Sound.DF.Uniform.Faust

Faust signal processing block diagram model.

Block diagram data type

type Rec_Id = (Id, Id, TypeRep)

The write and read Ids, and the wire type.

data BD

Block diagram.

Constructors

Constant (Maybe Id) K

Prim (Maybe Id) String [TypeRep] (Maybe TypeRep)

Par BD BD

Seq BD BD

Split BD BD

Rec (Maybe [Rec_Id]) BD BD

Instances

Eq BD

Fractional BD

Num BD

Show BD

Identifiers

bd_id :: BD -> Maybe Id

Read identifier.

bd_req_id :: BD -> Id

Erroring bd_id.

Pretty printing

bd_pp :: BD -> String

Pretty printer for BD.

Diagram types and signature

bd_signature :: BD -> ([TypeRep], [TypeRep])

Diagram type signature, ie. port_ty at ports.

bd_ty :: BD -> [TypeRep]

Type of output ports of BD.

bd_ty_uniform :: BD -> Maybe TypeRep

Type of uniform output ports of BD.

bd_ty1 :: BD -> Maybe TypeRep

Type of singular output port of BD.

Operator synonyms

(~~) :: BD -> BD -> BD

Faust uses single tilde, which is reserved by GHC.Exts.

(~.) :: BD -> BD -> BD

Faust uses comma, which is reserved by Data.Tuple, and indeed ~, is not legal either.

(~:) :: BD -> BD -> BD

Faust uses :, which is reserved by Data.List.

(~<:) :: BD -> BD -> BD

Faust uses <:, which is legal, however see ~:>.

(~:>) :: BD -> BD -> BD

Faust uses :>, however : is not allowed as a prefix.

 draw (graph (par_l [1,2,3,4] ~:> i_mul))
 draw (graph (par_l [1,2,3] ~:> i_negate))

Fold and traverse

bd_foldl :: (t -> BD -> t) -> t -> BD -> t

Fold over BD, signature as foldl.

bd_traverse :: (st -> BD -> (st, BD)) -> st -> BD -> (st, BD)

Traversal with state, signature as mapAccumL.

Introduce node identifiers

rec_ids :: Id -> Int -> [TypeRep] -> [Rec_Id]

Rec nodes introduce identifiers for each backward arc. k is the initial Id, n the number of arcs, and ty the arc types.

 rec_ids 5 2 [int32_t,float_t] == [(5,6,int32_t),(7,8,float_t)]

bd_set_id :: BD -> (Id, BD)

Set identifiers at Constant, Prim, and Rec nodes.

Degree

type Degree = (Int, Int)

Node degree as (input,output) pair.

degree :: BD -> Degree

Degree of block diagram BD.

in_degree :: BD -> Int

fst of degree.

out_degree :: BD -> Int

snd of degree.

Ports

type Port_Index = Int

The index of an Input_Port, all outputs are unary.

data Port

Port (input or output) at block diagram.

Constructors

Input_Port

Fields

port_bd :: BD

port_index :: Port_Index

Output_Port

Fields

port_bd :: BD

Instances

Eq Port

Show Port

ports :: BD -> ([Port], [Port])

The left and right outer ports of a block diagram.

port_ty :: Port -> TypeRep

Type of Port.

Wires

data Wire_Ty

Enumeration of wire types.

Constructors

Normal

Normal forward edge.

Backward Rec_Id

Backward edge.

Implicit_Normal

Implicit wire from recRd to node.

Implicit_Rec

Implicit wire from node to recWr.

Implicit_Backward

Implicit wire from recWr to recRd.

Instances

Eq Wire_Ty

Show Wire_Ty

type Wire = (Port, Port, Wire_Ty)

A Wire runs between two Ports.

normal_wires :: [Port] -> [Port] -> [Wire]

Set of Normal wires between Ports.

rec_back_wires :: [Rec_Id] -> [Port] -> [Port] -> [Wire]

Set of Backward wires between Ports.

wires_immed :: BD -> [Wire]

Immediate internal wires of a block diagram.

wires :: BD -> [Wire]

Internal wires of a block diagram.

Coherence

wire_coheres :: Wire -> Bool

A wire coheres if the port_ty of the left and right hand sides are equal.

bd_non_coherent :: BD -> [Wire]

The set of non-coherent wires at diagram.

bd_is_coherent :: BD -> Bool

Coherence predicate, ie. is bd_non_coherent empty.

Graph

data Node

Primitive block diagram elements.

Constructors

N_Constant

Fields

n_constant_id :: Id

n_constant_k :: K

N_Prim

Fields

n_prim_id :: Either Id (Id, Id)

n_prim_name :: String

n_prim_in_degree :: Int

n_prim_ty :: Maybe TypeRep

Instances

Eq Node

Show Node

actual_id :: Either Id (Id, Id) -> Id

Extract the current actual node id from n_prim_id.

node_ty :: Node -> Maybe TypeRep

Output type of Node, if out degree non-zero.

node_id :: Node -> Id

Either n_constant_id or actual_id of n_prim_id.

node_lift_id :: Node -> (Id, Node)

Pair Node Id with node.

node_pp :: Node -> String

Pretty printer, and Show instance.

type Edge = (Id, Id, (Port_Index, Wire_Ty))

Primitive edge, left hand Id, right hand side Id, right hand Port_Index and edge type.

type Graph = ([Node], [Edge])

A graph is a list of Node and a list of Edges.

edge_is_implicit_backward :: Edge -> Bool

Is Wire_Ty of Edge Implicit_Backward.

rec_nodes :: [Rec_Id] -> [Node]

Implicit rec nodes.

nodes :: Bool -> BD -> [Node]

Collect all primitive nodes at a block diagram.

wire_to_edges :: Bool -> Wire -> [Edge]

A backward Wire will introduce three implicit edges, a Normal wire introduces one Normal edge.

wires_to_edges :: Bool -> [Wire] -> [Edge]

concatMap of wire_to_edges.

edges :: Bool -> BD -> [Edge]

wires_to_edges of wires.

graph' :: Bool -> BD -> Graph

Construct Graph of block diagram, either with or without implicit edges.

graph :: BD -> Graph

Construct Graph of block diagram without implicit edges. This graph will include backward arcs if the graph contains recs.

Gr

type Gr = Gr Node (Port_Index, Wire_Ty)

FGL graph of BD.

gr :: BD -> Gr

Transform BD to Gr.

tsort :: BD -> Graph

Topological sort of nodes (via gr).

gr_dot :: BD -> String

Make dot rendering of graph at Node.

gr_draw :: BD -> IO ()

draw_dot of gr_dot.

Drawing

dot_node :: Node -> String

Dot description of Node.

wire_colour :: Wire_Ty -> String

Wires are coloured according to type.

dot_edge :: Edge -> String

Dot description of Edge.

dot_graph :: Graph -> [String]

Dot description of Graph.

draw_dot :: String -> IO ()

Draw dot graph.

draw :: Graph -> IO ()

draw_dot of dot_graph.

Composition

par_l :: [BD] -> BD

Fold of Par.

 degree (par_l [1,2,3,4]) == (0,4)
 draw (graph (par_l [1,2,3,4] ~:> i_mul))

bd_sum :: [BD] -> BD

Type-directed sum.

 draw (graph (bd_sum [1,2,3,4]))

split_r :: BD -> BD -> Bool

Predicate to determine if p can be split onto q.

split_m :: BD -> BD -> Maybe BD

split if diagrams cohere.

split :: BD -> BD -> BD

split if diagrams cohere, else error. Synonym of ~<:.

merge_degree :: BD -> BD -> Maybe Int

If merge is legal, the number of in-edges per port at q.

 merge_degree (par_l [1,2,3]) i_negate == Just 3
 merge_degree (par_l [1,2,3,4]) i_mul == Just 2

merge_m :: BD -> BD -> Maybe BD

merge if diagrams cohere.

 merge_m (par_l [1,2,3]) i_negate
 merge_m (par_l [1,2,3,4]) i_mul

merge :: BD -> BD -> BD

merge if diagrams cohere, else error. Synonym of ~:>.

rec_r :: BD -> BD -> Bool

Predicate to determine if p can be rec onto q.

rec_m :: BD -> BD -> Maybe BD

rec if diagrams cohere.

rec :: BD -> BD -> BD

rec if diagrams cohere, else error. Synonym of ~~.

Constants

i_constant :: Int -> BD

Integer constant.

r_constant :: Float -> BD

Real constant.

Primitives

u_prim :: TypeRep -> String -> Int -> BD

Construct uniform type primitive diagram.

i_prim :: String -> Int -> BD

u_prim of int32_t.

r_prim :: String -> Int -> BD

u_prim of float_t.

i_add :: BD

Adddition, ie. + of Num.

 (1 ~. 2) ~: i_add
 (1 :: BD) + 2

r_add :: BD

Adddition, ie. + of Num.

 (1 ~. 2) ~: i_add
 (1 :: BD) + 2

i_sub :: BD

Subtraction, ie. - of Num.

r_sub :: BD

Subtraction, ie. - of Num.

i_mul :: BD

Multiplication, ie. * of Num.

r_mul :: BD

Multiplication, ie. * of Num.

i_div :: BD

Division, ie. div of Integral.

r_div :: BD

Division, ie. / of Fractional.

i_abs :: BD

Absolute value, ie. abs of Num.

r_abs :: BD

Absolute value, ie. abs of Num.

i_negate :: BD

Negation, ie. negate of Num.

r_negate :: BD

Negation, ie. negate of Num.

i_identity :: BD

Identity diagram.

r_identity :: BD

Identity diagram.

float_to_int32 :: BD

Coerce float_t to int32_t.

int32_to_float :: BD

Coerce int32_t to float_t.

i32_to_normal_f32 :: BD

int32_to_float and then scale to be in (-1,1).

out1 :: BD

Single channel output.

 degree out1 == (1,0)
 bd_signature out1 == ([float_t],[])

Type following primitives

ty_uop :: (BD -> Maybe TypeRep) -> t -> t -> BD -> t

Type following unary operator.

ty_binop :: (BD -> Maybe TypeRep) -> t -> t -> BD -> BD -> t

Type following binary operator.

ty_add :: BD -> BD -> BD

Type following math operator, uniform types.

 1.0 `ty_add` 2.0 == r_add
 (1 ~. 2) `ty_add` (3 ~. 4) == i_add
 1.0 `ty_add` 2 == _|_
 draw (graph ((1 ~. 2) - (3 ~. 4)))

ty_div :: BD -> BD -> BD

Type following math operator, uniform types.

 1.0 `ty_add` 2.0 == r_add
 (1 ~. 2) `ty_add` (3 ~. 4) == i_add
 1.0 `ty_add` 2 == _|_
 draw (graph ((1 ~. 2) - (3 ~. 4)))

ty_mul :: BD -> BD -> BD

Type following math operator, uniform types.

 1.0 `ty_add` 2.0 == r_add
 (1 ~. 2) `ty_add` (3 ~. 4) == i_add
 1.0 `ty_add` 2 == _|_
 draw (graph ((1 ~. 2) - (3 ~. 4)))

ty_sub :: BD -> BD -> BD

Type following math operator, uniform types.

 1.0 `ty_add` 2.0 == r_add
 (1 ~. 2) `ty_add` (3 ~. 4) == i_add
 1.0 `ty_add` 2 == _|_
 draw (graph ((1 ~. 2) - (3 ~. 4)))

ty_add1 :: BD -> BD -> BD

Type following math operator, singular types.

 1.0 `ty_add1` 2.0 == r_add
 1.0 `ty_add1` 2 == _|_

ty_div1 :: BD -> BD -> BD

Type following math operator, singular types.

 1.0 `ty_add1` 2.0 == r_add
 1.0 `ty_add1` 2 == _|_

ty_mul1 :: BD -> BD -> BD

Type following math operator, singular types.

 1.0 `ty_add1` 2.0 == r_add
 1.0 `ty_add1` 2 == _|_

Code Gen

cg_k :: [Node] -> [(Id, K)]

List of constants for CGen.

cg_node_var :: Node -> Maybe Var

Var of Node.

node_output :: Node -> Maybe (Var_Ty, Id)

Output reference for Node.

node_inputs :: [Edge] -> Node -> [(Var_Ty, Id)]

Input references for Node.

cg_node_c_call :: [Edge] -> Node -> Maybe C_Call

C_Call of Node.

bd_instructions :: BD -> Instructions

Generate CGen Instructions for BD.

Audition

audition :: [Message] -> BD -> IO ()

Audition graph after sending initialisation messages.

Figures from Quick Reference

fig_3_2 :: BD

Figure illustrating ~..

 degree fig_3_2 == (2,2)
 draw (graph fig_3_2)

fig_3_3 :: BD

Figure illustrating ~:.

 degree fig_3_3 == (4,1)
 bd_signature fig_3_3
 draw (graph fig_3_3)

fig_3_4 :: BD

Figure illustrating ~<:.

 degree fig_3_4 == (0,3)
 draw (graph fig_3_4)

fig_3_5 :: BD

Figure illustrating ~:>.

 degree fig_3_5 == (0,1)
 draw (graph fig_3_5)

fig_3_6 :: BD

Figure illustrating ~~.

 degree fig_3_6 == (0,1)
 draw (graph fig_3_6)

fig_3_6' :: BD

Variant generating audible graph.

 draw (graph fig_3_6')
 gr_draw fig_3_6'
 audition [] fig_3_6'

i_counter :: BD

A counter, illustrating identity diagram.

 draw (graph (i_counter ~: i_negate))
 gr_draw (i_counter ~: i_negate)

List

adjacent :: [t] -> [(t, t)]

Adjacent elements of list.

 adjacent [1..4] == [(1,2),(3,4)]

Tuple

bimap :: (a -> b) -> (c -> d) -> (a, c) -> (b, d)

Bimap at tuple.

 bimap abs negate (-1,1) == (1,-1)