{
  "schema": "ailang/v0",
  "name": "prelude",
  "imports": [],
  "defs": [
    {
      "kind": "type",
      "name": "Ordering",
      "vars": [],
      "doc": "Result of a three-way comparison: LT (less than), EQ (equal), GT (greater than). Ships in milestone 23 as the codomain of Ord.compare.",
      "ctors": [
        { "name": "LT", "fields": [] },
        { "name": "EQ", "fields": [] },
        { "name": "GT", "fields": [] }
      ]
    },
    {
      "kind": "class",
      "name": "Eq",
      "param": "a",
      "doc": "Structural equality. Ships in milestone 23 alongside Ord. The primitive `==` operator stays as the surface-level comparator this iter; routing `==` through `Eq.eq` is the declared P2 follow-up (see docs/specs/2026-05-10-23-eq-ord-prelude.md, `Out of scope`).",
      "methods": [
        {
          "name": "eq",
          "type": {
            "k": "fn",
            "params": [
              { "k": "var", "name": "a" },
              { "k": "var", "name": "a" }
            ],
            "param_modes": ["borrow", "borrow"],
            "ret": { "k": "con", "name": "Bool" },
            "effects": []
          }
        }
      ]
    },
    {
      "kind": "instance",
      "class": "Eq",
      "type": { "k": "con", "name": "Int" },
      "doc": "Eq Int. Body lowers to `icmp eq i64` via the existing primitive `==` dispatch in `lower_eq`.",
      "methods": [
        {
          "name": "eq",
          "body": {
            "t": "lam",
            "params": ["x", "y"],
            "paramTypes": [
              { "k": "var", "name": "a" },
              { "k": "var", "name": "a" }
            ],
            "retType": { "k": "con", "name": "Bool" },
            "body": {
              "t": "app",
              "fn": { "t": "var", "name": "==" },
              "args": [
                { "t": "var", "name": "x" },
                { "t": "var", "name": "y" }
              ]
            }
          }
        }
      ]
    },
    {
      "kind": "instance",
      "class": "Eq",
      "type": { "k": "con", "name": "Bool" },
      "doc": "Eq Bool. Body lowers to `icmp eq i1` via the existing primitive `==` dispatch in `lower_eq`.",
      "methods": [
        {
          "name": "eq",
          "body": {
            "t": "lam",
            "params": ["x", "y"],
            "paramTypes": [
              { "k": "var", "name": "a" },
              { "k": "var", "name": "a" }
            ],
            "retType": { "k": "con", "name": "Bool" },
            "body": {
              "t": "app",
              "fn": { "t": "var", "name": "==" },
              "args": [
                { "t": "var", "name": "x" },
                { "t": "var", "name": "y" }
              ]
            }
          }
        }
      ]
    },
    {
      "kind": "instance",
      "class": "Eq",
      "type": { "k": "con", "name": "Str" },
      "doc": "Eq Str. The lambda body shape mirrors Int/Bool for round-trip stability, but the codegen intercept in `emit_fn` overrides the body to call `@ail_str_eq` directly — see `try_emit_primitive_instance_body` in `crates/ailang-codegen/src/lib.rs`.",
      "methods": [
        {
          "name": "eq",
          "body": {
            "t": "lam",
            "params": ["x", "y"],
            "paramTypes": [
              { "k": "var", "name": "a" },
              { "k": "var", "name": "a" }
            ],
            "retType": { "k": "con", "name": "Bool" },
            "body": {
              "t": "app",
              "fn": { "t": "var", "name": "==" },
              "args": [
                { "t": "var", "name": "x" },
                { "t": "var", "name": "y" }
              ]
            }
          }
        }
      ]
    },
    {
      "kind": "class",
      "name": "Ord",
      "param": "a",
      "superclass": { "class": "Eq", "type": "a" },
      "doc": "Total ordering. Ships in milestone 23 alongside Eq. `compare x y` returns LT, EQ, or GT (the three-ctor Ordering ADT also in the prelude). Decision 11's single-superclass closure requires `instance Eq T` for every `instance Ord T` — the three Ord instances below pair with the three Eq instances shipped in iter 23.2.3.",
      "methods": [
        {
          "name": "compare",
          "type": {
            "k": "fn",
            "params": [
              { "k": "var", "name": "a" },
              { "k": "var", "name": "a" }
            ],
            "param_modes": ["borrow", "borrow"],
            "ret": { "k": "con", "name": "Ordering" },
            "effects": []
          }
        }
      ]
    },
    {
      "kind": "instance",
      "class": "Ord",
      "type": { "k": "con", "name": "Int" },
      "doc": "Ord Int. The lambda body shape is a placeholder for round-trip stability; the codegen intercept `try_emit_primitive_instance_body::\"compare__Int\"` emits a three-way `icmp slt` / `icmp eq` branch ladder constructing LT / EQ / GT.",
      "methods": [
        {
          "name": "compare",
          "body": {
            "t": "lam",
            "params": ["x", "y"],
            "paramTypes": [
              { "k": "var", "name": "a" },
              { "k": "var", "name": "a" }
            ],
            "retType": { "k": "con", "name": "Ordering" },
            "body": {
              "t": "ctor",
              "type": "Ordering",
              "ctor": "EQ",
              "args": []
            }
          }
        }
      ]
    },
    {
      "kind": "instance",
      "class": "Ord",
      "type": { "k": "con", "name": "Bool" },
      "doc": "Ord Bool. Body lowered via `try_emit_primitive_instance_body::\"compare__Bool\"` — `icmp ult i1` LT-test, `icmp eq i1` EQ-test, GT default.",
      "methods": [
        {
          "name": "compare",
          "body": {
            "t": "lam",
            "params": ["x", "y"],
            "paramTypes": [
              { "k": "var", "name": "a" },
              { "k": "var", "name": "a" }
            ],
            "retType": { "k": "con", "name": "Ordering" },
            "body": {
              "t": "ctor",
              "type": "Ordering",
              "ctor": "EQ",
              "args": []
            }
          }
        }
      ]
    },
    {
      "kind": "instance",
      "class": "Ord",
      "type": { "k": "con", "name": "Str" },
      "doc": "Ord Str. Body lowered via `try_emit_primitive_instance_body::\"compare__Str\"` — `call i32 @ail_str_compare(ptr, ptr)` then branch on slt-0 / eq-0 against the normalised {-1, 0, +1} return.",
      "methods": [
        {
          "name": "compare",
          "body": {
            "t": "lam",
            "params": ["x", "y"],
            "paramTypes": [
              { "k": "var", "name": "a" },
              { "k": "var", "name": "a" }
            ],
            "retType": { "k": "con", "name": "Ordering" },
            "body": {
              "t": "ctor",
              "type": "Ordering",
              "ctor": "EQ",
              "args": []
            }
          }
        }
      ]
    },
    {
      "kind": "class",
      "name": "Show",
      "param": "a",
      "doc": "Producer of a human-readable Str representation. Ships in milestone 24 with primitive instances for Int/Bool/Str/Float; user types declare their own instance.",
      "methods": [
        {
          "name": "show",
          "type": {
            "k": "fn",
            "params": [{ "k": "var", "name": "a" }],
            "param_modes": ["borrow"],
            "ret": { "k": "con", "name": "Str" },
            "effects": []
          }
        }
      ]
    },
    {
      "kind": "instance",
      "class": "Show",
      "type": { "k": "con", "name": "Int" },
      "methods": [
        {
          "name": "show",
          "body": {
            "t": "lam",
            "params": ["x"],
            "paramTypes": [{ "k": "con", "name": "Int" }],
            "retType": { "k": "con", "name": "Str" },
            "body": {
              "t": "app",
              "fn": { "t": "var", "name": "int_to_str" },
              "args": [{ "t": "var", "name": "x" }]
            }
          }
        }
      ]
    },
    {
      "kind": "instance",
      "class": "Show",
      "type": { "k": "con", "name": "Bool" },
      "methods": [
        {
          "name": "show",
          "body": {
            "t": "lam",
            "params": ["x"],
            "paramTypes": [{ "k": "con", "name": "Bool" }],
            "retType": { "k": "con", "name": "Str" },
            "body": {
              "t": "app",
              "fn": { "t": "var", "name": "bool_to_str" },
              "args": [{ "t": "var", "name": "x" }]
            }
          }
        }
      ]
    },
    {
      "kind": "instance",
      "class": "Show",
      "type": { "k": "con", "name": "Str" },
      "methods": [
        {
          "name": "show",
          "body": {
            "t": "lam",
            "params": ["x"],
            "paramTypes": [{ "k": "con", "name": "Str" }],
            "retType": { "k": "con", "name": "Str" },
            "body": {
              "t": "app",
              "fn": { "t": "var", "name": "str_clone" },
              "args": [{ "t": "var", "name": "x" }]
            }
          }
        }
      ]
    },
    {
      "kind": "instance",
      "class": "Show",
      "type": { "k": "con", "name": "Float" },
      "methods": [
        {
          "name": "show",
          "body": {
            "t": "lam",
            "params": ["x"],
            "paramTypes": [{ "k": "con", "name": "Float" }],
            "retType": { "k": "con", "name": "Str" },
            "body": {
              "t": "app",
              "fn": { "t": "var", "name": "float_to_str" },
              "args": [{ "t": "var", "name": "x" }]
            }
          }
        }
      ]
    },
    {
      "kind": "fn",
      "name": "ne",
      "doc": "Polymorphic disequality. `ne x y` ≡ not (eq x y). Ships in milestone 23 as the Eq-class free helper.",
      "type": {
        "k": "forall",
        "vars": ["a"],
        "constraints": [{ "class": "Eq", "type": { "k": "var", "name": "a" } }],
        "body": {
          "k": "fn",
          "params": [
            { "k": "var", "name": "a" },
            { "k": "var", "name": "a" }
          ],
          "param_modes": ["borrow", "borrow"],
          "ret": { "k": "con", "name": "Bool" },
          "effects": []
        }
      },
      "params": ["x", "y"],
      "body": {
        "t": "app",
        "fn": { "t": "var", "name": "not" },
        "args": [{
          "t": "app",
          "fn": { "t": "var", "name": "eq" },
          "args": [
            { "t": "var", "name": "x" },
            { "t": "var", "name": "y" }
          ]
        }]
      }
    },
    {
      "kind": "fn",
      "name": "lt",
      "doc": "Polymorphic strict-less-than. `lt x y` ≡ case compare x y of LT -> True; _ -> False. Ships in milestone 23 as the Ord-class free helper.",
      "type": {
        "k": "forall",
        "vars": ["a"],
        "constraints": [{ "class": "Ord", "type": { "k": "var", "name": "a" } }],
        "body": {
          "k": "fn",
          "params": [
            { "k": "var", "name": "a" },
            { "k": "var", "name": "a" }
          ],
          "param_modes": ["borrow", "borrow"],
          "ret": { "k": "con", "name": "Bool" },
          "effects": []
        }
      },
      "params": ["x", "y"],
      "body": {
        "t": "match",
        "scrutinee": {
          "t": "app",
          "fn": { "t": "var", "name": "compare" },
          "args": [
            { "t": "var", "name": "x" },
            { "t": "var", "name": "y" }
          ]
        },
        "arms": [
          {
            "pat": { "p": "ctor", "ctor": "LT", "fields": [] },
            "body": { "t": "lit", "lit": { "kind": "bool", "value": true } }
          },
          {
            "pat": { "p": "wild" },
            "body": { "t": "lit", "lit": { "kind": "bool", "value": false } }
          }
        ]
      }
    },
    {
      "kind": "fn",
      "name": "le",
      "doc": "Polymorphic less-than-or-equal. `le x y` ≡ case compare x y of GT -> False; _ -> True. Ships in milestone 23 as the Ord-class free helper.",
      "type": {
        "k": "forall",
        "vars": ["a"],
        "constraints": [{ "class": "Ord", "type": { "k": "var", "name": "a" } }],
        "body": {
          "k": "fn",
          "params": [
            { "k": "var", "name": "a" },
            { "k": "var", "name": "a" }
          ],
          "param_modes": ["borrow", "borrow"],
          "ret": { "k": "con", "name": "Bool" },
          "effects": []
        }
      },
      "params": ["x", "y"],
      "body": {
        "t": "match",
        "scrutinee": {
          "t": "app",
          "fn": { "t": "var", "name": "compare" },
          "args": [
            { "t": "var", "name": "x" },
            { "t": "var", "name": "y" }
          ]
        },
        "arms": [
          {
            "pat": { "p": "ctor", "ctor": "GT", "fields": [] },
            "body": { "t": "lit", "lit": { "kind": "bool", "value": false } }
          },
          {
            "pat": { "p": "wild" },
            "body": { "t": "lit", "lit": { "kind": "bool", "value": true } }
          }
        ]
      }
    },
    {
      "kind": "fn",
      "name": "gt",
      "doc": "Polymorphic strict-greater-than. `gt x y` ≡ case compare x y of GT -> True; _ -> False. Ships in milestone 23 as the Ord-class free helper.",
      "type": {
        "k": "forall",
        "vars": ["a"],
        "constraints": [{ "class": "Ord", "type": { "k": "var", "name": "a" } }],
        "body": {
          "k": "fn",
          "params": [
            { "k": "var", "name": "a" },
            { "k": "var", "name": "a" }
          ],
          "param_modes": ["borrow", "borrow"],
          "ret": { "k": "con", "name": "Bool" },
          "effects": []
        }
      },
      "params": ["x", "y"],
      "body": {
        "t": "match",
        "scrutinee": {
          "t": "app",
          "fn": { "t": "var", "name": "compare" },
          "args": [
            { "t": "var", "name": "x" },
            { "t": "var", "name": "y" }
          ]
        },
        "arms": [
          {
            "pat": { "p": "ctor", "ctor": "GT", "fields": [] },
            "body": { "t": "lit", "lit": { "kind": "bool", "value": true } }
          },
          {
            "pat": { "p": "wild" },
            "body": { "t": "lit", "lit": { "kind": "bool", "value": false } }
          }
        ]
      }
    },
    {
      "kind": "fn",
      "name": "ge",
      "doc": "Polymorphic greater-than-or-equal. `ge x y` ≡ case compare x y of LT -> False; _ -> True. Ships in milestone 23 as the Ord-class free helper.",
      "type": {
        "k": "forall",
        "vars": ["a"],
        "constraints": [{ "class": "Ord", "type": { "k": "var", "name": "a" } }],
        "body": {
          "k": "fn",
          "params": [
            { "k": "var", "name": "a" },
            { "k": "var", "name": "a" }
          ],
          "param_modes": ["borrow", "borrow"],
          "ret": { "k": "con", "name": "Bool" },
          "effects": []
        }
      },
      "params": ["x", "y"],
      "body": {
        "t": "match",
        "scrutinee": {
          "t": "app",
          "fn": { "t": "var", "name": "compare" },
          "args": [
            { "t": "var", "name": "x" },
            { "t": "var", "name": "y" }
          ]
        },
        "arms": [
          {
            "pat": { "p": "ctor", "ctor": "LT", "fields": [] },
            "body": { "t": "lit", "lit": { "kind": "bool", "value": false } }
          },
          {
            "pat": { "p": "wild" },
            "body": { "t": "lit", "lit": { "kind": "bool", "value": true } }
          }
        ]
      }
    },
    {
      "kind": "fn",
      "name": "print",
      "doc": "Polymorphic console-print helper. `print x` ≡ `do io/print_str (show x)` with an explicit let-binder around `show x` for heap-Str RC discipline per eob.1 Str carve-out. Ships in milestone 24 as the second half of the Show prelude.",
      "type": {
        "k": "forall",
        "vars": ["a"],
        "constraints": [{ "class": "Show", "type": { "k": "var", "name": "a" } }],
        "body": {
          "k": "fn",
          "params": [{ "k": "var", "name": "a" }],
          "param_modes": ["borrow"],
          "ret": { "k": "con", "name": "Unit" },
          "effects": ["IO"]
        }
      },
      "params": ["x"],
      "body": {
        "t": "let",
        "name": "s",
        "value": {
          "t": "app",
          "fn": { "t": "var", "name": "show" },
          "args": [{ "t": "var", "name": "x" }]
        },
        "body": {
          "t": "do",
          "op": "io/print_str",
          "args": [{ "t": "var", "name": "s" }]
        }
      }
    }
  ]
}