diff --git a/ndc_analyser/src/analyser/assignments.rs b/ndc_analyser/src/analyser/assignments.rs
index a2f2b0a1..13d0abb8 100644
--- a/ndc_analyser/src/analyser/assignments.rs
+++ b/ndc_analyser/src/analyser/assignments.rs
@@ -296,30 +296,9 @@ impl Analyser {
             {
                 self.check_write(stored_type, value_type, span, Some(lvalue.id));
             }
-            AssignmentTarget::Member { .. } => {
+            AssignmentTarget::Member { .. } | AssignmentTarget::Index { .. } => {
                 self.check_write(stored_type, value_type, span, Some(lvalue.id));
             }
-            AssignmentTarget::Index { index, .. } => {
-                if self.accepts_write(stored_type, value_type, Some(lvalue.id)) {
-                    return;
-                }
-                // `xs[0..2] = (1, 2)` stores the tuple's elements.
-                let is_slice = self
-                    .result
-                    .analysis
-                    .expr_types
-                    .get(&index.id)
-                    .is_some_and(Self::index_type_is_slice);
-                if is_slice
-                    && let Some(stored_element) =
-                        self.vars.resolve(stored_type).index_element_type()
-                    && let Some(value_element) = value_type.sequence_element_type()
-                    && self.accepts_write(&stored_element, &value_element, None)
-                {
-                    return;
-                }
-                self.emit_rejected_write(stored_type, value_type, span);
-            }
             // Each target gets the element unpacked for it, as in a `let`.
             AssignmentTarget::Sequence(targets) => {
                 let StaticType::Tuple(stored_types) = stored_type else {
diff --git a/ndc_analyser/src/analyser/calls.rs b/ndc_analyser/src/analyser/calls.rs
index 18c9b38c..1623e6db 100644
--- a/ndc_analyser/src/analyser/calls.rs
+++ b/ndc_analyser/src/analyser/calls.rs
@@ -1,5 +1,5 @@
 use super::Analyser;
-use super::solver::{CallNodes, CallSite, Constraint};
+use super::solver::{CallNodes, CallSite};
 use crate::error::AnalysisError;
 use crate::overloads::{CallKind, Overloads};
 use itertools::Itertools;
@@ -124,20 +124,11 @@ impl Analyser {
                     ..
                 } => {
                     if let Some((typ, parameters)) = self.bind_signature(&callee, &arguments) {
-                        for (node, expected) in
-                            self.expected_of_any(&parameters, &arguments, &nodes)
-                        {
-                            self.expect(node, expected);
-                        }
-                        for (sequence, element) in
-                            self.iterations_waited_for(&parameters, &arguments)
-                        {
-                            self.wait(Constraint::Iterate {
-                                sequence,
-                                element,
-                                span,
-                            });
-                        }
+                        let checks = self.expected_of_any(&parameters, &arguments, &nodes);
+                        self.pending.checks.extend(checks);
+                        let iterations = self.iterations_waited_for(&parameters, &arguments);
+                        self.pending.iterations.extend(iterations);
+                        self.flush_copies(None, span);
                         typ
                     } else {
                         let arguments = arguments
diff --git a/ndc_analyser/src/analyser/declarations.rs b/ndc_analyser/src/analyser/declarations.rs
index 295c3a24..8d205185 100644
--- a/ndc_analyser/src/analyser/declarations.rs
+++ b/ndc_analyser/src/analyser/declarations.rs
@@ -20,6 +20,8 @@ pub(super) struct FunctionDeclaration<'a> {
     pub parameters: &'a [FunctionParameter],
     pub body: &'a ExpressionLocation,
     pub return_annotation: Option<&'a TypeExpr>,
+    /// Whether it's a `pure fn`, whose results are cached.
+    pub pure: bool,
     pub span: Span,
 }
 
@@ -40,6 +42,7 @@ impl Analyser {
             parameters,
             body,
             return_annotation,
+            pure,
             span,
         } = function;
         let declared = name.map(|name| (name, self.resolver.declared_symbol(id)));
@@ -164,7 +167,7 @@ impl Analyser {
                 self.vars.leave_level();
                 self.declaring = None;
                 self.declared_in_batch.insert(symbol);
-                let typ = self.generalize(symbol, &signature, id, [first_use, first_check]);
+                let typ = self.generalize(symbol, &signature, id, pure, [first_use, first_check]);
                 self.within_size_limit(symbol, name, typ, span)
             }
             _ => signature,
diff --git a/ndc_analyser/src/analyser/generics.rs b/ndc_analyser/src/analyser/generics.rs
index a8b50549..638ced00 100644
--- a/ndc_analyser/src/analyser/generics.rs
+++ b/ndc_analyser/src/analyser/generics.rs
@@ -40,6 +40,7 @@ impl Analyser {
         symbol: SymbolId,
         signature: &StaticType,
         declaration: NodeId,
+        pure: bool,
         [first_use, first_check]: [usize; 2],
     ) -> StaticType {
         self.solve_waiting();
@@ -157,12 +158,23 @@ impl Analyser {
         // An instance is for the types of the type parameters that what it
         // compiles differently depends on: the constraints and uses it
         // picks for, and the checks.
+        // A `pure fn` caches its results by its arguments' values, which can
+        // be equal across types, as `1` and `1.0` are, so each set of types
+        // gets an instance, and a cache, of its own.
+        let parameters = match self.vars.resolve(signature) {
+            StaticType::Function {
+                parameters: Some(parameters),
+                ..
+            } if pure => parameters,
+            _ => Vec::new(),
+        };
         let mut key: Vec<Box<str>> = Vec::new();
         for typ in scheme
             .iter()
             .flat_map(|waiting| waiting.constraint.inputs())
             .chain(uses.iter().flat_map(|generic_use| &generic_use.key))
             .chain(checks.iter().map(|(_, _, expected)| expected))
+            .chain(&parameters)
         {
             for name in typ.type_parameters() {
                 if !key.contains(&name) {
diff --git a/ndc_analyser/src/analyser/mod.rs b/ndc_analyser/src/analyser/mod.rs
index b708765c..73577587 100644
--- a/ndc_analyser/src/analyser/mod.rs
+++ b/ndc_analyser/src/analyser/mod.rs
@@ -489,6 +489,7 @@ impl Analyser {
                 parameters,
                 body,
                 return_annotation,
+                pure,
                 ..
             } => self.analyse_function_declaration(FunctionDeclaration {
                 id: *id,
@@ -496,6 +497,7 @@ impl Analyser {
                 parameters,
                 body,
                 return_annotation: return_annotation.as_ref(),
+                pure: *pure,
                 span: *span,
             }),
             Expression::Block { statements } => {
@@ -667,11 +669,11 @@ impl Analyser {
             }
             Expression::RangeInclusive { start, end }
             | Expression::RangeExclusive { start, end } => {
-                if let Some(start) = start {
-                    self.analyse_expr(start);
-                }
-                if let Some(end) = end {
-                    self.analyse_expr(end);
+                // A range counts in Ints, so its bounds are Ints: in `0..n`,
+                // `n` is one, whatever else it's used for.
+                for bound in [start, end].into_iter().flatten() {
+                    let typ = self.analyse_expr(bound);
+                    self.check_write(&StaticType::Int, &typ, bound.span, Some(bound.id));
                 }
 
                 StaticType::Iterator(Box::new(StaticType::Int))
diff --git a/ndc_analyser/src/analyser/solver.rs b/ndc_analyser/src/analyser/solver.rs
index 99ac6708..1ff42c29 100644
--- a/ndc_analyser/src/analyser/solver.rs
+++ b/ndc_analyser/src/analyser/solver.rs
@@ -1356,6 +1356,26 @@ impl Analyser {
             .flat_map(|argument| self.vars.unsettled(argument))
             .filter(|&var| self.vars.is_literal(var))
             .collect::<Vec<_>>();
+        // The nearest scope with an overload that takes the call hides those
+        // further out. When that scope has one overload, whose parameters
+        // take whatever the literals turn out to be, as a nested `fn d(x)`
+        // does, the call is its, though a literal isn't decided yet.
+        if !literals.is_empty()
+            && !Self::operand_could_be_a_tuple(kind, arguments)
+            && let Some(nearest) = self
+                .overloads()
+                .reachable_groups(candidates)
+                .into_iter()
+                .find(|group| {
+                    group
+                        .iter()
+                        .any(|&symbol| self.could_accept(symbol, arguments))
+                })
+            && let [only] = nearest[..]
+            && self.takes_any_literal(only, arguments)
+        {
+            return EarlyOverload::Only(only);
+        }
         let viable = reachable
             .iter()
             .copied()
@@ -1396,6 +1416,31 @@ impl Analyser {
         }
     }
 
+    /// Whether `symbol`'s parameter for each argument with a literal in it
+    /// takes any type, as an unannotated one does, and the other arguments
+    /// are known, so nothing still to come can change whether `symbol` takes
+    /// the call.
+    fn takes_any_literal(&self, symbol: SymbolId, arguments: &[StaticType]) -> bool {
+        let Some(parameters) = self.overloads().parameters_of(symbol) else {
+            return false;
+        };
+        parameters.len() == arguments.len()
+            && parameters
+                .iter()
+                .zip(arguments)
+                .all(|(parameter, argument)| {
+                    let unsettled = self.vars.unsettled(argument);
+                    if unsettled.iter().all(|&var| !self.vars.is_literal(var)) {
+                        return unsettled.is_empty();
+                    }
+                    match self.vars.resolve(parameter) {
+                        StaticType::Var(var) => !self.vars.is_literal(var),
+                        StaticType::Generic(_) => true,
+                        _ => false,
+                    }
+                })
+    }
+
     /// Whether one of `reachable` other than `except` takes `arguments`
     /// once each literal among them is `Any`.
     fn fits_once_any(
@@ -1955,8 +2000,8 @@ impl Analyser {
                     .zip(arguments)
                     .all(|(parameter, argument)| match (parameter, argument) {
                         (StaticType::Any, argument) => *argument == StaticType::Any,
-                        (StaticType::Iterable(_), StaticType::Var(var)) => {
-                            self.vars.is_literal(*var)
+                        (StaticType::Iterable(_), argument) => {
+                            !self.vars.waits_to_iterate(argument)
                         }
                         _ => true,
                     })
diff --git a/ndc_analyser/src/types.rs b/ndc_analyser/src/types.rs
index e49612ce..e62efb8c 100644
--- a/ndc_analyser/src/types.rs
+++ b/ndc_analyser/src/types.rs
@@ -135,15 +135,7 @@ impl TypeVars {
     /// A literal whose type the literal type `var` holds values of and that
     /// isn't settled yet, as `1`'s is in `[1]`.
     pub(crate) fn held_literal(&self, var: TypeVar) -> Option<TypeVar> {
-        self.bounds[var.0 as usize]
-            .iter()
-            .find_map(|bound| match bound {
-                Bound::Holds(held, _, _) => match self.resolve(held) {
-                    StaticType::Var(held) if held != var && self.is_literal(held) => Some(held),
-                    _ => None,
-                },
-                Bound::Number(..) => None,
-            })
+        self.held_literals(var).into_iter().next()
     }
 
     /// The unsettled literal types that each unsettled literal type is
@@ -366,28 +358,13 @@ impl TypeVars {
             return true;
         };
         let snapshot = self.snapshot();
-        let fits = defaults.iter().any(|default| self.try_settle(var, default));
+        let fits = defaults
+            .iter()
+            .any(|default| self.try_unify(&StaticType::Var(var), default));
         self.rollback(snapshot);
         fits
     }
 
-    /// Settles `var` as `typ` if `typ` is within its bounds, and returns
-    /// whether it did. A variable can't stand for a type that contains it.
-    fn try_settle(&mut self, var: TypeVar, typ: &StaticType) -> bool {
-        if self
-            .resolve(typ)
-            .contains(&|part| *part == StaticType::Var(var))
-        {
-            return false;
-        }
-        let snapshot = self.snapshot();
-        let settled = self.settle(var, typ.clone());
-        if !settled {
-            self.rollback(snapshot);
-        }
-        settled
-    }
-
     /// What the unsettled literal type `var` is shown as: what it would be
     /// if nothing said otherwise, as far as that's known.
     pub(crate) fn preview(&self, var: TypeVar) -> StaticType {
@@ -641,7 +618,10 @@ impl TypeVars {
                 Some(defaults) if !self.bounds[var.0 as usize].is_empty() => defaults,
                 _ => vec![self.fallbacks[var.0 as usize].clone()],
             };
-            if !defaults.iter().any(|default| self.try_settle(var, default)) {
+            if !defaults
+                .iter()
+                .any(|default| self.try_unify(&StaticType::Var(var), default))
+            {
                 // `Any` takes anything a literal holds.
                 self.settle(var, StaticType::Any);
             }
diff --git a/ndc_core/src/static_type.rs b/ndc_core/src/static_type.rs
index 4b7dbd8a..ec20a299 100644
--- a/ndc_core/src/static_type.rs
+++ b/ndc_core/src/static_type.rs
@@ -570,25 +570,6 @@ impl StaticType {
         }
     }
 
-    /// Returns a new type with the element type replaced. For container types
-    /// like `List<T>`, this returns `List<new_elem>`. Returns `None` if the
-    /// type does not have a replaceable element type.
-    pub fn with_element_type(&self, new_elem: Self) -> Self {
-        match self {
-            Self::List(_) => Self::List(Box::new(new_elem)),
-            Self::Iterable(_) => Self::Iterable(Box::new(new_elem)),
-            Self::Iterator(_) => Self::Iterator(Box::new(new_elem)),
-            Self::MinHeap(_) => Self::MinHeap(Box::new(new_elem)),
-            Self::MaxHeap(_) => Self::MaxHeap(Box::new(new_elem)),
-            Self::Deque(_) => Self::Deque(Box::new(new_elem)),
-            Self::Map { key, .. } => Self::Map {
-                key: key.clone(),
-                value: Box::new(new_elem),
-            },
-            _ => self.clone(),
-        }
-    }
-
     pub fn index_element_type(&self) -> Option<Self> {
         if let Self::Map { value, .. } = self {
             return Some(value.as_ref().clone());
diff --git a/ndc_stdlib/src/index.rs b/ndc_stdlib/src/index.rs
index f0381901..98b29ae6 100644
--- a/ndc_stdlib/src/index.rs
+++ b/ndc_stdlib/src/index.rs
@@ -455,21 +455,22 @@ fn vm_set_at_index(container: &Value, index_value: &Value, rhs: Value) -> Result
                         list[idx] = rhs;
                     }
                     VmOffset::Range(from, to) => {
-                        let rhs_vec = match rhs {
-                            Value::Object(o) => match o.as_ref() {
-                                Object::List(l) => l.borrow().clone(),
-                                Object::Tuple(t) => t.clone(),
-                                _ => {
-                                    return Err(VmError::native(
-                                        "cannot assign non-list to list slice",
-                                    ));
-                                }
-                            },
-                            _ => {
-                                return Err(VmError::native(
-                                    "cannot assign non-list to list slice",
-                                ));
+                        // Any sequence goes in a slice: a list, a tuple, a
+                        // range or another iterator.
+                        let rhs_vec = match &rhs {
+                            Value::Object(o) if matches!(o.as_ref(), Object::List(_)) => {
+                                let Object::List(l) = o.as_ref() else {
+                                    unreachable!("matched a list");
+                                };
+                                l.borrow().clone()
                             }
+                            _ => rhs
+                                .clone()
+                                .try_into_iter()
+                                .ok_or_else(|| {
+                                    VmError::native("cannot assign non-sequence to list slice")
+                                })?
+                                .collect(),
                         };
                         let tail: Vec<Value> = list.drain(from..).collect();
                         list.extend(rhs_vec);
diff --git a/tests/functional/programs/005_functions/105_a_nested_function_takes_a_literal_call_from_one_further_out.ndc b/tests/functional/programs/005_functions/105_a_nested_function_takes_a_literal_call_from_one_further_out.ndc
new file mode 100644
index 00000000..7e528d86
--- /dev/null
+++ b/tests/functional/programs/005_functions/105_a_nested_function_takes_a_literal_call_from_one_further_out.ndc
@@ -0,0 +1,7 @@
+// The nearest scope with a function that takes a call is the call's, so a
+// later call with another type can't hand an earlier one to an outer `d`.
+// expect-output: inner inner
+fn d(x: Int) => "outer";
+fn run() { fn d(x) => "inner"; d(1) }
+fn run2() { fn d(x) => "inner"; let r = d(1); d(2.5); r }
+print(run(), run2());
diff --git a/tests/functional/programs/005_functions/106_a_nested_function_waits_for_other_arguments_before_taking_a_call.ndc b/tests/functional/programs/005_functions/106_a_nested_function_waits_for_other_arguments_before_taking_a_call.ndc
new file mode 100644
index 00000000..66d32244
--- /dev/null
+++ b/tests/functional/programs/005_functions/106_a_nested_function_waits_for_other_arguments_before_taking_a_call.ndc
@@ -0,0 +1,9 @@
+// A call whose other arguments aren't known yet waits for them before the
+// nearest scope takes it: `y` may make the outer `d` the one that fits.
+// expect-output: outer
+fn d(x: Int, y: String) => "outer";
+fn run(y) {
+    fn d(x, y: Int) => "inner";
+    d(1, y)
+}
+print(run("s"));
diff --git a/tests/functional/programs/008_iterators/007_range_bound_types.ndc b/tests/functional/programs/008_iterators/007_range_bound_types.ndc
index 7cf89390..cc74bbb0 100644
--- a/tests/functional/programs/008_iterators/007_range_bound_types.ndc
+++ b/tests/functional/programs/008_iterators/007_range_bound_types.ndc
@@ -1,4 +1,4 @@
-// Every non-Int bound used to claim the integer was too large. Only an
-// integer that genuinely does not fit is a size problem.
-// expect-error: range bounds must be Int, got Number
+// Every non-Int bound used to claim the integer was too large. A range
+// counts in Ints, so a Number bound is reported before the program runs.
+// expect-error: mismatched types: found Number but expected Int
 for i in 0n..3n { print(i); }
diff --git a/tests/functional/programs/008_iterators/008_a_range_bound_is_an_int.ndc b/tests/functional/programs/008_iterators/008_a_range_bound_is_an_int.ndc
new file mode 100644
index 00000000..e4b80020
--- /dev/null
+++ b/tests/functional/programs/008_iterators/008_a_range_bound_is_an_int.ndc
@@ -0,0 +1,10 @@
+// A range counts in Ints, so a literal used as its bound is an Int, and a
+// list mixing it with a Float holds `Any`s.
+// expect-output: 3 [0.5,3]
+let n = 3;
+let xs = [0.5, n];
+let total = 0;
+for i in 0..n {
+    total += i;
+}
+print(total, xs);
diff --git a/tests/functional/programs/009_slicing/013_a_list_slice_takes_any_sequence.ndc b/tests/functional/programs/009_slicing/013_a_list_slice_takes_any_sequence.ndc
new file mode 100644
index 00000000..98288bb9
--- /dev/null
+++ b/tests/functional/programs/009_slicing/013_a_list_slice_takes_any_sequence.ndc
@@ -0,0 +1,7 @@
+// A list slice can be assigned any sequence of its element type.
+// expect-output: [1,5,6] [8,9,3]
+let xs = [1, 2, 3];
+xs[1..3] = 5..7;
+let ys = [1, 2, 3];
+ys[0..2] = (8, 9);
+print(xs, ys);
diff --git a/tests/functional/programs/010_memoization/006_a_pure_fn_caches_each_argument_type_apart.ndc b/tests/functional/programs/010_memoization/006_a_pure_fn_caches_each_argument_type_apart.ndc
new file mode 100644
index 00000000..2e0ea672
--- /dev/null
+++ b/tests/functional/programs/010_memoization/006_a_pure_fn_caches_each_argument_type_apart.ndc
@@ -0,0 +1,7 @@
+// A `pure fn` caches by its arguments, and `1` and `1.0` are equal, so each
+// argument type gets a cache of its own.
+// expect-output: 1 1.5
+pure fn same(x) => x;
+let n = same(1);
+let f = same(1.0);
+print(n, f + 0.5);
diff --git a/tests/functional/programs/020_tuples/004_a_tuple_of_values_still_waiting_on_a_literal_iterates_as_its_type.ndc b/tests/functional/programs/020_tuples/004_a_tuple_of_values_still_waiting_on_a_literal_iterates_as_its_type.ndc
new file mode 100644
index 00000000..01d972de
--- /dev/null
+++ b/tests/functional/programs/020_tuples/004_a_tuple_of_values_still_waiting_on_a_literal_iterates_as_its_type.ndc
@@ -0,0 +1,6 @@
+// A tuple whose elements wait for a literal's type iterates as that type
+// once it's known, as a list does.
+// expect-output: [2,5] [2,5]
+let x = 3;
+let y = 4;
+print((x - 1, y + 1).map(abs), [x - 1, y + 1].map(abs));
diff --git a/tests/functional/programs/998_not_desired/big_int_ranges.ndc b/tests/functional/programs/998_not_desired/big_int_ranges.ndc
index 75c9a00c..f75e7949 100644
--- a/tests/functional/programs/998_not_desired/big_int_ranges.ndc
+++ b/tests/functional/programs/998_not_desired/big_int_ranges.ndc
@@ -1,4 +1,4 @@
-// expect-error: Integer too large for range bounds
+// expect-error: mismatched types: found Number but expected Int
 // Not sure what to think of this one, but right now you cannot construct ranges with ints outside of the i64 range
 // it does make type analysis a tiny bit easier though
 (2n^1024n)..((2n^1024n)+1n)