EML-L1EML-L2EML-L3language kernelEML_LANGUAGE_KERNEL_FIXTURES_PASSno compiler change

EML Language Kernel

Inspect candidate EML programs before they lower into Expression Packet v0.

Programs

5

Inputs

8

Guards

4

Let bindings

1

Expansion tags

3

Canonical pairs

5

DAG unique ops

23

canonical operator tree lab

canonical match

eml primitive expansion

eml(x, y)exp(x) - ln(y)

Structural canonicalization only; not a semantic proof or compiler rewrite claim.

canonical match

softplus expansion

softplus(x)ln(1 + exp(x))

Structural canonicalization only; not a semantic proof or compiler rewrite claim.

canonical match

guarded softplus EML expanded shape

eml(x, softplus(y))exp(x) - ln(ln(1 + exp(y)))

Structural canonicalization only; not a semantic proof or compiler rewrite claim.

canonical match

commutative add canonicalization

exp(a) + exp(b)exp(b) + exp(a)

Structural canonicalization only; not a semantic proof or compiler rewrite claim.

canonical match

commutative mul canonicalization

x * yy * x

Structural canonicalization only; not a semantic proof or compiler rewrite claim.

internal language cost lab

no public SuperBEST claim change

Surface syntax, expanded trees, and DAG-style unique operator counts for reviewer inspection.

Program	Surface	Expanded	Delta	DAG unique	Repeated	Obligations	Checked
gaussian_energy_v0	7	7	0	4	3	1	0
guarded_eml_softplus_v0	1	6	5	6	0	4	0
raw_eml_primitive_v0	1	3	2	3	0	3	0
sigmoid_derivative_v0	10	10	0	6	4	2	1
softplus_pair_v0	4	4	0	4	0	3	1

forge_efrog_fixture0 guards0 lets

gaussian_energy_v0

exp(-(x * x)) + exp(-(x * x))

sha256:551c36f3c7a9a800aa83d84c3cdaabe33c774353bb4d8f52da15911571de6d3d

x

ASTs

surface

{
  "args": [
    {
      "args": [
        {
          "args": [
            {
              "args": [
                {
                  "kind": "var",
                  "name": "x"
                },
                {
                  "kind": "var",
                  "name": "x"
                }
              ],
              "kind": "op",
              "op": "mul"
            }
          ],
          "kind": "op",
          "op": "neg"
        }
      ],
      "kind": "op",
      "op": "exp"
    },
    {
      "args": [
        {
          "args": [
            {
              "args": [
                {
                  "kind": "var",
                  "name": "x"
                },
                {
                  "kind": "var",
                  "name": "x"
                }
              ],
              "kind": "op",
              "op": "mul"
            }
          ],
          "kind": "op",
          "op": "neg"
        }
      ],
      "kind": "op",
      "op": "exp"
    }
  ],
  "kind": "op",
  "op": "add"
}

expanded

{
  "args": [
    {
      "args": [
        {
          "args": [
            {
              "args": [
                {
                  "kind": "var",
                  "name": "x"
                },
                {
                  "kind": "var",
                  "name": "x"
                }
              ],
              "kind": "op",
              "op": "mul"
            }
          ],
          "kind": "op",
          "op": "neg"
        }
      ],
      "kind": "op",
      "op": "exp"
    },
    {
      "args": [
        {
          "args": [
            {
              "args": [
                {
                  "kind": "var",
                  "name": "x"
                },
                {
                  "kind": "var",
                  "name": "x"
                }
              ],
              "kind": "op",
              "op": "mul"
            }
          ],
          "kind": "op",
          "op": "neg"
        }
      ],
      "kind": "op",
      "op": "exp"
    }
  ],
  "kind": "op",
  "op": "add"
}

canonical

{
  "args": [
    {
      "args": [
        {
          "args": [
            {
              "args": [
                {
                  "kind": "var",
                  "name": "x"
                },
                {
                  "kind": "var",
                  "name": "x"
                }
              ],
              "kind": "op",
              "op": "mul"
            }
          ],
          "kind": "op",
          "op": "neg"
        }
      ],
      "kind": "op",
      "op": "exp"
    },
    {
      "args": [
        {
          "args": [
            {
              "args": [
                {
                  "kind": "var",
                  "name": "x"
                },
                {
                  "kind": "var",
                  "name": "x"
                }
              ],
              "kind": "op",
              "op": "mul"
            }
          ],
          "kind": "op",
          "op": "neg"
        }
      ],
      "kind": "op",
      "op": "exp"
    }
  ],
  "kind": "op",
  "op": "add"
}

guarded_eml1 guards1 lets

guarded_eml_softplus_v0

exp(x) - ln(ln(1 + exp(y)))

sha256:6a6fbd514b2283fdb15e2b1a58bf1a84ddbe379bf2b63c013f48860b636ca2f3

softplus expandseml expands

xy

guards

positive(ln(1 + exp(y)))

lets

y_safe = ln(1 + exp(y))

ASTs

surface

{
  "args": [
    {
      "kind": "var",
      "name": "x"
    },
    {
      "kind": "var",
      "name": "y_safe"
    }
  ],
  "kind": "op",
  "op": "eml"
}

expanded

{
  "args": [
    {
      "args": [
        {
          "kind": "var",
          "name": "x"
        }
      ],
      "kind": "op",
      "op": "exp"
    },
    {
      "args": [
        {
          "args": [
            {
              "args": [
                {
                  "kind": "const",
                  "value": 1
                },
                {
                  "args": [
                    {
                      "kind": "var",
                      "name": "y"
                    }
                  ],
                  "kind": "op",
                  "op": "exp"
                }
              ],
              "kind": "op",
              "op": "add"
            }
          ],
          "kind": "op",
          "op": "ln"
        }
      ],
      "kind": "op",
      "op": "ln"
    }
  ],
  "kind": "op",
  "op": "sub"
}

canonical

{
  "args": [
    {
      "args": [
        {
          "kind": "var",
          "name": "x"
        }
      ],
      "kind": "op",
      "op": "exp"
    },
    {
      "args": [
        {
          "args": [
            {
              "args": [
                {
                  "args": [
                    {
                      "kind": "var",
                      "name": "y"
                    }
                  ],
                  "kind": "op",
                  "op": "exp"
                },
                {
                  "kind": "const",
                  "value": 1
                }
              ],
              "kind": "op",
              "op": "add"
            }
          ],
          "kind": "op",
          "op": "ln"
        }
      ],
      "kind": "op",
      "op": "ln"
    }
  ],
  "kind": "op",
  "op": "sub"
}

eml_primitive1 guards0 lets

raw_eml_primitive_v0

exp(x) - ln(y)

sha256:870e00c09ae3236174b70fbb1dd0f27bef57c85481259c8180923991ad9e922c

eml expands

xy

guards

positive(y)

ASTs

surface

{
  "args": [
    {
      "kind": "var",
      "name": "x"
    },
    {
      "kind": "var",
      "name": "y"
    }
  ],
  "kind": "op",
  "op": "eml"
}

expanded

{
  "args": [
    {
      "args": [
        {
          "kind": "var",
          "name": "x"
        }
      ],
      "kind": "op",
      "op": "exp"
    },
    {
      "args": [
        {
          "kind": "var",
          "name": "y"
        }
      ],
      "kind": "op",
      "op": "ln"
    }
  ],
  "kind": "op",
  "op": "sub"
}

canonical

{
  "args": [
    {
      "args": [
        {
          "kind": "var",
          "name": "x"
        }
      ],
      "kind": "op",
      "op": "exp"
    },
    {
      "args": [
        {
          "kind": "var",
          "name": "y"
        }
      ],
      "kind": "op",
      "op": "ln"
    }
  ],
  "kind": "op",
  "op": "sub"
}

sigmoid_logistic1 guards0 lets

sigmoid_derivative_v0

1 / (1 + exp(-x)) * (1 - 1 / (1 + exp(-x)))

sha256:6eda998b3070f828b704bcef4476dfc764d8f4fe76ea0ee985036fb6b699606a

x

guards

nonzero(1 + exp(-x))

ASTs

surface

{
  "args": [
    {
      "args": [
        {
          "kind": "const",
          "value": 1
        },
        {
          "args": [
            {
              "kind": "const",
              "value": 1
            },
            {
              "args": [
                {
                  "args": [
                    {
                      "kind": "var",
                      "name": "x"
                    }
                  ],
                  "kind": "op",
                  "op": "neg"
                }
              ],
              "kind": "op",
              "op": "exp"
            }
          ],
          "kind": "op",
          "op": "add"
        }
      ],
      "kind": "op",
      "op": "div"
    },
    {
      "args": [
        {
          "kind": "const",
          "value": 1
        },
        {
          "args": [
            {
              "kind": "const",
              "value": 1
            },
            {
              "args": [
                {
                  "kind": "const",
                  "value": 1
                },
                {
                  "args": [
                    {
                      "args": [
                        {
                          "kind": "var",
                          "name": "x"
                        }
                      ],
                      "kind": "op",
                      "op": "neg"
                    }
                  ],
                  "kind": "op",
                  "op": "exp"
                }
              ],
              "kind": "op",
              "op": "add"
            }
          ],
          "kind": "op",
          "op": "div"
        }
      ],
      "kind": "op",
      "op": "sub"
    }
  ],
  "kind": "op",
  "op": "mul"
}

expanded

{
  "args": [
    {
      "args": [
        {
          "kind": "const",
          "value": 1
        },
        {
          "args": [
            {
              "kind": "const",
              "value": 1
            },
            {
              "args": [
                {
                  "args": [
                    {
                      "kind": "var",
                      "name": "x"
                    }
                  ],
                  "kind": "op",
                  "op": "neg"
                }
              ],
              "kind": "op",
              "op": "exp"
            }
          ],
          "kind": "op",
          "op": "add"
        }
      ],
      "kind": "op",
      "op": "div"
    },
    {
      "args": [
        {
          "kind": "const",
          "value": 1
        },
        {
          "args": [
            {
              "kind": "const",
              "value": 1
            },
            {
              "args": [
                {
                  "kind": "const",
                  "value": 1
                },
                {
                  "args": [
                    {
                      "args": [
                        {
                          "kind": "var",
                          "name": "x"
                        }
                      ],
                      "kind": "op",
                      "op": "neg"
                    }
                  ],
                  "kind": "op",
                  "op": "exp"
                }
              ],
              "kind": "op",
              "op": "add"
            }
          ],
          "kind": "op",
          "op": "div"
        }
      ],
      "kind": "op",
      "op": "sub"
    }
  ],
  "kind": "op",
  "op": "mul"
}

canonical

{
  "args": [
    {
      "args": [
        {
          "kind": "const",
          "value": 1
        },
        {
          "args": [
            {
              "args": [
                {
                  "args": [
                    {
                      "kind": "var",
                      "name": "x"
                    }
                  ],
                  "kind": "op",
                  "op": "neg"
                }
              ],
              "kind": "op",
              "op": "exp"
            },
            {
              "kind": "const",
              "value": 1
            }
          ],
          "kind": "op",
          "op": "add"
        }
      ],
      "kind": "op",
      "op": "div"
    },
    {
      "args": [
        {
          "kind": "const",
          "value": 1
        },
        {
          "args": [
            {
              "kind": "const",
              "value": 1
            },
            {
              "args": [
                {
                  "args": [
                    {
                      "args": [
                        {
                          "kind": "var",
                          "name": "x"
                        }
                      ],
                      "kind": "op",
                      "op": "neg"
                    }
                  ],
                  "kind": "op",
                  "op": "exp"
                },
                {
                  "kind": "const",
                  "value": 1
                }
              ],
              "kind": "op",
              "op": "add"
            }
          ],
          "kind": "op",
          "op": "div"
        }
      ],
      "kind": "op",
      "op": "sub"
    }
  ],
  "kind": "op",
  "op": "mul"
}

softplus_logsumexp1 guards0 lets

softplus_pair_v0

ln(exp(a) + exp(b))

sha256:d69591fc0d62cb7d8c6bfb8c53cb91e7a841217261d70c6e6813fc7aac95e58a

ab

guards

positive(exp(a) + exp(b))

ASTs

surface

{
  "args": [
    {
      "args": [
        {
          "args": [
            {
              "kind": "var",
              "name": "a"
            }
          ],
          "kind": "op",
          "op": "exp"
        },
        {
          "args": [
            {
              "kind": "var",
              "name": "b"
            }
          ],
          "kind": "op",
          "op": "exp"
        }
      ],
      "kind": "op",
      "op": "add"
    }
  ],
  "kind": "op",
  "op": "ln"
}

expanded

{
  "args": [
    {
      "args": [
        {
          "args": [
            {
              "kind": "var",
              "name": "a"
            }
          ],
          "kind": "op",
          "op": "exp"
        },
        {
          "args": [
            {
              "kind": "var",
              "name": "b"
            }
          ],
          "kind": "op",
          "op": "exp"
        }
      ],
      "kind": "op",
      "op": "add"
    }
  ],
  "kind": "op",
  "op": "ln"
}

canonical

{
  "args": [
    {
      "args": [
        {
          "args": [
            {
              "kind": "var",
              "name": "a"
            }
          ],
          "kind": "op",
          "op": "exp"
        },
        {
          "args": [
            {
              "kind": "var",
              "name": "b"
            }
          ],
          "kind": "op",
          "op": "exp"
        }
      ],
      "kind": "op",
      "op": "add"
    }
  ],
  "kind": "op",
  "op": "ln"
}