evinism / evinism/lambda-explorer
Partial application
- Dominant language
- JavaScript
- Stars
- 69
- Forks
- 10
- PR merge metrics
- No merged PRs in 30d
Description
`NAND TRUE` yields a function which works correctly (`λf₂.λa.λb.f₂ba`). But when using `(NAND TRUE) TRUE` get an incorrect result (`λa.λb.a`) which is different from manually writing `(λf₂.λa.λb.f₂ba) TRUE` which yields `λa.λb.b`.
Am I conceptualizing this incorrectly or is this a bug?
```
> TRUE
λa.λb.a
> NAND
λf₁.λf₂.λa.λb.f₁(f₂ba)a
> NAND TRUE
λf₂.λa.λb.f₂ba
> NAND TRUE TRUE
λa.λb.a
> (λf₂.λa.λb.f₂ba) TRUE
λa.λb.b
> (NAND TRUE) TRUE
λa.λb.a
```
```
> (λf₂.λa.λb.f₂ba) TRUE
λa.λb.b
(-)
Free Variables:
Rendered from AST: (λf₂.λa.λb.f₂ba)(λa.λb.a)
Beta-reduced: λa.λb.(λa.λb.a)ba
Eta-reduced: [eta irreducible]
Normal Form: λa.λb.b
Normal As Church Numeral: 0
Normal As Church Boolean: false
steps to normal form:
(λf₂.λa.λb.f₂ba)(λa.λb.a)
λa.λb.(λa.λb.a)ba
λa.λb.(λε₁.b)a
λa.λb.b
> (NAND TRUE) TRUE
λa.λb.a
Free Variables:
Rendered from AST: (λf₁.λf₂.λa.λb.f₁(f₂ba)a)(λa.λb.a)(λa.λb.a)
Beta-reduced: [beta irreducible]
Eta-reduced: [eta irreducible]
Normal Form: λa.λb.a
Normal As Church Numeral: [not a church numeral]
Normal As Church Boolean: true
steps to normal form:
(λf₁.λf₂.λa.λb.f₁(f₂ba)a)(λa.λb.a)(λa.λb.a)
(λf₂.λa.λb.(λa.λb.a)(f₂ba)a)(λa.λb.a)
λa.λb.(λa.λb.a)((λa.λb.a)ba)a
λa.λb.(λε₁.(λa.λb.a)ba)a
λa.λb.(λε₁.λb.a)ba
λa.λb.(λε₁.a)a
λa.λb.a
```
Contributor guide
No contributing guide indexed for this repository
Research direction
Start by reproducing the two expressions in the REPL and compare their reduction traces and normal forms. Investigate why partial application of NAND TRUE differs from the manually expanded lambda expression. Done means equivalent expressions produce the same expected result, with the existing reduction output still reporting the correct normal form.
Written by the indexing model from the issue text.
Assessment
- Tech stack
- javascript
- Domain
- compilers
- Issue type
- Bug
- Difficulty
- 4/5
- Estimated time
- 3-5 days
- Activity status
- Stale
- Clarity
- Mostly clear
- Newbie friendliness
- 35/100