ParametricInversion.jl

Julia in reverse: Parametric Inversion in pure Julia

Location in trace

Constant

Places refers to a subset of the axes (aka dimension, column, attributes) of relation

add v to vm[k]

All

Vars that are used in branching in block b

choose(ctx, loc, f, types, target, known. θ)

Parametrically choose a value for variables in relation defined by method f(::types..), given information about other values in relation.

Arguments

• f(::types...) - method to choose from
• loc - Location
• target - which axis we wish to choose onto
• given - what is given/known about values of the relation (e.g. value of input)
• θ - Parameter values which determine which element to choose

cycle(f, args...) yields xs_ such f(xs_...) == f(args...)`

Ensure there is single usage of a particular variable

For statement of the form v1 = f(v2, v3, ..., vn) produces [v1, v2, ..., vn]

Arguments of a statement

Head of expression defined by statement

What branchblocks are incoming into block b

Parameters that can be used to invert to x from y parameters(f, types, args...)

Produces parameters θ such that:

inverseparameters(f, types, f(args...), θ) == args

These parameters can be used for learning.

invert block b, store result in invb, assume v ∈ knownvars is known

ir::IR that computes inverse inverse of ir

Produce inverse ::CodeInfo

invertinvoke(f, t::Type{<:Tuple}, z, θ)

Parametric inverse application of method f(::t...) to args with parameters θ

Inputs:

f - function to invert t - Tuple of types which determines method of f to invert z - Input to inverse method θ - Parameter values

Returns

(a, b, c, ...) - tuple of values

f(x, y, z) = x * y + z
x, y, z = invertinvoke(f, Tuple{Float64, Float64, Float64}, 2.3, rand(3))
@assert f(x, y, z) == 2.3

invertir(f, t::Type{T})

Produce inverse ast for method f(::T)

When entering block at branchpoint brid, which variables are known?

Variables that are used in block b but neither defined in b nor inputs to b

Number of times var is used in block

Num times v is used in smt

passvars!(ir)

Removes implicit use of variable. Updates ir such that if a block uses some variable v then v is an input to that block.

Variables that are produced by b: inputs or lhs of statements

Undo each operation statement %a = f(%x, %y, %z) in b, add to invb

Argument types of statement stmt according to vartypes vtypes

vars used in statements of b

vars used in some form by block b

Repalce all occurances of x with y variable v1 with variable v2 in block b

Each statement of block b and associated Variable

Mapping from variables (including arguments) to inferred types