Expression syntax

Pointer expressions operate on the domain of bytes representing unsigned integers.

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YAML

ethdebug/format/pointer/expression

$schema: "https://json-schema.org/draft/2020-12/schema"
$id: "schema:ethdebug/format/pointer/expression"

title: ethdebug/format/pointer/expression
description: |
  A schema for describing expressions that evaluate to values.

oneOf:
  - $ref: "#/$defs/Literal"
  - $ref: "#/$defs/Variable"
  - $ref: "#/$defs/Constant"
  - $ref: "#/$defs/Arithmetic"
  - $ref: "#/$defs/Lookup"
  - $ref: "#/$defs/Read"
  - $ref: "#/$defs/Keccak256"

$defs:
  Literal:
    title: Literal value
    description: |
      An unsigned number or a `0x`-prefixed string of hexadecimal digits

    oneOf:
      - type: integer
        description: A non-negative integer literal
        min: 0

      - type: string
        description: |
          A `0x`-prefixed hexadecimal string representing literal bytes
        pattern: "^0x[0-9a-fA-F]{1,}$"

    examples:
      - 5
      - "0x0000000000000000000000000000000000000000000000000000000000000000"

  Constant:
    title: Constant value
    type: string
    enum:
      - $wordsize

  Variable:
    title: Variable identifier
    description: |
      A string that matches an identifier used in an earlier declaration of
      a scalar variable. This expression evaluates to the value of that
      variable.
    $ref: "schema:ethdebug/format/pointer/identifier"

  Arithmetic:
    title: Arithmetic operation
    type: object
    properties:
      "$sum":
        description: |
          A list of expressions to be added together.
        $ref: "#/$defs/Operands"
      "$difference":
        description: |
          A tuple of two expressions where the second is to be subtracted from
          the first.

          (i.e., `{ "$difference": [a, b] }` equals `a` minus `b`.)
        $ref: "#/$defs/Operands"
        minItems: 2
        maxItems: 2
      "$product":
        description: |
          A list of expressions to be multipled.
        $ref: "#/$defs/Operands"
      "$quotient":
        description: |
          A tuple of two expressions where the first corresponds to the
          dividend and the second corresponds to the divisor, for the purposes
          of doing integer division.

          (i.e., `{ "$quotient": [a, b] }` equals `a` divided by `b`.)
        $ref: "#/$defs/Operands"
        minItems: 2
        maxItems: 2
      "$remainder":
        description: |
          A tuple of two expressions where the first corresponds to the
          dividend and the second corresponds to the divisor, for the purposes
          of computing the modular-arithmetic remainder.

          (i.e., `{ "$remainder": [a, b] }` equals `a` mod `b`.)
        $ref: "#/$defs/Operands"
        minItems: 2
        maxItems: 2
    additionalProperties: false
    minProperties: 1
    maxProperties: 1
    examples:
      - "$sum": [5, 3, 4]
      - "$difference": [5, 3]
      - "$product": [5, 3, 0]
      - "$quotient": [5, 3]
      - "$remainder":
          - "$product":
            - 2
            - 2
            - 2
            - 2
          - 3

  Operands:
    type: array
    items:
      $ref: "schema:ethdebug/format/pointer/expression"

  Lookup:
    title: Lookup region definition
    description: |
      An object of the form `{ ".<property-name>": "<region>" }`, to
      denote that this expression is equivalent to the defined value for
      the property named `<property-name>` inside the region referenced as
      `<region>`.

      `<property-name>` **must** be a valid and present property on the
      corresponding region, or it **must** correspond to an optional property
      whose schema specifies a default value for that property.
    type: object
    patternProperties:
      "^\\.(offset|length|slot)$":
        $ref: "#/$defs/Reference"
    additionalProperties: false
    minProperties: 1
    maxProperties: 1

    examples:
      - .offset: "array-count"
      - .length: "array-item"
      - .offset: $this


  Read:
    title: Read region bytes
    description: |
      An object of the form `{ "$read": "<region>" }`. The value of this
      expression equals the raw bytes present in the running machine state
      in the referenced region.
    type: object
    properties:
      $read:
        $ref: "#/$defs/Reference"
    required:
      - $read
    additionalProperties: false
    examples:
      - $read: "struct-start"

  Reference:
    title: Region reference
    description: |
      A string value that **must** either be the `"name"` of at least one
      region declared with `{ "name": "<region>" }` previously in some root
      pointer representation, or it **must** be the literal value `"$this"`,
      which indicates a reference to the region containing this expression.

      If more than one region is defined with the same name, resolution is
      defined as firstly resolving to the latest earlier sibling that declares
      the matching name, then secondly resolving to the parent if it matches,
      then to parent's earlier siblings, and so on.
    type: string

    oneOf:
      - $ref: "schema:ethdebug/format/pointer/identifier"
      - const: "$this"
        description: |
          Indicates a reference to the region containing this expression.

  Keccak256:
    title: Keccak256 hash
    description: |
      An object of the form `{ "keccak256": [...values] }`, indicating that this
      expression evaluates to the Solidity-style keccak256 hash of the
      tightly-packed bytes encoded by `values`.
    type: object
    properties:
      $keccak256:
        title: Array of hashed values
        type: array
        items:
          $ref: "schema:ethdebug/format/pointer/expression"
    additionalProperties: false
    required:
      - $keccak256
    examples:
      - $keccak256:
          - 0
          - "0x00"

examples:
  - 0
  - $sum:
      - .offset: "array-start"
      - .length: "array-start"
      - 1
  - $keccak256:
      - 5
      - .offset: "array-start"

JSON

ethdebug/format/pointer/expression

{
  "$schema": "https://json-schema.org/draft/2020-12/schema",
  "$id": "schema:ethdebug/format/pointer/expression",
  "title": "ethdebug/format/pointer/expression",
  "description": "A schema for describing expressions that evaluate to values.\n",
  "oneOf": [
    {
      "$ref": "#/$defs/Literal"
    },
    {
      "$ref": "#/$defs/Variable"
    },
    {
      "$ref": "#/$defs/Constant"
    },
    {
      "$ref": "#/$defs/Arithmetic"
    },
    {
      "$ref": "#/$defs/Lookup"
    },
    {
      "$ref": "#/$defs/Read"
    },
    {
      "$ref": "#/$defs/Keccak256"
    }
  ],
  "$defs": {
    "Literal": {
      "title": "Literal value",
      "description": "An unsigned number or a `0x`-prefixed string of hexadecimal digits\n",
      "oneOf": [
        {
          "type": "integer",
          "description": "A non-negative integer literal",
          "min": 0
        },
        {
          "type": "string",
          "description": "A `0x`-prefixed hexadecimal string representing literal bytes\n",
          "pattern": "^0x[0-9a-fA-F]{1,}$"
        }
      ],
      "examples": [
        5,
        "0x0000000000000000000000000000000000000000000000000000000000000000"
      ]
    },
    "Constant": {
      "title": "Constant value",
      "type": "string",
      "enum": [
        "$wordsize"
      ]
    },
    "Variable": {
      "title": "Variable identifier",
      "description": "A string that matches an identifier used in an earlier declaration of\na scalar variable. This expression evaluates to the value of that\nvariable.\n",
      "$ref": "schema:ethdebug/format/pointer/identifier"
    },
    "Arithmetic": {
      "title": "Arithmetic operation",
      "type": "object",
      "properties": {
        "$sum": {
          "description": "A list of expressions to be added together.\n",
          "$ref": "#/$defs/Operands"
        },
        "$difference": {
          "description": "A tuple of two expressions where the second is to be subtracted from\nthe first.\n\n(i.e., `{ \"$difference\": [a, b] }` equals `a` minus `b`.)\n",
          "$ref": "#/$defs/Operands",
          "minItems": 2,
          "maxItems": 2
        },
        "$product": {
          "description": "A list of expressions to be multipled.\n",
          "$ref": "#/$defs/Operands"
        },
        "$quotient": {
          "description": "A tuple of two expressions where the first corresponds to the\ndividend and the second corresponds to the divisor, for the purposes\nof doing integer division.\n\n(i.e., `{ \"$quotient\": [a, b] }` equals `a` divided by `b`.)\n",
          "$ref": "#/$defs/Operands",
          "minItems": 2,
          "maxItems": 2
        },
        "$remainder": {
          "description": "A tuple of two expressions where the first corresponds to the\ndividend and the second corresponds to the divisor, for the purposes\nof computing the modular-arithmetic remainder.\n\n(i.e., `{ \"$remainder\": [a, b] }` equals `a` mod `b`.)\n",
          "$ref": "#/$defs/Operands",
          "minItems": 2,
          "maxItems": 2
        }
      },
      "additionalProperties": false,
      "minProperties": 1,
      "maxProperties": 1,
      "examples": [
        {
          "$sum": [
            5,
            3,
            4
          ]
        },
        {
          "$difference": [
            5,
            3
          ]
        },
        {
          "$product": [
            5,
            3,
            0
          ]
        },
        {
          "$quotient": [
            5,
            3
          ]
        },
        {
          "$remainder": [
            {
              "$product": [
                2,
                2,
                2,
                2
              ]
            },
            3
          ]
        }
      ]
    },
    "Operands": {
      "type": "array",
      "items": {
        "$ref": "schema:ethdebug/format/pointer/expression"
      }
    },
    "Lookup": {
      "title": "Lookup region definition",
      "description": "An object of the form `{ \".<property-name>\": \"<region>\" }`, to\ndenote that this expression is equivalent to the defined value for\nthe property named `<property-name>` inside the region referenced as\n`<region>`.\n\n`<property-name>` **must** be a valid and present property on the\ncorresponding region, or it **must** correspond to an optional property\nwhose schema specifies a default value for that property.\n",
      "type": "object",
      "patternProperties": {
        "^\\.(offset|length|slot)$": {
          "$ref": "#/$defs/Reference"
        }
      },
      "additionalProperties": false,
      "minProperties": 1,
      "maxProperties": 1,
      "examples": [
        {
          ".offset": "array-count"
        },
        {
          ".length": "array-item"
        },
        {
          ".offset": "$this"
        }
      ]
    },
    "Read": {
      "title": "Read region bytes",
      "description": "An object of the form `{ \"$read\": \"<region>\" }`. The value of this\nexpression equals the raw bytes present in the running machine state\nin the referenced region.\n",
      "type": "object",
      "properties": {
        "$read": {
          "$ref": "#/$defs/Reference"
        }
      },
      "required": [
        "$read"
      ],
      "additionalProperties": false,
      "examples": [
        {
          "$read": "struct-start"
        }
      ]
    },
    "Reference": {
      "title": "Region reference",
      "description": "A string value that **must** either be the `\"name\"` of at least one\nregion declared with `{ \"name\": \"<region>\" }` previously in some root\npointer representation, or it **must** be the literal value `\"$this\"`,\nwhich indicates a reference to the region containing this expression.\n\nIf more than one region is defined with the same name, resolution is\ndefined as firstly resolving to the latest earlier sibling that declares\nthe matching name, then secondly resolving to the parent if it matches,\nthen to parent's earlier siblings, and so on.\n",
      "type": "string",
      "oneOf": [
        {
          "$ref": "schema:ethdebug/format/pointer/identifier"
        },
        {
          "const": "$this",
          "description": "Indicates a reference to the region containing this expression.\n"
        }
      ]
    },
    "Keccak256": {
      "title": "Keccak256 hash",
      "description": "An object of the form `{ \"keccak256\": [...values] }`, indicating that this\nexpression evaluates to the Solidity-style keccak256 hash of the\ntightly-packed bytes encoded by `values`.\n",
      "type": "object",
      "properties": {
        "$keccak256": {
          "title": "Array of hashed values",
          "type": "array",
          "items": {
            "$ref": "schema:ethdebug/format/pointer/expression"
          }
        }
      },
      "additionalProperties": false,
      "required": [
        "$keccak256"
      ],
      "examples": [
        {
          "$keccak256": [
            0,
            "0x00"
          ]
        }
      ]
    }
  },
  "examples": [
    0,
    {
      "$sum": [
        {
          ".offset": "array-start"
        },
        {
          ".length": "array-start"
        },
        1
      ]
    },
    {
      "$keccak256": [
        5,
        {
          ".offset": "array-start"
        }
      ]
    }
  ]
}

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Literal values

An expression can be a literal value.

Literal values must be represented either as JSON numbers or as 0x-prefixed hexadecimal strings. Hexadecimal strings always represent a literal string of bytes.

For convenience, this schema does not restrict hexadecimal string representations to those that specify an even-number of digits (i.e., those that specify complete byte pairs); odd numbers of hexadecimal digits are fine.

Hexadecimal string representations may omit leading zeroes; values are assumed to be left-padded to the bytes width appropriate for the context.

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YAML

ethdebug/format/pointer/expression#/$defs/Literal

title: Literal value
description: |
  An unsigned number or a `0x`-prefixed string of hexadecimal digits

oneOf:
  - type: integer
    description: A non-negative integer literal
    min: 0

  - type: string
    description: |
      A `0x`-prefixed hexadecimal string representing literal bytes
    pattern: "^0x[0-9a-fA-F]{1,}$"

examples:
  - 5
  - "0x0000000000000000000000000000000000000000000000000000000000000000"

JSON

ethdebug/format/pointer/expression#/$defs/Literal

{
  "title": "Literal value",
  "description": "An unsigned number or a `0x`-prefixed string of hexadecimal digits\n",
  "oneOf": [
    {
      "type": "integer",
      "description": "A non-negative integer literal",
      "min": 0
    },
    {
      "type": "string",
      "description": "A `0x`-prefixed hexadecimal string representing literal bytes\n",
      "pattern": "^0x[0-9a-fA-F]{1,}$"
    }
  ],
  "examples": [
    5,
    "0x0000000000000000000000000000000000000000000000000000000000000000"
  ]
}

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Scalar variables

An expression can be a string value equal to the identifier for a known scalar variable introduced by some pointer representation.

For an example where scalar variables may appear, see the List collection schema.

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YAML

ethdebug/format/pointer/expression#/$defs/Literal

title: Literal value
description: |
  An unsigned number or a `0x`-prefixed string of hexadecimal digits

oneOf:
  - type: integer
    description: A non-negative integer literal
    min: 0

  - type: string
    description: |
      A `0x`-prefixed hexadecimal string representing literal bytes
    pattern: "^0x[0-9a-fA-F]{1,}$"

examples:
  - 5
  - "0x0000000000000000000000000000000000000000000000000000000000000000"

JSON

ethdebug/format/pointer/expression#/$defs/Literal

{
  "title": "Literal value",
  "description": "An unsigned number or a `0x`-prefixed string of hexadecimal digits\n",
  "oneOf": [
    {
      "type": "integer",
      "description": "A non-negative integer literal",
      "min": 0
    },
    {
      "type": "string",
      "description": "A `0x`-prefixed hexadecimal string representing literal bytes\n",
      "pattern": "^0x[0-9a-fA-F]{1,}$"
    }
  ],
  "examples": [
    5,
    "0x0000000000000000000000000000000000000000000000000000000000000000"
  ]
}

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Arithmetic operations

An expression can be an object of the form { <op>: [...] }, where <op> denotes an arithmetic operation.

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YAML

ethdebug/format/pointer/expression#/$defs/Arithmetic

title: Arithmetic operation
type: object
properties:
  "$sum":
    description: |
      A list of expressions to be added together.
    $ref: "#/$defs/Operands"
  "$difference":
    description: |
      A tuple of two expressions where the second is to be subtracted from
      the first.

      (i.e., `{ "$difference": [a, b] }` equals `a` minus `b`.)
    $ref: "#/$defs/Operands"
    minItems: 2
    maxItems: 2
  "$product":
    description: |
      A list of expressions to be multipled.
    $ref: "#/$defs/Operands"
  "$quotient":
    description: |
      A tuple of two expressions where the first corresponds to the
      dividend and the second corresponds to the divisor, for the purposes
      of doing integer division.

      (i.e., `{ "$quotient": [a, b] }` equals `a` divided by `b`.)
    $ref: "#/$defs/Operands"
    minItems: 2
    maxItems: 2
  "$remainder":
    description: |
      A tuple of two expressions where the first corresponds to the
      dividend and the second corresponds to the divisor, for the purposes
      of computing the modular-arithmetic remainder.

      (i.e., `{ "$remainder": [a, b] }` equals `a` mod `b`.)
    $ref: "#/$defs/Operands"
    minItems: 2
    maxItems: 2
additionalProperties: false
minProperties: 1
maxProperties: 1
examples:
  - "$sum": [ 5, 3, 4 ]
  - "$difference": [ 5, 3 ]
  - "$product": [ 5, 3, 0 ]
  - "$quotient": [ 5, 3 ]
  - "$remainder":
      - "$product":
          - 2
          - 2
          - 2
          - 2
      - 3

JSON

ethdebug/format/pointer/expression#/$defs/Arithmetic

{
  "title": "Arithmetic operation",
  "type": "object",
  "properties": {
    "$sum": {
      "description": "A list of expressions to be added together.\n",
      "$ref": "#/$defs/Operands"
    },
    "$difference": {
      "description": "A tuple of two expressions where the second is to be subtracted from\nthe first.\n\n(i.e., `{ \"$difference\": [a, b] }` equals `a` minus `b`.)\n",
      "$ref": "#/$defs/Operands",
      "minItems": 2,
      "maxItems": 2
    },
    "$product": {
      "description": "A list of expressions to be multipled.\n",
      "$ref": "#/$defs/Operands"
    },
    "$quotient": {
      "description": "A tuple of two expressions where the first corresponds to the\ndividend and the second corresponds to the divisor, for the purposes\nof doing integer division.\n\n(i.e., `{ \"$quotient\": [a, b] }` equals `a` divided by `b`.)\n",
      "$ref": "#/$defs/Operands",
      "minItems": 2,
      "maxItems": 2
    },
    "$remainder": {
      "description": "A tuple of two expressions where the first corresponds to the\ndividend and the second corresponds to the divisor, for the purposes\nof computing the modular-arithmetic remainder.\n\n(i.e., `{ \"$remainder\": [a, b] }` equals `a` mod `b`.)\n",
      "$ref": "#/$defs/Operands",
      "minItems": 2,
      "maxItems": 2
    }
  },
  "additionalProperties": false,
  "minProperties": 1,
  "maxProperties": 1,
  "examples": [
    {
      "$sum": [
        5,
        3,
        4
      ]
    },
    {
      "$difference": [
        5,
        3
      ]
    },
    {
      "$product": [
        5,
        3,
        0
      ]
    },
    {
      "$quotient": [
        5,
        3
      ]
    },
    {
      "$remainder": [
        {
          "$product": [
            2,
            2,
            2,
            2
          ]
        },
        3
      ]
    }
  ]
}

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Lookup region definition

An expression can reference properties defined for a particular region, such as another region's "offset" or "length". Such expressions resolve to the same value as the expression specified for that corresponding property.

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YAML

ethdebug/format/pointer/expression#/$defs/Lookup

title: Lookup region definition
description: |
  An object of the form `{ ".<property-name>": "<region>" }`, to
  denote that this expression is equivalent to the defined value for
  the property named `<property-name>` inside the region referenced as
  `<region>`.

  `<property-name>` **must** be a valid and present property on the
  corresponding region, or it **must** correspond to an optional property
  whose schema specifies a default value for that property.
type: object
patternProperties:
  "^\\.(offset|length|slot)$":
    $ref: "#/$defs/Reference"
additionalProperties: false
minProperties: 1
maxProperties: 1

examples:
  - .offset: "array-count"
  - .length: "array-item"
  - .offset: $this

JSON

ethdebug/format/pointer/expression#/$defs/Lookup

{
  "title": "Lookup region definition",
  "description": "An object of the form `{ \".<property-name>\": \"<region>\" }`, to\ndenote that this expression is equivalent to the defined value for\nthe property named `<property-name>` inside the region referenced as\n`<region>`.\n\n`<property-name>` **must** be a valid and present property on the\ncorresponding region, or it **must** correspond to an optional property\nwhose schema specifies a default value for that property.\n",
  "type": "object",
  "patternProperties": {
    "^\\.(offset|length|slot)$": {
      "$ref": "#/$defs/Reference"
    }
  },
  "additionalProperties": false,
  "minProperties": 1,
  "maxProperties": 1,
  "examples": [
    {
      ".offset": "array-count"
    },
    {
      ".length": "array-item"
    },
    {
      ".offset": "$this"
    }
  ]
}

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Reading from the EVM

An expression can be an object of the form { "$read": "<region>" }, where <region> references a particular region defined in some root pointer.

The value of such an expression is the concatenation of bytes present in the running machine state that correspond to the bytes addressed by the referenced region.

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YAML

ethdebug/format/pointer/expression#/$defs/Read

title: Read region bytes
description: |
  An object of the form `{ "$read": "<region>" }`. The value of this
  expression equals the raw bytes present in the running machine state
  in the referenced region.
type: object
properties:
  $read:
    $ref: "#/$defs/Reference"
required:
  - $read
additionalProperties: false
examples:
  - $read: "struct-start"

JSON

ethdebug/format/pointer/expression#/$defs/Read

{
  "title": "Read region bytes",
  "description": "An object of the form `{ \"$read\": \"<region>\" }`. The value of this\nexpression equals the raw bytes present in the running machine state\nin the referenced region.\n",
  "type": "object",
  "properties": {
    "$read": {
      "$ref": "#/$defs/Reference"
    }
  },
  "required": [
    "$read"
  ],
  "additionalProperties": false,
  "examples": [
    {
      "$read": "struct-start"
    }
  ]
}

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Keccak256 hashes

An expression can be an object of form { "$keccak256": [...] }, indicating that the value of the expression is a Solidity-style, tightly-packed keccak256 hash of the concatenation of bytes specified by the list.

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YAML

ethdebug/format/pointer/expression#/$defs/Keccak256

title: Keccak256 hash
description: |
  An object of the form `{ "keccak256": [...values] }`, indicating that this
  expression evaluates to the Solidity-style keccak256 hash of the
  tightly-packed bytes encoded by `values`.
type: object
properties:
  $keccak256:
    title: Array of hashed values
    type: array
    items:
      $ref: "schema:ethdebug/format/pointer/expression"
additionalProperties: false
required:
  - $keccak256
examples:
  - $keccak256:
      - 0
      - "0x00"

JSON

ethdebug/format/pointer/expression#/$defs/Keccak256

{
  "title": "Keccak256 hash",
  "description": "An object of the form `{ \"keccak256\": [...values] }`, indicating that this\nexpression evaluates to the Solidity-style keccak256 hash of the\ntightly-packed bytes encoded by `values`.\n",
  "type": "object",
  "properties": {
    "$keccak256": {
      "title": "Array of hashed values",
      "type": "array",
      "items": {
        "$ref": "schema:ethdebug/format/pointer/expression"
      }
    }
  },
  "additionalProperties": false,
  "required": [
    "$keccak256"
  ],
  "examples": [
    {
      "$keccak256": [
        0,
        "0x00"
      ]
    }
  ]
}

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Region references

Regions can be referenced either by name (which must be a defined region), or by use of the literal string value "$this" (which indicates that the referenced region is the region containing the expression itself).

In cases where an expression is used outside the context of a particular region definition, the use of "$this" is prohibited.

Individual properties may not be defined with any reference to themselves. Properties also may not be defined in terms of mutual reference to each other. (Don't make this harder than it has to be.)

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YAML

ethdebug/format/pointer/expression#/$defs/Reference

title: Region reference
description: |
  A string value that **must** either be the `"name"` of at least one
  region declared with `{ "name": "<region>" }` previously in some root
  pointer representation, or it **must** be the literal value `"$this"`,
  which indicates a reference to the region containing this expression.

  If more than one region is defined with the same name, resolution is
  defined as firstly resolving to the latest earlier sibling that declares
  the matching name, then secondly resolving to the parent if it matches,
  then to parent's earlier siblings, and so on.
type: string

oneOf:
  - $ref: "schema:ethdebug/format/pointer/identifier"
  - const: "$this"
    description: |
      Indicates a reference to the region containing this expression.

JSON

ethdebug/format/pointer/expression#/$defs/Reference

{
  "title": "Region reference",
  "description": "A string value that **must** either be the `\"name\"` of at least one\nregion declared with `{ \"name\": \"<region>\" }` previously in some root\npointer representation, or it **must** be the literal value `\"$this\"`,\nwhich indicates a reference to the region containing this expression.\n\nIf more than one region is defined with the same name, resolution is\ndefined as firstly resolving to the latest earlier sibling that declares\nthe matching name, then secondly resolving to the parent if it matches,\nthen to parent's earlier siblings, and so on.\n",
  "type": "string",
  "oneOf": [
    {
      "$ref": "schema:ethdebug/format/pointer/identifier"
    },
    {
      "const": "$this",
      "description": "Indicates a reference to the region containing this expression.\n"
    }
  ]
}

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