package mugen

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Binary products, but with the lexicographical order.

Parameters

Signature

include BoundedSemilattice
include Semilattice
include Shift.S
include StructuredType.PartiallyOrderedType
include StructuredType.EqualityType
type t

The type.

val equal : t -> t -> bool

equal x y checks whether x and y are equivalent.

val dump : Stdlib.Format.formatter -> t -> unit

Ugly printer.

val lt : t -> t -> bool

lt x y checks if x is strictly less than y. Note that trichotomy fails for general partial orders.

val leq : t -> t -> bool

leq x y checks if x is less than or equal to y. Note that trichotomy fails for general partial orders.

val id : t

id is the unit.

val is_id : t -> bool

is_id s checks whether s is the unit. It is equivalent to equal id s, but potentially faster.

val compose : t -> t -> t

compose s1 s2 composes the operators s1 and s2. Note that Foo^s1^s2 in McBride's notation is understood as compose (compose ... s2) s1 with the reversed order.

val join : t -> t -> t

join x y is the maximum of x and y.

val bot : t

bot is the minimum value.

val pair : X.t -> Y.t -> t

Forming a pair

val fst : t -> X.t

First projection

val snd : t -> Y.t

Second projection

val inl : X.t -> t

inl x is equivalent to pair x Y.id

val inr : Y.t -> t

inr y is equivalent to pair X.id y

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