Feat/fst order pred part3 & part4 (#457)

* support wildcard predicates in frontend

* suport wildcard predicate in podlang

* add validation test

* test full flow and apply some fixes

* fix clippy

* fix merge issues

* use desugared predicate

* Fix parsing of intro statement templates inside custom predicates

* Tidy up comments

* lang: handle wildcard predicate

* add unreachable message

---------

Co-authored-by: Rob Knight <mail@robknight.org.uk>

src/backends/plonky2/circuits/mainpod.rs

@@ -3255,8 +3255,12 @@ mod tests {
         use NativePredicate as NP;
         use StatementTmplBuilder as STB;
         let mut builder = CustomPredicateBatchBuilder::new(params.clone(), "batch".into());
-        let stb0 = STB::new(NP::Equal).arg(("id", "score")).arg(literal(42));
-        let stb1 = STB::new(NP::Equal).arg(("id", "key")).arg("secret");
+        let stb0 = STB::new_from_pred(NP::Equal)
+            .arg(("id", "score"))
+            .arg(literal(42));
+        let stb1 = STB::new_from_pred(NP::Equal)
+            .arg(("id", "key"))
+            .arg("secret");
         let _ = builder.predicate_and(
             "pred_and",
             &["id"],
@@ -3349,8 +3353,10 @@ mod tests {
         use NativePredicate as NP;
         use StatementTmplBuilder as STB;
         let mut builder = CustomPredicateBatchBuilder::new(params.clone(), "batch".into());
-        let stb0 = STB::new(NP::Equal).arg(("id", "score")).arg(literal(42));
-        let stb1 = STB::new(NP::Equal)
+        let stb0 = STB::new_from_pred(NP::Equal)
+            .arg(("id", "score"))
+            .arg(literal(42));
+        let stb1 = STB::new_from_pred(NP::Equal)
             .arg(("secret_id", "key"))
             .arg(("id", "score"));
         let _ = builder.predicate_and(

src/backends/plonky2/mainpod/mod.rs

@@ -1083,11 +1083,11 @@ pub mod tests {
         let vd_set = VDSet::new(&vds);
 
         let mut cpb_builder = CustomPredicateBatchBuilder::new(params.clone(), "cpb".into());
-        let stb0 = STB::new(NP::Contains)
+        let stb0 = STB::new_from_pred(NP::Contains)
             .arg("dict")
             .arg(literal("score"))
             .arg(literal(42));
-        let stb1 = STB::new(NP::Equal)
+        let stb1 = STB::new_from_pred(NP::Equal)
             .arg(("secret_dict", "key"))
             .arg(("dict", "score"));
         let _ = cpb_builder.predicate_and(

src/frontend/custom.rs

@@ -7,7 +7,7 @@ use crate::{
     frontend::{AnchoredKey, Error, Result, Statement, StatementArg},
     middleware::{
         self, hash_str, CustomPredicate, CustomPredicateBatch, Hash, Key, NativePredicate, Params,
-        Predicate, PredicateOrWildcard, StatementTmpl, StatementTmplArg, ToFields, Value, Wildcard,
+        Predicate, StatementTmpl, StatementTmplArg, ToFields, Value, Wildcard,
     },
 };
 
@@ -41,16 +41,34 @@ pub fn literal(v: impl Into<Value>) -> BuilderArg {
     BuilderArg::Literal(v.into())
 }
 
+#[derive(Clone, Debug)]
+pub enum PredicateOrWildcard {
+    Predicate(Predicate),
+    Wildcard(String),
+}
+
 #[derive(Clone)]
 pub struct StatementTmplBuilder {
-    pub(crate) predicate: Predicate,
+    pub(crate) pred_or_wc: PredicateOrWildcard,
     pub(crate) args: Vec<BuilderArg>,
 }
 
 impl StatementTmplBuilder {
-    pub fn new(p: impl Into<Predicate>) -> StatementTmplBuilder {
+    pub fn new_from_pred(p: impl Into<Predicate>) -> StatementTmplBuilder {
         StatementTmplBuilder {
-            predicate: p.into(),
+            pred_or_wc: PredicateOrWildcard::Predicate(p.into()),
+            args: Vec::new(),
+        }
+    }
+    pub fn new_from_wc(p: impl Into<String>) -> StatementTmplBuilder {
+        StatementTmplBuilder {
+            pred_or_wc: PredicateOrWildcard::Wildcard(p.into()),
+            args: Vec::new(),
+        }
+    }
+    pub fn new(pred_or_wc: PredicateOrWildcard) -> StatementTmplBuilder {
+        StatementTmplBuilder {
+            pred_or_wc,
             args: Vec::new(),
         }
     }
@@ -62,68 +80,48 @@ impl StatementTmplBuilder {
 
     /// Desugar the predicate to a simpler form
     /// Should mirror the logic in `MainPodBuilder::lower_op`
-    pub(crate) fn desugar(self) -> StatementTmplBuilder {
-        match self.predicate {
-            Predicate::Native(NativePredicate::Gt) => {
-                let mut stb = StatementTmplBuilder {
-                    predicate: Predicate::Native(NativePredicate::Lt),
-                    args: self.args,
+    pub(crate) fn desugar(mut self) -> StatementTmplBuilder {
+        let pred = match self.pred_or_wc {
+            PredicateOrWildcard::Predicate(p) => p,
+            PredicateOrWildcard::Wildcard(_) => return self,
         };
-                stb.args.swap(0, 1);
-                stb
+        let pred = match pred {
+            Predicate::Native(nat_pred) => Predicate::Native(match nat_pred {
+                NativePredicate::Gt => {
+                    self.args.swap(0, 1);
+                    NativePredicate::Lt
                 }
-            Predicate::Native(NativePredicate::GtEq) => {
-                let mut stb = StatementTmplBuilder {
-                    predicate: Predicate::Native(NativePredicate::LtEq),
-                    args: self.args,
+                NativePredicate::GtEq => {
+                    self.args.swap(0, 1);
+                    NativePredicate::LtEq
+                }
+                NativePredicate::ArrayContains | NativePredicate::DictContains => {
+                    NativePredicate::Contains
+                }
+                NativePredicate::DictNotContains | NativePredicate::SetNotContains => {
+                    NativePredicate::NotContains
+                }
+                NativePredicate::SetContains => {
+                    self.args.push(self.args[1].clone());
+                    NativePredicate::Contains
+                }
+                NativePredicate::DictInsert => NativePredicate::ContainerInsert,
+                NativePredicate::SetInsert => {
+                    self.args.push(self.args[2].clone());
+                    NativePredicate::ContainerInsert
+                }
+                NativePredicate::DictUpdate | NativePredicate::ArrayUpdate => {
+                    NativePredicate::ContainerUpdate
+                }
+                NativePredicate::DictDelete => NativePredicate::ContainerDelete,
+                NativePredicate::SetDelete => NativePredicate::ContainerDelete,
+                _ => nat_pred,
+            }),
+            _ => pred,
         };
-                stb.args.swap(0, 1);
-                stb
-            }
-            Predicate::Native(NativePredicate::ArrayContains)
-            | Predicate::Native(NativePredicate::DictContains) => StatementTmplBuilder {
-                predicate: Predicate::Native(NativePredicate::Contains),
-                args: self.args,
-            },
-            Predicate::Native(NativePredicate::DictNotContains)
-            | Predicate::Native(NativePredicate::SetNotContains) => StatementTmplBuilder {
-                predicate: Predicate::Native(NativePredicate::NotContains),
-                args: self.args,
-            },
-            Predicate::Native(NativePredicate::SetContains) => {
-                let mut new_args = self.args.clone();
-                new_args.push(self.args[1].clone());
         StatementTmplBuilder {
-                    predicate: Predicate::Native(NativePredicate::Contains),
-                    args: new_args,
-                }
-            }
-            Predicate::Native(NativePredicate::DictInsert) => StatementTmplBuilder {
-                predicate: Predicate::Native(NativePredicate::ContainerInsert),
+            pred_or_wc: PredicateOrWildcard::Predicate(pred),
             args: self.args,
-            },
-            Predicate::Native(NativePredicate::SetInsert) => {
-                let mut new_args = self.args.clone();
-                new_args.push(self.args[2].clone());
-                StatementTmplBuilder {
-                    predicate: Predicate::Native(NativePredicate::ContainerInsert),
-                    args: new_args,
-                }
-            }
-            Predicate::Native(NativePredicate::DictUpdate)
-            | Predicate::Native(NativePredicate::ArrayUpdate) => StatementTmplBuilder {
-                predicate: Predicate::Native(NativePredicate::ContainerUpdate),
-                args: self.args,
-            },
-            Predicate::Native(NativePredicate::DictDelete) => StatementTmplBuilder {
-                predicate: Predicate::Native(NativePredicate::ContainerDelete),
-                args: self.args,
-            },
-            Predicate::Native(NativePredicate::SetDelete) => StatementTmplBuilder {
-                predicate: Predicate::Native(NativePredicate::ContainerDelete),
-                args: self.args,
-            },
-            _ => self,
         }
     }
 }
@@ -200,7 +198,7 @@ impl CustomPredicateBatchBuilder {
             .iter()
             .map(|sb| {
                 let stb = sb.clone().desugar();
-                let args = stb
+                let st_tmpl_args = stb
                     .args
                     .iter()
                     .map(|a| {
@@ -216,10 +214,17 @@ impl CustomPredicateBatchBuilder {
                         })
                     })
                     .collect::<Result<_>>()?;
+                let pred_or_wc = match stb.pred_or_wc {
+                    PredicateOrWildcard::Predicate(p) => {
+                        middleware::PredicateOrWildcard::Predicate(p)
+                    }
+                    PredicateOrWildcard::Wildcard(v) => middleware::PredicateOrWildcard::Wildcard(
+                        resolve_wildcard(args, priv_args, &v)?,
+                    ),
+                };
                 Ok(StatementTmpl {
-                    // TODO: Support wildcard
-                    pred_or_wc: PredicateOrWildcard::Predicate(stb.predicate.clone()),
-                    args,
+                    pred_or_wc,
+                    args: st_tmpl_args,
                 })
             })
             .collect::<Result<_>>()?;
@@ -299,7 +304,7 @@ mod tests {
         let vd_set = &*MOCK_VD_SET;
         let mut builder = CustomPredicateBatchBuilder::new(params.clone(), "gt_custom_pred".into());
 
-        let gt_stb = StatementTmplBuilder::new(NativePredicate::Gt)
+        let gt_stb = StatementTmplBuilder::new_from_pred(NativePredicate::Gt)
             .arg("s1")
             .arg("s2");
 
@@ -344,7 +349,7 @@ mod tests {
         let mut builder =
             CustomPredicateBatchBuilder::new(params.clone(), "set_contains_custom_pred".into());
 
-        let set_contains_stb = StatementTmplBuilder::new(NativePredicate::SetContains)
+        let set_contains_stb = StatementTmplBuilder::new_from_pred(NativePredicate::SetContains)
             .arg("s1")
             .arg("s2");
 

src/frontend/error.rs

@@ -1,34 +1,13 @@
 use std::{backtrace::Backtrace, fmt::Debug};
 
-use crate::middleware::{BackendError, Statement, StatementTmpl, Value};
+use crate::middleware::BackendError;
 
 pub type Result<T, E = Error> = core::result::Result<T, E>;
 
-fn display_wc_map(wc_map: &[Option<Value>]) -> String {
-    let mut out = String::new();
-    use std::fmt::Write;
-    for (i, v) in wc_map.iter().enumerate() {
-        write!(out, "- {}: ", i).unwrap();
-        if let Some(v) = v {
-            writeln!(out, "{}", v).unwrap();
-        } else {
-            writeln!(out, "none").unwrap();
-        }
-    }
-    out
-}
-
 #[derive(thiserror::Error, Debug)]
 pub enum InnerError {
     #[error("{0} {1} is over the limit {2}")]
     MaxLength(String, usize, usize),
-    #[error("{0} doesn't match {1:#}.\nWildcard map:\n{map}\nInternal error: {3}", map=display_wc_map(.2))]
-    StatementsDontMatch(
-        Statement,
-        StatementTmpl,
-        Vec<Option<Value>>,
-        crate::middleware::Error,
-    ),
     #[error("invalid arguments to {0} operation")]
     OpInvalidArgs(String),
     #[error("Podlang parse error: {0}")]
@@ -99,14 +78,6 @@ impl Error {
     pub(crate) fn op_invalid_args(s: String) -> Self {
         new!(OpInvalidArgs(s))
     }
-    pub(crate) fn statements_dont_match(
-        s0: Statement,
-        s1: StatementTmpl,
-        wc_map: Vec<Option<Value>>,
-        mid_error: crate::middleware::Error,
-    ) -> Self {
-        new!(StatementsDontMatch(s0, s1, wc_map, mid_error))
-    }
     pub(crate) fn max_length(obj: String, found: usize, expect: usize) -> Self {
         new!(MaxLength(obj, found, expect))
     }

src/frontend/mod.rs

@@ -13,10 +13,10 @@ use serde::{Deserialize, Serialize};
 pub use serialization::SerializedMainPod;
 
 use crate::middleware::{
-    self, check_custom_pred, check_st_tmpl, containers::Dictionary, hash_op, max_op, prod_op,
-    sum_op, AnchoredKey, Hash, Key, MainPodInputs, MainPodProver, NativeOperation, OperationAux,
-    OperationType, Params, PublicKey, RawValue, Signature, Signer, Statement, StatementArg, VDSet,
-    Value, ValueRef,
+    self, check_custom_pred, containers::Dictionary, fill_wildcard_values, hash_op, max_op,
+    prod_op, sum_op, AnchoredKey, Hash, Key, MainPodInputs, MainPodProver, NativeOperation,
+    OperationAux, OperationType, Params, PublicKey, RawValue, Signature, Signer, Statement,
+    StatementArg, VDSet, Value, ValueRef,
 };
 
 mod custom;
@@ -600,21 +600,7 @@ impl MainPodBuilder {
                     }
                     wildcard_map[index] = Some(value);
                 }
-                for (st_tmpl, st) in pred.statements.iter().zip(args.iter()) {
-                    let st_args = st.args();
-                    for (st_tmpl_arg, st_arg) in st_tmpl.args.iter().zip(&st_args) {
-                        if let Err(st_tmpl_check_error) =
-                            check_st_tmpl(st_tmpl_arg, st_arg, &mut wildcard_map)
-                        {
-                            return Err(Error::statements_dont_match(
-                                st.clone(),
-                                st_tmpl.clone(),
-                                wildcard_map,
-                                st_tmpl_check_error,
-                            ));
-                        }
-                    }
-                }
+                fill_wildcard_values(&self.params, pred, &args, &mut wildcard_map)?;
                 let v_default = Value::from(0);
                 let st_args: Vec<_> = wildcard_map
                     .into_iter()
@@ -817,7 +803,8 @@ pub mod tests {
     use super::*;
     use crate::{
         backends::plonky2::{
-            mock::mainpod::MockProver, primitives::ec::schnorr::SecretKey, signer::Signer,
+            basetypes::DEFAULT_VD_SET, mainpod::Prover, mock::mainpod::MockProver,
+            primitives::ec::schnorr::SecretKey, signer::Signer,
         },
         dict,
         examples::{
@@ -1423,6 +1410,75 @@ pub mod tests {
         Ok(())
     }
 
+    #[test]
+    fn test_wildcard_predicate() -> Result<()> {
+        let mock = true;
+        let params = Params::default();
+
+        let mock_prover = MockProver {};
+        let real_prover = Prover {};
+        let (vd_set, prover): (_, &dyn MainPodProver) = if mock {
+            (&VDSet::new(&[]), &mock_prover)
+        } else {
+            println!("Prebuilding circuits to calculate vd_set...");
+            let vd_set = &*DEFAULT_VD_SET;
+            println!("vd_set calculation complete");
+            (vd_set, &real_prover)
+        };
+
+        let input = r#"
+        Test(a, b, private: c) = AND(
+            Equal(a, 5)
+            b(1, 5)
+            c(6, 3)
+        )
+        "#;
+        let batch = parse(input, &params, &[])
+            .unwrap()
+            .first_batch()
+            .unwrap()
+            .clone();
+        let pred_test = batch.predicate_ref_by_name("Test").unwrap();
+
+        let mut builder = MainPodBuilder::new(&params, vd_set);
+        let st0 = builder.priv_op(Operation::eq(5, 5)).unwrap();
+        let st1 = builder.priv_op(Operation::lt(1, 5)).unwrap();
+        let st2 = builder.priv_op(Operation::ne(6, 3)).unwrap();
+        let _st = builder
+            .op(true, vec![], Operation::custom(pred_test, [st0, st1, st2]))
+            .unwrap();
+
+        let pod = builder.prove(prover).unwrap();
+        pod.pod.verify().unwrap();
+
+        let input = r#"
+        Test(a, b, private: c) = OR(
+            Equal(a, 5)
+            b(1, 5)
+            c(6, 3)
+        )
+        "#;
+        let batch = parse(input, &params, &[])
+            .unwrap()
+            .first_batch()
+            .unwrap()
+            .clone();
+        let pred_test = batch.predicate_ref_by_name("Test").unwrap();
+
+        let mut builder = MainPodBuilder::new(&params, vd_set);
+        let st0 = Statement::None;
+        let st1 = builder.priv_op(Operation::lt(1, 5)).unwrap();
+        let st2 = Statement::None;
+        let _st = builder
+            .op(true, vec![], Operation::custom(pred_test, [st0, st1, st2]))
+            .unwrap();
+
+        let pod = builder.prove(prover).unwrap();
+        pod.pod.verify().unwrap();
+
+        Ok(())
+    }
+
     #[test]
     fn test_apply_predicate_e2e() -> Result<()> {
         // End-to-end test of apply_predicate with MockProver

src/lang/error.rs

@@ -88,6 +88,9 @@ pub enum ValidationError {
         first_span: Option<Span>,
         second_span: Option<Span>,
     },
+
+    #[error("Wildcard '{name}' collides with a predicate name")]
+    WildcardPredicateNameCollision { name: String },
 }
 
 /// Lowering errors from frontend AST lowering to middleware

src/lang/frontend_ast_batch.rs

@@ -619,6 +619,7 @@ fn build_single_batch(
                     batch_idx,
                     reference_map,
                     existing_batches,
+                    name,
                     symbols,
                 )
             })
@@ -648,6 +649,7 @@ fn build_statement_with_resolved_refs(
     current_batch_idx: usize,
     reference_map: &HashMap<String, (usize, usize)>,
     existing_batches: &[Arc<CustomPredicateBatch>],
+    custom_predicate_name: &str, // custom pred that defines this statement template
     symbols: &SymbolTable,
 ) -> Result<StatementTmplBuilder, BatchingError> {
     let callee_name = &stmt.predicate.name;
@@ -657,16 +659,17 @@ fn build_statement_with_resolved_refs(
         current_batch_idx,
         reference_map,
         existing_batches,
+        custom_predicate_name,
     };
 
-    let predicate = resolve_predicate(callee_name, symbols, &context).ok_or_else(|| {
+    let pred_or_wc = resolve_predicate(callee_name, symbols, &context).ok_or_else(|| {
         BatchingError::Internal {
             message: format!("Unknown predicate reference: '{}'", callee_name),
         }
     })?;
 
     // Build the statement template
-    let mut builder = StatementTmplBuilder::new(predicate);
+    let mut builder = StatementTmplBuilder::new(pred_or_wc);
 
     for arg in &stmt.args {
         builder = builder.arg(lower_statement_arg(arg));

src/lang/frontend_ast_lower.rs

@@ -10,7 +10,7 @@ use std::{
 };
 
 use crate::{
-    frontend::{BuilderArg, StatementTmplBuilder},
+    frontend::{BuilderArg, PredicateOrWildcard, StatementTmplBuilder},
     lang::{
         frontend_ast::*,
         frontend_ast_batch::{self, PredicateBatches},
@@ -18,8 +18,8 @@ use crate::{
         frontend_ast_validate::{PredicateKind, SymbolTable, ValidatedAST},
     },
     middleware::{
-        containers, CustomPredicateBatch, CustomPredicateRef, IntroPredicateRef, Key,
-        NativePredicate, Params, Predicate, PredicateOrWildcard, StatementTmpl as MWStatementTmpl,
+        self, containers, CustomPredicateBatch, CustomPredicateRef, IntroPredicateRef, Key,
+        NativePredicate, Params, Predicate, StatementTmpl as MWStatementTmpl,
         StatementTmplArg as MWStatementTmplArg, Value, Wildcard,
     },
 };
@@ -35,6 +35,7 @@ pub enum ResolutionContext<'a> {
         current_batch_idx: usize,
         reference_map: &'a HashMap<String, (usize, usize)>,
         existing_batches: &'a [Arc<CustomPredicateBatch>],
+        custom_predicate_name: &'a str,
     },
 }
 
@@ -43,10 +44,23 @@ pub fn resolve_predicate(
     pred_name: &str,
     symbols: &SymbolTable,
     context: &ResolutionContext,
-) -> Option<Predicate> {
-    // 1. Try native predicate first
+) -> Option<PredicateOrWildcard> {
+    // 0. Try wildcard first
+    if let ResolutionContext::Batch {
+        custom_predicate_name,
+        ..
+    } = context
+    {
+        if let Some(wc_scope) = symbols.wildcard_scopes.get(*custom_predicate_name) {
+            if wc_scope.wildcards.contains_key(pred_name) {
+                return Some(PredicateOrWildcard::Wildcard(pred_name.to_string()));
+            }
+        }
+    }
+
+    // 1. Try native predicate second
     if let Ok(native) = NativePredicate::from_str(pred_name) {
-        return Some(Predicate::Native(native));
+        return Some(PredicateOrWildcard::Predicate(Predicate::Native(native)));
     }
 
     // 2. Look up in symbol table
@@ -64,6 +78,7 @@ pub fn resolve_predicate(
                     current_batch_idx,
                     reference_map,
                     existing_batches,
+                    ..
                 } => resolve_local_predicate(
                     pred_name,
                     *current_batch_idx,
@@ -85,7 +100,7 @@ pub fn resolve_predicate(
                 verifier_data_hash: *verifier_data_hash,
             }),
         };
-        return Some(predicate);
+        return Some(PredicateOrWildcard::Predicate(predicate));
     }
 
     // 3. In batch context, also check reference_map for split chain pieces
@@ -94,6 +109,7 @@ pub fn resolve_predicate(
         current_batch_idx,
         reference_map,
         existing_batches,
+        ..
     } = context
     {
         if reference_map.contains_key(pred_name) {
@@ -102,7 +118,8 @@ pub fn resolve_predicate(
                 *current_batch_idx,
                 reference_map,
                 existing_batches,
-            );
+            )
+            .map(PredicateOrWildcard::Predicate);
         }
     }
 
@@ -328,7 +345,7 @@ impl<'a> Lowerer<'a> {
         })?;
 
         // Create a builder with the resolved predicate and desugar
-        let mut builder = StatementTmplBuilder::new(predicate);
+        let mut builder = StatementTmplBuilder::new(predicate.clone());
         for arg in &stmt.args {
             let builder_arg = lower_statement_arg(arg);
             builder = builder.arg(builder_arg);
@@ -356,9 +373,14 @@ impl<'a> Lowerer<'a> {
             mw_args.push(mw_arg);
         }
 
+        let predicate = match desugared.pred_or_wc {
+            PredicateOrWildcard::Predicate(p) => p,
+            PredicateOrWildcard::Wildcard(_) => {
+                unreachable!("wildcard predicates aren't considered in requests")
+            }
+        };
         Ok(MWStatementTmpl {
-            // TODO: Support wildcard
-            pred_or_wc: PredicateOrWildcard::Predicate(desugared.predicate),
+            pred_or_wc: middleware::PredicateOrWildcard::Predicate(predicate),
             args: mw_args,
         })
     }
@@ -424,7 +446,6 @@ impl<'a> Lowerer<'a> {
             let result = frontend_ast_split::split_predicate_if_needed(pred, self.params)?;
             split_results.push(result);
         }
-
         Ok(split_results)
     }
 }
@@ -601,7 +622,7 @@ mod tests {
         // Should be BatchSelf(0) referring to pred1
         assert!(matches!(
             stmt.pred_or_wc,
-            PredicateOrWildcard::Predicate(Predicate::BatchSelf(0))
+            middleware::PredicateOrWildcard::Predicate(Predicate::BatchSelf(0))
         ));
     }
 
@@ -639,10 +660,25 @@ mod tests {
         // Should desugar to the Contains predicate
         assert!(matches!(
             stmt.pred_or_wc,
-            PredicateOrWildcard::Predicate(Predicate::Native(NativePredicate::Contains))
+            middleware::PredicateOrWildcard::Predicate(Predicate::Native(
+                NativePredicate::Contains
+            ))
         ));
     }
 
+    #[test]
+    fn test_wc_pred() {
+        let input = r#"
+            my_pred(X, DynPred) = AND (
+                Equal(X["pred"], DynPred)
+                DynPred(X)
+            )
+        "#;
+
+        let params = Params::default();
+        parse_validate_and_lower(input, &params).unwrap();
+    }
+
     #[test]
     fn test_multi_batch_packing() {
         // Create more predicates than fit in a single batch
@@ -749,7 +785,7 @@ mod tests {
         // Verify the second statement is an intro predicate reference
         let intro_stmt = &pred.statements()[1];
         match intro_stmt.pred_or_wc() {
-            PredicateOrWildcard::Predicate(Predicate::Intro(intro_ref)) => {
+            middleware::PredicateOrWildcard::Predicate(Predicate::Intro(intro_ref)) => {
                 assert_eq!(intro_ref.name, "external_check");
                 assert_eq!(intro_ref.args_len, 1);
                 assert_eq!(intro_ref.verifier_data_hash, EMPTY_HASH);

src/lang/frontend_ast_validate.rs

@@ -3,7 +3,11 @@
 //! This module provides semantic validation for parsed AST documents,
 //! including name resolution, arity checking, and wildcard validation.
 
-use std::{collections::HashMap, str::FromStr, sync::Arc};
+use std::{
+    collections::{HashMap, HashSet},
+    str::FromStr,
+    sync::Arc,
+};
 
 use hex::ToHex;
 
@@ -411,6 +415,21 @@ impl Validator {
         Ok(())
     }
 
+    /// Validate that no wildcard name collides with a predicate name to avoid ambiguity when using
+    /// wildcard predicates.
+    fn validate_wildcard_names(&self, names: &HashSet<&String>) -> Result<(), ValidationError> {
+        for name in names {
+            if NativePredicate::from_str(name).is_ok()
+                || self.symbols.predicates.contains_key(*name)
+            {
+                return Err(ValidationError::WildcardPredicateNameCollision {
+                    name: (*name).clone(),
+                });
+            }
+        }
+        Ok(())
+    }
+
     fn validate_statement(
         &self,
         stmt: &StatementTmpl,
@@ -418,18 +437,26 @@ impl Validator {
     ) -> Result<(), ValidationError> {
         let pred_name = &stmt.predicate.name;
 
+        let wc_names = match wildcard_context {
+            Some((_, wc_scope)) => wc_scope.wildcards.keys().collect(),
+            None => HashSet::new(),
+        };
+        self.validate_wildcard_names(&wc_names)?;
+
         // Check if predicate exists
         let pred_info = if let Ok(native) = NativePredicate::from_str(pred_name) {
             // Native predicate
-            PredicateInfo {
+            Some(PredicateInfo {
                 kind: PredicateKind::Native(native),
                 arity: native.arity(),
                 public_arity: native.arity(),
                 source_span: None,
-            }
+            })
         } else if let Some(info) = self.symbols.predicates.get(pred_name) {
             // Custom or imported predicate
-            info.clone()
+            Some(info.clone())
+        } else if wc_names.contains(pred_name) {
+            None
         } else {
             return Err(ValidationError::UndefinedPredicate {
                 name: pred_name.clone(),
@@ -437,8 +464,8 @@ impl Validator {
             });
         };
 
+        if let Some(ref pred_info) = pred_info {
             let expected_arity = pred_info.public_arity;
-
             if stmt.args.len() != expected_arity {
                 return Err(ValidationError::ArgumentCountMismatch {
                     predicate: pred_name.clone(),
@@ -447,9 +474,10 @@ impl Validator {
                     span: stmt.span,
                 });
             }
+        }
 
         // Validate arguments
-        self.validate_statement_args(stmt, &pred_info, wildcard_context)?;
+        self.validate_statement_args(stmt, pred_info.as_ref(), wildcard_context)?;
 
         Ok(())
     }
@@ -457,13 +485,13 @@ impl Validator {
     fn validate_statement_args(
         &self,
         stmt: &StatementTmpl,
-        pred_info: &PredicateInfo,
+        pred_info: Option<&PredicateInfo>,
         wildcard_context: Option<(&str, &WildcardScope)>,
     ) -> Result<(), ValidationError> {
         // For custom predicates, only wildcards and literals are allowed
         if matches!(
-            pred_info.kind,
-            PredicateKind::Custom { .. } | PredicateKind::BatchImported { .. }
+            pred_info.map(|i| &i.kind),
+            Some(PredicateKind::Custom { .. }) | Some(PredicateKind::BatchImported { .. })
         ) {
             for arg in &stmt.args {
                 match arg {
@@ -631,6 +659,18 @@ mod tests {
         ));
     }
 
+    #[test]
+    fn test_wildcard_predicate_collision() {
+        let input = r#"
+            my_pred(A, Lt) = AND (Equal(A["x"], Lt))
+        "#;
+        let result = parse_and_validate(input, &[]);
+        assert!(matches!(
+            result,
+            Err(ValidationError::WildcardPredicateNameCollision { .. })
+        ));
+    }
+
     #[test]
     fn test_custom_predicate_with_anchored_key() {
         let input = r#"

src/middleware/error.rs

@@ -3,12 +3,26 @@
 use std::{backtrace::Backtrace, fmt::Debug};
 
 use crate::middleware::{
-    CustomPredicate, Hash, Key, Operation, Predicate, Statement, StatementArg, StatementTmplArg,
-    Value, Wildcard,
+    CustomPredicate, Hash, Key, Operation, Predicate, Statement, StatementArg, StatementTmpl,
+    StatementTmplArg, Value, Wildcard,
 };
 
 pub type Result<T, E = Error> = core::result::Result<T, E>;
 
+fn display_wc_map(wc_map: &[Option<Value>]) -> String {
+    let mut out = String::new();
+    use std::fmt::Write;
+    for (i, v) in wc_map.iter().enumerate() {
+        write!(out, "- {}: ", i).unwrap();
+        if let Some(v) = v {
+            writeln!(out, "{}", v).unwrap();
+        } else {
+            writeln!(out, "none").unwrap();
+        }
+    }
+    out
+}
+
 #[derive(Debug, thiserror::Error)]
 pub enum MiddlewareInnerError {
     #[error("incorrect statement args")]
@@ -33,6 +47,13 @@ pub enum MiddlewareInnerError {
     MismatchedStatementWildcardPredicate(Value, Value, Predicate),
     #[error("Value {0} does not match argument {1} with index {2} in the following custom predicate:\n{3}")]
     MismatchedWildcardValueAndStatementArg(Value, Value, usize, CustomPredicate),
+    #[error("{0} doesn't match {1:#}.\nWildcard map:\n{map}\nInternal error: {3}", map=display_wc_map(.2))]
+    StatementsDontMatch(
+        Statement,
+        StatementTmpl,
+        Vec<Option<Value>>,
+        crate::middleware::Error,
+    ),
     #[error(
         "None of the statement templates of the following custom predicate have been matched:\n{0}"
     )]
@@ -132,6 +153,14 @@ impl Error {
             wc_value, st_arg, arg_index, pred
         ))
     }
+    pub(crate) fn statements_dont_match(
+        s0: Statement,
+        s1: StatementTmpl,
+        wc_map: Vec<Option<Value>>,
+        mid_error: crate::middleware::Error,
+    ) -> Self {
+        new!(StatementsDontMatch(s0, s1, wc_map, mid_error))
+    }
     pub(crate) fn unsatisfied_custom_predicate_disjunction(pred: CustomPredicate) -> Self {
         new!(UnsatisfiedCustomPredicateDisjunction(pred))
     }

src/middleware/operation.rs

@@ -611,17 +611,21 @@ pub fn fill_wildcard_values(
     wildcard_map: &mut [Option<Value>],
 ) -> Result<()> {
     for (st_tmpl, st) in pred.statements.iter().zip(args) {
-        let st_args = st.args();
         if let PredicateOrWildcard::Wildcard(wc) = &st_tmpl.pred_or_wc {
             wc_check_or_set(Value::from(st.predicate().hash(params)), wc, wildcard_map)?;
         }
-        st_tmpl
-            .args
-            .iter()
-            .zip(&st_args)
-            .try_for_each(|(st_tmpl_arg, st_arg)| {
-                check_st_tmpl(st_tmpl_arg, st_arg, wildcard_map)
-            })?;
+        let st_args = st.args();
+
+        for (st_tmpl_arg, st_arg) in st_tmpl.args.iter().zip(&st_args) {
+            if let Err(st_tmpl_check_error) = check_st_tmpl(st_tmpl_arg, st_arg, wildcard_map) {
+                return Err(Error::statements_dont_match(
+                    st.clone(),
+                    st_tmpl.clone(),
+                    wildcard_map.to_vec(),
+                    st_tmpl_check_error,
+                ));
+            }
+        }
     }
     Ok(())
 }
@@ -741,16 +745,7 @@ pub(crate) fn check_custom_pred(
     for (st_tmpl, st) in pred.statements.iter().zip(args) {
         // For `or` predicates, only one statement needs to match the template.
         // The rest of the statements can be `None`.
-        let expected_pred_is_none = match &st_tmpl.pred_or_wc {
-            PredicateOrWildcard::Predicate(st_tmpl_pred) => {
-                *st_tmpl_pred == Predicate::Native(NativePredicate::None)
-            }
-            PredicateOrWildcard::Wildcard(wc) => {
-                wc_values[wc.index]
-                    == Value::from(Predicate::Native(NativePredicate::None).hash(params))
-            }
-        };
-        if !pred.conjunction && matches!(st, Statement::None) && !expected_pred_is_none {
+        if !pred.conjunction && matches!(st, Statement::None) {
             continue;
         }
         check_custom_pred_argument(params, custom_pred_ref, st_tmpl, st, &wc_values)?;