package mugen

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Parameters
Signature

mugen
- Mugen
  - Semantics
    
    Endo
    
    Make
    
    P
    
    Shift
    
    Param
    
    Shift
    
    S
    
    Free
    
    Make
    
    Infix
    
    P
    
    Shift
    
    Param
    
    Shift
    
    S
    
    Infix
  - Shift
    
    Constant
    
    Act
    
    Const
    
    FiniteSupport
    
    Base
    
    Fractal
    
    Base
    
    Int
    
    Lexicographic
    
    X
    
    Y
    
    Nat
    
    NearlyConstant
    
    Base
    
    NonPositive
    
    Opposite
    
    Base
    
    Prefix
    
    Base
    
    Product
    
    X
    
    Y
    
    S
  - ShiftWithJoin
    
    BoundedSemilattice
    
    FiniteSupport
    
    Base
    
    Int
    
    Lexicographic
    
    X
    
    Y
    
    Nat
    
    NearlyConstant
    
    Base
    
    NonPositive
    
    Product
    
    X
    
    Y
    
    Semilattice
  - StructuredType
    
    EqualityType
    
    PartiallyOrderedType
    
    PartiallyOrderedTypeWithRightAction
  - Syntax
    
    Endo
    
    Free

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Library
Module
Module type
Parameter
Class
Class type

The implementation of smart constructors.

Parameters

module P : Param

Signature

type level = (P.Shift.t, P.var) Syntax.free

The type of freely generated levels.

val var : P.var -> level

var is Syntax.Free.var

val shifted : level -> P.Shift.t -> level

Smarter version of Syntax.Endo.shifted that collapses multiple displacements

raises Invalid_argument
When it attempts to shift the top level.

val top : level

top is Syntax.Endo.top

val equal : level -> level -> bool

equal l1 l2 checks whether l1 and l2 are the same universe level.

raises Invalid_argument
When l1 or l2 is shifted top.

val lt : level -> level -> bool

lt l1 l2 checks whether l1 is strictly less than l2. Note that trichotomy fails for general universe levels.

raises Invalid_argument
When l1 or l2 is shifted top.

val leq : level -> level -> bool

leq l1 l2 checks whether l1 is less than or equal to l2. Note that trichotomy fails for general universe levels.

raises Invalid_argument
When l1 or l2 is shifted top.

val gt : level -> level -> bool

gt l1 l2 is lt l2 l1.

val geq : level -> level -> bool

geq l1 l2 is leq l2 l1.

module Infix : sig ... end

Infix notation.