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Questions tagged [equality]

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3 votes
2 answers
820 views

Canonical representation of finite maps on non-overlapping finite rational intervals

I would like to have a canonical representation of a map from rational intervals (f, t] with f, t ∈ ℚ to some irrelevant value type. These intervals are non-overlapping and there exist only finitely ...
Janno's user avatar
  • 31
8 votes
2 answers
326 views

Decidability of Equality of Radical Expressions

Consider terms built from elements of $\mathbb Q$ and the operations $+,\times,-,/$, and $\sqrt[n]{\,\cdot\,}$ for each natural number $n$. Given the promise that two terms are well-formed -- that is, ...
Mees de Vries's user avatar
7 votes
2 answers
209 views

Computability of equality to zero for a simple language

Suppose we have a tree in which leaves are labeled with a set of numbers $L$, and internal nodes with a set of operations $O$. In particular $L$ can be $\mathbb{N}, \mathbb{Z}$ or $\mathbb{Q}$, and ...
miniBill's user avatar
  • 419
4 votes
1 answer
151 views

Decidability of equality, and soundness of expressions involving elementary arithmetic and exponentials

Let's have expressions that are composed of elements of $\mathbb N$ and a limited set of binary operations {$+,\times,-,/$} and functions {$\exp, \ln$}. The expressions are always well-formed and form ...
GolDDranks's user avatar
4 votes
1 answer
242 views

Definition of extensional and propositional equality in Martin-Lof extensional type theory

Martin Hofmann states in Extensional Concepts in Intensional Type Theory (§1.1 p.[4-5]) that: A similar situation occurs in extensional Martin-Lof type theory where propositional and definitional ...
al pal's user avatar
  • 621
5 votes
1 answer
411 views

Definitional equality of two propositions about propositional equality

Martin Hofmann states in Extensional Concepts in Intensional Type Theory (§1.1 p.3) that: It is important that definition equality is pervasive so if M and N are definitionally equal then P(M) is ...
al pal's user avatar
  • 621
3 votes
1 answer
78 views

Equality of lambda terms which do not have normal form

In the context of lambda calculus, how should one prove $\beta$-equality of terms that do not have normal form? In particular, how to prove that these are different combinators: $$ Y = λf.(λx.f(xx))(...
prog's user avatar
  • 105
1 vote
0 answers
49 views

Decidability of equality of expressions involving exponentiation

Let's have expressions that are finite-sized trees, with elements of $\mathbb N$ as leaf nodes and the operations {$+,\times,-,/$, ^} with their usual semantics as the internal nodes, with the special ...
GolDDranks's user avatar