diff --git a/src/algo/all_pairs_shortest_path.rs b/src/algo/all_pairs_shortest_path.rs
index 820b8d63..1dfdfd00 100644
--- a/src/algo/all_pairs_shortest_path.rs
+++ b/src/algo/all_pairs_shortest_path.rs
@@ -6,12 +6,16 @@ use miette::Result;
 use ordered_float::OrderedFloat;
 use priority_queue::PriorityQueue;
 use rayon::prelude::*;
+use smartstring::{LazyCompact, SmartString};
 
-use crate::algo::AlgoImpl;
 use crate::algo::shortest_path_dijkstra::dijkstra_keep_ties;
+use crate::algo::AlgoImpl;
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -75,6 +79,15 @@ impl AlgoImpl for BetweennessCentrality {
 
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(2)
+    }
 }
 
 pub(crate) struct ClosenessCentrality;
@@ -116,6 +129,15 @@ impl AlgoImpl for ClosenessCentrality {
         }
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(2)
+    }
 }
 
 pub(crate) fn dijkstra_cost_only(
diff --git a/src/algo/astar.rs b/src/algo/astar.rs
index 1484cbbd..b13ed6b5 100644
--- a/src/algo/astar.rs
+++ b/src/algo/astar.rs
@@ -4,12 +4,15 @@ use std::collections::BTreeMap;
 use miette::{ensure, Result};
 use ordered_float::OrderedFloat;
 use priority_queue::PriorityQueue;
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::{AlgoImpl, BadExprValueError, NodeNotFoundError};
 use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicAlgoRuleArg, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -63,6 +66,15 @@ impl AlgoImpl for ShortestPathAStar {
 
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(4)
+    }
 }
 
 fn astar(
diff --git a/src/algo/bfs.rs b/src/algo/bfs.rs
index 55f5a4cb..a389f5ef 100644
--- a/src/algo/bfs.rs
+++ b/src/algo/bfs.rs
@@ -1,11 +1,15 @@
 use std::collections::{BTreeMap, BTreeSet, VecDeque};
 
-use miette::Result;
+use miette::{Result};
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::{AlgoImpl, NodeNotFoundError};
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -96,4 +100,13 @@ impl AlgoImpl for Bfs {
         }
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(1)
+    }
 }
diff --git a/src/algo/csv.rs b/src/algo/csv.rs
index c89d8a3e..a79a2a9f 100644
--- a/src/algo/csv.rs
+++ b/src/algo/csv.rs
@@ -2,15 +2,19 @@ use std::collections::BTreeMap;
 
 use csv::StringRecord;
 use miette::{bail, ensure, IntoDiagnostic, Result};
-use smartstring::SmartString;
+use smartstring::{LazyCompact, SmartString};
 
-use crate::algo::AlgoImpl;
+use crate::algo::{AlgoImpl, CannotDetermineArity};
+use crate::data::expr::Expr;
 use crate::data::functions::{op_to_float, op_to_uuid};
-use crate::data::program::{MagicAlgoApply, MagicSymbol, WrongAlgoOptionError};
+use crate::data::program::{
+    AlgoOptionNotFoundError, MagicAlgoApply, MagicSymbol, WrongAlgoOptionError,
+};
 use crate::data::relation::{ColType, NullableColType};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
-use crate::parse::parse_type;
+use crate::parse::{parse_type, SourceSpan};
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -149,9 +153,7 @@ impl AlgoImpl for CsvReader {
                 }
             }
             None => {
-                let content = minreq::get(&url as &str)
-                    .send()
-                    .into_diagnostic()?;
+                let content = minreq::get(&url as &str).send().into_diagnostic()?;
                 let mut rdr = rdr_builder.from_reader(content.as_bytes());
                 for record in rdr.records() {
                     let record = record.into_diagnostic()?;
@@ -161,4 +163,44 @@ impl AlgoImpl for CsvReader {
         }
         Ok(())
     }
+
+    fn arity(
+        &self,
+        options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        span: SourceSpan,
+    ) -> Result<usize> {
+        let with_row_num = match options.get("prepend_index") {
+            None => 0,
+            Some(Expr::Const {
+                val: DataValue::Bool(true),
+                ..
+            }) => 1,
+            Some(Expr::Const {
+                val: DataValue::Bool(false),
+                ..
+            }) => 0,
+            _ => bail!(CannotDetermineArity(
+                "CsvReader".to_string(),
+                "invalid option 'prepend_index' given, expect a boolean".to_string(),
+                span
+            )),
+        };
+        let columns = options
+            .get("types")
+            .ok_or_else(|| AlgoOptionNotFoundError {
+                name: "types".to_string(),
+                span,
+                algo_name: "CsvReader".to_string(),
+            })?;
+        let columns = columns.clone().eval_to_const()?;
+        if let Some(l) = columns.get_list() {
+            return Ok(l.len() + with_row_num);
+        }
+        bail!(CannotDetermineArity(
+            "CsvReader".to_string(),
+            "invalid option 'types' given, expect positive number or list".to_string(),
+            span
+        ))
+    }
 }
diff --git a/src/algo/degree_centrality.rs b/src/algo/degree_centrality.rs
index 0adfa358..47e882ce 100644
--- a/src/algo/degree_centrality.rs
+++ b/src/algo/degree_centrality.rs
@@ -1,11 +1,15 @@
 use std::collections::BTreeMap;
 
 use miette::Result;
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::AlgoImpl;
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -60,4 +64,13 @@ impl AlgoImpl for DegreeCentrality {
         }
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(4)
+    }
 }
diff --git a/src/algo/dfs.rs b/src/algo/dfs.rs
index 1da3ba7b..4625f4f1 100644
--- a/src/algo/dfs.rs
+++ b/src/algo/dfs.rs
@@ -1,11 +1,15 @@
 use std::collections::{BTreeMap, BTreeSet};
 
 use miette::Result;
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::{AlgoImpl, NodeNotFoundError};
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -99,4 +103,13 @@ impl AlgoImpl for Dfs {
         }
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(1)
+    }
 }
diff --git a/src/algo/jlines.rs b/src/algo/jlines.rs
index 5211e109..587614ca 100644
--- a/src/algo/jlines.rs
+++ b/src/algo/jlines.rs
@@ -5,11 +5,14 @@ use std::{fs, io};
 
 use itertools::Itertools;
 use miette::{bail, miette, Diagnostic, IntoDiagnostic, Result};
+use smartstring::{LazyCompact, SmartString};
 use thiserror::Error;
 
-use crate::algo::AlgoImpl;
+use crate::algo::{AlgoImpl, CannotDetermineArity};
+use crate::data::expr::Expr;
 use crate::data::json::JsonValue;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
 use crate::parse::SourceSpan;
@@ -121,4 +124,43 @@ impl AlgoImpl for JsonReader {
         }
         Ok(())
     }
+
+    fn arity(
+        &self,
+        opts: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        span: SourceSpan,
+    ) -> Result<usize> {
+        let with_row_num = match opts.get("prepend_index") {
+            None => 0,
+            Some(Expr::Const {
+                val: DataValue::Bool(true),
+                ..
+            }) => 1,
+            Some(Expr::Const {
+                val: DataValue::Bool(false),
+                ..
+            }) => 0,
+            _ => bail!(CannotDetermineArity(
+                "JsonReader".to_string(),
+                "invalid option 'prepend_index' given, expect a boolean".to_string(),
+                span
+            )),
+        };
+        let fields = opts.get("fields").ok_or_else(|| {
+            CannotDetermineArity(
+                "JsonReader".to_string(),
+                "option 'fields' not provided".to_string(),
+                span,
+            )
+        })?;
+        Ok(match fields.clone().eval_to_const()? {
+            DataValue::List(l) => l.len() + with_row_num,
+            _ => bail!(CannotDetermineArity(
+                "JsonReader".to_string(),
+                "invalid option 'fields' given, expect a list".to_string(),
+                span
+            )),
+        })
+    }
 }
diff --git a/src/algo/kruskal.rs b/src/algo/kruskal.rs
index 77a7f1ca..d6001624 100644
--- a/src/algo/kruskal.rs
+++ b/src/algo/kruskal.rs
@@ -5,11 +5,15 @@ use itertools::Itertools;
 use miette::Result;
 use ordered_float::OrderedFloat;
 use priority_queue::PriorityQueue;
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::AlgoImpl;
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -45,6 +49,15 @@ impl AlgoImpl for MinimumSpanningForestKruskal {
 
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(3)
+    }
 }
 
 fn kruskal(edges: &[Vec<(usize, f64)>], poison: Poison) -> Result<Vec<(usize, usize, f64)>> {
diff --git a/src/algo/label_propagation.rs b/src/algo/label_propagation.rs
index 1bb41cbd..492a8b3c 100644
--- a/src/algo/label_propagation.rs
+++ b/src/algo/label_propagation.rs
@@ -3,11 +3,15 @@ use std::collections::BTreeMap;
 use itertools::Itertools;
 use miette::Result;
 use rand::prelude::*;
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::AlgoImpl;
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -35,6 +39,15 @@ impl AlgoImpl for LabelPropagation {
         }
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(2)
+    }
 }
 
 fn label_propagation(
diff --git a/src/algo/louvain.rs b/src/algo/louvain.rs
index 83ea960d..b969b0ff 100644
--- a/src/algo/louvain.rs
+++ b/src/algo/louvain.rs
@@ -3,11 +3,15 @@ use std::collections::{BTreeMap, BTreeSet};
 use itertools::Itertools;
 use log::debug;
 use miette::Result;
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::AlgoImpl;
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -59,6 +63,15 @@ impl AlgoImpl for CommunityDetectionLouvain {
 
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(2)
+    }
 }
 
 fn louvain(
diff --git a/src/algo/mod.rs b/src/algo/mod.rs
index 73af7650..1396085b 100644
--- a/src/algo/mod.rs
+++ b/src/algo/mod.rs
@@ -1,6 +1,5 @@
 use std::collections::BTreeMap;
 
-use either::Either;
 use miette::{bail, ensure, Diagnostic, Result};
 use smartstring::{LazyCompact, SmartString};
 use thiserror::Error;
@@ -25,10 +24,7 @@ use crate::algo::top_sort::TopSort;
 use crate::algo::triangles::ClusteringCoefficients;
 use crate::algo::yen::KShortestPathYen;
 use crate::data::expr::Expr;
-use crate::data::functions::OP_LIST;
-use crate::data::program::{
-    AlgoOptionNotFoundError, AlgoRuleArg, MagicAlgoApply, MagicAlgoRuleArg, MagicSymbol,
-};
+use crate::data::program::{MagicAlgoApply, MagicAlgoRuleArg, MagicSymbol};
 use crate::data::symb::Symbol;
 use crate::data::tuple::{Tuple, TupleIter};
 use crate::data::value::DataValue;
@@ -66,8 +62,23 @@ pub(crate) trait AlgoImpl {
         out: &InMemRelation,
         poison: Poison,
     ) -> Result<()>;
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize>;
 }
 
+#[derive(Debug, Error, Diagnostic)]
+#[error("Cannot determine arity for algo {0} since {1}")]
+#[diagnostic(code(parser::no_algo_arity))]
+pub(crate) struct CannotDetermineArity(
+    pub(crate) String,
+    pub(crate) String,
+    #[label] pub(crate) SourceSpan,
+);
+
 #[derive(Clone, Debug)]
 pub(crate) struct AlgoHandle {
     pub(crate) name: Symbol,
@@ -79,124 +90,6 @@ impl AlgoHandle {
             name: Symbol::new(name, span),
         }
     }
-    pub(crate) fn arity(
-        &self,
-        _args: Either<&[AlgoRuleArg], &[MagicAlgoRuleArg]>,
-        opts: &BTreeMap<SmartString<LazyCompact>, Expr>,
-    ) -> Result<usize> {
-        #[derive(Debug, Error, Diagnostic)]
-        #[error("Cannot determine arity for algo {0} since {1}")]
-        #[diagnostic(code(parser::no_algo_arity))]
-        struct CannotDetermineArity(String, String, #[label] SourceSpan);
-
-        Ok(match &self.name.name as &str {
-            "ClusteringCoefficients" => 4,
-            "DegreeCentrality" => 4,
-            "ClosenessCentrality" => 2,
-            "BetweennessCentrality" => 2,
-            "DepthFirstSearch" | "DFS" => 1,
-            "BreadthFirstSearch" | "BFS" => 1,
-            "ShortestPathDijkstra" => 4,
-            "ShortestPathAStar" => 4,
-            "KShortestPathYen" => 4,
-            "MinimumSpanningTreePrim" => 3,
-            "MinimumSpanningTreeKruskal" => 3,
-            "TopSort" => 2,
-            "ConnectedComponents" => 2,
-            "StronglyConnectedComponents" | "SCC" => 2,
-            "PageRank" => 2,
-            "CommunityDetectionLouvain" => 2,
-            "LabelPropagation" => 2,
-            "RandomWalk" => 3,
-            n @ "ReorderSort" => {
-                let out_opts = opts.get("out").ok_or_else(|| {
-                    CannotDetermineArity(
-                        n.to_string(),
-                        "option 'out' not provided".to_string(),
-                        self.name.span,
-                    )
-                })?;
-                match out_opts {
-                    Expr::Const {
-                        val: DataValue::List(l),
-                        ..
-                    } => l.len() + 1,
-                    Expr::Apply { op, args, .. } if **op == OP_LIST => args.len() + 1,
-                    _ => bail!(CannotDetermineArity(
-                        n.to_string(),
-                        "invalid option 'out' given, expect a list".to_string(),
-                        self.name.span
-                    )),
-                }
-            }
-            n @ "CsvReader" => {
-                let with_row_num = match opts.get("prepend_index") {
-                    None => 0,
-                    Some(Expr::Const {
-                        val: DataValue::Bool(true),
-                        ..
-                    }) => 1,
-                    Some(Expr::Const {
-                        val: DataValue::Bool(false),
-                        ..
-                    }) => 0,
-                    _ => bail!(CannotDetermineArity(
-                        n.to_string(),
-                        "invalid option 'prepend_index' given, expect a boolean".to_string(),
-                        self.name.span
-                    )),
-                };
-                let columns = opts.get("types").ok_or_else(|| AlgoOptionNotFoundError {
-                    name: "types".to_string(),
-                    span: self.name.span,
-                    algo_name: n.to_string(),
-                })?;
-                let columns = columns.clone().eval_to_const()?;
-                if let Some(l) = columns.get_list() {
-                    return Ok(l.len() + with_row_num);
-                }
-                bail!(CannotDetermineArity(
-                    n.to_string(),
-                    "invalid option 'types' given, expect positive number or list".to_string(),
-                    self.name.span
-                ))
-            }
-            n @ "JsonReader" => {
-                let with_row_num = match opts.get("prepend_index") {
-                    None => 0,
-                    Some(Expr::Const {
-                        val: DataValue::Bool(true),
-                        ..
-                    }) => 1,
-                    Some(Expr::Const {
-                        val: DataValue::Bool(false),
-                        ..
-                    }) => 0,
-                    _ => bail!(CannotDetermineArity(
-                        n.to_string(),
-                        "invalid option 'prepend_index' given, expect a boolean".to_string(),
-                        self.name.span
-                    )),
-                };
-                let fields = opts.get("fields").ok_or_else(|| {
-                    CannotDetermineArity(
-                        n.to_string(),
-                        "option 'fields' not provided".to_string(),
-                        self.name.span,
-                    )
-                })?;
-                match fields.clone().eval_to_const()? {
-                    DataValue::List(l) => l.len() + with_row_num,
-                    _ => bail!(CannotDetermineArity(
-                        n.to_string(),
-                        "invalid option 'fields' given, expect a list".to_string(),
-                        self.name.span
-                    )),
-                }
-            }
-            n => bail!(AlgoNotFoundError(n.to_string(), self.name.span)),
-        })
-    }
 
     pub(crate) fn get_impl(&self) -> Result<Box<dyn AlgoImpl>> {
         Ok(match &self.name.name as &str {
diff --git a/src/algo/pagerank.rs b/src/algo/pagerank.rs
index 84751f41..de49412b 100644
--- a/src/algo/pagerank.rs
+++ b/src/algo/pagerank.rs
@@ -4,11 +4,15 @@ use std::mem;
 use approx::AbsDiffEq;
 use miette::Result;
 use nalgebra::{Dynamic, OMatrix, U1};
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::AlgoImpl;
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -39,6 +43,15 @@ impl AlgoImpl for PageRank {
         }
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(2)
+    }
 }
 
 fn pagerank(
diff --git a/src/algo/prim.rs b/src/algo/prim.rs
index d7d6ab17..1d5c8d23 100644
--- a/src/algo/prim.rs
+++ b/src/algo/prim.rs
@@ -5,10 +5,13 @@ use miette::Diagnostic;
 use miette::Result;
 use ordered_float::OrderedFloat;
 use priority_queue::PriorityQueue;
+use smartstring::{LazyCompact, SmartString};
 use thiserror::Error;
 
 use crate::algo::AlgoImpl;
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
 use crate::parse::SourceSpan;
@@ -68,6 +71,15 @@ impl AlgoImpl for MinimumSpanningTreePrim {
         }
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(3)
+    }
 }
 
 fn prim(
diff --git a/src/algo/random_walk.rs b/src/algo/random_walk.rs
index 206cac13..46f96701 100644
--- a/src/algo/random_walk.rs
+++ b/src/algo/random_walk.rs
@@ -4,11 +4,15 @@ use itertools::Itertools;
 use miette::{bail, ensure, Result};
 use rand::distributions::WeightedIndex;
 use rand::prelude::*;
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::{AlgoImpl, BadExprValueError, NodeNotFoundError};
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -119,4 +123,13 @@ impl AlgoImpl for RandomWalk {
         }
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(3)
+    }
 }
diff --git a/src/algo/reorder_sort.rs b/src/algo/reorder_sort.rs
index c668968a..204eab6a 100644
--- a/src/algo/reorder_sort.rs
+++ b/src/algo/reorder_sort.rs
@@ -2,11 +2,13 @@ use std::collections::BTreeMap;
 
 use itertools::Itertools;
 use miette::{bail, Result};
+use smartstring::{LazyCompact, SmartString};
 
-use crate::algo::AlgoImpl;
+use crate::algo::{AlgoImpl, CannotDetermineArity};
 use crate::data::expr::Expr;
 use crate::data::functions::OP_LIST;
 use crate::data::program::{MagicAlgoApply, MagicSymbol, WrongAlgoOptionError};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
 use crate::parse::SourceSpan;
@@ -112,4 +114,31 @@ impl AlgoImpl for ReorderSort {
         }
         Ok(())
     }
+
+    fn arity(
+        &self,
+        opts: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        span: SourceSpan,
+    ) -> Result<usize> {
+        let out_opts = opts.get("out").ok_or_else(|| {
+            CannotDetermineArity(
+                "ReorderSort".to_string(),
+                "option 'out' not provided".to_string(),
+                span,
+            )
+        })?;
+        Ok(match out_opts {
+            Expr::Const {
+                val: DataValue::List(l),
+                ..
+            } => l.len() + 1,
+            Expr::Apply { op, args, .. } if **op == OP_LIST => args.len() + 1,
+            _ => bail!(CannotDetermineArity(
+                "ReorderSort".to_string(),
+                "invalid option 'out' given, expect a list".to_string(),
+                span
+            )),
+        })
+    }
 }
diff --git a/src/algo/shortest_path_dijkstra.rs b/src/algo/shortest_path_dijkstra.rs
index 5f9700fe..fa098ba2 100644
--- a/src/algo/shortest_path_dijkstra.rs
+++ b/src/algo/shortest_path_dijkstra.rs
@@ -8,11 +8,15 @@ use ordered_float::OrderedFloat;
 use priority_queue::PriorityQueue;
 use rayon::prelude::*;
 use smallvec::{smallvec, SmallVec};
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::AlgoImpl;
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -139,6 +143,15 @@ impl AlgoImpl for ShortestPathDijkstra {
 
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(4)
+    }
 }
 
 #[derive(PartialEq)]
diff --git a/src/algo/strongly_connected_components.rs b/src/algo/strongly_connected_components.rs
index 86139365..0364bc77 100644
--- a/src/algo/strongly_connected_components.rs
+++ b/src/algo/strongly_connected_components.rs
@@ -3,11 +3,15 @@ use std::collections::BTreeMap;
 
 use itertools::Itertools;
 use miette::Result;
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::AlgoImpl;
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -62,6 +66,15 @@ impl AlgoImpl for StronglyConnectedComponent {
 
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(2)
+    }
 }
 
 pub(crate) struct TarjanScc<'a> {
diff --git a/src/algo/top_sort.rs b/src/algo/top_sort.rs
index c58d459b..e81a00fc 100644
--- a/src/algo/top_sort.rs
+++ b/src/algo/top_sort.rs
@@ -1,11 +1,15 @@
 use std::collections::BTreeMap;
 
 use miette::Result;
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::AlgoImpl;
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -35,6 +39,15 @@ impl AlgoImpl for TopSort {
 
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(2)
+    }
 }
 
 pub(crate) fn kahn(graph: &[Vec<usize>], poison: Poison) -> Result<Vec<usize>> {
diff --git a/src/algo/triangles.rs b/src/algo/triangles.rs
index de4811cb..39b32b7c 100644
--- a/src/algo/triangles.rs
+++ b/src/algo/triangles.rs
@@ -2,11 +2,15 @@ use std::collections::{BTreeMap, BTreeSet};
 
 use miette::Result;
 use rayon::prelude::*;
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::AlgoImpl;
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -41,6 +45,15 @@ impl AlgoImpl for ClusteringCoefficients {
 
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(4)
+    }
 }
 
 fn clustering_coefficients(
diff --git a/src/algo/yen.rs b/src/algo/yen.rs
index 8ce16d6c..5f713593 100644
--- a/src/algo/yen.rs
+++ b/src/algo/yen.rs
@@ -3,12 +3,16 @@ use std::collections::{BTreeMap, BTreeSet};
 use itertools::Itertools;
 use miette::Result;
 use rayon::prelude::*;
+use smartstring::{LazyCompact, SmartString};
 
 use crate::algo::shortest_path_dijkstra::dijkstra;
 use crate::algo::AlgoImpl;
+use crate::data::expr::Expr;
 use crate::data::program::{MagicAlgoApply, MagicSymbol};
+use crate::data::symb::Symbol;
 use crate::data::tuple::Tuple;
 use crate::data::value::DataValue;
+use crate::parse::SourceSpan;
 use crate::runtime::db::Poison;
 use crate::runtime::in_mem::InMemRelation;
 use crate::runtime::transact::SessionTx;
@@ -96,6 +100,15 @@ impl AlgoImpl for KShortestPathYen {
         }
         Ok(())
     }
+
+    fn arity(
+        &self,
+        _options: &BTreeMap<SmartString<LazyCompact>, Expr>,
+        _rule_head: &[Symbol],
+        _span: SourceSpan,
+    ) -> Result<usize> {
+        Ok(4)
+    }
 }
 
 fn k_shortest_path_yen(
diff --git a/src/data/program.rs b/src/data/program.rs
index f95700fe..f7d4b985 100644
--- a/src/data/program.rs
+++ b/src/data/program.rs
@@ -2,13 +2,12 @@ use std::collections::btree_map::Entry;
 use std::collections::{BTreeMap, BTreeSet};
 use std::fmt::{Debug, Display, Formatter};
 
-use either::{Left, Right};
 use miette::{ensure, Diagnostic, Result};
 use smallvec::SmallVec;
 use smartstring::{LazyCompact, SmartString};
 use thiserror::Error;
 
-use crate::algo::AlgoHandle;
+use crate::algo::{AlgoHandle, AlgoImpl};
 use crate::data::aggr::Aggregation;
 use crate::data::expr::Expr;
 use crate::data::relation::StoredRelationMetadata;
@@ -193,18 +192,33 @@ impl InputRulesOrAlgo {
     }
 }
 
-#[derive(Clone)]
 pub(crate) struct AlgoApply {
     pub(crate) algo: AlgoHandle,
     pub(crate) rule_args: Vec<AlgoRuleArg>,
     pub(crate) options: BTreeMap<SmartString<LazyCompact>, Expr>,
     pub(crate) head: Vec<Symbol>,
+    pub(crate) arity: usize,
     pub(crate) span: SourceSpan,
+    pub(crate) algo_impl: Box<dyn AlgoImpl>,
+}
+
+impl Clone for AlgoApply {
+    fn clone(&self) -> Self {
+        Self {
+            algo: self.algo.clone(),
+            rule_args: self.rule_args.clone(),
+            options: self.options.clone(),
+            head: self.head.clone(),
+            arity: self.arity,
+            span: self.span.clone(),
+            algo_impl: self.algo.get_impl().unwrap(),
+        }
+    }
 }
 
 impl AlgoApply {
     pub(crate) fn arity(&self) -> Result<usize> {
-        self.algo.arity(Left(&self.rule_args), &self.options)
+        self.algo_impl.arity(&self.options, &self.head, self.span)
     }
 }
 
@@ -224,6 +238,7 @@ pub(crate) struct MagicAlgoApply {
     pub(crate) rule_args: Vec<MagicAlgoRuleArg>,
     pub(crate) options: BTreeMap<SmartString<LazyCompact>, Expr>,
     pub(crate) span: SourceSpan,
+    pub(crate) arity: usize,
 }
 
 #[derive(Error, Diagnostic, Debug)]
@@ -249,9 +264,6 @@ pub(crate) struct WrongAlgoOptionError {
 }
 
 impl MagicAlgoApply {
-    pub(crate) fn arity(&self) -> Result<usize> {
-        self.algo.arity(Right(&self.rule_args), &self.options)
-    }
     pub(crate) fn relation_with_min_len(
         &self,
         idx: usize,
@@ -879,7 +891,7 @@ impl MagicRulesOrAlgo {
     pub(crate) fn arity(&self) -> Result<usize> {
         Ok(match self {
             MagicRulesOrAlgo::Rules { rules } => rules.first().unwrap().head.len(),
-            MagicRulesOrAlgo::Algo { algo } => algo.arity()?,
+            MagicRulesOrAlgo::Algo { algo } => algo.arity,
         })
     }
     pub(crate) fn mut_rules(&mut self) -> Option<&mut Vec<MagicRule>> {
diff --git a/src/parse/query.rs b/src/parse/query.rs
index fe9ef6d5..60218d25 100644
--- a/src/parse/query.rs
+++ b/src/parse/query.rs
@@ -820,7 +820,6 @@ fn parse_algo_rule(
     }
 
     let algo = AlgoHandle::new(algo_name, name_pair.extract_span());
-    let algo_arity = algo.arity(Left(&rule_args), &options)?;
 
     #[derive(Debug, Error, Diagnostic)]
     #[error("Algorithm rule head arity mismatch")]
@@ -828,9 +827,12 @@ fn parse_algo_rule(
     #[diagnostic(help("Expected arity: {0}, number of arguments given: {1}"))]
     struct AlgoRuleHeadArityMismatch(usize, usize, #[label] SourceSpan);
 
+    let algo_impl = algo.get_impl()?;
+    let arity = algo_impl.arity(&options, &head, args_list_span)?;
+
     ensure!(
-        head.is_empty() || algo_arity == head.len(),
-        AlgoRuleHeadArityMismatch(algo_arity, head.len(), args_list_span)
+        head.is_empty() || arity == head.len(),
+        AlgoRuleHeadArityMismatch(arity, head.len(), args_list_span)
     );
 
     Ok((
@@ -840,7 +842,9 @@ fn parse_algo_rule(
             rule_args,
             options,
             head,
+            arity,
             span: args_list_span,
+            algo_impl,
         },
     ))
 }
diff --git a/src/query/magic.rs b/src/query/magic.rs
index 2b61ab54..5d5a14d1 100644
--- a/src/query/magic.rs
+++ b/src/query/magic.rs
@@ -374,6 +374,7 @@ impl NormalFormProgram {
                                     })
                                     .try_collect()?,
                                 options: algo_apply.options.clone(),
+                                arity: algo_apply.arity
                             },
                         },
                     );