This combinator handles left-associative parsing, and the application of, zero or more binary operators between one or more values.

First parse p, then parse op followed by a p repeatedly. The results of the ps, x₁ through xₙ, are combined with the results of the ops, f₁ through fₙ₋₁, with left-associative application: fₙ₋₁ (fₙ₋₂ (..(f₁ x₁ x₂)..) xₙ₋₁) xₙ. This application is then returned as the result of the combinator. If p or op fails having consumed input at any point, the whole combinator fails.

Compared with chainl1, this combinator allows the types of the operators to more accurately encode their associativity in their types. However, chainl1, in which a and b must match, allows for more flexibility to change the associativity.

This combinator handles right-associative parsing, and the application of, zero or more binary operators between one or more values.

First parse p, then parse op followed by a p repeatedly. The results of the ps, x₁ through xₙ, are combined with the results of the ops, f₁ through fₙ, with right-associative application: f₁ x₁ (f₂ x₂ (...(fₙ₋₁ xₙ₋₁ xₙ)...)). This application is then returned as the result of the combinator. If p or op fails having consumed input at any point, the whole combinator fails.

Compared with chainr1, this combinator allows the types of the operators to more accurately encode their associativity in their types. However, chainr1, in which a and b must match, allows for more flexibility to change the associativity.

This combinator handles non-associative parsing, and the application of, zero or one binary operators between one or two values.

First parse p. Then:

• If this not is followed by an op, simply return p.
• Otherwise, parse this op followed by a single p. Then ensure that this is not followed by a further op, to enforce non-associativity. The results of the ps, x and y, are combined with the result of op, f with the application f x y. This application is then returned as the result of the combinator.

If p or op fails having consumed input at any point, the whole combinator fails. This combinator also fails if the second p is followed by another op.

This combinator handles right-assocative parsing, and application of, zero or more prefix unary operators to a single value.

First parse many repeated ops. When there are no more ops left to parse, parse a single p. The result of p, x, is applied first to wrap, and then to each of the results of the ops, f₁ through fₙ, such that fₙ is applied first and f₁ last: f₁ (f₂ (..(fₙ (wrap x))..)). This application is then returned as the result of the combinator.

If p or op fails having consumed input at any point, the whole combinator fails.

This combinator handles left-assocative parsing, and application of, zero or more postfix unary operators to a single value.

First parse a single p. Then, parse many repeated ops. The result of p, x, is applied first to wrap, and then to each of the results of the ops, f₁ through fₙ, such that f₁ is applied first and fₙ last: fₙ( fₙ₋₁(..f₁ (wrap x)..)). This application is then returned as the result of the combinator.

If p or op fails having consumed input at any point, the whole combinator fails.

Constructs a precedence parser.

This combinator builds an expression parser given a heterogeneous precedence table.

An expression parser will be formed by collapsing the given precedence table layer-by-layer. Since this table is heterogeneous, each level of the table produces a difference type, which is then consumed by the next level above.

This combinator builds an expression parser given a collection of homogeneous atoms and operators.

An expression parser will be formed by treating the given parser as the base Atom, then each successive layer in the given list as another Level in a tightest-to-weakest binding. This means the last element of the given list will be at the top of the precedence table.

Each level must consume and produce the same type.

Constructs a single layer of operators in the precedence tree.

Constructs a single layer of operators in the precedence tree for values of Op a b, where a is a Subtype of b. This provides support for subtyped heterogeneous precedence parsing.

Constructs a single layer of operators Op a b, supporting fully heterogeneous precedence parsing.

This function builds an Ops object representing many operators found at the same precedence level, with a given fixity.

The operators found on the level constructed by this function are heterogeneous: the type of the level below may vary from the types of the values produced at this level. To make this work, a function must be provided that can transform the values from the layer below into the types generated by this layer.

The fixity describes the shape of the operators expected.

Denotes the fixity and associativity of an operator.

Importantly, it also specifies the types of the operations themselves.

Describes a single layer of operators in the precedence tree.

The parameters are:

• a: the base tyep consumed by the operators.
• b: the type produced/consumed by the operators.

The base type for precedence tables.

The parameter a is the type of structure produced by the list of levels.

For more complex expression parser types, Prec describes the precedence table whilst preserving the intermediate structure between each level.

The base of the table will always be an Atom, and each layer built on top of the last using the Level constructor.

Adds a new layer to this precedence table on the left, in a weakest-to-tightest ordering. This is an alias for Level.

This method associates to the left, so left-most applications are tighter binding (closer to the atoms) than those to the right.

It should not be mixed with (+<), as this can be create a confusing and less predictable precedence table.

Adds a new layer to this precedence table on the right, in a tightest-to-weakest ordering.

This method associates to the right (with this table on the right!), so right-most applications are tighter binding (closer to the atoms) than those to the left.

It should not be mixed with (>+), as this can be create a confusing and less predictable precedence table.

The base type for precedence tables.

The parameter a is the type of structure produced by the list of levels.

For more complex expression parser types, Prec describes the precedence table whilst preserving the intermediate structure between each level.

The base of the table will always be an Atom, and each layer built on top of the last using the Level constructor.

Denotes the fixity and associativity of an operator.

Importantly, it also specifies the types of the operations themselves.

Describes a single layer of operators in the precedence tree.

The parameters are:

• a: the base tyep consumed by the operators.
• b: the type produced/consumed by the operators.

Constructs a precedence parser.

This combinator builds an expression parser given a heterogeneous precedence table.

An expression parser will be formed by collapsing the given precedence table layer-by-layer. Since this table is heterogeneous, each level of the table produces a difference type, which is then consumed by the next level above.

This combinator builds an expression parser given a collection of homogeneous atoms and operators.

An expression parser will be formed by treating the given parser as the base Atom, then each successive layer in the given list as another Level in a tightest-to-weakest binding. This means the last element of the given list will be at the top of the precedence table.

Each level must consume and produce the same type.

Constructs a single layer of operators in the precedence tree.

Constructs a single layer of operators in the precedence tree for values of Op a b, where a is a Subtype of b. This provides support for subtyped heterogeneous precedence parsing.

Constructs a single layer of operators Op a b, supporting fully heterogeneous precedence parsing.

This function builds an Ops object representing many operators found at the same precedence level, with a given fixity.

The operators found on the level constructed by this function are heterogeneous: the type of the level below may vary from the types of the values produced at this level. To make this work, a function must be provided that can transform the values from the layer below into the types generated by this layer.

The fixity describes the shape of the operators expected.

Adds a new layer to this precedence table on the left, in a weakest-to-tightest ordering. This is an alias for Level.

This method associates to the left, so left-most applications are tighter binding (closer to the atoms) than those to the right.

It should not be mixed with (+<), as this can be create a confusing and less predictable precedence table.

Adds a new layer to this precedence table on the right, in a tightest-to-weakest ordering.

This method associates to the right (with this table on the right!), so right-most applications are tighter binding (closer to the atoms) than those to the left.

It should not be mixed with (>+), as this can be create a confusing and less predictable precedence table.