{
  "esm": "1.0.0",
  "metadata": {
    "name": "Interp",
    "description": "Standard-library interpolation subsystem. Demonstrates the canonical AST recipe for 1-D linear and 2-D bilinear interpolation built from `interp.searchsorted` (esm-spec.md §9.2) + the `index` op (§4.3.3) + arithmetic. The closed registry deliberately ships *only* `searchsorted`; this file is the reference composition and a copy-paste template — it is not an exhaustive `linear_interp_1d(x, xs, ys)` 'function' (the spec has no closed function over inline-array arguments). To use, copy the variable definitions into the consuming subsystem and replace the inline `xs`/`ys`/`table` const arrays with the caller's data. See docs/standard_library.md for the design rationale.",
    "authors": [
      "EarthSciML"
    ],
    "created": "2026-04-25T00:00:00Z",
    "tags": [
      "standard-library",
      "interpolation",
      "searchsorted",
      "closed-function-registry"
    ],
    "references": [
      {
        "citation": "esm-spec.md §9.2 (interp.searchsorted closed function); §4.3.3 (index op)."
      }
    ]
  },
  "models": {
    "Interp": {
      "variables": {
        "x": {
          "type": "parameter",
          "units": "1",
          "default": 0.5,
          "description": "1-D query point. Replace at composition time with the caller's value."
        },
        "y_linear": {
          "type": "unknown",
          "units": "1",
          "description": "1-D linear interpolation of the inline table (xs = 0,0.25,0.5,0.75,1.0; ys = 0,1,4,9,16) at `x`. Recipe: `i_raw = searchsorted(xs, x); i = min(N, max(2, i_raw)); t = clamp((x - xs[i-1])/(xs[i] - xs[i-1]), 0, 1); y = ys[i-1] + t*(ys[i] - ys[i-1])`. The clamp on `t` provides constant-value extrapolation outside [xs[1], xs[N]] (matching the spec's recommended boundary behavior; see esm-spec.md §9.2 note on `searchsorted` out-of-range queries)."
        }
      },
      "equations": [
        {
          "lhs": "y_linear",
          "rhs": {
            "op": "+",
            "args": [
              {
                "op": "index",
                "args": [
                  {
                    "op": "const",
                    "args": [],
                    "value": [
                      0.0,
                      1.0,
                      4.0,
                      9.0,
                      16.0
                    ]
                  },
                  {
                    "op": "-",
                    "args": [
                      {
                        "op": "min",
                        "args": [
                          5,
                          {
                            "op": "max",
                            "args": [
                              2,
                              {
                                "op": "fn",
                                "name": "interp.searchsorted",
                                "args": [
                                  "x",
                                  {
                                    "op": "const",
                                    "args": [],
                                    "value": [
                                      0.0,
                                      0.25,
                                      0.5,
                                      0.75,
                                      1.0
                                    ]
                                  }
                                ]
                              }
                            ]
                          }
                        ]
                      },
                      1
                    ]
                  }
                ]
              },
              {
                "op": "*",
                "args": [
                  {
                    "op": "min",
                    "args": [
                      1.0,
                      {
                        "op": "max",
                        "args": [
                          0.0,
                          {
                            "op": "/",
                            "args": [
                              {
                                "op": "-",
                                "args": [
                                  "x",
                                  {
                                    "op": "index",
                                    "args": [
                                      {
                                        "op": "const",
                                        "args": [],
                                        "value": [
                                          0.0,
                                          0.25,
                                          0.5,
                                          0.75,
                                          1.0
                                        ]
                                      },
                                      {
                                        "op": "-",
                                        "args": [
                                          {
                                            "op": "min",
                                            "args": [
                                              5,
                                              {
                                                "op": "max",
                                                "args": [
                                                  2,
                                                  {
                                                    "op": "fn",
                                                    "name": "interp.searchsorted",
                                                    "args": [
                                                      "x",
                                                      {
                                                        "op": "const",
                                                        "args": [],
                                                        "value": [
                                                          0.0,
                                                          0.25,
                                                          0.5,
                                                          0.75,
                                                          1.0
                                                        ]
                                                      }
                                                    ]
                                                  }
                                                ]
                                              }
                                            ]
                                          },
                                          1
                                        ]
                                      }
                                    ]
                                  }
                                ]
                              },
                              {
                                "op": "-",
                                "args": [
                                  {
                                    "op": "index",
                                    "args": [
                                      {
                                        "op": "const",
                                        "args": [],
                                        "value": [
                                          0.0,
                                          0.25,
                                          0.5,
                                          0.75,
                                          1.0
                                        ]
                                      },
                                      {
                                        "op": "min",
                                        "args": [
                                          5,
                                          {
                                            "op": "max",
                                            "args": [
                                              2,
                                              {
                                                "op": "fn",
                                                "name": "interp.searchsorted",
                                                "args": [
                                                  "x",
                                                  {
                                                    "op": "const",
                                                    "args": [],
                                                    "value": [
                                                      0.0,
                                                      0.25,
                                                      0.5,
                                                      0.75,
                                                      1.0
                                                    ]
                                                  }
                                                ]
                                              }
                                            ]
                                          }
                                        ]
                                      }
                                    ]
                                  },
                                  {
                                    "op": "index",
                                    "args": [
                                      {
                                        "op": "const",
                                        "args": [],
                                        "value": [
                                          0.0,
                                          0.25,
                                          0.5,
                                          0.75,
                                          1.0
                                        ]
                                      },
                                      {
                                        "op": "-",
                                        "args": [
                                          {
                                            "op": "min",
                                            "args": [
                                              5,
                                              {
                                                "op": "max",
                                                "args": [
                                                  2,
                                                  {
                                                    "op": "fn",
                                                    "name": "interp.searchsorted",
                                                    "args": [
                                                      "x",
                                                      {
                                                        "op": "const",
                                                        "args": [],
                                                        "value": [
                                                          0.0,
                                                          0.25,
                                                          0.5,
                                                          0.75,
                                                          1.0
                                                        ]
                                                      }
                                                    ]
                                                  }
                                                ]
                                              }
                                            ]
                                          },
                                          1
                                        ]
                                      }
                                    ]
                                  }
                                ]
                              }
                            ]
                          }
                        ]
                      }
                    ]
                  },
                  {
                    "op": "-",
                    "args": [
                      {
                        "op": "index",
                        "args": [
                          {
                            "op": "const",
                            "args": [],
                            "value": [
                              0.0,
                              1.0,
                              4.0,
                              9.0,
                              16.0
                            ]
                          },
                          {
                            "op": "min",
                            "args": [
                              5,
                              {
                                "op": "max",
                                "args": [
                                  2,
                                  {
                                    "op": "fn",
                                    "name": "interp.searchsorted",
                                    "args": [
                                      "x",
                                      {
                                        "op": "const",
                                        "args": [],
                                        "value": [
                                          0.0,
                                          0.25,
                                          0.5,
                                          0.75,
                                          1.0
                                        ]
                                      }
                                    ]
                                  }
                                ]
                              }
                            ]
                          }
                        ]
                      },
                      {
                        "op": "index",
                        "args": [
                          {
                            "op": "const",
                            "args": [],
                            "value": [
                              0.0,
                              1.0,
                              4.0,
                              9.0,
                              16.0
                            ]
                          },
                          {
                            "op": "-",
                            "args": [
                              {
                                "op": "min",
                                "args": [
                                  5,
                                  {
                                    "op": "max",
                                    "args": [
                                      2,
                                      {
                                        "op": "fn",
                                        "name": "interp.searchsorted",
                                        "args": [
                                          "x",
                                          {
                                            "op": "const",
                                            "args": [],
                                            "value": [
                                              0.0,
                                              0.25,
                                              0.5,
                                              0.75,
                                              1.0
                                            ]
                                          }
                                        ]
                                      }
                                    ]
                                  }
                                ]
                              },
                              1
                            ]
                          }
                        ]
                      }
                    ]
                  }
                ]
              }
            ]
          }
        }
      ]
    }
  }
}