evinism / evinism/lambda-explorer

Partial application

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Dominant language
JavaScript
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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

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