hugr_core/

import.rs

//! Importing HUGR graphs from their `hugr-model` representation.
//!
//! **Warning**: This module is still under development and is expected to change.
//! It is included in the library to allow for early experimentation, and for
//! the core and model to converge incrementally.
use std::sync::Arc;

use crate::{
    Direction, Hugr, HugrView, Node, Port,
    extension::{
        ExtensionId, ExtensionRegistry, SignatureError, resolution::ExtensionResolutionError,
    },
    hugr::{HugrMut, NodeMetadata},
    ops::{
        AliasDecl, AliasDefn, CFG, Call, CallIndirect, Case, Conditional, Const, DFG,
        DataflowBlock, ExitBlock, FuncDecl, FuncDefn, Input, LoadConstant, LoadFunction, OpType,
        OpaqueOp, Output, Tag, TailLoop, Value,
        constant::{CustomConst, CustomSerialized, OpaqueValue},
    },
    package::Package,
    std_extensions::{
        arithmetic::{float_types::ConstF64, int_types::ConstInt},
        collections::array::ArrayValue,
    },
    types::{
        CustomType, FuncTypeBase, MaybeRV, PolyFuncType, PolyFuncTypeBase, RowVariable, Signature,
        Term, Type, TypeArg, TypeBase, TypeBound, TypeEnum, TypeName, TypeRow,
        type_param::{SeqPart, TypeParam},
        type_row::TypeRowBase,
    },
};
use fxhash::FxHashMap;
use hugr_model::v0::table;
use hugr_model::v0::{self as model};
use itertools::{Either, Itertools};
use smol_str::{SmolStr, ToSmolStr};
use thiserror::Error;

fn gen_str(generator: &Option<String>) -> String {
    match generator {
        Some(g) => format!(" generated by {g}"),
        None => String::new(),
    }
}

/// An error that can occur during import.
#[derive(Debug, Clone, Error)]
#[error("failed to import hugr{}", gen_str(&self.generator))]
pub struct ImportError {
    #[source]
    inner: ImportErrorInner,
    generator: Option<String>,
}

const UNSUPPORTED_HINT: &str = concat!(
    "Hint: The import process encountered a `hugr-model` feature ",
    "that is currently unsupported in `hugr-core`. ",
    "As `hugr-core` evolves towards the same expressivity as `hugr-model` ",
    "we expect that errors of this kind will be removed.",
);

const UNINFERRED_HINT: &str = concat!(
    "Hint: The import process encountered implicit information in the `hugr-model` ",
    "package that it can not yet fill in. ",
    "Such implicit information can be signatures for nodes and regions, ",
    "wildcard terms or symbol applications with fewer arguments than the symbol has parameters. ",
    "Until more comprehensive inference is implemented, `hugr-model` packages will need to be very explicit. ",
    "To avoid this error, make sure to include as much information as possible when generating packages."
);

/// Error hint explaining the concept of a closed tuple.
const CLOSED_TUPLE_HINT: &str = concat!(
    "Hint: A tuple is closed if all of its items are known. ",
    "Closed tuples can contain spliced subtuples, as long as they can be recursively flattened ",
    "into a tuple that only contains individual items."
);

/// Error hint explaining the concept of a closed list.
const CLOSED_LIST_HINT: &str = concat!(
    "Hint: A list is closed if all of its items are known. ",
    "Closed lists can contain spliced sublists, as long as they can be recursively flattened ",
    "into a list that only contains individual items."
);

#[derive(Debug, Clone, Error)]
enum ImportErrorInner {
    /// The model contains a feature that is not supported by the importer yet.
    /// Errors of this kind are expected to be removed as the model format and
    /// the core HUGR representation converge.
    #[error("Unsupported: {0}\n{hint}", hint = UNSUPPORTED_HINT)]
    Unsupported(String),

    /// The model contains implicit information that has not yet been inferred.
    /// This includes wildcards and application of functions with implicit parameters.
    #[error("Uninferred implicit: {0}\n{hint}", hint = UNINFERRED_HINT)]
    Uninferred(String),

    /// The model is not well-formed.
    #[error("{0}")]
    Invalid(String),

    /// An error with additional context.
    #[error("import failed in context: {1}")]
    Context(#[source] Box<ImportErrorInner>, String),

    /// A signature mismatch was detected during import.
    #[error("signature error")]
    Signature(#[from] SignatureError),

    /// An error relating to the loaded extension registry.
    #[error("extension error")]
    Extension(#[from] ExtensionError),

    /// Incorrect order hints.
    #[error("incorrect order hint")]
    OrderHint(#[from] OrderHintError),

    /// Extension resolution.
    #[error("extension resolution error")]
    ExtensionResolution(#[from] ExtensionResolutionError),
}

#[derive(Debug, Clone, Error)]
enum ExtensionError {
    /// An extension is missing.
    #[error("Importing the hugr requires extension {missing_ext}, which was not found in the registry. The available extensions are: [{}]",
            available.iter().map(std::string::ToString::to_string).collect::<Vec<_>>().join(", "))]
    Missing {
        /// The missing extension.
        missing_ext: ExtensionId,
        /// The available extensions in the registry.
        available: Vec<ExtensionId>,
    },

    /// An extension type is missing.
    #[error(
        "Importing the hugr requires extension {ext} to have a type named {name}, but it was not found."
    )]
    MissingType {
        /// The extension that is missing the type.
        ext: ExtensionId,
        /// The name of the missing type.
        name: TypeName,
    },
}

/// Import error caused by incorrect order hints.
#[derive(Debug, Clone, Error)]
enum OrderHintError {
    /// Duplicate order hint key in the same region.
    #[error("duplicate order hint key {0}")]
    DuplicateKey(table::RegionId, u64),
    /// Order hint including a key not defined in the region.
    #[error("order hint with unknown key {0}")]
    UnknownKey(u64),
    /// Order hint involving a node with no order port.
    #[error("order hint on node with no order port: {0}")]
    NoOrderPort(table::NodeId),
}

/// Helper macro to create an `ImportErrorInner::Unsupported` error with a formatted message.
macro_rules! error_unsupported {
    ($($e:expr),*) => { ImportErrorInner::Unsupported(format!($($e),*)) }
}

/// Helper macro to create an `ImportErrorInner::Uninferred` error with a formatted message.
macro_rules! error_uninferred {
    ($($e:expr),*) => { ImportErrorInner::Uninferred(format!($($e),*)) }
}

/// Helper macro to create an `ImportErrorInner::Invalid` error with a formatted message.
macro_rules! error_invalid {
    ($($e:expr),*) => { ImportErrorInner::Invalid(format!($($e),*)) }
}

/// Helper macro to create an `ImportErrorInner::Context` error with a formatted message.
macro_rules! error_context {
    ($err:expr, $($e:expr),*) => {
        {
            ImportErrorInner::Context(Box::new($err), format!($($e),*))
        }
    }
}

/// Import a [`Package`] from its model representation.
pub fn import_package(
    package: &table::Package,
    extensions: &ExtensionRegistry,
) -> Result<Package, ImportError> {
    let modules = package
        .modules
        .iter()
        .map(|module| import_hugr(module, extensions))
        .collect::<Result<Vec<_>, _>>()?;

    // This does not panic since the import already requires a module root.
    let package = Package::new(modules);
    Ok(package)
}

/// Get the name of the generator from the metadata of the module.
/// If no generator is found, `None` is returned.
fn get_generator(ctx: &Context<'_>) -> Option<String> {
    ctx.module
        .get_region(ctx.module.root)
        .map(|r| r.meta.iter())
        .into_iter()
        .flatten()
        .find_map(|meta| {
            let (name, json_val) = ctx.decode_json_meta(*meta).ok()??;

            (name == crate::envelope::GENERATOR_KEY)
                .then_some(crate::envelope::format_generator(&json_val))
        })
}

/// Import a [`Hugr`] module from its model representation.
pub fn import_hugr(
    module: &table::Module,
    extensions: &ExtensionRegistry,
) -> Result<Hugr, ImportError> {
    // TODO: Module should know about the number of edges, so that we can use a vector here.
    // For now we use a hashmap, which will be slower.
    let mut ctx = Context {
        module,
        hugr: Hugr::new(),
        link_ports: FxHashMap::default(),
        static_edges: Vec::new(),
        extensions,
        nodes: FxHashMap::default(),
        local_vars: FxHashMap::default(),
        custom_name_cache: FxHashMap::default(),
        region_scope: table::RegionId::default(),
    };

    let import_steps: [fn(&mut Context) -> _; 3] = [
        |ctx| ctx.import_root(),
        |ctx| ctx.link_ports(),
        |ctx| ctx.link_static_ports(),
    ];

    for step in import_steps {
        if let Err(e) = step(&mut ctx) {
            return Err(ImportError {
                inner: e,
                generator: get_generator(&ctx),
            });
        }
    }
    ctx.hugr
        .resolve_extension_defs(extensions)
        .map_err(|e| ImportError {
            inner: ImportErrorInner::ExtensionResolution(e),
            generator: get_generator(&ctx),
        })?;
    Ok(ctx.hugr)
}

struct Context<'a> {
    /// The module being imported.
    module: &'a table::Module<'a>,

    /// The HUGR graph being constructed.
    hugr: Hugr,

    /// The ports that are part of each link. This is used to connect the ports at the end of the
    /// import process.
    link_ports: FxHashMap<(table::RegionId, table::LinkIndex), Vec<(Node, Port)>>,

    /// Pairs of nodes that should be connected by a static edge.
    /// These are collected during the import process and connected at the end.
    static_edges: Vec<(table::NodeId, table::NodeId)>,

    /// The ambient extension registry to use for importing.
    extensions: &'a ExtensionRegistry,

    /// A map from `NodeId` to the imported `Node`.
    nodes: FxHashMap<table::NodeId, Node>,

    local_vars: FxHashMap<table::VarId, LocalVar>,

    custom_name_cache: FxHashMap<&'a str, (ExtensionId, SmolStr)>,

    region_scope: table::RegionId,
}

impl<'a> Context<'a> {
    /// Get the signature of the node with the given `NodeId`.
    fn get_node_signature(&mut self, node: table::NodeId) -> Result<Signature, ImportErrorInner> {
        let node_data = self.get_node(node)?;
        let signature = node_data
            .signature
            .ok_or_else(|| error_uninferred!("node signature"))?;
        self.import_func_type(signature)
    }

    /// Get the node with the given `NodeId`, or return an error if it does not exist.
    #[inline]
    fn get_node(&self, node_id: table::NodeId) -> Result<&'a table::Node<'a>, ImportErrorInner> {
        self.module
            .get_node(node_id)
            .ok_or_else(|| error_invalid!("unknown node {}", node_id))
    }

    /// Get the term with the given `TermId`, or return an error if it does not exist.
    #[inline]
    fn get_term(&self, term_id: table::TermId) -> Result<&'a table::Term<'a>, ImportErrorInner> {
        self.module
            .get_term(term_id)
            .ok_or_else(|| error_invalid!("unknown term {}", term_id))
    }

    /// Get the region with the given `RegionId`, or return an error if it does not exist.
    #[inline]
    fn get_region(
        &self,
        region_id: table::RegionId,
    ) -> Result<&'a table::Region<'a>, ImportErrorInner> {
        self.module
            .get_region(region_id)
            .ok_or_else(|| error_invalid!("unknown region {}", region_id))
    }

    fn make_node(
        &mut self,
        node_id: table::NodeId,
        op: OpType,
        parent: Node,
    ) -> Result<Node, ImportErrorInner> {
        let node = self.hugr.add_node_with_parent(parent, op);
        self.nodes.insert(node_id, node);

        let node_data = self.get_node(node_id)?;
        self.record_links(node, Direction::Incoming, node_data.inputs);
        self.record_links(node, Direction::Outgoing, node_data.outputs);

        for meta_item in node_data.meta {
            self.import_node_metadata(node, *meta_item)
                .map_err(|err| error_context!(err, "node metadata"))?;
        }

        Ok(node)
    }

    fn import_node_metadata(
        &mut self,
        node: Node,
        meta_item: table::TermId,
    ) -> Result<(), ImportErrorInner> {
        // Import the JSON metadata
        if let Some((name, json_value)) = self.decode_json_meta(meta_item)? {
            self.hugr.set_metadata(node, name, json_value);
        }

        // Set the entrypoint
        if let Some([]) = self.match_symbol(meta_item, model::CORE_ENTRYPOINT)? {
            self.hugr.set_entrypoint(node);
        }

        Ok(())
    }

    fn decode_json_meta(
        &self,
        meta_item: table::TermId,
    ) -> Result<Option<(SmolStr, serde_json::Value)>, ImportErrorInner> {
        Ok(
            if let Some([name_arg, json_arg]) =
                self.match_symbol(meta_item, model::COMPAT_META_JSON)?
            {
                let table::Term::Literal(model::Literal::Str(name)) = self.get_term(name_arg)?
                else {
                    return Err(error_invalid!(
                        "`{}` expects a string literal as its first argument",
                        model::COMPAT_META_JSON
                    ));
                };

                let table::Term::Literal(model::Literal::Str(json_str)) =
                    self.get_term(json_arg)?
                else {
                    return Err(error_invalid!(
                        "`{}` expects a string literal as its second argument",
                        model::COMPAT_CONST_JSON
                    ));
                };

                let json_value: NodeMetadata = serde_json::from_str(json_str).map_err(|_| {
                    error_invalid!(
                        "failed to parse JSON string for `{}` metadata",
                        model::COMPAT_CONST_JSON
                    )
                })?;
                Some((name.to_owned(), json_value))
            } else {
                None
            },
        )
    }

    /// Associate links with the ports of the given node in the given direction.
    fn record_links(&mut self, node: Node, direction: Direction, links: &'a [table::LinkIndex]) {
        let optype = self.hugr.get_optype(node);
        // NOTE: `OpType::port_count` copies the signature, which significantly slows down the import.
        debug_assert!(links.len() <= optype.port_count(direction));

        for (link, port) in links.iter().zip(self.hugr.node_ports(node, direction)) {
            self.link_ports
                .entry((self.region_scope, *link))
                .or_default()
                .push((node, port));
        }
    }

    /// Link up the ports in the hugr graph, according to the connectivity information that
    /// has been gathered in the `link_ports` map.
    fn link_ports(&mut self) -> Result<(), ImportErrorInner> {
        // For each edge, we group the ports by their direction. We reuse the `inputs` and
        // `outputs` vectors to avoid unnecessary allocations.
        let mut inputs = Vec::new();
        let mut outputs = Vec::new();

        for (link_id, link_ports) in std::mem::take(&mut self.link_ports) {
            // Skip the edge if it doesn't have any ports.
            if link_ports.is_empty() {
                continue;
            }

            for (node, port) in link_ports {
                match port.as_directed() {
                    Either::Left(input) => inputs.push((node, input)),
                    Either::Right(output) => outputs.push((node, output)),
                }
            }

            match (inputs.as_slice(), outputs.as_slice()) {
                ([], []) => {
                    unreachable!();
                }
                (_, [output]) => {
                    for (node, port) in &inputs {
                        self.hugr.connect(output.0, output.1, *node, *port);
                    }
                }
                ([input], _) => {
                    for (node, port) in &outputs {
                        self.hugr.connect(*node, *port, input.0, input.1);
                    }
                }
                _ => {
                    return Err(error_unsupported!(
                        concat!(
                            "Link {:?} would require a hyperedge because it connects more ",
                            "than one input port with more than one output port."
                        ),
                        link_id
                    ));
                }
            }

            inputs.clear();
            outputs.clear();
        }

        Ok(())
    }

    /// Connects static ports according to the connections in [`self.static_edges`].
    fn link_static_ports(&mut self) -> Result<(), ImportErrorInner> {
        for (src_id, dst_id) in std::mem::take(&mut self.static_edges) {
            // None of these lookups should fail given how we constructed `static_edges`.
            let src = self.nodes[&src_id];
            let dst = self.nodes[&dst_id];
            let src_port = self.hugr.get_optype(src).static_output_port().unwrap();
            let dst_port = self.hugr.get_optype(dst).static_input_port().unwrap();
            self.hugr.connect(src, src_port, dst, dst_port);
        }

        Ok(())
    }

    fn get_symbol_name(&self, node_id: table::NodeId) -> Result<&'a str, ImportErrorInner> {
        let node_data = self.get_node(node_id)?;
        let name = node_data
            .operation
            .symbol()
            .ok_or_else(|| error_invalid!("node {} is expected to be a symbol", node_id))?;
        Ok(name)
    }

    fn get_func_signature(
        &mut self,
        func_node: table::NodeId,
    ) -> Result<PolyFuncType, ImportErrorInner> {
        let symbol = match self.get_node(func_node)?.operation {
            table::Operation::DefineFunc(symbol) => symbol,
            table::Operation::DeclareFunc(symbol) => symbol,
            _ => {
                return Err(error_invalid!(
                    "node {} is expected to be a function declaration or definition",
                    func_node
                ));
            }
        };

        self.import_poly_func_type(func_node, *symbol, |_, signature| Ok(signature))
    }

    /// Import the root region of the module.
    fn import_root(&mut self) -> Result<(), ImportErrorInner> {
        self.region_scope = self.module.root;
        let region_data = self.get_region(self.module.root)?;

        for node in region_data.children {
            self.import_node(*node, self.hugr.module_root())?;
        }

        for meta_item in region_data.meta {
            self.import_node_metadata(self.hugr.module_root(), *meta_item)?;
        }

        Ok(())
    }

    fn import_node(
        &mut self,
        node_id: table::NodeId,
        parent: Node,
    ) -> Result<Option<Node>, ImportErrorInner> {
        let node_data = self.get_node(node_id)?;

        let result = match node_data.operation {
            table::Operation::Invalid => {
                return Err(error_invalid!(concat!(
                    "Tried to import an `invalid` operation.\n",
                    "The `invalid` operation in `hugr-model` is a placeholder indicating a missing operation. ",
                    "It currently has no equivalent in `hugr-core`."
                )));
            }

            table::Operation::Dfg => Some(
                self.import_node_dfg(node_id, parent, node_data)
                    .map_err(|err| error_context!(err, "`dfg` node with id {}", node_id))?,
            ),

            table::Operation::Cfg => Some(
                self.import_node_cfg(node_id, parent, node_data)
                    .map_err(|err| error_context!(err, "`cfg` node with id {}", node_id))?,
            ),

            table::Operation::Block => Some(
                self.import_node_block(node_id, parent)
                    .map_err(|err| error_context!(err, "`block` node with id {}", node_id))?,
            ),

            table::Operation::DefineFunc(symbol) => Some(
                self.import_node_define_func(node_id, symbol, node_data, parent)
                    .map_err(|err| error_context!(err, "`define-func` node with id {}", node_id))?,
            ),

            table::Operation::DeclareFunc(symbol) => Some(
                self.import_node_declare_func(node_id, symbol, parent)
                    .map_err(|err| {
                        error_context!(err, "`declare-func` node with id {}", node_id)
                    })?,
            ),

            table::Operation::TailLoop => Some(
                self.import_tail_loop(node_id, parent)
                    .map_err(|err| error_context!(err, "`tail-loop` node with id {}", node_id))?,
            ),

            table::Operation::Conditional => Some(
                self.import_conditional(node_id, parent)
                    .map_err(|err| error_context!(err, "`cond` node with id {}", node_id))?,
            ),

            table::Operation::Custom(operation) => Some(
                self.import_node_custom(node_id, operation, node_data, parent)
                    .map_err(|err| error_context!(err, "custom node with id {}", node_id))?,
            ),

            table::Operation::DefineAlias(symbol, value) => Some(
                self.import_node_define_alias(node_id, symbol, value, parent)
                    .map_err(|err| {
                        error_context!(err, "`define-alias` node with id {}", node_id)
                    })?,
            ),

            table::Operation::DeclareAlias(symbol) => Some(
                self.import_node_declare_alias(node_id, symbol, parent)
                    .map_err(|err| {
                        error_context!(err, "`declare-alias` node with id {}", node_id)
                    })?,
            ),

            table::Operation::Import { .. } => None,

            table::Operation::DeclareConstructor { .. } => None,
            table::Operation::DeclareOperation { .. } => None,
        };

        Ok(result)
    }

    fn import_node_dfg(
        &mut self,
        node_id: table::NodeId,
        parent: Node,
        node_data: &'a table::Node<'a>,
    ) -> Result<Node, ImportErrorInner> {
        let signature = self
            .get_node_signature(node_id)
            .map_err(|err| error_context!(err, "node signature"))?;

        let optype = OpType::DFG(DFG { signature });
        let node = self.make_node(node_id, optype, parent)?;

        let [region] = node_data.regions else {
            return Err(error_invalid!("dfg region expects a single region"));
        };

        self.import_dfg_region(*region, node)?;
        Ok(node)
    }

    fn import_node_cfg(
        &mut self,
        node_id: table::NodeId,
        parent: Node,
        node_data: &'a table::Node<'a>,
    ) -> Result<Node, ImportErrorInner> {
        let signature = self
            .get_node_signature(node_id)
            .map_err(|err| error_context!(err, "node signature"))?;

        let optype = OpType::CFG(CFG { signature });
        let node = self.make_node(node_id, optype, parent)?;

        let [region] = node_data.regions else {
            return Err(error_invalid!("cfg nodes expect a single region"));
        };

        self.import_cfg_region(*region, node)?;
        Ok(node)
    }

    fn import_dfg_region(
        &mut self,
        region: table::RegionId,
        node: Node,
    ) -> Result<(), ImportErrorInner> {
        let region_data = self.get_region(region)?;

        let prev_region = self.region_scope;
        if region_data.scope.is_some() {
            self.region_scope = region;
        }

        if region_data.kind != model::RegionKind::DataFlow {
            return Err(error_invalid!("expected dfg region"));
        }

        let signature = self
            .import_func_type(
                region_data
                    .signature
                    .ok_or_else(|| error_uninferred!("region signature"))?,
            )
            .map_err(|err| error_context!(err, "signature of dfg region with id {}", region))?;

        // Create the input and output nodes
        let input = self.hugr.add_node_with_parent(
            node,
            OpType::Input(Input {
                types: signature.input,
            }),
        );
        let output = self.hugr.add_node_with_parent(
            node,
            OpType::Output(Output {
                types: signature.output,
            }),
        );

        // Make sure that the ports of the input/output nodes are connected correctly
        self.record_links(input, Direction::Outgoing, region_data.sources);
        self.record_links(output, Direction::Incoming, region_data.targets);

        for child in region_data.children {
            self.import_node(*child, node)?;
        }

        self.create_order_edges(region, input, output)?;

        for meta_item in region_data.meta {
            self.import_node_metadata(node, *meta_item)?;
        }

        self.region_scope = prev_region;

        Ok(())
    }

    /// Create order edges between nodes of a dataflow region based on order hint metadata.
    ///
    /// This method assumes that the nodes for the children of the region have already been imported.
    fn create_order_edges(
        &mut self,
        region_id: table::RegionId,
        input: Node,
        output: Node,
    ) -> Result<(), ImportErrorInner> {
        let region_data = self.get_region(region_id)?;
        debug_assert_eq!(region_data.kind, model::RegionKind::DataFlow);

        // Collect order hint keys
        // PERFORMANCE: It might be worthwhile to reuse the map to avoid allocations.
        let mut order_keys = FxHashMap::<u64, Node>::default();

        for child_id in region_data.children {
            let child_data = self.get_node(*child_id)?;

            for meta_id in child_data.meta {
                let Some([key]) = self.match_symbol(*meta_id, model::ORDER_HINT_KEY)? else {
                    continue;
                };

                let table::Term::Literal(model::Literal::Nat(key)) = self.get_term(key)? else {
                    continue;
                };

                // NOTE: The lookups here are expected to succeed since we only
                // process the order metadata after we have imported the nodes.
                let child_node = self.nodes[child_id];
                let child_optype = self.hugr.get_optype(child_node);

                // Check that the node has order ports.
                // NOTE: This assumes that a node has an input order port iff it has an output one.
                if child_optype.other_output_port().is_none() {
                    return Err(OrderHintError::NoOrderPort(*child_id).into());
                }

                if order_keys.insert(*key, child_node).is_some() {
                    return Err(OrderHintError::DuplicateKey(region_id, *key).into());
                }
            }
        }

        // Collect the order hint keys for the input and output nodes
        for meta_id in region_data.meta {
            if let Some([key]) = self.match_symbol(*meta_id, model::ORDER_HINT_INPUT_KEY)? {
                let table::Term::Literal(model::Literal::Nat(key)) = self.get_term(key)? else {
                    continue;
                };

                if order_keys.insert(*key, input).is_some() {
                    return Err(OrderHintError::DuplicateKey(region_id, *key).into());
                }
            }

            if let Some([key]) = self.match_symbol(*meta_id, model::ORDER_HINT_OUTPUT_KEY)? {
                let table::Term::Literal(model::Literal::Nat(key)) = self.get_term(key)? else {
                    continue;
                };

                if order_keys.insert(*key, output).is_some() {
                    return Err(OrderHintError::DuplicateKey(region_id, *key).into());
                }
            }
        }

        // Insert order edges
        for meta_id in region_data.meta {
            let Some([a, b]) = self.match_symbol(*meta_id, model::ORDER_HINT_ORDER)? else {
                continue;
            };

            let table::Term::Literal(model::Literal::Nat(a)) = self.get_term(a)? else {
                continue;
            };

            let table::Term::Literal(model::Literal::Nat(b)) = self.get_term(b)? else {
                continue;
            };

            let a = order_keys.get(a).ok_or(OrderHintError::UnknownKey(*a))?;
            let b = order_keys.get(b).ok_or(OrderHintError::UnknownKey(*b))?;

            // NOTE: The unwrap here must succeed:
            // - For all ordinary nodes we checked that they have an order port.
            // - Input and output nodes always have an order port.
            let a_port = self.hugr.get_optype(*a).other_output_port().unwrap();
            let b_port = self.hugr.get_optype(*b).other_input_port().unwrap();

            self.hugr.connect(*a, a_port, *b, b_port);
        }

        Ok(())
    }

    /// Imports a closed list whose first element is an ADT with a closed list
    /// of variants. The variants and the remaining elements of the list are
    /// returned as type rows.
    fn import_adt_and_rest(
        &mut self,
        list: table::TermId,
    ) -> Result<(Vec<TypeRow>, TypeRow), ImportErrorInner> {
        let items = self.import_closed_list(list)?;

        let Some((first, rest)) = items.split_first() else {
            return Err(error_invalid!("expected list to have at least one element"));
        };

        let sum_rows: Vec<_> = {
            let [variants] = self.expect_symbol(*first, model::CORE_ADT)?;
            self.import_type_rows(variants)?
        };

        let rest = rest
            .iter()
            .map(|term| self.import_type(*term))
            .collect::<Result<Vec<_>, _>>()?
            .into();

        Ok((sum_rows, rest))
    }

    fn import_tail_loop(
        &mut self,
        node_id: table::NodeId,
        parent: Node,
    ) -> Result<Node, ImportErrorInner> {
        let node_data = self.get_node(node_id)?;
        debug_assert_eq!(node_data.operation, table::Operation::TailLoop);

        let [region] = node_data.regions else {
            return Err(error_invalid!(
                "loop node {} expects a single region",
                node_id
            ));
        };

        let region_data = self.get_region(*region)?;

        let (just_inputs, just_outputs, rest) = (|| {
            let [_, region_outputs] = self.get_func_type(
                region_data
                    .signature
                    .ok_or_else(|| error_uninferred!("region signature"))?,
            )?;
            let (sum_rows, rest) = self.import_adt_and_rest(region_outputs)?;

            if sum_rows.len() != 2 {
                return Err(error_invalid!(
                    "Loop nodes expect their first target to be an ADT with two variants."
                ));
            }

            let mut sum_rows = sum_rows.into_iter();
            let just_inputs = sum_rows.next().unwrap();
            let just_outputs = sum_rows.next().unwrap();

            Ok((just_inputs, just_outputs, rest))
        })()
        .map_err(|err| error_context!(err, "region signature"))?;

        let optype = OpType::TailLoop(TailLoop {
            just_inputs,
            just_outputs,
            rest,
        });

        let node = self.make_node(node_id, optype, parent)?;

        self.import_dfg_region(*region, node)?;
        Ok(node)
    }

    fn import_conditional(
        &mut self,
        node_id: table::NodeId,
        parent: Node,
    ) -> Result<Node, ImportErrorInner> {
        let node_data = self.get_node(node_id)?;
        debug_assert_eq!(node_data.operation, table::Operation::Conditional);

        let (sum_rows, other_inputs, outputs) = (|| {
            let [inputs, outputs] = self.get_func_type(
                node_data
                    .signature
                    .ok_or_else(|| error_uninferred!("node signature"))?,
            )?;
            let (sum_rows, other_inputs) = self.import_adt_and_rest(inputs)?;
            let outputs = self.import_type_row(outputs)?;

            Ok((sum_rows, other_inputs, outputs))
        })()
        .map_err(|err| error_context!(err, "node signature"))?;

        let optype = OpType::Conditional(Conditional {
            sum_rows,
            other_inputs,
            outputs,
        });

        let node = self.make_node(node_id, optype, parent)?;

        for region in node_data.regions {
            let region_data = self.get_region(*region)?;
            let signature = self.import_func_type(
                region_data
                    .signature
                    .ok_or_else(|| error_uninferred!("region signature"))?,
            )?;

            let case_node = self
                .hugr
                .add_node_with_parent(node, OpType::Case(Case { signature }));

            self.import_dfg_region(*region, case_node)?;
        }

        Ok(node)
    }

    /// Imports a control flow region.
    ///
    /// The `hugr-model` and `hugr-core` representations of control flow are
    /// slightly different, and so this method needs to perform some conversion.
    ///
    /// In `hugr-core` the first node in the region is a [`BasicBlock`] that by
    /// virtue of its position is the designated entry block. The second node in
    /// the region is an [`ExitBlock`]. The [`ExitBlock`] is analogous to an
    /// [`Output`] node in a dataflow graph, while there is no direct control flow
    /// equivalent to [`Input`] nodes.
    ///
    /// In `hugr-model` control flow regions have a single source and target port,
    /// respectively, mirroring data flow regions. The region's source port needs
    /// to be connected to either the input port of a block in the region or to the
    /// target port.
    fn import_cfg_region(
        &mut self,
        region: table::RegionId,
        node: Node,
    ) -> Result<(), ImportErrorInner> {
        let region_data = self.get_region(region)?;

        if region_data.kind != model::RegionKind::ControlFlow {
            return Err(error_invalid!("expected cfg region"));
        }

        let prev_region = self.region_scope;
        if region_data.scope.is_some() {
            self.region_scope = region;
        }

        let region_target_types = (|| {
            let [_, region_targets] = self.get_ctrl_type(
                region_data
                    .signature
                    .ok_or_else(|| error_uninferred!("region signature"))?,
            )?;

            self.import_closed_list(region_targets)
        })()
        .map_err(|err| error_context!(err, "signature of cfg region with id {}", region))?;

        // Identify the entry node of the control flow region by looking for
        // a block whose input is linked to the sole source port of the CFG region.
        let entry_node = 'find_entry: {
            let [entry_link] = region_data.sources else {
                return Err(error_invalid!("cfg region expects a single source"));
            };

            for child in region_data.children {
                let child_data = self.get_node(*child)?;
                let is_entry = child_data.inputs.iter().any(|link| link == entry_link);

                if is_entry {
                    break 'find_entry *child;
                }
            }

            // TODO: We should allow for the case in which control flows
            // directly from the source to the target of the region. This is
            // currently not allowed in hugr core directly, but may be simulated
            // by constructing an empty entry block.
            return Err(error_invalid!("cfg region without entry node"));
        };

        // The entry node in core control flow regions is identified by being
        // the first child node of the CFG node. We therefore import the entry node first.
        self.import_node(entry_node, node)?;

        // Create the exit node for the control flow region. This always needs
        // to be second in the node list.
        {
            let cfg_outputs = {
                let [target_types] = region_target_types.as_slice() else {
                    return Err(error_invalid!("cfg region expects a single target"));
                };

                self.import_type_row(*target_types)?
            };

            let exit = self
                .hugr
                .add_node_with_parent(node, OpType::ExitBlock(ExitBlock { cfg_outputs }));
            self.record_links(exit, Direction::Incoming, region_data.targets);
        }

        // Finally we import all other nodes.
        for child in region_data.children {
            if *child != entry_node {
                self.import_node(*child, node)?;
            }
        }

        for meta_item in region_data.meta {
            self.import_node_metadata(node, *meta_item)
                .map_err(|err| error_context!(err, "node metadata"))?;
        }

        self.region_scope = prev_region;

        Ok(())
    }

    fn import_node_block(
        &mut self,
        node_id: table::NodeId,
        parent: Node,
    ) -> Result<Node, ImportErrorInner> {
        let node_data = self.get_node(node_id)?;
        debug_assert_eq!(node_data.operation, table::Operation::Block);

        let [region] = node_data.regions else {
            return Err(error_invalid!("basic block expects a single region"));
        };
        let region_data = self.get_region(*region)?;
        let [inputs, outputs] = self.get_func_type(
            region_data
                .signature
                .ok_or_else(|| error_uninferred!("region signature"))?,
        )?;
        let inputs = self.import_type_row(inputs)?;
        let (sum_rows, other_outputs) = self.import_adt_and_rest(outputs)?;

        let optype = OpType::DataflowBlock(DataflowBlock {
            inputs,
            other_outputs,
            sum_rows,
        });
        let node = self.make_node(node_id, optype, parent)?;

        self.import_dfg_region(*region, node).map_err(|err| {
            error_context!(err, "block body defined by region with id {}", *region)
        })?;
        Ok(node)
    }

    fn import_node_define_func(
        &mut self,
        node_id: table::NodeId,
        symbol: &'a table::Symbol<'a>,
        node_data: &'a table::Node<'a>,
        parent: Node,
    ) -> Result<Node, ImportErrorInner> {
        let visibility = symbol.visibility.clone().ok_or(ImportErrorInner::Invalid(
            "No visibility for FuncDefn".to_string(),
        ))?;
        self.import_poly_func_type(node_id, *symbol, |ctx, signature| {
            let func_name = ctx.import_title_metadata(node_id)?.unwrap_or(symbol.name);

            let optype =
                OpType::FuncDefn(FuncDefn::new_vis(func_name, signature, visibility.into()));

            let node = ctx.make_node(node_id, optype, parent)?;

            let [region] = node_data.regions else {
                return Err(error_invalid!(
                    "function definition nodes expect a single region"
                ));
            };

            ctx.import_dfg_region(*region, node).map_err(|err| {
                error_context!(err, "function body defined by region with id {}", *region)
            })?;

            Ok(node)
        })
    }

    fn import_node_declare_func(
        &mut self,
        node_id: table::NodeId,
        symbol: &'a table::Symbol<'a>,
        parent: Node,
    ) -> Result<Node, ImportErrorInner> {
        let visibility = symbol.visibility.clone().ok_or(ImportErrorInner::Invalid(
            "No visibility for FuncDecl".to_string(),
        ))?;
        self.import_poly_func_type(node_id, *symbol, |ctx, signature| {
            let func_name = ctx.import_title_metadata(node_id)?.unwrap_or(symbol.name);

            let optype =
                OpType::FuncDecl(FuncDecl::new_vis(func_name, signature, visibility.into()));
            let node = ctx.make_node(node_id, optype, parent)?;
            Ok(node)
        })
    }

    /// Import a node with a custom operation.
    ///
    /// A custom operation in `hugr-model` referred to by a symbol application
    /// term. The name of the symbol specifies the name of the custom operation,
    /// and the arguments supplied to the symbol are the arguments to be passed
    /// to the custom operation. This method imports the custom operations as
    /// [`OpaqueOp`]s. The [`OpaqueOp`]s are then resolved later against the
    /// [`ExtensionRegistry`].
    ///
    /// Some operations that needed to be builtins in `hugr-core` are custom
    /// operations in `hugr-model`. This method detects these and converts them
    /// to the corresponding `hugr-core` builtins.
    fn import_node_custom(
        &mut self,
        node_id: table::NodeId,
        operation: table::TermId,
        node_data: &'a table::Node<'a>,
        parent: Node,
    ) -> Result<Node, ImportErrorInner> {
        if let Some([inputs, outputs]) = self.match_symbol(operation, model::CORE_CALL_INDIRECT)? {
            let inputs = self.import_type_row(inputs)?;
            let outputs = self.import_type_row(outputs)?;
            let signature = Signature::new(inputs, outputs);
            let optype = OpType::CallIndirect(CallIndirect { signature });
            let node = self.make_node(node_id, optype, parent)?;
            return Ok(node);
        }

        if let Some([_, _, func]) = self.match_symbol(operation, model::CORE_CALL)? {
            let (symbol, args) = match self.get_term(func)? {
                table::Term::Apply(symbol, args) => (symbol, args),
                table::Term::Var(_) => {
                    // TODO: Allow calling functions that are passed as variables.
                    //
                    // This would be necessary to allow functions which take
                    // other functions as static parameters and then call them.
                    // See #2301.
                    return Err(error_unsupported!(
                        "`{}` does not yet support function variables.",
                        model::CORE_CALL
                    ));
                }
                table::Term::Func(_) => {
                    // TODO: Allow importing and calling anonymous functions.
                    //
                    // This could be implemented in `hugr-core` by lifting the anonymous function
                    // into a function to be added into the containing module and then calling that
                    // function. See #2559.
                    return Err(error_unsupported!(
                        "`{}` does not yet support anonymous functions.",
                        model::CORE_CALL
                    ));
                }
                _ => {
                    return Err(error_invalid!(
                        concat!(
                            "Expected a function to be passed to `{}`.\n",
                            "Currently this is restricted to symbols that refer to functions."
                        ),
                        model::CORE_CALL
                    ));
                }
            };

            let func_sig = self.get_func_signature(*symbol)?;

            let type_args = args
                .iter()
                .map(|term| self.import_term(*term))
                .collect::<Result<Vec<TypeArg>, _>>()?;

            self.static_edges.push((*symbol, node_id));
            let optype = OpType::Call(
                Call::try_new(func_sig, type_args).map_err(ImportErrorInner::Signature)?,
            );

            let node = self.make_node(node_id, optype, parent)?;
            return Ok(node);
        }

        if let Some([_, value]) = self.match_symbol(operation, model::CORE_LOAD_CONST)? {
            // If the constant refers directly to a function, import this as the `LoadFunc` operation.
            if let table::Term::Apply(symbol, args) = self.get_term(value)? {
                let func_node_data = self.get_node(*symbol)?;

                if let table::Operation::DefineFunc(_) | table::Operation::DeclareFunc(_) =
                    func_node_data.operation
                {
                    let func_sig = self.get_func_signature(*symbol)?;
                    let type_args = args
                        .iter()
                        .map(|term| self.import_term(*term))
                        .collect::<Result<Vec<TypeArg>, _>>()?;

                    self.static_edges.push((*symbol, node_id));

                    let optype = OpType::LoadFunction(
                        LoadFunction::try_new(func_sig, type_args)
                            .map_err(ImportErrorInner::Signature)?,
                    );

                    let node = self.make_node(node_id, optype, parent)?;
                    return Ok(node);
                }
            }

            // Otherwise use const nodes
            let signature = node_data
                .signature
                .ok_or_else(|| error_uninferred!("node signature"))?;
            let [_, outputs] = self.get_func_type(signature)?;
            let outputs = self.import_closed_list(outputs)?;
            let output = outputs.first().ok_or_else(|| {
                error_invalid!("`{}` expects a single output", model::CORE_LOAD_CONST)
            })?;
            let datatype = self.import_type(*output)?;

            let imported_value = self.import_value(value, *output)?;

            let load_const_node = self.make_node(
                node_id,
                OpType::LoadConstant(LoadConstant {
                    datatype: datatype.clone(),
                }),
                parent,
            )?;

            let const_node = self
                .hugr
                .add_node_with_parent(parent, OpType::Const(Const::new(imported_value)));

            self.hugr.connect(const_node, 0, load_const_node, 0);

            return Ok(load_const_node);
        }

        if let Some([_, _, tag]) = self.match_symbol(operation, model::CORE_MAKE_ADT)? {
            let tag = match self.get_term(tag)? {
                table::Term::Literal(model::Literal::Nat(tag)) => tag,
                table::Term::Var(_) => {
                    return Err(error_unsupported!(
                        concat!(
                            "`{}` does not yet support passing a variable as the tag.\n",
                            "The `hugr-core` builtin `Tag` operation expects a concrete value for the tag. ",
                            "Therefore we must insist on a tag given as a natural number literal on import.",
                        ),
                        model::CORE_MAKE_ADT
                    ));
                }
                _ => {
                    return Err(error_invalid!(
                        "`{}` expects a nat literal tag",
                        model::CORE_MAKE_ADT
                    ));
                }
            };

            let signature = node_data
                .signature
                .ok_or_else(|| error_uninferred!("node signature"))?;
            let [_, outputs] = self.get_func_type(signature)?;
            let (variants, _) = self.import_adt_and_rest(outputs)?;
            let node = self.make_node(
                node_id,
                OpType::Tag(Tag {
                    variants,
                    tag: *tag as usize,
                }),
                parent,
            )?;
            return Ok(node);
        }

        let table::Term::Apply(node, params) = self.get_term(operation)? else {
            return Err(error_invalid!(
                "custom operations expect a symbol application referencing an operation"
            ));
        };
        let name = self.get_symbol_name(*node)?;
        let args = params
            .iter()
            .map(|param| self.import_term(*param))
            .collect::<Result<Vec<_>, _>>()?;
        let (extension, name) = self.import_custom_name(name)?;
        let signature = self.get_node_signature(node_id)?;

        // TODO: Currently we do not have the description or any other metadata for
        // the custom op. This will improve with declarative extensions being able
        // to declare operations as a node, in which case the description will be attached
        // to that node as metadata.

        let optype = OpType::OpaqueOp(OpaqueOp::new(extension, name, args, signature));
        self.make_node(node_id, optype, parent)
    }

    fn import_node_define_alias(
        &mut self,
        node_id: table::NodeId,
        symbol: &'a table::Symbol<'a>,
        value: table::TermId,
        parent: Node,
    ) -> Result<Node, ImportErrorInner> {
        if !symbol.params.is_empty() {
            return Err(error_unsupported!(
                "parameters or constraints in alias definition"
            ));
        }

        let optype = OpType::AliasDefn(AliasDefn {
            name: symbol.name.to_smolstr(),
            definition: self.import_type(value)?,
        });

        let node = self.make_node(node_id, optype, parent)?;
        Ok(node)
    }

    fn import_node_declare_alias(
        &mut self,
        node_id: table::NodeId,
        symbol: &'a table::Symbol<'a>,
        parent: Node,
    ) -> Result<Node, ImportErrorInner> {
        if !symbol.params.is_empty() {
            return Err(error_unsupported!(
                "parameters or constraints in alias declaration"
            ));
        }

        let optype = OpType::AliasDecl(AliasDecl {
            name: symbol.name.to_smolstr(),
            bound: TypeBound::Copyable,
        });

        let node = self.make_node(node_id, optype, parent)?;
        Ok(node)
    }

    fn import_poly_func_type<RV: MaybeRV, T>(
        &mut self,
        node: table::NodeId,
        symbol: table::Symbol<'a>,
        in_scope: impl FnOnce(&mut Self, PolyFuncTypeBase<RV>) -> Result<T, ImportErrorInner>,
    ) -> Result<T, ImportErrorInner> {
        (|| {
            let mut imported_params = Vec::with_capacity(symbol.params.len());

            for (index, param) in symbol.params.iter().enumerate() {
                self.local_vars
                    .insert(table::VarId(node, index as _), LocalVar::new(param.r#type));
            }

            for constraint in symbol.constraints {
                if let Some([term]) = self.match_symbol(*constraint, model::CORE_NON_LINEAR)? {
                    let table::Term::Var(var) = self.get_term(term)? else {
                        return Err(error_unsupported!(
                            "constraint on term that is not a variable"
                        ));
                    };

                    self.local_vars
                        .get_mut(var)
                        .ok_or_else(|| error_invalid!("unknown variable {}", var))?
                        .bound = TypeBound::Copyable;
                } else {
                    return Err(error_unsupported!(
                        concat!(
                            "Constraints other than `{}` can not yet be imported.\n",
                            "`hugr-core` does not have support for arbitrary constraints yet, ",
                            "instead relying on operation-specific Rust code to compute and ",
                            "validate signatures of custom operations."
                        ),
                        model::CORE_NON_LINEAR
                    ));
                }
            }

            for (index, param) in symbol.params.iter().enumerate() {
                let bound = self.local_vars[&table::VarId(node, index as _)].bound;
                imported_params.push(
                    self.import_term_with_bound(param.r#type, bound)
                        .map_err(|err| error_context!(err, "type of parameter `{}`", param.name))?,
                );
            }

            let body = self.import_func_type::<RV>(symbol.signature)?;
            in_scope(self, PolyFuncTypeBase::new(imported_params, body))
        })()
        .map_err(|err| error_context!(err, "symbol `{}` defined by node {}", symbol.name, node))
    }

    /// Import a [`Term`] from a term that represents a static type or value.
    fn import_term(&mut self, term_id: table::TermId) -> Result<Term, ImportErrorInner> {
        self.import_term_with_bound(term_id, TypeBound::Linear)
    }

    fn import_term_with_bound(
        &mut self,
        term_id: table::TermId,
        bound: TypeBound,
    ) -> Result<Term, ImportErrorInner> {
        (|| {
            if let Some([]) = self.match_symbol(term_id, model::CORE_STR_TYPE)? {
                return Ok(Term::StringType);
            }

            if let Some([]) = self.match_symbol(term_id, model::CORE_NAT_TYPE)? {
                return Ok(Term::max_nat_type());
            }

            if let Some([]) = self.match_symbol(term_id, model::CORE_BYTES_TYPE)? {
                return Ok(Term::BytesType);
            }

            if let Some([]) = self.match_symbol(term_id, model::CORE_FLOAT_TYPE)? {
                return Ok(Term::FloatType);
            }

            if let Some([]) = self.match_symbol(term_id, model::CORE_TYPE)? {
                return Ok(TypeParam::RuntimeType(bound));
            }

            if let Some([]) = self.match_symbol(term_id, model::CORE_CONSTRAINT)? {
                return Err(error_unsupported!("`{}`", model::CORE_CONSTRAINT));
            }

            if let Some([]) = self.match_symbol(term_id, model::CORE_STATIC)? {
                return Ok(Term::StaticType);
            }

            if let Some([ty]) = self.match_symbol(term_id, model::CORE_CONST)? {
                let ty = self
                    .import_type(ty)
                    .map_err(|err| error_context!(err, "type of a constant"))?;
                return Ok(TypeParam::new_const(ty));
            }

            if let Some([item_type]) = self.match_symbol(term_id, model::CORE_LIST_TYPE)? {
                // At present `hugr-model` has no way to express that the item
                // type of a list must be copyable. Therefore we import it as `Any`.
                let item_type = self
                    .import_term(item_type)
                    .map_err(|err| error_context!(err, "item type of list type"))?;
                return Ok(TypeParam::new_list_type(item_type));
            }

            if let Some([item_types]) = self.match_symbol(term_id, model::CORE_TUPLE_TYPE)? {
                // At present `hugr-model` has no way to express that the item
                // types of a tuple must be copyable. Therefore we import it as `Any`.
                let item_types = self
                    .import_term(item_types)
                    .map_err(|err| error_context!(err, "item types of tuple type"))?;
                return Ok(TypeParam::new_tuple_type(item_types));
            }

            match self.get_term(term_id)? {
                table::Term::Wildcard => Err(error_uninferred!("wildcard")),

                table::Term::Var(var) => {
                    let var_info = self
                        .local_vars
                        .get(var)
                        .ok_or_else(|| error_invalid!("unknown variable {}", var))?;
                    let decl = self.import_term_with_bound(var_info.r#type, var_info.bound)?;
                    Ok(Term::new_var_use(var.1 as _, decl))
                }

                table::Term::List(parts) => {
                    // PERFORMANCE: Can we do this without the additional allocation?
                    let parts: Vec<_> = parts
                        .iter()
                        .map(|part| self.import_seq_part(part))
                        .collect::<Result<_, _>>()
                        .map_err(|err| error_context!(err, "list parts"))?;
                    Ok(TypeArg::new_list_from_parts(parts))
                }

                table::Term::Tuple(parts) => {
                    // PERFORMANCE: Can we do this without the additional allocation?
                    let parts: Vec<_> = parts
                        .iter()
                        .map(|part| self.import_seq_part(part))
                        .try_collect()
                        .map_err(|err| error_context!(err, "tuple parts"))?;
                    Ok(TypeArg::new_tuple_from_parts(parts))
                }

                table::Term::Literal(model::Literal::Str(value)) => {
                    Ok(Term::String(value.to_string()))
                }

                table::Term::Literal(model::Literal::Nat(value)) => Ok(Term::BoundedNat(*value)),

                table::Term::Literal(model::Literal::Bytes(value)) => {
                    Ok(Term::Bytes(value.clone()))
                }
                table::Term::Literal(model::Literal::Float(value)) => Ok(Term::Float(*value)),
                table::Term::Func { .. } => Err(error_unsupported!("function constant")),

                table::Term::Apply { .. } => {
                    let ty: Type = self.import_type(term_id)?;
                    Ok(ty.into())
                }
            }
        })()
        .map_err(|err| error_context!(err, "term {}", term_id))
    }

    fn import_seq_part(
        &mut self,
        seq_part: &'a table::SeqPart,
    ) -> Result<SeqPart<TypeArg>, ImportErrorInner> {
        Ok(match seq_part {
            table::SeqPart::Item(term_id) => SeqPart::Item(self.import_term(*term_id)?),
            table::SeqPart::Splice(term_id) => SeqPart::Splice(self.import_term(*term_id)?),
        })
    }

    /// Import a `Type` from a term that represents a runtime type.
    fn import_type<RV: MaybeRV>(
        &mut self,
        term_id: table::TermId,
    ) -> Result<TypeBase<RV>, ImportErrorInner> {
        (|| {
            if let Some([_, _]) = self.match_symbol(term_id, model::CORE_FN)? {
                let func_type = self.import_func_type::<RowVariable>(term_id)?;
                return Ok(TypeBase::new_function(func_type));
            }

            if let Some([variants]) = self.match_symbol(term_id, model::CORE_ADT)? {
                let variants = (|| {
                    self.import_closed_list(variants)?
                        .iter()
                        .map(|variant| self.import_type_row::<RowVariable>(*variant))
                        .collect::<Result<Vec<_>, _>>()
                })()
                .map_err(|err| error_context!(err, "adt variants"))?;

                return Ok(TypeBase::new_sum(variants));
            }

            match self.get_term(term_id)? {
                table::Term::Wildcard => Err(error_uninferred!("wildcard")),

                table::Term::Apply(symbol, args) => {
                    let name = self.get_symbol_name(*symbol)?;

                    let args = args
                        .iter()
                        .map(|arg| self.import_term(*arg))
                        .collect::<Result<Vec<_>, _>>()
                        .map_err(|err| {
                            error_context!(err, "type argument of custom type `{}`", name)
                        })?;

                    let (extension, id) = self.import_custom_name(name)?;

                    let extension_ref =
                        self.extensions
                            .get(&extension)
                            .ok_or_else(|| ExtensionError::Missing {
                                missing_ext: extension.clone(),
                                available: self.extensions.ids().cloned().collect(),
                            })?;

                    let ext_type =
                        extension_ref
                            .get_type(&id)
                            .ok_or_else(|| ExtensionError::MissingType {
                                ext: extension.clone(),
                                name: id.clone(),
                            })?;

                    let bound = ext_type.bound(&args);

                    Ok(TypeBase::new_extension(CustomType::new(
                        id,
                        args,
                        extension,
                        bound,
                        &Arc::downgrade(extension_ref),
                    )))
                }

                table::Term::Var(var @ table::VarId(_, index)) => {
                    let local_var = self
                        .local_vars
                        .get(var)
                        .ok_or(error_invalid!("unknown var {}", var))?;
                    Ok(TypeBase::new_var_use(*index as _, local_var.bound))
                }

                // The following terms are not runtime types, but the core `Type` only contains runtime types.
                // We therefore report a type error here.
                table::Term::Literal(_)
                | table::Term::List { .. }
                | table::Term::Tuple { .. }
                | table::Term::Func { .. } => Err(error_invalid!("expected a runtime type")),
            }
        })()
        .map_err(|err| error_context!(err, "term {} as `Type`", term_id))
    }

    fn get_func_type(
        &mut self,
        term_id: table::TermId,
    ) -> Result<[table::TermId; 2], ImportErrorInner> {
        self.match_symbol(term_id, model::CORE_FN)?
            .ok_or(error_invalid!("expected a function type"))
    }

    fn get_ctrl_type(
        &mut self,
        term_id: table::TermId,
    ) -> Result<[table::TermId; 2], ImportErrorInner> {
        self.match_symbol(term_id, model::CORE_CTRL)?
            .ok_or(error_invalid!("expected a control type"))
    }

    /// Import a [`Signature`] or [`FuncValueType`].
    ///
    /// When importing a [`Signature`] the lists of input and output types need
    /// to be closed. In constrast [`FuncValueType`] admits importing open lists
    /// of input and output types via "row variables".
    ///
    /// Function types are not special-cased in `hugr-model` but are represented
    /// via the `core.fn` term constructor.
    fn import_func_type<RV: MaybeRV>(
        &mut self,
        term_id: table::TermId,
    ) -> Result<FuncTypeBase<RV>, ImportErrorInner> {
        (|| {
            let [inputs, outputs] = self.get_func_type(term_id)?;
            let inputs = self
                .import_type_row(inputs)
                .map_err(|err| error_context!(err, "function inputs"))?;
            let outputs = self
                .import_type_row(outputs)
                .map_err(|err| error_context!(err, "function outputs"))?;
            Ok(FuncTypeBase::new(inputs, outputs))
        })()
        .map_err(|err| error_context!(err, "function type"))
    }

    /// Import a closed list as a vector of term ids.
    ///
    /// This method supports list terms that contain spliced sublists as long as
    /// the list can be recursively flattened to only contain individual items.
    ///
    /// To allow for IR constructions that are parameterised by static
    /// parameters, open lists with spliced variables should be supported where
    /// possible. Closed lists might be required in some places of the IR that
    /// are not supposed to be parameterised with variables or where such
    /// parameterisation is not yet supported by the `hugr-core` structures that
    /// we are importing into.
    fn import_closed_list(
        &mut self,
        term_id: table::TermId,
    ) -> Result<Vec<table::TermId>, ImportErrorInner> {
        fn import_into(
            ctx: &mut Context,
            term_id: table::TermId,
            types: &mut Vec<table::TermId>,
        ) -> Result<(), ImportErrorInner> {
            match ctx.get_term(term_id)? {
                table::Term::List(parts) => {
                    types.reserve(parts.len());

                    for part in *parts {
                        match part {
                            table::SeqPart::Item(term_id) => {
                                types.push(*term_id);
                            }
                            table::SeqPart::Splice(term_id) => {
                                import_into(ctx, *term_id, types)?;
                            }
                        }
                    }
                }
                _ => {
                    return Err(error_invalid!(
                        "Expected a closed list.\n{}",
                        CLOSED_LIST_HINT
                    ));
                }
            }

            Ok(())
        }

        let mut types = Vec::new();
        import_into(self, term_id, &mut types)?;
        Ok(types)
    }

    /// Import a closed tuple as a vector of term ids.
    ///
    /// This is the tuple version of [`Self::import_closed_list`].
    fn import_closed_tuple(
        &mut self,
        term_id: table::TermId,
    ) -> Result<Vec<table::TermId>, ImportErrorInner> {
        fn import_into(
            ctx: &mut Context,
            term_id: table::TermId,
            types: &mut Vec<table::TermId>,
        ) -> Result<(), ImportErrorInner> {
            match ctx.get_term(term_id)? {
                table::Term::Tuple(parts) => {
                    types.reserve(parts.len());

                    for part in *parts {
                        match part {
                            table::SeqPart::Item(term_id) => {
                                types.push(*term_id);
                            }
                            table::SeqPart::Splice(term_id) => {
                                import_into(ctx, *term_id, types)?;
                            }
                        }
                    }
                }
                _ => {
                    return Err(error_invalid!(
                        "Expected a closed tuple term.\n{}",
                        CLOSED_TUPLE_HINT
                    ));
                }
            }

            Ok(())
        }

        let mut types = Vec::new();
        import_into(self, term_id, &mut types)?;
        Ok(types)
    }

    /// Imports a list of lists as a vector of type rows.
    ///
    /// See [`Self::import_type_row`].
    fn import_type_rows<RV: MaybeRV>(
        &mut self,
        term_id: table::TermId,
    ) -> Result<Vec<TypeRowBase<RV>>, ImportErrorInner> {
        self.import_closed_list(term_id)?
            .into_iter()
            .map(|term_id| self.import_type_row::<RV>(term_id))
            .collect()
    }

    /// Imports a list as a type row.
    ///
    /// This method works to produce a [`TypeRow`] or a [`TypeRowRV`], depending
    /// on the `RV` type argument. For [`TypeRow`] a closed list is expected.
    /// For [`TypeRowRV`] we import spliced variables as row variables.
    fn import_type_row<RV: MaybeRV>(
        &mut self,
        term_id: table::TermId,
    ) -> Result<TypeRowBase<RV>, ImportErrorInner> {
        fn import_into<RV: MaybeRV>(
            ctx: &mut Context,
            term_id: table::TermId,
            types: &mut Vec<TypeBase<RV>>,
        ) -> Result<(), ImportErrorInner> {
            match ctx.get_term(term_id)? {
                table::Term::List(parts) => {
                    types.reserve(parts.len());

                    for item in *parts {
                        match item {
                            table::SeqPart::Item(term_id) => {
                                types.push(ctx.import_type::<RV>(*term_id)?);
                            }
                            table::SeqPart::Splice(term_id) => {
                                import_into(ctx, *term_id, types)?;
                            }
                        }
                    }
                }
                table::Term::Var(table::VarId(_, index)) => {
                    let var = RV::try_from_rv(RowVariable(*index as _, TypeBound::Linear))
                        .map_err(|_| {
                            error_invalid!("Expected a closed list.\n{}", CLOSED_LIST_HINT)
                        })?;
                    types.push(TypeBase::new(TypeEnum::RowVar(var)));
                }
                _ => return Err(error_invalid!("expected a list")),
            }

            Ok(())
        }

        let mut types = Vec::new();
        import_into(self, term_id, &mut types)?;
        Ok(types.into())
    }

    fn import_custom_name(
        &mut self,
        symbol: &'a str,
    ) -> Result<(ExtensionId, SmolStr), ImportErrorInner> {
        use std::collections::hash_map::Entry;
        match self.custom_name_cache.entry(symbol) {
            Entry::Occupied(occupied_entry) => Ok(occupied_entry.get().clone()),
            Entry::Vacant(vacant_entry) => {
                let qualified_name = ExtensionId::new(symbol)
                    .map_err(|_| error_invalid!("`{}` is not a valid symbol name", symbol))?;

                let (extension, id) = qualified_name
                    .split_last()
                    .ok_or_else(|| error_invalid!("`{}` is not a valid symbol name", symbol))?;

                vacant_entry.insert((extension.clone(), id.clone()));
                Ok((extension, id))
            }
        }
    }

    /// Import a constant term as a [`Value`].
    ///
    /// This method supports the JSON compatibility constants and a small selection of built in
    /// constant constructors. It is a compatibility shim until constants can be represented as
    /// terms in `hugr-core` at which point this method will become redundant.
    fn import_value(
        &mut self,
        term_id: table::TermId,
        type_id: table::TermId,
    ) -> Result<Value, ImportErrorInner> {
        let term_data = self.get_term(term_id)?;

        // NOTE: We have special cased arrays, integers, and floats for now.
        // TODO: Allow arbitrary extension values to be imported from terms.

        if let Some([runtime_type, json]) = self.match_symbol(term_id, model::COMPAT_CONST_JSON)? {
            let table::Term::Literal(model::Literal::Str(json)) = self.get_term(json)? else {
                return Err(error_invalid!(
                    "`{}` expects a string literal",
                    model::COMPAT_CONST_JSON
                ));
            };

            // We attempt to deserialize as the custom const directly.
            // This might fail due to the custom const struct not being included when
            // this code was compiled; in that case, we fall back to the serialized form.
            let value: Option<Box<dyn CustomConst>> = serde_json::from_str(json).ok();

            if let Some(value) = value {
                let opaque_value = OpaqueValue::from(value);
                return Ok(Value::Extension { e: opaque_value });
            } else {
                let runtime_type = self.import_type(runtime_type)?;
                let value: serde_json::Value = serde_json::from_str(json).map_err(|_| {
                    error_invalid!(
                        "unable to parse JSON string for `{}`",
                        model::COMPAT_CONST_JSON
                    )
                })?;
                let custom_const = CustomSerialized::new(runtime_type, value);
                let opaque_value = OpaqueValue::new(custom_const);
                return Ok(Value::Extension { e: opaque_value });
            }
        }

        if let Some([_, element_type_term, contents]) =
            self.match_symbol(term_id, ArrayValue::CTR_NAME)?
        {
            let element_type = self.import_type(element_type_term)?;
            let contents = self.import_closed_list(contents)?;
            let contents = contents
                .iter()
                .map(|item| self.import_value(*item, element_type_term))
                .collect::<Result<Vec<_>, _>>()?;
            return Ok(ArrayValue::new(element_type, contents).into());
        }

        if let Some([bitwidth, value]) = self.match_symbol(term_id, ConstInt::CTR_NAME)? {
            let bitwidth = {
                let table::Term::Literal(model::Literal::Nat(bitwidth)) =
                    self.get_term(bitwidth)?
                else {
                    return Err(error_invalid!(
                        "`{}` expects a nat literal in its `bitwidth` argument",
                        ConstInt::CTR_NAME
                    ));
                };
                if *bitwidth > 6 {
                    return Err(error_invalid!(
                        "`{}` expects the bitwidth to be at most 6, got {}",
                        ConstInt::CTR_NAME,
                        bitwidth
                    ));
                }
                *bitwidth as u8
            };

            let value = {
                let table::Term::Literal(model::Literal::Nat(value)) = self.get_term(value)? else {
                    return Err(error_invalid!(
                        "`{}` expects a nat literal value",
                        ConstInt::CTR_NAME
                    ));
                };
                *value
            };

            return Ok(ConstInt::new_u(bitwidth, value)
                .map_err(|_| error_invalid!("failed to create int constant"))?
                .into());
        }

        if let Some([value]) = self.match_symbol(term_id, ConstF64::CTR_NAME)? {
            let table::Term::Literal(model::Literal::Float(value)) = self.get_term(value)? else {
                return Err(error_invalid!(
                    "`{}` expects a float literal value",
                    ConstF64::CTR_NAME
                ));
            };

            return Ok(ConstF64::new(value.into_inner()).into());
        }

        if let Some([_, _, tag, values]) = self.match_symbol(term_id, model::CORE_CONST_ADT)? {
            let [variants] = self.expect_symbol(type_id, model::CORE_ADT)?;
            let values = self.import_closed_tuple(values)?;
            let variants = self.import_closed_list(variants)?;

            let table::Term::Literal(model::Literal::Nat(tag)) = self.get_term(tag)? else {
                return Err(error_invalid!(
                    "`{}` expects a nat literal tag",
                    model::CORE_ADT
                ));
            };

            let variant = variants.get(*tag as usize).ok_or(error_invalid!(
                "the tag of a `{}` must be a valid index into the list of variants",
                model::CORE_CONST_ADT
            ))?;

            let variant = self.import_closed_list(*variant)?;

            let items = values
                .iter()
                .zip(variant.iter())
                .map(|(value, typ)| self.import_value(*value, *typ))
                .collect::<Result<Vec<_>, _>>()?;

            let typ = {
                // TODO: Import as a `SumType` directly and avoid the copy.
                let typ: Type = self.import_type(type_id)?;
                match typ.as_type_enum() {
                    TypeEnum::Sum(sum) => sum.clone(),
                    _ => unreachable!(),
                }
            };

            return Ok(Value::sum(*tag as _, items, typ).unwrap());
        }

        match term_data {
            table::Term::Wildcard => Err(error_uninferred!("wildcard")),
            table::Term::Var(_) => Err(error_unsupported!(concat!(
                "Constant value containing a variable.\n",
                "The constant system in `hugr-core` is not set up yet to support ",
                "constants that depend on variables.",
            ))),

            table::Term::Apply(symbol, _) => {
                let symbol_name = self.get_symbol_name(*symbol)?;
                Err(error_unsupported!(
                    concat!(
                        "Unknown custom constant constructor `{}`.\n",
                        "Importing constants from `hugr-model` to `hugr-core` currently only supports a small ",
                        "and hard-coded list of constant constructors. To support JSON encoded constants ",
                        "use the constant constructor `{}`."
                    ),
                    symbol_name,
                    model::COMPAT_CONST_JSON
                ))
                // TODO: This should ultimately include the following cases:
                // - function definitions
                // - custom constructors for values
            }

            table::Term::List { .. } | table::Term::Tuple(_) | table::Term::Literal(_) => {
                Err(error_invalid!("expected constant"))
            }

            table::Term::Func { .. } => Err(error_unsupported!("Constant function value.")),
        }
    }

    /// Check if a term is an application of a symbol with the given name. If
    /// so, return the arguments of the application.
    ///
    /// We allow the match even if the symbol is applied to fewer arguments than
    /// expected. In that case, the arguments are considered implicit and the
    /// return array is padded with wildcard terms at the beginning. The match
    /// fails if the symbol is applied to more arguments than expected.
    ///
    /// # Errors
    ///
    /// An error is returned in the following cases:
    ///
    /// - The term id does not exist in the module to be imported.
    /// - The term is a symbol application but the node id in the application does not refer to a symbol.
    ///
    /// Failed matches return `Ok(None)` instead of an error so that this method can be used
    /// in sequence to probe for applications of different symbol constructors.
    fn match_symbol<const N: usize>(
        &self,
        term_id: table::TermId,
        name: &str,
    ) -> Result<Option<[table::TermId; N]>, ImportErrorInner> {
        let term = self.get_term(term_id)?;

        // TODO: Follow alias chains?

        let table::Term::Apply(symbol, args) = term else {
            return Ok(None);
        };

        if name != self.get_symbol_name(*symbol)? {
            return Ok(None);
        }

        if args.len() > N {
            return Ok(None);
        }

        let result = std::array::from_fn(|i| {
            (i + args.len())
                .checked_sub(N)
                .map(|i| args[i])
                .unwrap_or_default()
        });

        Ok(Some(result))
    }

    /// Expects a term to be an application of a symbol with the given name and
    /// returns the arguments of the application.
    ///
    /// See [`Self::match_symbol`].
    ///
    /// # Errors
    ///
    /// In addition to the error cases described in [`Self::match_symbol`], this
    /// method also returns an error when the match failed.
    fn expect_symbol<const N: usize>(
        &self,
        term_id: table::TermId,
        name: &str,
    ) -> Result<[table::TermId; N], ImportErrorInner> {
        self.match_symbol(term_id, name)?.ok_or(error_invalid!(
            "Expected symbol `{}` with arity {}.",
            name,
            N
        ))
    }

    /// Searches for `core.title` metadata on the given node.
    ///
    /// The `core.title` metadata is used as the `hugr-core` name for private function symbols.
    /// This is necessary as a compatibility shim to bridge between the different concepts of name
    /// in `hugr-core` and `hugr-model`: In `hugr-model` the name of a symbol uniquely identifies
    /// that symbol within a module, while in `hugr-core` the name started out as procedurally
    /// irrelevant debug metadata. With linking, the `hugr-core` name has become significant,
    /// but only for public functions.
    fn import_title_metadata(
        &self,
        node_id: table::NodeId,
    ) -> Result<Option<&'a str>, ImportErrorInner> {
        let node_data = self.get_node(node_id)?;
        for meta in node_data.meta {
            let Some([name]) = self.match_symbol(*meta, model::CORE_TITLE)? else {
                continue;
            };

            let table::Term::Literal(model::Literal::Str(name)) = self.get_term(name)? else {
                return Err(error_invalid!(
                    "`{}` metadata expected a string literal as argument",
                    model::CORE_TITLE
                ));
            };

            return Ok(Some(name.as_str()));
        }

        Ok(None)
    }
}

/// Information about a local variable.
#[derive(Debug, Clone, Copy)]
struct LocalVar {
    /// The type of the variable.
    r#type: table::TermId,
    /// The type bound of the variable.
    bound: TypeBound,
}

impl LocalVar {
    pub fn new(r#type: table::TermId) -> Self {
        Self {
            r#type,
            bound: TypeBound::Linear,
        }
    }
}