Partial application

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#126 opened on Dec 4, 2023 1 comment 0 reactions 0 assignees View on GitHub

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Assessment

Difficulty: 4/5
Estimated time: 3-5 days
Newbie friendliness: 35/100

Issue type: Bug
Clarity: Mostly clear
Activity status: Stale
Tech stack: javascript
Domain: compilers

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.

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
<function, church boolean true>
> NAND
λf₁.λf₂.λa.λb.f₁(f₂ba)a
<function>
> NAND TRUE
λf₂.λa.λb.f₂ba
<function>
> NAND TRUE TRUE
λa.λb.a
<function, church boolean true>
> (λf₂.λa.λb.f₂ba) TRUE
λa.λb.b
<function, church numeral 0, church boolean false>
> (NAND TRUE) TRUE
λa.λb.a
<function, church boolean true>

> (λf₂.λa.λb.f₂ba) TRUE
λa.λb.b
<function, church numeral 0, church boolean false>(-)
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
<function, church boolean true>
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

Dominant language: JavaScript
Stars: 69
Forks: 10
PR merge metrics: No merged PRs in 30d

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