| Copyright | (c) 2021-2023 Dakotah Lambert |
|---|---|
| License | MIT |
| Safe Haskell | Safe-Inferred |
| Language | Haskell2010 |
LTK.Algebra
Description
This module centralizes definitions of some commonly used algebraic properties.
Since: 1.0
Synopsis
- type SynMon n e = FSA ([Maybe n], [Symbol e]) e
- isCommutative :: (Ord n, Ord e) => FSA (n, [Symbol e]) e -> Set (State (n, [Symbol e])) -> Bool
- me :: (Ord n, Ord e) => FSA (n, [Symbol e]) e -> State (n, [Symbol e]) -> Set (State (n, [Symbol e]))
- emee :: (Ord n, Ord e) => FSA (n, [Symbol e]) e -> State (n, [Symbol e]) -> Set (State (n, [Symbol e]))
- ese :: (Ord n, Ord e) => FSA (n, [Symbol e]) e -> State (n, [Symbol e]) -> Set (State (n, [Symbol e]))
- syntacticOrder :: (Ord n, Ord e) => SynMon n e -> FSA [e] ()
- emblock :: (Ord n, Ord e) => SynMon n e -> SynMon Integer Integer
- idempotents :: (Ord n, Ord e) => FSA (n, [Symbol e]) e -> Set (State (n, [Symbol e]))
- omega :: (Ord n, Ord e) => FSA (n, [Symbol e]) e -> State (n, [Symbol e]) -> State (n, [Symbol e])
Type
type SynMon n e = FSA ([Maybe n], [Symbol e]) e #
A simpler way to denote syntactic monoids in type signatures.
Tests
isCommutative :: (Ord n, Ord e) => FSA (n, [Symbol e]) e -> Set (State (n, [Symbol e])) -> Bool #
True iff the supplied elements commute with one another in the provided monoid.
Generated Submonoids and Subsemigroups
me :: (Ord n, Ord e) => FSA (n, [Symbol e]) e -> State (n, [Symbol e]) -> Set (State (n, [Symbol e])) #
For a given idempotent \(e\), return the set generated by \(\{m : (\exists u,v)[umv=e]\}\).
emee :: (Ord n, Ord e) => FSA (n, [Symbol e]) e -> State (n, [Symbol e]) -> Set (State (n, [Symbol e])) #
For a given idempotent \(e\), return the set me monoid e
multiplied on the left and right by \(e\).
ese :: (Ord n, Ord e) => FSA (n, [Symbol e]) e -> State (n, [Symbol e]) -> Set (State (n, [Symbol e])) #
The semigroup multiplied on the left and right by the given idempotent.
Other generation
syntacticOrder :: (Ord n, Ord e) => SynMon n e -> FSA [e] () #
Returns a machine whose states represent monoid elements and where a transition exists from \(p\) to \(q\) if and only if \(p\leq q\).
Since: 1.1
emblock :: (Ord n, Ord e) => SynMon n e -> SynMon Integer Integer #
Construct a monoid based on the idempotent paths as described by Straubing (1985). Elements are of the form \((e,esf,f)\) for idempotents \(e\) and \(f\) and arbitrary \(s\).
Since: 1.1