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+
+

OCaml package documentation

+
    +
  1. mugen
    2. +
+
+
+ + \ No newline at end of file diff --git a/mugen/Mugen/Builder/Endo/Make/argument-1-P/Shift/index.html b/mugen/Mugen/Builder/Endo/Make/argument-1-P/Shift/index.html new file mode 100644 index 0000000..edcd25e --- /dev/null +++ b/mugen/Mugen/Builder/Endo/Make/argument-1-P/Shift/index.html @@ -0,0 +1,2 @@ + +Shift (mugen.Mugen.Builder.Endo.Make.P.Shift)

Module P.Shift

The displacement algebra.

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Builder/Endo/Make/argument-1-P/index.html b/mugen/Mugen/Builder/Endo/Make/argument-1-P/index.html new file mode 100644 index 0000000..df89475 --- /dev/null +++ b/mugen/Mugen/Builder/Endo/Make/argument-1-P/index.html @@ -0,0 +1,2 @@ + +P (mugen.Mugen.Builder.Endo.Make.P)

Parameter Make.P

module Shift : Shift.S

The displacement algebra.

type level

The type that embeds level expressions.

val level : (Shift.t, level) Syntax.endo -> level

The embedding of level expressions into level.

val unlevel : level -> (Shift.t, level) Syntax.endo option

Extract the embedded level, if any.

diff --git a/mugen/Mugen/Builder/Endo/Make/index.html b/mugen/Mugen/Builder/Endo/Make/index.html new file mode 100644 index 0000000..b14e5be --- /dev/null +++ b/mugen/Mugen/Builder/Endo/Make/index.html @@ -0,0 +1,2 @@ + +Make (mugen.Mugen.Builder.Endo.Make)

Module Endo.Make

The implementation of smart constructors.

Parameters

module P : Param

Signature

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

shifted s l is the smarter version of Syntax.Endo.shifted that collapses multiple displacements, representing the level l shifted by the displacement s.

  • raises Invalid_argument

    When it (directly or indirectly) attempts to shift the top level.

val top : P.level

top is Syntax.Endo.top, the additional top level for convenience.

diff --git a/mugen/Mugen/Builder/Endo/index.html b/mugen/Mugen/Builder/Endo/index.html new file mode 100644 index 0000000..53b9fcb --- /dev/null +++ b/mugen/Mugen/Builder/Endo/index.html @@ -0,0 +1,4 @@ + +Endo (mugen.Mugen.Builder.Endo)

Module Builder.Endo

Semantic operations for Syntax.endo.

module type Param = sig ... end

Parameters of smart constructors.

module type S = sig ... end

The signature of smart constructors.

module Make + (P : Param) : + S with type shift := P.Shift.t and type level := P.level

The implementation of smart constructors.

diff --git a/mugen/Mugen/Builder/Endo/module-type-Param/Shift/index.html b/mugen/Mugen/Builder/Endo/module-type-Param/Shift/index.html new file mode 100644 index 0000000..a620b41 --- /dev/null +++ b/mugen/Mugen/Builder/Endo/module-type-Param/Shift/index.html @@ -0,0 +1,2 @@ + +Shift (mugen.Mugen.Builder.Endo.Param.Shift)

Module Param.Shift

The displacement algebra.

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Builder/Endo/module-type-Param/index.html b/mugen/Mugen/Builder/Endo/module-type-Param/index.html new file mode 100644 index 0000000..d0c5721 --- /dev/null +++ b/mugen/Mugen/Builder/Endo/module-type-Param/index.html @@ -0,0 +1,2 @@ + +Param (mugen.Mugen.Builder.Endo.Param)

Module type Endo.Param

Parameters of smart constructors.

module Shift : Shift.S

The displacement algebra.

type level

The type that embeds level expressions.

val level : (Shift.t, level) Syntax.endo -> level

The embedding of level expressions into level.

val unlevel : level -> (Shift.t, level) Syntax.endo option

Extract the embedded level, if any.

diff --git a/mugen/Mugen/Builder/Endo/module-type-S/index.html b/mugen/Mugen/Builder/Endo/module-type-S/index.html new file mode 100644 index 0000000..3867721 --- /dev/null +++ b/mugen/Mugen/Builder/Endo/module-type-S/index.html @@ -0,0 +1,2 @@ + +S (mugen.Mugen.Builder.Endo.S)

Module type Endo.S

The signature of smart constructors.

type shift

The displacement algebra.

type level

The type that embeds levels.

val shifted : level -> shift -> level

shifted s l is the smarter version of Syntax.Endo.shifted that collapses multiple displacements, representing the level l shifted by the displacement s.

  • raises Invalid_argument

    When it (directly or indirectly) attempts to shift the top level.

val top : level

top is Syntax.Endo.top, the additional top level for convenience.

diff --git a/mugen/Mugen/Builder/Free/Make/argument-1-P/Shift/index.html b/mugen/Mugen/Builder/Free/Make/argument-1-P/Shift/index.html new file mode 100644 index 0000000..e7a17e1 --- /dev/null +++ b/mugen/Mugen/Builder/Free/Make/argument-1-P/Shift/index.html @@ -0,0 +1,2 @@ + +Shift (mugen.Mugen.Builder.Free.Make.P.Shift)

Module P.Shift

The displacement algebra.

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Builder/Free/Make/argument-1-P/index.html b/mugen/Mugen/Builder/Free/Make/argument-1-P/index.html new file mode 100644 index 0000000..6942a07 --- /dev/null +++ b/mugen/Mugen/Builder/Free/Make/argument-1-P/index.html @@ -0,0 +1,2 @@ + +P (mugen.Mugen.Builder.Free.Make.P)

Parameter Make.P

module Shift : Shift.S

The displacement algebra.

type var

The type of level variables.

diff --git a/mugen/Mugen/Builder/Free/Make/index.html b/mugen/Mugen/Builder/Free/Make/index.html new file mode 100644 index 0000000..109d10e --- /dev/null +++ b/mugen/Mugen/Builder/Free/Make/index.html @@ -0,0 +1,2 @@ + +Make (mugen.Mugen.Builder.Free.Make)

Module Free.Make

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, representing the variable level v.

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

shifted s l is the smarter version of Syntax.Endo.shifted that collapses multiple displacements, representing the level l shifted by the displacement s.

  • raises Invalid_argument

    When it (directly or indirectly) attempts to shift the top level.

val top : level

top is Syntax.Endo.top, the additional top level for convenience.

diff --git a/mugen/Mugen/Builder/Free/index.html b/mugen/Mugen/Builder/Free/index.html new file mode 100644 index 0000000..c0414cf --- /dev/null +++ b/mugen/Mugen/Builder/Free/index.html @@ -0,0 +1,2 @@ + +Free (mugen.Mugen.Builder.Free)

Module Builder.Free

Semantic operations for Syntax.free.

module type Param = sig ... end

Parameters of smart constructors.

module type S = sig ... end

The signature of smart constructors.

module Make (P : Param) : S with type shift := P.Shift.t and type var := P.var

The implementation of smart constructors.

diff --git a/mugen/Mugen/Builder/Free/module-type-Param/Shift/index.html b/mugen/Mugen/Builder/Free/module-type-Param/Shift/index.html new file mode 100644 index 0000000..96210b7 --- /dev/null +++ b/mugen/Mugen/Builder/Free/module-type-Param/Shift/index.html @@ -0,0 +1,2 @@ + +Shift (mugen.Mugen.Builder.Free.Param.Shift)

Module Param.Shift

The displacement algebra.

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Builder/Free/module-type-Param/index.html b/mugen/Mugen/Builder/Free/module-type-Param/index.html new file mode 100644 index 0000000..59b14af --- /dev/null +++ b/mugen/Mugen/Builder/Free/module-type-Param/index.html @@ -0,0 +1,2 @@ + +Param (mugen.Mugen.Builder.Free.Param)

Module type Free.Param

Parameters of smart constructors.

module Shift : Shift.S

The displacement algebra.

type var

The type of level variables.

diff --git a/mugen/Mugen/Builder/Free/module-type-S/index.html b/mugen/Mugen/Builder/Free/module-type-S/index.html new file mode 100644 index 0000000..36a2367 --- /dev/null +++ b/mugen/Mugen/Builder/Free/module-type-S/index.html @@ -0,0 +1,2 @@ + +S (mugen.Mugen.Builder.Free.S)

Module type Free.S

The signature of smart constructors.

type shift

The displacement algebra.

type var

The type of level variables.

type level = (shift, var) Syntax.free

The type of freely generated levels.

val var : var -> level

var is Syntax.Free.var, representing the variable level v.

val shifted : level -> shift -> level

shifted s l is the smarter version of Syntax.Endo.shifted that collapses multiple displacements, representing the level l shifted by the displacement s.

  • raises Invalid_argument

    When it (directly or indirectly) attempts to shift the top level.

val top : level

top is Syntax.Endo.top, the additional top level for convenience.

diff --git a/mugen/Mugen/Builder/index.html b/mugen/Mugen/Builder/index.html new file mode 100644 index 0000000..3f7a3d4 --- /dev/null +++ b/mugen/Mugen/Builder/index.html @@ -0,0 +1,2 @@ + +Builder (mugen.Mugen.Builder)

Module Mugen.Builder

Smart constructors for level expressions

module Endo : sig ... end

Semantic operations for Syntax.endo.

module Free : sig ... end

Semantic operations for Syntax.free.

diff --git a/mugen/Mugen/Shift/Constant/argument-1-Act/index.html b/mugen/Mugen/Shift/Constant/argument-1-Act/index.html new file mode 100644 index 0000000..8b497f1 --- /dev/null +++ b/mugen/Mugen/Shift/Constant/argument-1-Act/index.html @@ -0,0 +1,2 @@ + +Act (mugen.Mugen.Shift.Constant.Act)

Parameter Constant.Act

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Shift/Constant/argument-2-Const/index.html b/mugen/Mugen/Shift/Constant/argument-2-Const/index.html new file mode 100644 index 0000000..5e0065b --- /dev/null +++ b/mugen/Mugen/Shift/Constant/argument-2-Const/index.html @@ -0,0 +1,2 @@ + +Const (mugen.Mugen.Shift.Constant.Const)

Parameter Constant.Const

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 act : t -> Act.t -> t

the right action

diff --git a/mugen/Mugen/Shift/Constant/index.html b/mugen/Mugen/Shift/Constant/index.html new file mode 100644 index 0000000..4e32a22 --- /dev/null +++ b/mugen/Mugen/Shift/Constant/index.html @@ -0,0 +1,2 @@ + +Constant (mugen.Mugen.Shift.Constant)

Module Shift.Constant

Constant displacements.

Parameters

module Act : S
module Const : sig ... end

Signature

include S
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 act : Act.t -> t

act s represents actions.

val const : Const.t -> t

const s represents constants.

val to_either : t -> (Act.t, Const.t) Stdlib.Either.t

to_either convert an element to a value of type Either.t

diff --git a/mugen/Mugen/Shift/FiniteSupport/argument-1-Base/index.html b/mugen/Mugen/Shift/FiniteSupport/argument-1-Base/index.html new file mode 100644 index 0000000..db30b13 --- /dev/null +++ b/mugen/Mugen/Shift/FiniteSupport/argument-1-Base/index.html @@ -0,0 +1,2 @@ + +Base (mugen.Mugen.Shift.FiniteSupport.Base)

Parameter FiniteSupport.Base

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Shift/FiniteSupport/index.html b/mugen/Mugen/Shift/FiniteSupport/index.html new file mode 100644 index 0000000..3ccb2e9 --- /dev/null +++ b/mugen/Mugen/Shift/FiniteSupport/index.html @@ -0,0 +1,8 @@ + +FiniteSupport (mugen.Mugen.Shift.FiniteSupport)

Module Shift.FiniteSupport

Infinite products with finite supports. A special case of NearlyConstant where the base is id.

Parameters

module Base : S

Signature

include S
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 of_list : Base.t list -> t

Conversion from a list; a list l represents the following infinite product (as a function from natural numbers to Base.t)

f 0 = List.nth l 0
+f 1 = List.nth l 1
+...
+f (n-1) = List.nth l (n-1)
+f n = Base.id
+f (n+1) = Base.id
+...
val to_list : t -> Base.t list

List representation of an infinite product. Right inverse of of_list. It is not a left inverse of of_list because trailing Base.id will be stripped.

diff --git a/mugen/Mugen/Shift/Int/index.html b/mugen/Mugen/Shift/Int/index.html new file mode 100644 index 0000000..d4e48d2 --- /dev/null +++ b/mugen/Mugen/Shift/Int/index.html @@ -0,0 +1,2 @@ + +Int (mugen.Mugen.Shift.Int)

Module Shift.Int

Integers with addition. Caveats: it does not handle integer overflow.

include S
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 of_int : int -> t

Conversion from int

val to_int : t -> int

Conversion to int

diff --git a/mugen/Mugen/Shift/Lexicographic/argument-1-X/index.html b/mugen/Mugen/Shift/Lexicographic/argument-1-X/index.html new file mode 100644 index 0000000..07f24e4 --- /dev/null +++ b/mugen/Mugen/Shift/Lexicographic/argument-1-X/index.html @@ -0,0 +1,2 @@ + +X (mugen.Mugen.Shift.Lexicographic.X)

Parameter Lexicographic.X

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Shift/Lexicographic/argument-2-Y/index.html b/mugen/Mugen/Shift/Lexicographic/argument-2-Y/index.html new file mode 100644 index 0000000..a2fc9bb --- /dev/null +++ b/mugen/Mugen/Shift/Lexicographic/argument-2-Y/index.html @@ -0,0 +1,2 @@ + +Y (mugen.Mugen.Shift.Lexicographic.Y)

Parameter Lexicographic.Y

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Shift/Lexicographic/index.html b/mugen/Mugen/Shift/Lexicographic/index.html new file mode 100644 index 0000000..3c6f0ed --- /dev/null +++ b/mugen/Mugen/Shift/Lexicographic/index.html @@ -0,0 +1,2 @@ + +Lexicographic (mugen.Mugen.Shift.Lexicographic)

Module Shift.Lexicographic

Binary products, but with the lexicographical order.

Parameters

module X : S
module Y : S

Signature

include S
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 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

diff --git a/mugen/Mugen/Shift/Nat/index.html b/mugen/Mugen/Shift/Nat/index.html new file mode 100644 index 0000000..0e2a26e --- /dev/null +++ b/mugen/Mugen/Shift/Nat/index.html @@ -0,0 +1,2 @@ + +Nat (mugen.Mugen.Shift.Nat)

Module Shift.Nat

Natural numbers with addition. Caveats: it does not handle integer overflow.

include S
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 of_int : int -> t

Conversion from int

val to_int : t -> int

Conversion to int

diff --git a/mugen/Mugen/Shift/NearlyConstant/argument-1-Base/index.html b/mugen/Mugen/Shift/NearlyConstant/argument-1-Base/index.html new file mode 100644 index 0000000..1cc6438 --- /dev/null +++ b/mugen/Mugen/Shift/NearlyConstant/argument-1-Base/index.html @@ -0,0 +1,2 @@ + +Base (mugen.Mugen.Shift.NearlyConstant.Base)

Parameter NearlyConstant.Base

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Shift/NearlyConstant/index.html b/mugen/Mugen/Shift/NearlyConstant/index.html new file mode 100644 index 0000000..714ba81 --- /dev/null +++ b/mugen/Mugen/Shift/NearlyConstant/index.html @@ -0,0 +1,8 @@ + +NearlyConstant (mugen.Mugen.Shift.NearlyConstant)

Module Shift.NearlyConstant

Infinite products with finite elements different from a fixed displacement.

Parameters

module Base : S

Signature

include S
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 of_based_list : (Base.t * Base.t list) -> t

Conversion from a based list; a based list (b, l) represents the following infinite product (as a function from natural numbers to Base.t)

f 0 = List.nth l 0
+f 1 = List.nth l 1
+...
+f (n-1) = List.nth l (n-1)
+f n = b
+f (n+1) = b
+...
val to_based_list : t -> Base.t * Base.t list

Right inverse of of_based_list. It is not a left inverse of of_based_list because trailing values that are equal to the base will be stripped.

diff --git a/mugen/Mugen/Shift/NonPositive/index.html b/mugen/Mugen/Shift/NonPositive/index.html new file mode 100644 index 0000000..ec5d97d --- /dev/null +++ b/mugen/Mugen/Shift/NonPositive/index.html @@ -0,0 +1,2 @@ + +NonPositive (mugen.Mugen.Shift.NonPositive)

Module Shift.NonPositive

Non-positive integers with addition. Caveats: it does not handle integer overflow.

include S
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 of_int : int -> t

Conversion from int

val to_int : t -> int

Conversion to int

diff --git a/mugen/Mugen/Shift/Opposite/argument-1-Base/index.html b/mugen/Mugen/Shift/Opposite/argument-1-Base/index.html new file mode 100644 index 0000000..06ad284 --- /dev/null +++ b/mugen/Mugen/Shift/Opposite/argument-1-Base/index.html @@ -0,0 +1,2 @@ + +Base (mugen.Mugen.Shift.Opposite.Base)

Parameter Opposite.Base

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Shift/Opposite/index.html b/mugen/Mugen/Shift/Opposite/index.html new file mode 100644 index 0000000..218e9d9 --- /dev/null +++ b/mugen/Mugen/Shift/Opposite/index.html @@ -0,0 +1,2 @@ + +Opposite (mugen.Mugen.Shift.Opposite)

Module Shift.Opposite

Opposite displacements

Parameters

module Base : S

Signature

include S
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 of_base : Base.t -> t

of_base b gives the same level b in the opposite algebra.

val to_base : t -> Base.t

to_base b gives the same level b in the original algebra.

diff --git a/mugen/Mugen/Shift/Prefix/argument-1-Base/index.html b/mugen/Mugen/Shift/Prefix/argument-1-Base/index.html new file mode 100644 index 0000000..a1349ae --- /dev/null +++ b/mugen/Mugen/Shift/Prefix/argument-1-Base/index.html @@ -0,0 +1,2 @@ + +Base (mugen.Mugen.Shift.Prefix.Base)

Parameter Prefix.Base

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.

diff --git a/mugen/Mugen/Shift/Prefix/index.html b/mugen/Mugen/Shift/Prefix/index.html new file mode 100644 index 0000000..7f59089 --- /dev/null +++ b/mugen/Mugen/Shift/Prefix/index.html @@ -0,0 +1,2 @@ + +Prefix (mugen.Mugen.Shift.Prefix)

Module Shift.Prefix

Prefix displacements.

Parameters

module Base : sig ... end

Signature

include S
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 prepend : Base.t -> t -> t

Prepend a symbol to a displacement.

val to_list : t -> Base.t list

Conversion to a list

diff --git a/mugen/Mugen/Shift/Product/argument-1-X/index.html b/mugen/Mugen/Shift/Product/argument-1-X/index.html new file mode 100644 index 0000000..c6018d3 --- /dev/null +++ b/mugen/Mugen/Shift/Product/argument-1-X/index.html @@ -0,0 +1,2 @@ + +X (mugen.Mugen.Shift.Product.X)

Parameter Product.X

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Shift/Product/argument-2-Y/index.html b/mugen/Mugen/Shift/Product/argument-2-Y/index.html new file mode 100644 index 0000000..e4e7631 --- /dev/null +++ b/mugen/Mugen/Shift/Product/argument-2-Y/index.html @@ -0,0 +1,2 @@ + +Y (mugen.Mugen.Shift.Product.Y)

Parameter Product.Y

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Shift/Product/index.html b/mugen/Mugen/Shift/Product/index.html new file mode 100644 index 0000000..1672007 --- /dev/null +++ b/mugen/Mugen/Shift/Product/index.html @@ -0,0 +1,2 @@ + +Product (mugen.Mugen.Shift.Product)

Module Shift.Product

Binary products.

Parameters

module X : S
module Y : S

Signature

include S
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 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

diff --git a/mugen/Mugen/Shift/index.html b/mugen/Mugen/Shift/index.html new file mode 100644 index 0000000..d21dd69 --- /dev/null +++ b/mugen/Mugen/Shift/index.html @@ -0,0 +1,2 @@ + +Shift (mugen.Mugen.Shift)

Module Mugen.Shift

Stock displacement algebras

module type S = sig ... end

The signature of a displacement algebra.

module Nat : sig ... end

Natural numbers with addition. Caveats: it does not handle integer overflow.

module Int : sig ... end

Integers with addition. Caveats: it does not handle integer overflow.

module NonPositive : sig ... end

Non-positive integers with addition. Caveats: it does not handle integer overflow.

module Constant (Act : S) (Const : sig ... end) : sig ... end

Constant displacements.

module Product (X : S) (Y : S) : sig ... end

Binary products.

module Lexicographic (X : S) (Y : S) : sig ... end

Binary products, but with the lexicographical order.

module NearlyConstant (Base : S) : sig ... end

Infinite products with finite elements different from a fixed displacement.

module FiniteSupport (Base : S) : sig ... end

Infinite products with finite supports. A special case of NearlyConstant where the base is id.

module Prefix (Base : sig ... end) : sig ... end

Prefix displacements.

module Opposite (Base : S) : sig ... end

Opposite displacements

diff --git a/mugen/Mugen/Shift/module-type-S/index.html b/mugen/Mugen/Shift/module-type-S/index.html new file mode 100644 index 0000000..c191153 --- /dev/null +++ b/mugen/Mugen/Shift/module-type-S/index.html @@ -0,0 +1,2 @@ + +S (mugen.Mugen.Shift.S)

Module type Shift.S

The signature of a displacement algebra.

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/ShiftWithJoin/FiniteSupport/argument-1-Base/index.html b/mugen/Mugen/ShiftWithJoin/FiniteSupport/argument-1-Base/index.html new file mode 100644 index 0000000..41d8078 --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/FiniteSupport/argument-1-Base/index.html @@ -0,0 +1,2 @@ + +Base (mugen.Mugen.ShiftWithJoin.FiniteSupport.Base)

Parameter FiniteSupport.Base

include Shift.S
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.

diff --git a/mugen/Mugen/ShiftWithJoin/FiniteSupport/index.html b/mugen/Mugen/ShiftWithJoin/FiniteSupport/index.html new file mode 100644 index 0000000..b08f0f8 --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/FiniteSupport/index.html @@ -0,0 +1,2 @@ + +FiniteSupport (mugen.Mugen.ShiftWithJoin.FiniteSupport)

Module ShiftWithJoin.FiniteSupport

Infinite products with finite supports. A special case of NearlyConstant.

Parameters

module Base : Semilattice

Signature

include Semilattice
include Shift.S
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 of_list : Base.t list -> t

Conversion from a list

val to_list : t -> Base.t list

Conversion to a list

diff --git a/mugen/Mugen/ShiftWithJoin/Int/index.html b/mugen/Mugen/ShiftWithJoin/Int/index.html new file mode 100644 index 0000000..6ed4224 --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/Int/index.html @@ -0,0 +1,2 @@ + +Int (mugen.Mugen.ShiftWithJoin.Int)

Module ShiftWithJoin.Int

Integers with addition. Caveats: it does not handle integer overflow.

include Semilattice
include Shift.S
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 of_int : int -> t

Conversion from int

val to_int : t -> int

Conversion to int

diff --git a/mugen/Mugen/ShiftWithJoin/Lexicographic/argument-1-X/index.html b/mugen/Mugen/ShiftWithJoin/Lexicographic/argument-1-X/index.html new file mode 100644 index 0000000..c723996 --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/Lexicographic/argument-1-X/index.html @@ -0,0 +1,2 @@ + +X (mugen.Mugen.ShiftWithJoin.Lexicographic.X)

Parameter Lexicographic.X

include Semilattice
include Shift.S
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.

diff --git a/mugen/Mugen/ShiftWithJoin/Lexicographic/argument-2-Y/index.html b/mugen/Mugen/ShiftWithJoin/Lexicographic/argument-2-Y/index.html new file mode 100644 index 0000000..5a4617a --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/Lexicographic/argument-2-Y/index.html @@ -0,0 +1,2 @@ + +Y (mugen.Mugen.ShiftWithJoin.Lexicographic.Y)

Parameter Lexicographic.Y

include Semilattice
include Shift.S
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.

diff --git a/mugen/Mugen/ShiftWithJoin/Lexicographic/index.html b/mugen/Mugen/ShiftWithJoin/Lexicographic/index.html new file mode 100644 index 0000000..e8999a2 --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/Lexicographic/index.html @@ -0,0 +1,2 @@ + +Lexicographic (mugen.Mugen.ShiftWithJoin.Lexicographic)

Module ShiftWithJoin.Lexicographic

Binary products, but with the lexicographical order.

Parameters

Signature

include BoundedSemilattice
include Semilattice
include Shift.S
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

diff --git a/mugen/Mugen/ShiftWithJoin/Nat/index.html b/mugen/Mugen/ShiftWithJoin/Nat/index.html new file mode 100644 index 0000000..2731643 --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/Nat/index.html @@ -0,0 +1,2 @@ + +Nat (mugen.Mugen.ShiftWithJoin.Nat)

Module ShiftWithJoin.Nat

Natural numbers with addition. Caveats: it does not handle integer overflow.

include BoundedSemilattice
include Semilattice
include Shift.S
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 of_int : int -> t

Conversion from int

val to_int : t -> int

Conversion to int

diff --git a/mugen/Mugen/ShiftWithJoin/NearlyConstant/argument-1-Base/index.html b/mugen/Mugen/ShiftWithJoin/NearlyConstant/argument-1-Base/index.html new file mode 100644 index 0000000..86b42cd --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/NearlyConstant/argument-1-Base/index.html @@ -0,0 +1,2 @@ + +Base (mugen.Mugen.ShiftWithJoin.NearlyConstant.Base)

Parameter NearlyConstant.Base

include Semilattice
include Shift.S
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.

diff --git a/mugen/Mugen/ShiftWithJoin/NearlyConstant/index.html b/mugen/Mugen/ShiftWithJoin/NearlyConstant/index.html new file mode 100644 index 0000000..321f7a7 --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/NearlyConstant/index.html @@ -0,0 +1,2 @@ + +NearlyConstant (mugen.Mugen.ShiftWithJoin.NearlyConstant)

Module ShiftWithJoin.NearlyConstant

Infinite products with finite elements different from a fixed displacement.

Parameters

Signature

include BoundedSemilattice
include Semilattice
include Shift.S
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 of_based_list : (Base.t * Base.t list) -> t

Conversion from a based list

val to_based_list : t -> Base.t * Base.t list

Conversion to a based list

diff --git a/mugen/Mugen/ShiftWithJoin/NonPositive/index.html b/mugen/Mugen/ShiftWithJoin/NonPositive/index.html new file mode 100644 index 0000000..102ea1d --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/NonPositive/index.html @@ -0,0 +1,2 @@ + +NonPositive (mugen.Mugen.ShiftWithJoin.NonPositive)

Module ShiftWithJoin.NonPositive

Non-positive integers with addition. Caveats: it does not handle integer overflow.

include Semilattice
include Shift.S
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 of_int : int -> t

Conversion from int

val to_int : t -> int

Conversion to int

diff --git a/mugen/Mugen/ShiftWithJoin/Product/argument-1-X/index.html b/mugen/Mugen/ShiftWithJoin/Product/argument-1-X/index.html new file mode 100644 index 0000000..d62bf2f --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/Product/argument-1-X/index.html @@ -0,0 +1,2 @@ + +X (mugen.Mugen.ShiftWithJoin.Product.X)

Parameter Product.X

include Shift.S
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.

diff --git a/mugen/Mugen/ShiftWithJoin/Product/argument-2-Y/index.html b/mugen/Mugen/ShiftWithJoin/Product/argument-2-Y/index.html new file mode 100644 index 0000000..fb9cb96 --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/Product/argument-2-Y/index.html @@ -0,0 +1,2 @@ + +Y (mugen.Mugen.ShiftWithJoin.Product.Y)

Parameter Product.Y

include Shift.S
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.

diff --git a/mugen/Mugen/ShiftWithJoin/Product/index.html b/mugen/Mugen/ShiftWithJoin/Product/index.html new file mode 100644 index 0000000..68fc155 --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/Product/index.html @@ -0,0 +1,2 @@ + +Product (mugen.Mugen.ShiftWithJoin.Product)

Module ShiftWithJoin.Product

Binary products.

Parameters

module X : Semilattice
module Y : Semilattice

Signature

include Semilattice
include Shift.S
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 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

diff --git a/mugen/Mugen/ShiftWithJoin/index.html b/mugen/Mugen/ShiftWithJoin/index.html new file mode 100644 index 0000000..829cdff --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/index.html @@ -0,0 +1,5 @@ + +ShiftWithJoin (mugen.Mugen.ShiftWithJoin)

Module Mugen.ShiftWithJoin

Stock displacement algebras with joins

module type Semilattice = sig ... end

The signature of a displacement algebra with binary joins. (Note that this refers to joins of displacements, not joins of universe levels.)

module type BoundedSemilattice = sig ... end

A displacement algebra with joins and a bottom element.

module Nat : sig ... end

Natural numbers with addition. Caveats: it does not handle integer overflow.

module Int : sig ... end

Integers with addition. Caveats: it does not handle integer overflow.

module NonPositive : sig ... end

Non-positive integers with addition. Caveats: it does not handle integer overflow.

module Product (X : Semilattice) (Y : Semilattice) : sig ... end

Binary products.

module Lexicographic + (X : BoundedSemilattice) + (Y : BoundedSemilattice) : + sig ... end

Binary products, but with the lexicographical order.

module NearlyConstant (Base : BoundedSemilattice) : sig ... end

Infinite products with finite elements different from a fixed displacement.

module FiniteSupport (Base : Semilattice) : sig ... end

Infinite products with finite supports. A special case of NearlyConstant.

diff --git a/mugen/Mugen/ShiftWithJoin/module-type-BoundedSemilattice/index.html b/mugen/Mugen/ShiftWithJoin/module-type-BoundedSemilattice/index.html new file mode 100644 index 0000000..e5c6bd3 --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/module-type-BoundedSemilattice/index.html @@ -0,0 +1,2 @@ + +BoundedSemilattice (mugen.Mugen.ShiftWithJoin.BoundedSemilattice)

Module type ShiftWithJoin.BoundedSemilattice

A displacement algebra with joins and a bottom element.

include Semilattice
include Shift.S
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.

diff --git a/mugen/Mugen/ShiftWithJoin/module-type-Semilattice/index.html b/mugen/Mugen/ShiftWithJoin/module-type-Semilattice/index.html new file mode 100644 index 0000000..f1ea213 --- /dev/null +++ b/mugen/Mugen/ShiftWithJoin/module-type-Semilattice/index.html @@ -0,0 +1,2 @@ + +Semilattice (mugen.Mugen.ShiftWithJoin.Semilattice)

Module type ShiftWithJoin.Semilattice

The signature of a displacement algebra with binary joins. (Note that this refers to joins of displacements, not joins of universe levels.)

include Shift.S
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.

diff --git a/mugen/Mugen/Syntax/Endo/index.html b/mugen/Mugen/Syntax/Endo/index.html new file mode 100644 index 0000000..5e26d18 --- /dev/null +++ b/mugen/Mugen/Syntax/Endo/index.html @@ -0,0 +1,7 @@ + +Endo (mugen.Mugen.Syntax.Endo)

Module Syntax.Endo

Stupid constructors for endo.

type ('s, 'a) t = ('s, 'a) endo =
  1. | Shifted of 'a * 's
  2. | Top

A family of polynomial endofunctors ('s, -) t indexed by the type of displacements 's.

val shifted : 'a -> 's -> ('s, 'a) t

shifted l s is Shifted (l, s), representing the level l shifted by the displacement s.

val top : ('s, 'a) t

top is Top, the additional top level for convenience.

val dump : + (Stdlib.Format.formatter -> 's -> unit) -> + (Stdlib.Format.formatter -> 'a -> unit) -> + Stdlib.Format.formatter -> + ('s, 'a) t -> + unit

dump dump_s dump_a is the ugly printer for levels, where dump_s is the printer for displacements and dump_a is the printer for inner sub-expressions.

diff --git a/mugen/Mugen/Syntax/Free/index.html b/mugen/Mugen/Syntax/Free/index.html new file mode 100644 index 0000000..2ce4a28 --- /dev/null +++ b/mugen/Mugen/Syntax/Free/index.html @@ -0,0 +1,7 @@ + +Free (mugen.Mugen.Syntax.Free)

Module Syntax.Free

Stupid constructors for free.

type ('s, 'v) t = ('s, 'v) free =
  1. | Level of ('s, ('s, 'v) free) endo
  2. | Var of 'v

The free monad ('s, -) t on the endofunctor ('s, -) endo indexed by the type of displacements 's.

val shifted : ('s, 'v) t -> 's -> ('s, 'v) t

shifted l s is Level (Shifted (l, s)), representing the level l shifted by the displacement s.

val top : ('s, 'v) t

top is Top, the additional top level for convenience.

val var : 'v -> ('s, 'v) t

var v is Var v, representing the variable level v.

val dump : + (Stdlib.Format.formatter -> 's -> unit) -> + (Stdlib.Format.formatter -> 'v -> unit) -> + Stdlib.Format.formatter -> + ('s, 'v) t -> + unit

dump dump_s dump_v is the ugly printer for levels, where dump_s is the printer for displacements and dump_v is the printer for variables.

diff --git a/mugen/Mugen/Syntax/index.html b/mugen/Mugen/Syntax/index.html new file mode 100644 index 0000000..1368a16 --- /dev/null +++ b/mugen/Mugen/Syntax/index.html @@ -0,0 +1,2 @@ + +Syntax (mugen.Mugen.Syntax)

Module Mugen.Syntax

Definitions of level expressions

type ('s, 'a) endo =
  1. | Shifted of 'a * 's
  2. | Top

A family of polynomial endofunctors ('s, -) endo indexed by the type of displacements 's.

type ('s, 'v) free =
  1. | Level of ('s, ('s, 'v) free) endo
  2. | Var of 'v

The free monad ('s, -) free on the endofunctor ('s, -) endo indexed by the type of displacements 's.

module Endo : sig ... end

Stupid constructors for endo.

module Free : sig ... end

Stupid constructors for free.

diff --git a/mugen/Mugen/Theory/Make/Infix/index.html b/mugen/Mugen/Theory/Make/Infix/index.html new file mode 100644 index 0000000..8ba9d10 --- /dev/null +++ b/mugen/Mugen/Theory/Make/Infix/index.html @@ -0,0 +1,2 @@ + +Infix (mugen.Mugen.Theory.Make.Infix)

Module Make.Infix

Infix notation.

val (=) : level -> level -> bool

Alias of equal.

val (<) : level -> level -> bool

Alias of lt.

val (<=) : level -> level -> bool

Alias of leq.

val (>) : level -> level -> bool

Alias of gt.

val (>=) : level -> level -> bool

Alias of geq.

diff --git a/mugen/Mugen/Theory/Make/argument-1-P/Shift/index.html b/mugen/Mugen/Theory/Make/argument-1-P/Shift/index.html new file mode 100644 index 0000000..7259417 --- /dev/null +++ b/mugen/Mugen/Theory/Make/argument-1-P/Shift/index.html @@ -0,0 +1,2 @@ + +Shift (mugen.Mugen.Theory.Make.P.Shift)

Module P.Shift

The displacement algebra.

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Theory/Make/argument-1-P/index.html b/mugen/Mugen/Theory/Make/argument-1-P/index.html new file mode 100644 index 0000000..ba629da --- /dev/null +++ b/mugen/Mugen/Theory/Make/argument-1-P/index.html @@ -0,0 +1,2 @@ + +P (mugen.Mugen.Theory.Make.P)

Parameter Make.P

module Shift : Shift.S

The displacement algebra.

type var

The type of level variables.

val equal_var : var -> var -> bool

equal_var x y checks whether two level variables x and y are the same.

diff --git a/mugen/Mugen/Theory/Make/index.html b/mugen/Mugen/Theory/Make/index.html new file mode 100644 index 0000000..1051493 --- /dev/null +++ b/mugen/Mugen/Theory/Make/index.html @@ -0,0 +1,2 @@ + +Make (mugen.Mugen.Theory.Make)

Module Theory.Make

The implementation of the theory.

Parameters

module P : Param

Signature

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

The type of freely generated levels.

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.

diff --git a/mugen/Mugen/Theory/index.html b/mugen/Mugen/Theory/index.html new file mode 100644 index 0000000..7c1531c --- /dev/null +++ b/mugen/Mugen/Theory/index.html @@ -0,0 +1,2 @@ + +Theory (mugen.Mugen.Theory)

Module Mugen.Theory

Semantic comparators for free level expressions

module type Param = sig ... end

Parameters of the theory.

module type S = sig ... end

The signature of the theory.

module Make (P : Param) : S with type shift := P.Shift.t and type var := P.var

The implementation of the theory.

diff --git a/mugen/Mugen/Theory/module-type-Param/Shift/index.html b/mugen/Mugen/Theory/module-type-Param/Shift/index.html new file mode 100644 index 0000000..50a62cc --- /dev/null +++ b/mugen/Mugen/Theory/module-type-Param/Shift/index.html @@ -0,0 +1,2 @@ + +Shift (mugen.Mugen.Theory.Param.Shift)

Module Param.Shift

The displacement algebra.

To form a valid displacement algebra, compose and id should form a monoid, and lt (the strict order) must be left-invariant respect to compose.

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.

diff --git a/mugen/Mugen/Theory/module-type-Param/index.html b/mugen/Mugen/Theory/module-type-Param/index.html new file mode 100644 index 0000000..619bc2f --- /dev/null +++ b/mugen/Mugen/Theory/module-type-Param/index.html @@ -0,0 +1,2 @@ + +Param (mugen.Mugen.Theory.Param)

Module type Theory.Param

Parameters of the theory.

module Shift : Shift.S

The displacement algebra.

type var

The type of level variables.

val equal_var : var -> var -> bool

equal_var x y checks whether two level variables x and y are the same.

diff --git a/mugen/Mugen/Theory/module-type-S/Infix/index.html b/mugen/Mugen/Theory/module-type-S/Infix/index.html new file mode 100644 index 0000000..8bcfe0d --- /dev/null +++ b/mugen/Mugen/Theory/module-type-S/Infix/index.html @@ -0,0 +1,2 @@ + +Infix (mugen.Mugen.Theory.S.Infix)

Module S.Infix

Infix notation.

val (=) : level -> level -> bool

Alias of equal.

val (<) : level -> level -> bool

Alias of lt.

val (<=) : level -> level -> bool

Alias of leq.

val (>) : level -> level -> bool

Alias of gt.

val (>=) : level -> level -> bool

Alias of geq.

diff --git a/mugen/Mugen/Theory/module-type-S/index.html b/mugen/Mugen/Theory/module-type-S/index.html new file mode 100644 index 0000000..5551359 --- /dev/null +++ b/mugen/Mugen/Theory/module-type-S/index.html @@ -0,0 +1,2 @@ + +S (mugen.Mugen.Theory.S)

Module type Theory.S

The signature of the theory.

type shift

The displacement algebra.

type var

The type of level variables.

type level = (shift, var) Syntax.free

The type of freely generated levels.

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.

diff --git a/mugen/Mugen/index.html b/mugen/Mugen/index.html new file mode 100644 index 0000000..808ce47 --- /dev/null +++ b/mugen/Mugen/index.html @@ -0,0 +1,2 @@ + +Mugen (mugen.Mugen)

Module Mugen

module Shift : module type of Shift

Stock displacement algebras

module ShiftWithJoin : module type of ShiftWithJoin

Stock displacement algebras with joins

Syntax of Level Expressions

module Syntax : module type of Syntax

Definitions of level expressions

module Builder : module type of Builder

Smart constructors for level expressions

Comparators of Level Expressions

module Theory : module type of Theory

Semantic comparators for free level expressions

diff --git a/mugen/index.html b/mugen/index.html new file mode 100644 index 0000000..0782e96 --- /dev/null +++ b/mugen/index.html @@ -0,0 +1,2 @@ + +index (mugen.index)

mugen: Universe Levels

What is "mugen"?

"mugen" is the transliteration of "無限" in Japanese, possibly a learned borrowing of "無限" from Chinese. It literally means "without limits", and is widely used in anime for the obvious reason. It is fitting in the context of universe polymorphism.

diff --git a/mugen/quickstart.html b/mugen/quickstart.html new file mode 100644 index 0000000..48a8793 --- /dev/null +++ b/mugen/quickstart.html @@ -0,0 +1,73 @@ + +quickstart (mugen.quickstart)

Quickstart Tutorial

This tutorial is for an implementer (you!) to integrate this library into your type theory implementation as quickly as possible. We will assume you are already familiar with OCaml and dependent type theory, and are using a typical OCaml package structure.

Introduction

Following Conor McBride’s crude but effective stratification and our algebraic reformulation, a universe level in this library is represented as a pair of a variable together with some displacement. For example, a universe level might be x + 10, meaning the variable level x shifted (bumped) by 10 levels. The shifting of 10 levels is the displacement. For the same variable x, the level x + n is larger than x + m if n is larger than m, while levels x + n and y + m are in general incomparable for different variables x and y. Substituting x + n1 for y in y + n2 results in the level x + (n1 + n2).

While this scheme (with only a variable and some displacement) looks limited, we proved that it is in a sense universal if you allow all mathematically possible displacements beyond natural numbers. We also call the minimum algebra of displacements that would make the scheme work a displacement algebra. See our POPL paper for more details.

This library implements several displacement algebras you could choose from, along with a uniform interface to construct and compare universe levels.

Choose Your Displacements

The first step is to choose your favorite displacements. We will use Mugen.Shift.Int (integers) as the starting point, and it is easy to switch to another displacement algebra later. Other displacements are under Mugen.Shift and Mugen.ShiftWithJoin.

Free Level Expressions

Free level expressions are expressions freely generated by only variables and shifting operators. In contrast, we will have a different kind of level expressions embedded in your datatype holding terms or types. The free level expressions are the only ones that can be compared against each other; the embedded ones must be converted to free ones for comparison. More on this point later.

Save the following content as the file ULvl.ml for free level expressions, assuming that you are using integers to represent variables.

module Param =
+struct
+  (** Your chosen displacement algebra *)
+  module Shift = Mugen.Shift.Int
+
+  (** The representation of variables in free level expressions *)
+  type var = int
+
+  (** The equality checker for variables *)
+  let equal_var : var -> var -> bool = Int.equal
+end
+include Param
+
+(** An alias of the type of displacements *)
+type shift = Shift.t
+
+(** An alias of the type of free level expressions *)
+type t = (shift, int) Mugen.Syntax.free
+
+(** Smart constructors for free level expressions *)
+include Mugen.Builder.Free.Make (Param)
+
+(** Comparators for free level expressions *)
+include Mugen.Theory.Make (Param)

Take a look at Mugen.Syntax.free for the definition of free level expressions.

Extend Your Syntax

Now we have the free level expressions ready, you need to extend your datatype to embed levels and define the conversion functions to free ones. A typical datatype holding terms or types will have the following pattern:

type t =
+  | Var of int (* maybe using De Bruijn indexes or levels *)
+  (* ... more syntax follows ... *)

There are three steps to add level expressions to your datatype

Change the Datatype

The idea is to use Mugen.Syntax.endo, instead of Mugen.Syntax.free, so that displacements can syntactically apply to any term or type in your language (but most of them will be ill-formed terms or types). The first parameter of Mugen.Syntax.endo is the type of displacements, and the second parameter is your datatype. It needs to be defined together with your datatype due to the mutual recursion; in the following example, we choose to add a new constructor, ULvl, to embed level expressions:

(** Use [endo] to embed levels into your datatype. *)
+type ulvl = (ULvl.shift, t) Mugen.Syntax.endo
+
+(** The datatype of terms. *)
+and t =
+  | Var of int
+  (* ... more syntax follows ... *)
+  | ULvl of ulvl

You can take a look at Mugen.Syntax.endo for the definition of embedded level expressions.

Add Converters

(** Conversion to free level expressions *)
+let rec to_ulvl : t -> ULvl.t =
+  function
+  | Var i -> Mugen.Syntax.Var i
+  | ULvl endo -> endo_to_ulvl endo
+  | _ -> invalid_arg "to_ulvl"
+
+and endo_to_ulvl : ulvl -> ULvl.t =
+  let module M = Mugen.Syntax in
+  function
+  | M.Shifted (l, s) -> ULvl.shifted (to_ulvl l) s
+  | M.Top -> ULvl.top

Add Smart Constructors

Comparing Levels

The most common tasks are to compare two embedded levels. The code is straightforward---the ULvl module you have created comes with comparators for free level expressions. It is sufficient to convert embedded level expressions to free ones and compare them accordingly. Copy and paste the following code snippet after the definition of your datatype:

(** Conversion to free level expressions *)
+let rec to_ulvl : t -> ULvl.t =
+  function
+  | Var i -> Mugen.Syntax.Var i
+  | ULvl endo -> endo_to_ulvl endo
+  | _ -> invalid_arg "to_ulvl"
+
+and endo_to_ulvl : ulvl -> ULvl.t =
+  let module M = Mugen.Syntax in
+  function
+  | M.Shifted (l, s) -> ULvl.shifted (to_ulvl l) s
+  | M.Top -> ULvl.top

Now, the comparators for embedded level expressions can be defined as followed:

let equal_ulvl l1 l2 = ULvl.equal (to_ulvl l1) (to_ulvl l2)
+let leq_ulvl l1 l2 = ULvl.leq (to_ulvl l1) (to_ulvl l2)
+let lt_ulvl l1 l2 = ULvl.lt (to_ulvl l1) (to_ulvl l2)

You might have noticed that there is a "top" level---we added the top level for convenience.

Building Levels

Another common task in a real system is to parse user inputs and construct corresponding (embedded) level expressions. The recommended approach is to use smart constructors that will consolidate displacements when building level expressions. To do so, these smart constructors need to know how to check whether an expression in your datatype is a level expression. Here is the snippet to copy and paste to summon smart constructors:

(** Include smart constructors for universe levels *)
+include
+  Mugen.Builder.Endo.Make
+    (struct
+      (** Your chosen displacement algebra *)
+      module Shift = ULvl.Shift
+
+      (** The type of embedded level expressions *)
+      type level = t
+
+      (** A function to embed a level expression *)
+      let level (l : ulvl) : t = ULvl l
+
+      (** A function to check whether an expression is an embedded level expression *)
+      let unlevel : t -> ulvl option = function ULvl l -> Some l | _ -> None
+    end)

See Remember that you have included the smart constructors in previous steps.

The essential one

let _ = shifted l s

to obtain the level l shifted by the displacement s. Constructing the displacement s depends on your chosen displacement algebra. If you were using integers, aliasing the stock Mugen.Shift.Int as ULvl.Shift), then the shifting by 10 levels can be implemented as:

let _ = shifted l (ULvl.Shift.of_int 10)

For convenience, we also introduced the top level

let _ = top

that will be greater than any other level. (Note that you cannot shift the distinguished top level!)

Concluding Notes

That's it! Now you have rich universe levels. Here are a few remarks:

Ugly Printers for Debugging

It is recommended to write your own pretty printer. However, if you wish to dump the universe levels, check out Mugen.Syntax.Free.dump for free level expressions and Mugen.Syntax.Endo.dump for embedded ones.

Changing the Displacement Algebra

It is trivial to switch to another displacement algebra by aliasing ULvl.Shift to another module implementing the interface Mugen.Shift.S. Changing the displacement algebra only affects how displacements are constructed and printed.

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t||!t.unexpandable:Nn.hasOwnProperty(e)&&!Nn[e].primitive},e}(),Un={"\u0301":{text:"\\'",math:"\\acute"},"\u0300":{text:"\\`",math:"\\grave"},"\u0308":{text:'\\"',math:"\\ddot"},"\u0303":{text:"\\~",math:"\\tilde"},"\u0304":{text:"\\=",math:"\\bar"},"\u0306":{text:"\\u",math:"\\breve"},"\u030c":{text:"\\v",math:"\\check"},"\u0302":{text:"\\^",math:"\\hat"},"\u0307":{text:"\\.",math:"\\dot"},"\u030a":{text:"\\r",math:"\\mathring"},"\u030b":{text:"\\H"},"\u0327":{text:"\\c"}},Yn={"\xe1":"a\u0301","\xe0":"a\u0300","\xe4":"a\u0308","\u01df":"a\u0308\u0304","\xe3":"a\u0303","\u0101":"a\u0304","\u0103":"a\u0306","\u1eaf":"a\u0306\u0301","\u1eb1":"a\u0306\u0300","\u1eb5":"a\u0306\u0303","\u01ce":"a\u030c","\xe2":"a\u0302","\u1ea5":"a\u0302\u0301","\u1ea7":"a\u0302\u0300","\u1eab":"a\u0302\u0303","\u0227":"a\u0307","\u01e1":"a\u0307\u0304","\xe5":"a\u030a","\u01fb":"a\u030a\u0301","\u1e03":"b\u0307","\u0107":"c\u0301","\u1e09":"c\u0327\u0301","\u010d":"c\u030c","\u0109":"c\u0302","\u010b":"c\u0307","\xe7":"c\u0327","\u010f":"d\u030c","\u1e0b":"d\u0307","\u1e11":"d\u0327","\xe9":"e\u0301","\xe8":"e\u0300","\xeb":"e\u0308","\u1ebd":"e\u0303","\u0113":"e\u0304","\u1e17":"e\u0304\u0301","\u1e15":"e\u0304\u0300","\u0115":"e\u0306","\u1e1d":"e\u0327\u0306","\u011b":"e\u030c","\xea":"e\u0302","\u1ebf":"e\u0302\u0301","\u1ec1":"e\u0302\u0300","\u1ec5":"e\u0302\u0303","\u0117":"e\u0307","\u0229":"e\u0327","\u1e1f":"f\u0307","\u01f5":"g\u0301","\u1e21":"g\u0304","\u011f":"g\u0306","\u01e7":"g\u030c","\u011d":"g\u0302","\u0121":"g\u0307","\u0123":"g\u0327","\u1e27":"h\u0308","\u021f":"h\u030c","\u0125":"h\u0302","\u1e23":"h\u0307","\u1e29":"h\u0327","\xed":"i\u0301","\xec":"i\u0300","\xef":"i\u0308","\u1e2f":"i\u0308\u0301","\u0129":"i\u0303","\u012b":"i\u0304","\u012d":"i\u0306","\u01d0":"i\u030c","\xee":"i\u0302","\u01f0":"j\u030c","\u0135":"j\u0302","\u1e31":"k\u0301","\u01e9":"k\u030c","\u0137":"k\u0327","\u013a":"l\u0301","\u013e":"l\u030c","\u013c":"l\u0327","\u1e3f":"m\u0301","\u1e41":"m\u0307","\u0144":"n\u0301","\u01f9":"n\u0300","\xf1":"n\u0303","\u0148":"n\u030c","\u1e45":"n\u0307","\u0146":"n\u0327","\xf3":"o\u0301","\xf2":"o\u0300","\xf6":"o\u0308","\u022b":"o\u0308\u0304","\xf5":"o\u0303","\u1e4d":"o\u0303\u0301","\u1e4f":"o\u0303\u0308","\u022d":"o\u0303\u0304","\u014d":"o\u0304","\u1e53":"o\u0304\u0301","\u1e51":"o\u0304\u0300","\u014f":"o\u0306","\u01d2":"o\u030c","\xf4":"o\u0302","\u1ed1":"o\u0302\u0301","\u1ed3":"o\u0302\u0300","\u1ed7":"o\u0302\u0303","\u022f":"o\u0307","\u0231":"o\u0307\u0304","\u0151":"o\u030b","\u1e55":"p\u0301","\u1e57":"p\u0307","\u0155":"r\u0301","\u0159":"r\u030c","\u1e59":"r\u0307","\u0157":"r\u0327","\u015b":"s\u0301","\u1e65":"s\u0301\u0307","\u0161":"s\u030c","\u1e67":"s\u030c\u0307","\u015d":"s\u0302","\u1e61":"s\u0307","\u015f":"s\u0327","\u1e97":"t\u0308","\u0165":"t\u030c","\u1e6b":"t\u0307","\u0163":"t\u0327","\xfa":"u\u0301","\xf9":"u\u0300","\xfc":"u\u0308","\u01d8":"u\u0308\u0301","\u01dc":"u\u0308\u0300","\u01d6":"u\u0308\u0304","\u01da":"u\u0308\u030c","\u0169":"u\u0303","\u1e79":"u\u0303\u0301","\u016b":"u\u0304","\u1e7b":"u\u0304\u0308","\u016d":"u\u0306","\u01d4":"u\u030c","\xfb":"u\u0302","\u016f":"u\u030a","\u0171":"u\u030b","\u1e7d":"v\u0303","\u1e83":"w\u0301","\u1e81":"w\u0300","\u1e85":"w\u0308","\u0175":"w\u0302","\u1e87":"w\u0307","\u1e98":"w\u030a","\u1e8d":"x\u0308","\u1e8b":"x\u0307","\xfd":"y\u0301","\u1ef3":"y\u0300","\xff":"y\u0308","\u1ef9":"y\u0303","\u0233":"y\u0304","\u0177":"y\u0302","\u1e8f":"y\u0307","\u1e99":"y\u030a","\u017a":"z\u0301","\u017e":"z\u030c","\u1e91":"z\u0302","\u017c":"z\u0307","\xc1":"A\u0301","\xc0":"A\u0300","\xc4":"A\u0308","\u01de":"A\u0308\u0304","\xc3":"A\u0303","\u0100":"A\u0304","\u0102":"A\u0306","\u1eae":"A\u0306\u0301","\u1eb0":"A\u0306\u0300","\u1eb4":"A\u0306\u0303","\u01cd":"A\u030c","\xc2":"A\u0302","\u1ea4":"A\u0302\u0301","\u1ea6":"A\u0302\u0300","\u1eaa":"A\u0302\u0303","\u0226":"A\u0307","\u01e0":"A\u0307\u0304","\xc5":"A\u030a","\u01fa":"A\u030a\u0301","\u1e02":"B\u0307","\u0106":"C\u0301","\u1e08":"C\u0327\u0301","\u010c":"C\u030c","\u0108":"C\u0302","\u010a":"C\u0307","\xc7":"C\u0327","\u010e":"D\u030c","\u1e0a":"D\u0307","\u1e10":"D\u0327","\xc9":"E\u0301","\xc8":"E\u0300","\xcb":"E\u0308","\u1ebc":"E\u0303","\u0112":"E\u0304","\u1e16":"E\u0304\u0301","\u1e14":"E\u0304\u0300","\u0114":"E\u0306","\u1e1c":"E\u0327\u0306","\u011a":"E\u030c","\xca":"E\u0302","\u1ebe":"E\u0302\u0301","\u1ec0":"E\u0302\u0300","\u1ec4":"E\u0302\u0303","\u0116":"E\u0307","\u0228":"E\u0327","\u1e1e":"F\u0307","\u01f4":"G\u0301","\u1e20":"G\u0304","\u011e":"G\u0306","\u01e6":"G\u030c","\u011c":"G\u0302","\u0120":"G\u0307","\u0122":"G\u0327","\u1e26":"H\u0308","\u021e":"H\u030c","\u0124":"H\u0302","\u1e22":"H\u0307","\u1e28":"H\u0327","\xcd":"I\u0301","\xcc":"I\u0300","\xcf":"I\u0308","\u1e2e":"I\u0308\u0301","\u0128":"I\u0303","\u012a":"I\u0304","\u012c":"I\u0306","\u01cf":"I\u030c","\xce":"I\u0302","\u0130":"I\u0307","\u0134":"J\u0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e(e,t){this.mode=void 0,this.gullet=void 0,this.settings=void 0,this.leftrightDepth=void 0,this.nextToken=void 0,this.mode="math",this.gullet=new Gn(e,t,this.mode),this.settings=t,this.leftrightDepth=0}var t=e.prototype;return t.expect=function(e,t){if(void 0===t&&(t=!0),this.fetch().text!==e)throw new n("Expected '"+e+"', got '"+this.fetch().text+"'",this.fetch());t&&this.consume()},t.consume=function(){this.nextToken=null},t.fetch=function(){return null==this.nextToken&&(this.nextToken=this.gullet.expandNextToken()),this.nextToken},t.switchMode=function(e){this.mode=e,this.gullet.switchMode(e)},t.parse=function(){this.settings.globalGroup||this.gullet.beginGroup(),this.settings.colorIsTextColor&&this.gullet.macros.set("\\color","\\textcolor");try{var e=this.parseExpression(!1);return this.expect("EOF"),this.settings.globalGroup||this.gullet.endGroup(),e}finally{this.gullet.endGroups()}},t.subparse=function(e){var t=this.nextToken;this.consume(),this.gullet.pushToken(new Dr("}")),this.gullet.pushTokens(e);var r=this.parseExpression(!1);return this.expect("}"),this.nextToken=t,r},t.parseExpression=function(t,r){for(var n=[];;){"math"===this.mode&&this.consumeSpaces();var a=this.fetch();if(-1!==e.endOfExpression.indexOf(a.text))break;if(r&&a.text===r)break;if(t&&Nn[a.text]&&Nn[a.text].infix)break;var i=this.parseAtom(r);if(!i)break;"internal"!==i.type&&n.push(i)}return"text"===this.mode&&this.formLigatures(n),this.handleInfixNodes(n)},t.handleInfixNodes=function(e){for(var t,r=-1,a=0;a=0&&this.settings.reportNonstrict("unicodeTextInMathMode",'Latin-1/Unicode text character "'+t[0]+'" used in math mode',e);var s,l=ae[this.mode][t].group,h=Lr.range(e);if(te.hasOwnProperty(l)){var m=l;s={type:"atom",mode:this.mode,family:m,loc:h,text:t}}else s={type:l,mode:this.mode,loc:h,text:t};i=s}else{if(!(t.charCodeAt(0)>=128))return null;this.settings.strict&&(S(t.charCodeAt(0))?"math"===this.mode&&this.settings.reportNonstrict("unicodeTextInMathMode",'Unicode text character "'+t[0]+'" used in math mode',e):this.settings.reportNonstrict("unknownSymbol",'Unrecognized Unicode character "'+t[0]+'" ('+t.charCodeAt(0)+")",e)),i={type:"textord",mode:"text",loc:Lr.range(e),text:t}}if(this.consume(),o)for(var c=0;c *:first-child { + /* This make the first thing in the preamble align with the sidebar */ + padding-top: 0; + margin-top: 0; +} + +header { + margin-bottom: 30px; +} + +header.odoc-preamble { + grid-column: 2; + grid-row: 3; +} + +nav { + font-family: "Fira Sans", sans-serif; +} + +nav.odoc-nav { + grid-column: 2; + grid-row: 2; +} + +/* Basic markup elements */ + +b, strong { + font-weight: bold; +} + +i { + font-style: italic; +} + +em, i em.odd{ + font-style: italic; +} + +em.odd, i em { + font-style: normal; +} + +sup { + vertical-align: super; +} + +sub { + vertical-align: sub; +} + +sup, sub { + font-size: 12px; + line-height: 0; + margin-left: 0.2ex; +} + +ul, ol { + list-style-position: outside +} + +ul>li { + margin-left: 22px; +} + +ol>li { + margin-left: 27.2px; +} + +li>*:first-child { + margin-top: 0 +} + +/* Text alignements, this should be forbidden. */ + +.left { + text-align: left; +} + +.right { + text-align: right; +} + +.center { + text-align: center; +} + +/* Links and anchors */ + +a { + text-decoration: none; + color: var(--link-color); +} + +.odoc-src pre a { + color: inherit; +} + +a:hover { + box-shadow: 0 1px 0 0 var(--link-color); +} + +/* Linked highlight */ +*:target { + background-color: var(--target-background) !important; + box-shadow: 0 0px 0 1px var(--target-shadow) !important; + border-radius: 1px; +} + +*:hover > a.anchor { + visibility: visible; +} + +a.anchor:before { + content: "#"; +} + +a.anchor:hover { + box-shadow: none; + text-decoration: none; + color: var(--anchor-hover); +} + +a.anchor { + visibility: hidden; + position: absolute; + /* top: 0px; */ + /* margin-left: -3ex; */ + margin-left: -1.3em; + font-weight: normal; + font-style: normal; + padding-right: 0.4em; + padding-left: 0.4em; + /* To remain selectable */ + color: var(--anchor-color); +} + +.spec > a.anchor { + margin-left: -2.3em; + padding-right: 0.9em; +} + +.xref-unresolved { + color: #2C94BD; +} +.xref-unresolved:hover { + box-shadow: 0 1px 0 0 var(--xref-shadow); +} + +/* Source links float inside preformated text or headings. */ +a.source_link { + float: right; + color: var(--source-color); + font-family: "Fira Sans", sans-serif; + font-size: initial; +} + +/* Section and document divisions. + Until at least 4.03 many of the modules of the stdlib start at .h7, + we restart the sequence there like h2 */ + +h1, h2, h3, h4, h5, h6, .h7, .h8, .h9, .h10 { + font-family: "Fira Sans", sans-serif; + font-weight: 400; + padding-top: 0.1em; + line-height: 1.2; + overflow-wrap: break-word; +} + +.odoc-preamble h1 { + margin-top: 10px; +} + +h1 { + font-weight: 500; + font-size: 2.441em; +} + +h1 { + font-weight: 500; + font-size: 1.953em; + box-shadow: 0 1px 0 0 var(--header-shadow); +} + +h2 { + font-size: 1.563em; +} + +h3 { + font-size: 1.25em; +} + +small, .font_small { + font-size: 0.8em; +} + +h1 code, h1 tt { + font-size: inherit; + font-weight: inherit; +} + +h2 code, h2 tt { + font-size: inherit; + font-weight: inherit; +} + +h3 code, h3 tt { + font-size: inherit; + font-weight: inherit; +} + +h3 code, h3 tt { + font-size: inherit; + font-weight: inherit; +} + +h4 { + font-size: 1.12em; +} + +/* Comment delimiters, hidden but accessible to screen readers and + selected for copy/pasting */ + +/* Taken from bootstrap */ +/* See also https://stackoverflow.com/a/27769435/4220738 */ +.comment-delim { + position: absolute; + width: 1px; + height: 1px; + padding: 0; + margin: -1px; + overflow: hidden; + clip: rect(0, 0, 0, 0); + white-space: nowrap; + border: 0; +} + +/* Preformatted and code */ + +tt, code, pre { + font-family: "Fira Mono", monospace; + font-weight: 400; +} + +.odoc pre { + padding: 0.1em; + border: 1px solid var(--pre-border-color); + border-radius: 5px; + overflow-x: auto; +} + +.odoc p code, +.odoc li code { + background-color: var(--li-code-background); + color: var(--li-code-color); + border-radius: 3px; + padding: 0 0.3ex; +} + +p a > code, li a > code { + color: var(--link-color); +} + +.odoc code { + white-space: pre-wrap; +} + +/* Code blocks (e.g. Examples) */ + +.odoc pre code { + font-size: 0.893rem; +} + +/* Code lexemes */ + +.keyword { + font-weight: 500; +} + +.arrow { white-space: nowrap } + +/* Module member specification */ + +.spec { + background-color: var(--spec-summary-background); + border-radius: 3px; + border-left: 4px solid var(--spec-summary-border-color); + border-right: 5px solid transparent; + padding: 0.35em 0.5em; +} + +.spec .label, .spec .optlabel { + color: var(--spec-label-color); +} + +li:not(:last-child) > .def-doc { + margin-bottom: 15px; +} + +/* Spacing between items */ +div.odoc-spec,.odoc-include { + margin-bottom: 2em; +} + +.spec.type .variant p, .spec.type .record p { + margin: 5px; +} + +.spec.type .variant, .spec.type .record { + margin-left: 2ch; +} + +.spec.type li.variant, .spec.type li.record { + list-style: none; +} + +.spec.type .record > code, .spec.type .variant > code { + min-width: 40%; +} + +.spec.type > ol { + margin-top: 0; + margin-bottom: 0; +} + +.spec.type .record > .def-doc, .spec.type .variant > .def-doc { + min-width:50%; + padding: 0.25em 0.5em; + margin-left: 10%; + border-radius: 3px; + background: var(--main-background); + box-shadow: 1px 1px 2px lightgrey; +} + +div.def { + margin-top: 0; + text-indent: -2ex; + padding-left: 2ex; +} + +div.def-doc>*:first-child { + margin-top: 0; +} + +/* Collapsible inlined include and module */ + +.odoc-include details { + position: relative; +} + +.odoc-include.shadowed-include { + display: none; +} + +.odoc-include details:after { + z-index: -100; + display: block; + content: " "; + position: absolute; + border-radius: 0 1ex 1ex 0; + right: -20px; + top: 1px; + bottom: 1px; + width: 15px; + background: var(--spec-details-after-background, rgba(0, 4, 15, 0.05)); + box-shadow: 0 0px 0 1px var(--spec-details-after-shadow, rgba(204, 204, 204, 0.53)); +} + +.odoc-include summary { + position: relative; + margin-bottom: 1em; + cursor: pointer; + outline: none; +} + +.odoc-include summary:hover { + background-color: var(--spec-summary-hover-background); +} + +/* FIXME: Does not work in Firefox. */ +.odoc-include summary::-webkit-details-marker { + color: #888; + transform: scaleX(-1); + position: absolute; + top: calc(50% - 5px); + height: 11px; + right: -29px; +} + +/* Records and variants FIXME */ + +div.def table { + text-indent: 0em; + padding: 0; + margin-left: -2ex; +} + +td.def { + padding-left: 2ex; +} + +td.def-doc *:first-child { + margin-top: 0em; +} + +/* Lists of @tags */ + +.at-tags { list-style-type: none; margin-left: -3ex; } +.at-tags li { padding-left: 3ex; text-indent: -3ex; } +.at-tags .at-tag { text-transform: capitalize } + +/* Alert emoji */ + +.alert::before, .deprecated::before { + content: '⚠️ '; +} + +/* Lists of modules */ + +.modules { list-style-type: none; margin-left: -3ex; } +.modules li { padding-left: 3ex; text-indent: -3ex; margin-top: 5px } +.modules .synopsis { padding-left: 1ch; } + +/* Odig package index */ + +.packages { list-style-type: none; margin-left: -3ex; } +.packages li { padding-left: 3ex; text-indent: -3ex } +.packages li a.anchor { padding-right: 0.5ch; padding-left: 3ch; } +.packages .version { font-size: 10px; color: var(--by-name-version-color); } +.packages .synopsis { padding-left: 1ch } + +.by-name nav a { + text-transform: uppercase; + font-size: 18px; + margin-right: 1ex; + color: var(--by-name-nav-link-color,); + display: inline-block; +} + +.by-tag nav a { + margin-right: 1ex; + color: var(--by-name-nav-link-color); + display: inline-block; +} + +.by-tag ol { list-style-type: none; } +.by-tag ol.tags li { margin-left: 1ch; display: inline-block } +.by-tag td:first-child { text-transform: uppercase; } + +/* Odig package page */ + +.package nav { + display: inline; + font-size: 14px; + font-weight: normal; +} + +.package .version { + font-size: 14px; +} + +.package.info { + margin: 0; +} + +.package.info td:first-child { + font-style: italic; + padding-right: 2ex; +} + +.package.info ul { + list-style-type: none; + display: inline; + margin: 0; +} + +.package.info li { + display: inline-block; + margin: 0; + margin-right: 1ex; +} + +#info-authors li, #info-maintainers li { + display: block; +} + +/* Sidebar and TOC */ + +.odoc-toc:before { + display: block; + content: "Contents"; + text-transform: uppercase; + font-size: 1em; + margin: 1.414em 0 0.5em; + font-weight: 500; + color: var(--toc-before-color); + line-height: 1.2; +} + +/* When a search bar is present, we need the sticky sidebar to be a bit lower, + so `top` is higher */ + +.odoc-search + * + .odoc-toc { + --toc-top: calc(var(--search-bar-height) + var(--search-padding-top) + 20px); + max-height: calc(100vh - 2 * var(--toc-top)); + top: var(--toc-top) +} + +.odoc-toc { + --toc-top: 20px; + width: 28ex; + background: var(--toc-background); + overflow: auto; + color: var(--toc-color); + padding-left: 2ex; + padding-right: 2ex; + grid-row-start: 3; + grid-row-end: 5; + grid-column: 1; + height: fit-content; + border: solid 1px var(--border); + border-radius: 5px; + position:sticky; + max-height: calc(100vh - 2 * var(--toc-top)); + top: var(--toc-top) +} + +.odoc-toc ul li a { + font-family: "Fira Sans", sans-serif; + font-size: 0.95em; + color: var(--color); + font-weight: 400; + line-height: 1.2em; + display: block; +} + +.odoc-sidebar ul li a:hover { + box-shadow: none; + text-decoration: underline; +} + +:root { + --search-bar-height: 25px; + --search-padding-top: 1rem; +} + +.odoc-search { + position: sticky; + top: 0; + background: var(--main-background); + /* This amounts to fit-content when the search is not active, but when you + have the search results displayed, you do not want the height of the search + container to change. */ + height: calc(var(--search-bar-height) + var(--search-padding-top)); + width: 100%; + padding-top: var(--search-padding-top); + z-index: 1; + grid-row: 1; + grid-column-start: 1; + grid-column-end: 3; +} + + +.odoc-search .search-inner { + width: 100%; + position: relative; + left: 0; + display: grid; + /* The second column is for the search snake, which has 0 width */ + grid-template-columns: 1fr 0fr; + grid-row-gap: 1rem; + /* The second row is for the search results. It has a width, but only */ + grid-template-rows: min-content 0px; + background: transparent; +} + +.odoc-search .search-bar { + position: relative; + z-index: 2; + font-size: 1em; + transition: font-size 0.3s; + box-shadow: 0px 0px 0.2rem 0.3em var(--main-background); + height: var(--search-bar-height); +} + +.odoc-search:focus-within .search-bar { + font-size: 1.1em; +} + +.odoc-search:not(:focus-within) .search-result { + display: none; +} + +.odoc-search .search-result:empty { + display: none; +} + +.odoc-search .search-result { + grid-row: 2; + background: var(--toc-background); + position: absolute; + left: 0; + right: 0; + border: solid; + border-color: var(--search-results-border); + border-width: 1px; + border-radius: 6px; + box-shadow: 0 3px 10px 2px var(--search-results-shadow), 0 0 3px 4px var(--main-background), 0px -1rem 0px 0px var(--main-background); + /* Works better on smallish screens with this */ + max-height: calc(min(40rem, 50vh)); + overflow-y: auto; +} + +.search-bar { + /* inputs are of fixed size by default, even if you display:block them */ + width: 100%; +} + + +.odoc-search .search-no-result { + color: var(--color); + border-bottom: var(--search-results-border) solid 1px; + background-color: inherit; + outline: 0; + padding: 10px; + padding-right: 0.5rem; +} + +.search-bar-container { + display: flex; + align-items: stretch; + border-bottom: 1rem solid var(--main-background); +} + +.search-snake { + grid-row: 1; + grid-column: 2; + display: flex; + align-items: center; + width: 0; + z-index: 2; + position: relative; + left: 0; + margin-top: 4px; + margin-bottom: 4px; + /* Otherwise the search snake flickers for very fast searches. */ + transition: opacity 0.2s; + opacity: 0; +} + +.search-snake.search-busy { + opacity: 1; +} + +.search-snake:before { + content: " "; + display: block; + aspect-ratio: 1 / 1; + height: 100%; + margin-right: 4px; + border-radius: 50%; + border: 3px solid #aaa; + border-color: var(--search-snake) transparent var(--search-snake) transparent; + animation: search-snake 1.2s linear infinite; + position: absolute; + right: 0; +} + +@keyframes search-snake { + 0% { + transform: rotate(0deg); + } + + 100% { + transform: rotate(360deg); + } +} + +:root { + --kind-font-size-factor: 0.8; +} + +.odoc-search .search-entry { + color: var(--color); + display: grid; + /* Possible kinds are the following : + "doc" "type" "mod" "exn" "class" "meth" "cons" "sig" "cons" "field" "val" + and "ext". + As the longest is 5 characters (and the font monospace), we give 5 + character size to the column. However the font used for kind is a little + smaller, so we adjust by this factor. + */ + grid-template-columns: [kinds] calc(var(--kind-font-size-factor) * 5ch) [titles] 1fr; + column-gap: 0.5rem; + border-bottom: var(--search-results-border) solid 1px; + background-color: inherit; + outline: 0; + padding: 0.4rem 0.4rem 0.7rem 0.7rem; +} +.odoc-search .search-entry p { + margin: 0; + overflow: hidden; + text-overflow: ellipsis; + white-space: nowrap; +} + +.odoc-search .search-entry:focus-visible { + box-shadow: none; + background-color: var(--target-background); +} + +.odoc-search .search-entry:hover { + box-shadow: none; + background-color: var(--toc-background-emph); +} + +.odoc-search .search-entry .entry-kind { + grid-row: 1/2; + grid-column: 1/2; + line-height: 1.4rem; + font-size: calc(var(--kind-font-size-factor) * 1em); + font-weight: bold; + text-align: right; + position: relative; + bottom: 0; +} + +.odoc-search .search-entry pre { + border: none; + margin: 0; +} + +.odoc-search .search-entry pre code { + font-size: 1em; + background-color: var(--li-code-background); + color: var(--li-code-color); + border-radius: 3px; + padding: 0 0.3ex; +} + +.odoc-search .search-entry .entry-title { + width: 100%; + display: block; + grid-column: 2/2; + grid-row: 1/2; + align-self: end; + line-height: 1.4rem; + white-space: nowrap; + overflow: hidden; + text-overflow: ellipsis; +} + +.odoc-search .entry-name { + font-weight: bold; +} + +.odoc-search .prefix-name { + font-weight: bold; +} + +.odoc-search .search-entry .prefix-name { + opacity: 0.7; +} + +.odoc-search .entry-rhs { + white-space: nowrap; +} + +.odoc-search .search-entry .entry-content { + flex-grow: 1; + flex-shrink: 1; + min-width: 0; +} + +.odoc-search .search-entry .entry-comment { + max-height: 1.5em; + overflow: hidden; + text-overflow: ellipsis; + white-space: nowrap; + font-size: 0.95em; + grid-row: 2/2; + grid-column: 2/2; +} + +.odoc-search .search-entry .entry-comment ul { + white-space: nowrap; + display: inline; +} + +.odoc-search .search-entry .entry-comment li { + display: inline; + white-space: nowrap; +} + +.odoc-search .search-entry .entry-comment ul>li::before { + content: '•'; +} + +.odoc-search .search-entry .entry-comment div { + display: inline; + white-space: nowrap; +} + +.odoc-search .search-entry .entry-comment p { + display: inline; + white-space: nowrap; +} + +.odoc-search .search-entry .entry-comment code { + display: inline; + white-space: nowrap; +} + +/* First level titles */ + +.odoc-toc>ul>li>a { + font-weight: 500; +} + +.odoc-toc li ul { + margin: 0px; + padding-top: 0.25em; +} + +.odoc-toc ul { + list-style-type: none; +} + +.odoc-toc ul li { + padding: 0.25em 0; +} + +.odoc-toc>ul>li { + margin-bottom: 0.3em; +} + +.odoc-toc ul li li { + border-left: 1px solid var(--toc-list-border); + margin-left: 5px; + padding-left: 12px; +} + +/* Tables */ + +.odoc-table { + margin: 1em; +} + +.odoc-table td, +.odoc-table th { + padding-left: 0.5em; + padding-right: 0.5em; + border: 1px solid black; +} + +.odoc-table th { + font-weight: bold; +} + +/* Mobile adjustements. */ + +@media only screen and (max-width: 110ex) { + body { + margin: 2em; + padding: 0; + } + + body.odoc { + display: block; + } + + .odoc-toc { + position: static; + width: auto; + min-width: unset; + max-width: unset; + border: none; + padding: 0.2em 1em; + border-radius: 5px; + margin-bottom: 2em; + } +} + +/* Print adjustements. */ + +@media print { + body { + color: black; + background: white; + } + + body nav:first-child { + visibility: hidden; + } +} + +/* Source code. */ + +.source_container { + display: flex; +} + +.source_line_column { + padding-right: 0.5em; + text-align: right; + background: #eee8d5; +} + +.source_line { + padding: 0 1em; +} + +.source_code { + flex-grow: 1; + background: #fdf6e3; + padding: 0 0.3em; + color: #657b83; +} + +/* Source directories */ + +.odoc-directory::before { + content: "📁"; + margin: 0.3em; + font-size: 1.3em; +} + +.odoc-file::before { + content: "📄"; + margin: 0.3em; + font-size: 1.3em; +} + +.odoc-folder-list { + list-style: none; +} + +/* Syntax highlighting (based on github-gist) */ + +.hljs { + display: block; + background: var(--code-background); + padding: 0.5em; + color: var(--color); + overflow-x: auto; +} + +.hljs-comment, +.hljs-meta { + color: #969896; +} + +.hljs-string, +.hljs-variable, +.hljs-template-variable, +.hljs-strong, +.hljs-emphasis, +.hljs-quote { + color: #df5000; +} + +.hljs-keyword, +.hljs-selector-tag { + color: #a71d5d; +} + +.hljs-type, +.hljs-class .hljs-title { + color: #458; + font-weight: 500; +} + +.hljs-literal, +.hljs-symbol, +.hljs-bullet, +.hljs-attribute { + color: #0086b3; +} + +.hljs-section, +.hljs-name { + color: #63a35c; +} + +.hljs-tag { + color: #333333; +} + +.hljs-attr, +.hljs-selector-id, +.hljs-selector-class, +.hljs-selector-attr, +.hljs-selector-pseudo { + color: #795da3; +} + +.hljs-addition { + color: #55a532; + background-color: #eaffea; +} + +.hljs-deletion { + color: #bd2c00; + background-color: #ffecec; +} + +.hljs-link { + text-decoration: underline; +} + +.VAL, +.TYPE, +.LET, +.REC, +.IN, +.OPEN, +.NONREC, +.MODULE, +.METHOD, +.LETOP, +.INHERIT, +.INCLUDE, +.FUNCTOR, +.EXTERNAL, +.CONSTRAINT, +.ASSERT, +.AND, +.END, +.CLASS, +.STRUCT, +.SIG { + color: #859900; + ; +} + +.WITH, +.WHILE, +.WHEN, +.VIRTUAL, +.TRY, +.TO, +.THEN, +.PRIVATE, +.OF, +.NEW, +.MUTABLE, +.MATCH, +.LAZY, +.IF, +.FUNCTION, +.FUN, +.FOR, +.EXCEPTION, +.ELSE, +.TO, +.DOWNTO, +.DO, +.DONE, +.BEGIN, +.AS { + color: #cb4b16; +} + +.TRUE, +.FALSE { + color: #b58900; +} + +.failwith, +.INT, +.SEMISEMI, +.LIDENT { + color: #2aa198; +} + +.STRING, +.CHAR, +.UIDENT { + color: #b58900; +} + +.DOCSTRING { + color: #268bd2; +} + +.COMMENT { + color: #93a1a1; +} + +/*--------------------------------------------------------------------------- + Copyright (c) 2016 The odoc contributors + + Permission to use, copy, modify, and/or distribute this software for any + purpose with or without fee is hereby granted, provided that the above + copyright notice and this permission notice appear in all copies. + + THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES + WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF + MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR + ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES + WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN + ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF + OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. + ---------------------------------------------------------------------------*/ \ No newline at end of file diff --git a/odoc.support/odoc_search.js b/odoc.support/odoc_search.js new file mode 100644 index 0000000..0dc659d --- /dev/null +++ b/odoc.support/odoc_search.js @@ -0,0 +1,66 @@ +/* The browsers interpretation of the CORS origin policy prevents to run + webworkers from javascript files fetched from the file:// protocol. This hack + is to workaround this restriction. */ +function createWebWorker() { + var searchs = search_urls.map((search_url) => { + let parts = document.location.href.split("/"); + parts[parts.length - 1] = search_url; + return '"' + parts.join("/") + '"'; + }); + blobContents = ["importScripts(" + searchs.join(",") + ");"]; + var blob = new Blob(blobContents, { type: "application/javascript" }); + var blobUrl = URL.createObjectURL(blob); + + var worker = new Worker(blobUrl); + URL.revokeObjectURL(blobUrl); + + return worker; +} + +var worker; +var waiting = 0; + +function wait() { + waiting = waiting + 1; + document.querySelector(".search-snake").classList.add("search-busy"); +} + +function stop_waiting() { + if (waiting > 0) waiting = waiting - 1; + else waiting = 0; + if (waiting == 0) { + document.querySelector(".search-snake").classList.remove("search-busy"); + } +} + +document.querySelector(".search-bar").addEventListener("focus", (ev) => { + if (typeof worker == "undefined") { + worker = createWebWorker(); + worker.onmessage = (e) => { + stop_waiting(); + let results = e.data; + let search_results = document.querySelector(".search-result"); + search_results.innerHTML = ""; + let f = (entry) => { + let search_result = document.createElement("a"); + search_result.classList.add("search-entry"); + search_result.href = base_url + entry.url; + search_result.innerHTML = entry.html; + search_results.appendChild(search_result); + }; + results.forEach(f); + let search_request = document.querySelector(".search-bar").value; + if (results.length == 0 && search_request != "") { + let no_result = document.createElement("div"); + no_result.classList.add("search-no-result"); + no_result.innerText = "No result..."; + search_results.appendChild(no_result); + } + }; + } +}); + +document.querySelector(".search-bar").addEventListener("input", (ev) => { + wait(); + worker.postMessage(ev.target.value); +});