# Programs

`Catlab.Programs.GenerateJuliaPrograms`

— ModuleCompile or evaluate morphisms as Julia programs.

`Catlab.Programs.GenerateJuliaPrograms.Block`

— TypeA block of Julia code with input and output variables.

`Catlab.Programs.GenerateJuliaPrograms.CompileState`

— TypeInternal state for compilation of morphism into Julia code.

`Catlab.Programs.GenerateJuliaPrograms.compile`

— MethodCompile a morphism expression into a Julia function.

`Catlab.Programs.GenerateJuliaPrograms.compile_block`

— MethodCompile a morphism expression into a block of Julia code.

`Catlab.Programs.GenerateJuliaPrograms.compile_expr`

— MethodCompile a morphism expression into a Julia function expression.

`Catlab.Programs.GenerateJuliaPrograms.evaluate`

— MethodEvaluate a morphism as a function.

If the morphism will be evaluated only once (possibly with vectorized inputs), then direct evaluation will be much faster than compiling (via `compile`

) and evaluating a standard Julia function.

Compare with `functor`

.

`Catlab.Programs.ParseJuliaPrograms`

— ModuleParse Julia programs into morphisms represented as wiring diagrams.

`Catlab.Programs.ParseJuliaPrograms.parse_wiring_diagram`

— MethodParse a wiring diagram from a Julia function expression.

For more information, see the corresponding macro `@program`

.

`Catlab.Programs.ParseJuliaPrograms.@program`

— MacroParse a wiring diagram from a Julia program.

For the most part, this is standard Julia code but we take a few liberties with the syntax. Products are represented as tuples. So if `x`

and `y`

are variables of type $X$ and $Y$, then `(x,y)`

has type $X \otimes Y$. Also, both `()`

and `nothing`

are interpreted as the monoidal unit $I$.

Unlike in standard Julia, the call expressions `f(x,y)`

and `f((x,y))`

are equivalent. Consequently, given morphisms $f: W \to X \otimes Y$ and $g: X \otimes Y \to Z$, the code

```
x, y = f(w)
g(x,y)
```

is equivalent to `g(f(w))`

. In standard Julia, at most one of these calls to `g`

would be valid, unless `g`

had multiple signatures.

The diagonals (copying and deleting) are implicit in the Julia syntax: copying is variable reuse and deleting is variable non-use. For the codiagonals (merging and creating), a special syntax is provided, reinterpreting Julia's vector literals. The merge of `x1`

and `x2`

is represented by the vector `[x1,x2]`

and creation by the empty vector `[]`

. For example, `f([x1,x2])`

translates to `compose(mmerge(X),f)`

.

This macro is a wrapper around `parse_wiring_diagram`

.

`Catlab.Programs.RelationalPrograms`

— ModuleParse relation expressions in Julia syntax into undirected wiring diagrams.

`Catlab.Programs.RelationalPrograms.parse_relation_diagram`

— MethodParse an undirected wiring diagram from a relation expression.

For more information, see the corresponding macro `@relation`

.

`Catlab.Programs.RelationalPrograms.@relation`

— MacroConstruct an undirected wiring diagram using relation notation.

Unlike the `@program`

macro for directed wiring diagrams, this macro departs from the usual semantics of the Julia programming language. Function calls with n arguments are now interpreted as assertions that an n-ary relation holds at a particular point. For example, the composition of binary relations R ⊆ X × Y and S ⊆ Y × Z can be represented as an undirected wiring diagram by the macro call

```
@relation (x,z) where (x::X, y::Y, z::Z) begin
R(x,y)
S(y,z)
end
```

In general, the context in the `where`

clause defines the set of junctions in the diagram and variable sharing defines the wiring of ports to junctions.

The ports and junctions of the diagram may be typed or untyped, and the ports may be named or unnamed. Thus four possible types of diagrams may be returned, with the type determined by the form of relation header:

- Untyped, unnamed:
`@relation (x,z) where (x,y,z) ...`

- Typed, unnamed:
`@relation (x,z) where (x::X, y::Y, z::Z) ...`

- Untyped, named:
`@relation (out1=x, out2=z) where (x,y,z) ...`

- Typed, named:
`@relation (out=1, out2=z) where (x::X, y::Y, z::Z) ...`