type-inference-validation

Type Inference Validation

Core Concept

Static type validation that rejects invalid path compositions before caching. Every Navigator path must prove type compatibility with its input structure—this skill enforces that proof.

Works alongside Möbius filtering as a second line of defense: Möbius eliminates topological impossibilities, Type Inference eliminates structural impossibilities.

Why Type Validation?

Consider this dangerous scenario:

data_numbers = [1, 2, 3, 4, 5]
data_dict = Dict("x" => 10, "y" => 20)

# This path makes sense for numbers
nav1 = @late_nav([ALL, pred(iseven)])  # Type ✓: Vector → Numbers → Numbers

# But what if someone mistakenly uses it on the dict?
nav_select(nav1, data_dict, x -> [x])
# => IndexError! (dicts don't support ALL enumeration this way)

Type Inference Validation prevents this at compile time, not runtime.

Architecture

Type System

Each Navigator carries a type signature:

Navigator{InputType, OutputType, PathSteps}

Examples:

nav_vector = Navigator{Vector, Vector, [ALL, pred(f)]}
nav_dict = Navigator{Dict, Vector, [keypath(k), ALL]}
nav_sexp = Navigator{SExpression, Symbol, [sexp_nth(2), SEXP_HEAD]}

Type Refinement Pipeline

Input Type
    ↓
@late_nav(path_expr) triggers validation
    ↓
Type each step in path:
  [ALL] : Vector{T} → T
  [keypath(k)] : Dict{K,V} → V
  [pred(f)] : T → T (preserves type)
  [INDEX(i)] : Vector{T} → T
  [SEXP_HEAD] : SExpr → Symbol
    ↓
Unify step outputs with next step inputs
    ↓
Final output type computed
    ↓
Cache with type signature
    ↓
Accept or Reject

Type Incompatibility Detection

Step	Input Type	Output Type	Valid?
[ALL]	Vector{T}	T	✓
[ALL]	Dict{K,V}	⚠️ (ambiguous)	✗
[keypath(k)]	Dict{K,V}	V	✓
[keypath(k)]	Vector{T}	✗	✗
[pred(f)]	T	T	✓
[INDEX(i)]	Vector{T}	T	✓
[INDEX(i)]	Dict	✗	✗