feat: add De Bruijn indexed reduction engine

Add a new interpreter option (-i debruijn) that uses De Bruijn indices
for variable representation, eliminating the need for variable renaming
during substitution.

- Add -i flag to select interpreter (lambda or debruijn)
- Create debruijn package with Expression types (Variable with index,
  Abstraction without parameter, Application)
- Implement shift and substitute operations for De Bruijn indices
- Add conversion functions between lambda and De Bruijn representations
- Update CLI to support switching between interpreters
- Add De Bruijn tests to verify all samples pass

Closes #26
This commit is contained in:
2026-01-16 19:36:05 -05:00
parent 1974ad582f
commit 528956b033
12 changed files with 621 additions and 9 deletions

32
pkg/debruijn/shift.go Normal file
View File

@@ -0,0 +1,32 @@
package debruijn
// Shift increments all free variable indices in an expression by the given amount.
// A variable is free if its index is >= the cutoff (depth of nested abstractions).
// This is necessary when substituting an expression into a different binding context.
func Shift(expr Expression, amount int, cutoff int) Expression {
switch e := expr.(type) {
case *Variable:
if e.index >= cutoff {
return NewVariable(e.index+amount, e.label)
}
return e
case *Abstraction:
newBody := Shift(e.body, amount, cutoff+1)
if newBody == e.body {
return e
}
return NewAbstraction(newBody)
case *Application:
newAbs := Shift(e.abstraction, amount, cutoff)
newArg := Shift(e.argument, amount, cutoff)
if newAbs == e.abstraction && newArg == e.argument {
return e
}
return NewApplication(newAbs, newArg)
default:
return expr
}
}