlib">>, <<"5508E169E20369FC8D400481D3F37CCB2CFD880509F63D6E2B6D85F939BC991B">>}]} 11 | ]. 12 | -------------------------------------------------------------------------------- /src/gleam_logic/stream.gleam: -------------------------------------------------------------------------------- 1 | pub type Stream(a) { 2 | Empty 3 | Mature(a, Stream(a)) 4 | Immature(fn() -> Stream(a)) 5 | } 6 | 7 | pub fn pull(s: Stream(a)) -> Stream(a) { 8 | case s { 9 | Empty -> Empty 10 | Mature(x, xs) -> Mature(x, xs) 11 | Immature(f) -> pull(f()) 12 | } 13 | } 14 | 15 | pub fn take_all(s: Stream(a)) -> List(a) { 16 | case pull(s) { 17 | Empty -> [] 18 | Mature(x, xs) -> [x, ..take_all(xs)] 19 | } 20 | } 21 | 22 | pub fn take(n: Int, s: Stream(a)) -> List(a) { 23 | case n { 24 | 0 -> [] 25 | n -> 26 | case pull(s) { 27 | Empty -> [] 28 | Mature(x, xs) -> [x, ..take(n - 1, xs)] 29 | } 30 | } 31 | } 32 | 33 | pub fn mzero() -> Stream(a) { 34 | Empty 35 | } 36 | 37 | pub fn unit(x: a) -> Stream(a) { 38 | Mature(x, Empty) 39 | } 40 | 41 | pub fn mplus(s1: Stream(a), s2: Stream(a)) { 42 | case s1 { 43 | Empty -> s2 44 | Mature(x, xs) -> Mature(x, mplus(xs, s2)) 45 | Immature(f) -> Immature(fn() { mplus(s2, f()) }) 46 | } 47 | } 48 | 49 | pub fn bind(s1: Stream(a), g: fn(a) -> Stream(a)) -> Stream(a) { 50 | case s1 { 51 | Empty -> mzero() 52 | Mature(x, xs) -> mplus(g(x), bind(xs, g)) 53 | Immature(f) -> Immature(fn() { bind(f(), g) }) 54 | } 55 | } 56 | -------------------------------------------------------------------------------- /test/gleam_logic_test.gleam: -------------------------------------------------------------------------------- 1 | import gleam_logic 2 | import gleam/map 3 | import gleam/should 4 | 5 | fn fives(x) { 6 | gleam_logic.disj( 7 | gleam_logic.equal(x, gleam_logic.Symbol("5")), 8 | gleam_logic.zzz(fn(state) { fives(x)(state) }), 9 | ) 10 | } 11 | 12 | pub fn fives_test() { 13 | let result = gleam_logic.run(1, gleam_logic.call_fresh(fives)) 14 | 15 | should.equal(result, [gleam_logic.Symbol("5")]) 16 | } 17 | 18 | pub fn disj_all_test() { 19 | let result = 20 | gleam_logic.run_all(gleam_logic.call_fresh(fn(x) { 21 | gleam_logic.disj_all([ 22 | gleam_logic.equal(x, gleam_logic.Symbol("2")), 23 | gleam_logic.equal(x, gleam_logic.Symbol("1")), 24 | gleam_logic.equal(x, gleam_logic.Symbol("8")), 25 | ]) 26 | })) 27 | 28 | should.equal( 29 | result, 30 | [gleam_logic.Symbol("2"), gleam_logic.Symbol("1"), gleam_logic.Symbol("8")], 31 | ) 32 | } 33 | 34 | pub fn conde_test() { 35 | let result = 36 | gleam_logic.run_all(gleam_logic.call_fresh(fn(x) { 37 | gleam_logic.call_fresh(fn(y) { 38 | gleam_logic.conde([ 39 | [ 40 | gleam_logic.equal(x, gleam_logic.Symbol("5")), 41 | gleam_logic.equal(y, gleam_logic.Symbol("3")), 42 | ], 43 | [ 44 | gleam_logic.equal(x, gleam_logic.Symbol("8")), 45 | gleam_logic.equal(y, gleam_logic.Symbol("2")), 46 | ], 47 | ]) 48 | }) 49 | })) 50 | 51 | should.equal(result, [gleam_logic.Symbol("5"), gleam_logic.Symbol("8")]) 52 | } 53 | 54 | pub fn reifier_test() { 55 | let result = 56 | gleam_logic.run_all(gleam_logic.call_fresh(fn(x) { 57 | gleam_logic.call_fresh(fn(y) { gleam_logic.equal(x, y) }) 58 | })) 59 | 60 | should.equal(result, [gleam_logic.Symbol("_.0")]) 61 | } 62 | -------------------------------------------------------------------------------- /src/gleam_logic.gleam: -------------------------------------------------------------------------------- 1 | import gleam/int 2 | import gleam/list 3 | import gleam/map 4 | import gleam/option 5 | import gleam/string 6 | import gleam_logic/stream 7 | 8 | pub type Term { 9 | Symbol(String) 10 | Variable(VariableIndex) 11 | Pair(Term, Term) 12 | } 13 | 14 | pub type VariableIndex = 15 | Int 16 | 17 | pub type Substitution = 18 | map.Map(VariableIndex, Term) 19 | 20 | pub type State { 21 | State(substitution: Substitution, counter: Int) 22 | } 23 | 24 | pub type Goal = 25 | fn(State) -> stream.Stream(State) 26 | 27 | pub fn empty_state() -> State { 28 | State(map.new(), 0) 29 | } 30 | 31 | pub fn call_empty_state(g: Goal) -> stream.Stream(State) { 32 | g(empty_state()) 33 | } 34 | 35 | pub fn run(n: Int, g: Goal) { 36 | mk_reify(stream.take(n, call_empty_state(g))) 37 | } 38 | 39 | pub fn run_all(g: Goal) { 40 | mk_reify(stream.take_all(call_empty_state(g))) 41 | } 42 | 43 | pub fn walk(u: Term, s: Substitution) -> Term { 44 | case u { 45 | Variable(index) -> 46 | case map.get(s, index) { 47 | Error(Nil) -> Variable(index) 48 | Ok(v) -> walk(v, s) 49 | } 50 | _ -> u 51 | } 52 | } 53 | 54 | pub fn walk_all(u: Term, s: Substitution) -> Term { 55 | case walk(u, s) { 56 | Variable(_) -> u 57 | Pair(u1, u2) -> Pair(walk_all(u1, s), walk_all(u2, s)) 58 | u -> u 59 | } 60 | } 61 | 62 | pub fn extend_substitution( 63 | index: VariableIndex, 64 | u: Term, 65 | s: Substitution, 66 | ) -> option.Option(Substitution) { 67 | case occurs_check(index, u, s) { 68 | True -> option.None 69 | False -> option.Some(map.insert(s, index, u)) 70 | } 71 | } 72 | 73 | pub fn occurs_check(index: VariableIndex, v: Term, s: Substitution) -> Bool { 74 | case walk(v, s) { 75 | Variable(v_index) -> index == v_index 76 | Pair(v1, v2) -> occurs_check(index, v1, s) || occurs_check(index, v2, s) 77 | _ -> False 78 | } 79 | } 80 | 81 | pub fn unify(u: Term, v: Term, s: Substitution) -> option.Option(Substitution) { 82 | let u = walk(u, s) 83 | let v = walk(v, s) 84 | 85 | case tuple(u, v) { 86 | tuple(Variable(u_index), Variable(v_index)) if u_index == v_index -> 87 | option.Some(s) 88 | tuple(Variable(index), _) -> extend_substitution(index, v, s) 89 | tuple(_, Variable(index)) -> extend_substitution(index, u, s) 90 | tuple(Pair(u1, u2), Pair(v1, v2)) -> 91 | case unify(u1, v1, s) { 92 | option.None -> option.None 93 | option.Some(s) -> unify(u2, v2, s) 94 | } 95 | tuple(Symbol(u_name), Symbol(v_name)) if u_name == v_name -> option.Some(s) 96 | _ -> option.None 97 | } 98 | } 99 | 100 | pub fn zzz(g: Goal) -> Goal { 101 | fn(a) { stream.Immature(fn() { g(a) }) } 102 | } 103 | 104 | pub fn conj_all(gs: List(Goal)) -> Goal { 105 | case gs { 106 | [g] -> zzz(g) 107 | [g, ..gs] -> conj(zzz(g), conj_all(gs)) 108 | } 109 | } 110 | 111 | pub fn disj_all(gs: List(Goal)) -> Goal { 112 | case gs { 113 | [g] -> zzz(g) 114 | [g, ..gs] -> disj(zzz(g), disj_all(gs)) 115 | } 116 | } 117 | 118 | pub fn conde(gs: List(List(Goal))) -> Goal { 119 | gs 120 | |> list.map(conj_all) 121 | |> disj_all() 122 | } 123 | 124 | pub fn equal(u: Term, v: Term) -> Goal { 125 | fn(state: State) { 126 | case unify(u, v, state.substitution) { 127 | option.None -> stream.mzero() 128 | option.Some(s) -> stream.unit(State(..state, substitution: s)) 129 | } 130 | } 131 | } 132 | 133 | pub fn call_fresh(f: fn(Term) -> Goal) -> Goal { 134 | fn(state: State) { 135 | let u = Variable(state.counter) 136 | 137 | f(u)(State(..state, counter: state.counter + 1)) 138 | } 139 | } 140 | 141 | pub fn disj(g1: Goal, g2: Goal) -> Goal { 142 | fn(state) { 143 | let s1 = g1(state) 144 | let s2 = g2(state) 145 | 146 | stream.mplus(s1, s2) 147 | } 148 | } 149 | 150 | pub fn conj(g1: Goal, g2: Goal) -> Goal { 151 | fn(state) { 152 | let s = g1(state) 153 | 154 | stream.bind(s, g2) 155 | } 156 | } 157 | 158 | pub fn mk_reify(states: List(State)) { 159 | list.map(states, reify_state_first_variable) 160 | } 161 | 162 | pub fn reify_state_first_variable(state: State) { 163 | let v = walk_all(Variable(0), state.substitution) 164 | 165 | walk_all(v, reify_substitution(v, map.new())) 166 | } 167 | 168 | pub fn reify_substitution(u: Term, s: Substitution) { 169 | case walk(u, s) { 170 | Variable(index) -> { 171 | let n = reify_name(map.size(s)) 172 | case extend_substitution(index, n, s) { 173 | option.None -> s 174 | option.Some(s) -> s 175 | } 176 | } 177 | Pair(u1, u2) -> reify_substitution(u2, reify_substitution(u1, s)) 178 | _ -> s 179 | } 180 | } 181 | 182 | pub fn reify_name(n: Int) { 183 | Symbol(string.append("_.", int.to_string(n))) 184 | } 185 | 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