REInfer: Runtime Extended Inference

REInfer performs Runtime Extended type Inference on json data. Compared to traditional types, the extended types incorporate some numerical information, such as the number of times a field appears in the data, or the number of times it is null.

A facility is provided to compare inferred types. This follows the idea of a diff algorithm which takes two values and returns the difference. The difference consists of a common part plus two deltas. Deltas are applied using a sum operation for extended types. The diff algorithm borrows and extends ideas from abduction for shape analysis, applied to type theory instead of program logic.

A simple UI is provided to experiment with the primitives: it can be used to visualize inferred types and their difference.

There is a thought experiment exploring of the use of runtime type inference in conjunction with runtime type checking. This combination gives an instrumented semantics that can be used to execute programs. This instrumented semantics has the peculiar property that it can fail at run time in cases where the program is not statically typable. In contrast to ordinary testing, this also applies to programs that do not fail when executed under a normal semantics.

Run Project

npm install
npm start
npm run webpack
# in another tab
npm run serve

Then open the served page in the browser and edit Demo.re.

Example of type inference

val1:
{"x":"hello"}

val2:
{"x":null, "y":0}

Type inference will produce types styp1 and styp2

The numerical information indicates that fied x occurs once. But in the second value it has optional type ? 1, indicating that 1 (out of 1) value of x is null.

Numbers begin to add up when using arrays, or when sampling multiple values. For example, [null,2,3,4] has this type:

Example of diff

Once the types for val1 and val2 have been computed, a difference algorithm computes a type stypB:

The type highlights what sub-parts which are in common. Also, lhs highlights the subpart that the first type has in addition to the common part, and correspondingly for rhs.

It is also possible to look at stypA1 and stypA2 that indicate the overall difference between the common type and the two resulting ones:

Example of union types

Some data formats allow differet types of data in the same position.

For example: [ "hell", 0, "world"] has this inferred type:

Diff is also supported with union types.

Example of singleton types

While by default basic types are at the granularity of string/number/boolean, it's possible to turn on singleton types mode so each constant has a different type.

For example, ["h", "e", "l", "l", "o", "w", "o", "r", "l", "d"] in singleton type mode has inferred type:

References

• Sean Grove's talk at ReasonConf 2018 https://www.youtube.com/watch?v=OT7xOpPCGds.

• Tree view UI adapted from react-treeview.

• Abduction in shape analysis https://dl.acm.org/citation.cfm?id=2049700.

License

This project is MIT-licensed.

Formalisation

Values

val ::=
  123 |
  “abc” |
  true | false |
  null |
  obj |
  [ val1, …, valn ]

obj ::= { x1:val, …, xn:val }

Types

Types: t are ordinary types of a programming language, with t? an optional type.

t ::=
  empty |
  number |
  string |
  boolean |
  t? |
  {x1:t, …, xn:t} |
  [ t ]

Statistical Types

Statistical types are a mutual definition of styp and typ.

o ::= opt(p) | notOpt

styp ::= (typ,o)::p

typ ::=
  empty |
  number |
  string |
  boolean |
  {x1:styp1, …, xn:stypn} |
  [styp]

Abbreviation: write typ?n::p or typ::p.

Type checking for Types

Type checking for t: |- val : t

Erasure of Statistical Types

Erasure: |- |styp| = t

Type checking for Statistical Types

Type checking for styp: |- val : styp

Sum of Statistical Types

Sum operations: |- styp1 + styp2 = styp and |- typ1 + typ2 = typ and |- o1 + o2 = o.

Notice this defines a partial commutative monoid.

Inference of Statistical Types from value samples

Given a set of sampled data val1, …, valn define a process of type inference |- val1, …, valn -> styp. The process consists of using the existing inference for arrays:

|- [val1, …, valn] : [styp]
———————————————————————————
 |- val1, …, valn -> styp

Abduction for Statistical Types

Abduction: |- styp1 + <stypA> = styp2 and |- typ1 + <typA> = typ2 and |- o1 + <oA> = o2.

With abduction, the inputs are styp1 and styp2, and the output is stypA, the abduced value.

There are many solutions to the abduction question. We want smallest solution w.r.t. <= where styp1 <= styp2 if there is styp such that |- styp1 + styp = styp2.

Abduction aims to compute the smallest representation of the difference between statistical types.

It turns out that this form of difference is not sufficient because there are incomparable types and the negation corresponding to + does not exist. So another form of diff is required.

Diff for Statistical Types

Diff: |- <stypA1,stypA2> + <stypB> = styp1,styp2 and |- <typA1,typA2> + <typB> = typ1,typ2 and |- <oA1,oA2> + <oB> = o1,o2.

The inputs are styp1 and styp2 and the outputs are stypB and stypA1 and stypA2. The common part is stypB and the two deltas are stypA1 and stypA2. The correctness critera are that stypA1 + stypB = styp1 and stypA2 + stypB = styp2.

There are many solutions to the diff question. We want the largest solution w.r.t. <= for the B part, and smallest for the A1 and A2 parts, where styp1 <= styp2 if there is styp such that |- styp1 + styp = styp2.

Extension: Union Types

stypU ::= styp1 | ... | stypn

typ += union(stypU)

Write typ1 # typ2 when there is no typ such that |- typ1 + typ2 = typ, with the corresponding extension styp1 # styp2.

The sum of stypU written |- stypU1 + stypU2 = stypU is defined below. The conversion |- u(styp) = stypU is also defined below.

Union Extension of |- styp1 + styp2 = styp and |- <stypA1,stypA2> + <stypB> = styp1,styp2.

Extension: Singleton Types

typ ::=
  number | 0 | 1 | 2 | ...
  string | "hello" | ...
  boolean | true | false
  ...