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README.md

Pando

Usage

TODO

Tags

A tag is a dictionary of tag category (key) and tag value (value) pairs. We denote a tag category and a tag value by cat: and cat:val, respectively. When there is no ambiguity, val may be used instead of cat:val. We also define a "combination" of tags T1 and T2, denoted by T1/T2, as a tag such that for any tag category cat:,

  • If cat:v ∈ T2, then cat:v ∈ T1/T2,
  • If cat: ∉ T2 and cat:v ∈ T1, then cat:v ∈ T1/T2, and
  • If cat: ∉ T2 and cat: ∉ T1, then cat: ∉ T1/T2.

Note the asymmetry between T1 and T2. As an example, the combination { c1:v1 c2:v2 }/{ c2:v3 c3:v4 } is the tag { c1:v1 c2:v3 c3:v4 }. In this example, c1: and c3: exist in only one of the tags, and so their values are used. For c2:, both tags contain different values, and so the value in the right tag is preferred.

Tag Database Gathering

A calculator calc contains an array of tag-node pairs, called Tag Database. Each entry { tag, value } in the tag database signifies that the computation of tag should include value. We denote a tag database entry with tag <- value. If value is a reread to tag2, we may instead denote the entry with tag <= tag2. Note the different arrow type between the two, as well as the type difference on the right side of the arrow.

With tag database, calc can gather a tag T via calc.get(T), returning all entries in the tag database with matching tags. An entry tag <- value in the tag database is included in a gathering iff for every k:v ∈ tag, v == null or k:v ∈ T. If the value in the included entry is a node, its value is computed using tag T. If the value is a Reread with tag T2, another gather is performed using T/T2, and its result is appended to the final result. As an example, consider calc.get({ c1:v1 c2:vA }) when the calculator has the following Tag Database,

[
  { c1:v1       } <- node1, // entry 1
  { c1:v2       } <- node2, // entry 2
  { c1:v1 c2:vA } <- node3, // entry 3
  { c1:v1 c2:vB } <- node4, // entry 4
  {       c2:vA } <- node5, // entry 5
  { c1:v1 c2:vA } <= { c2:vB } // entry 6
].

In this case, calc first selects the matching entries 1, 3, 5, and 6. As entries 1, 3, and 5 contain nodes, calc computes nodes 1, 3, and 5 with tag { c1:v1 c2:vA }. Next, the the calculator resolves entry 6, by performing a gathering with tag { c1:v1 c2:vA }/{ c2:vB } = { c1:v1 c2:vB }, computing nodes 1 and 4 with tag { c1:v1 c2:vB }. The calculator then returns the following:

  • Value of node1 computed with tag { c1:v1 c2:vA },
  • Value of node3 computed with tag { c1:v1 c2:vA },
  • Value of node5 computed with tag { c1:v1 c2:vA },
  • Value of node1 computed with tag { c1:v1 c2:vB }, and
  • Value of node4 computed with tag { c1:v1 c2:vB }.

Note that node1 is computed twice, each with different tags, due to reread operation.

Node Operations

This section outlines all operations supported by Pando. Operations are separated into three types, arithmetic, branching, and tag-related.

Arithmetic Operations

  • constant(c): values of a constant c (converting it to a Node),
    • This is normally unneeded as most functions permit both Node and constants,
  • sum(x1, x2, ...) := x1 + x2 + ...,
  • prod(x1, x2, ...) := x1 * x2 * ...,
  • min(x1, x2, ...) := Math.min(x1, x2, ...),
  • max(x1, x2, ...) := Math.max(x1, x2, ...),
  • sumfrac(x1, x2) := x1 / (x1 + x2),
  • subscript(index, array) := array[index]. array can be either array of strings or of numbers,
  • custom(op, x1, x2, ...) is for custom node for non-standard computations,

Branching Operations

Most branching functions are of the form cmp<<CMP>>(x1, x2, pass, fail) where a comparator CMP (e.g., Eq) is used to compare x1 and x2. If the comparison yields true (e.g., x1 == x2 for cmpEq), then pass branch is chosen. Otherwise, fail branch is chosen. Unchosen branch is not evaluated. fail can be omitted if it is 0. Supported comparators include

  • Eq (x1 == x2) and NE (x1 != x2),
  • GE (x1 >= x2) and GT (x1 > x2), and
  • LE (x1 <= x2) and LT (x1 < x2).

Another branching function is lookup(key, table, defaultV) := table[key] ?? defaultV. There are two main distinctions between subscript and lookup:

  • lookup indices are strings while subscript indices are numbers, and
  • lookup table may contain complex nodes while subscript array can contain only constants.

Nodes other than table[key] are not evaluated. When both lookup and subscript are applicable, prefer subscript for performance reason.

Tag-Related Operations

By default, all arithmetic and branching operations preserve the tags, e.g., calculating sum(x1, x2) with a tag T, the calculation of x1 and x2 also use the same tag T. When computing with a current tag Tcur

  • tagVal(cat) reads the value of Tcur at category cat, or "" if cat: ∉ Tcur,
  • tag(v, tag) calculates v using Tcur/tag,
  • dynTag(v, tag) calculates v using Tcur/tag. The main difference compared to tag operation is that the tag values in dynTag can be other nodes, which are computed with Tcur tag. When both dynTag and tag are applicable, prefer tag for performance reason.
  • read(tag, accu) performs a gather with tag Tcur/tag, then combine the results using accumulator the accumulators include sum/prod/min/max, corresponding to the arithmetic operations. Accumulator may be undefined, in which case, the gathering is assumed to contain exactly one entry.

Calculator Customization

Calculator can be customized via subclassing. Functions that are designed to be overriden by such subclasses include

- computeMeta(n: AnyNode, value: number | string,
    x: (CalcResult<number | string, M> | undefined)[],
    br: CalcResult<number | string, M>[],
    tag: Tag | undefined): M
- computeCustom(args: (number | string)[], op: string): any