Abstract
It is commonly understood that Countable Choice holds constructively due to the underlying computational nature of constructivism. However, in this paper we demonstrate that invoking different notions of computation result in radically different behaviors regarding Countable Choice. In particular, we illustrate that, although deterministic computation guarantees Countable Choice, non-deterministic computation can negate Countable Choice. We then further show that using stateful computation can restore Countable Choice even in the presence of non-determinism. This finding suggests that much of the modern discourse of constructivism assumes a deterministic underlying computational system, despite non-determinism being a fundamental aspect of modern-day computation.
Original language | American English |
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Pages (from-to) | 87-120 |
Number of pages | 34 |
Journal | Electronic Notes in Theoretical Computer Science |
Volume | 347 |
DOIs | |
State | Published - 1 Jan 2019 |
Externally published | Yes |
Event | 35th Conference on the Mathematical Foundations of Programming Semantics, MFPS 2019 - London, United Kingdom Duration: 4 Jun 2019 → 7 Jun 2019 |
Keywords
- constructivism
- countable choice
- effects
- non-determinism
- stateful computation
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- General Computer Science