diff --git a/problemtools/judge/execute.py b/problemtools/judge/execute.py
index 0e22caf3..fe366f0e 100644
--- a/problemtools/judge/execute.py
+++ b/problemtools/judge/execute.py
@@ -196,7 +196,7 @@ def _run_multipass(
     base_dir: Path,
     diag: Diagnostics,
 ) -> SubmissionResult:
-    infile = testcase.infile
+    infile: Path = testcase.infile
     slowest = 0.0
     feedback_dir = execution_dir / 'feedback'
     for _ in range(metadata.limits.validation_passes):
diff --git a/problemtools/model/attachments.py b/problemtools/model/attachments.py
index d2d63ae2..ed0efea2 100644
--- a/problemtools/model/attachments.py
+++ b/problemtools/model/attachments.py
@@ -3,15 +3,17 @@
 from dataclasses import dataclass, field
 from pathlib import Path
 
+from .paths import AbsolutePath, abspath, resolve
+
 
 @dataclass(frozen=True)
 class Attachments:
     """A problem's attachments: files found under the attachments/ directory."""
 
-    paths: list[Path] = field(default_factory=list)
+    paths: list[AbsolutePath] = field(default_factory=list)
 
 
 def load_attachments(probdir: Path) -> Attachments:
-    attachments_dir = probdir / 'attachments'
-    paths = list(attachments_dir.iterdir()) if attachments_dir.is_dir() else []
+    attachments_dir = resolve(probdir) / 'attachments'
+    paths = [abspath(p) for p in attachments_dir.iterdir()] if attachments_dir.is_dir() else []
     return Attachments(paths=paths)
diff --git a/problemtools/model/graders.py b/problemtools/model/graders.py
index d818afbc..2480511c 100644
--- a/problemtools/model/graders.py
+++ b/problemtools/model/graders.py
@@ -4,7 +4,8 @@
 from pathlib import Path
 
 from ..languages import Languages
-from ..run import Program, find_programs, get_tool
+from ..run import BuildRun, SourceCode, as_source_or_buildrun, find_programs, get_tool
+from .paths import resolve
 
 DEFAULT_GRADER = get_tool('default_grader')
 
@@ -13,10 +14,10 @@
 class Graders:
     """A problem's graders: custom grader programs found on disk, if any."""
 
-    graders: list[Program] = field(default_factory=list)
+    graders: list[SourceCode | BuildRun] = field(default_factory=list)
 
     @property
-    def grader(self) -> Program | None:
+    def grader(self) -> SourceCode | BuildRun | None:
         """The custom grader, if there's exactly one; None if there are zero (default grading is used).
 
         Does not validate that there's at most one grader; callers that care about the invalid
@@ -25,5 +26,6 @@ def grader(self) -> Program | None:
 
 
 def load_graders(probdir: Path, language_config: Languages) -> Graders:
-    graders = find_programs(str(probdir / 'graders'), language_config=language_config)
+    probdir = resolve(probdir)
+    graders = as_source_or_buildrun(find_programs(str(probdir / 'graders'), language_config=language_config))
     return Graders(graders=graders)
diff --git a/problemtools/model/includes.py b/problemtools/model/includes.py
index 3dff54ed..b1be33b5 100644
--- a/problemtools/model/includes.py
+++ b/problemtools/model/includes.py
@@ -2,6 +2,7 @@
 from pathlib import Path
 
 from ..languages import Language, Languages
+from .paths import RelativePath, relpath, resolve
 
 #: Pseudo-language whose include files are added for every language.
 DEFAULT_LANGUAGE = 'default'
@@ -15,7 +16,7 @@ class IncludeFile:
     include/cpp/Vector/Vector.h, path is Vector/Vector.h.
     """
 
-    path: Path
+    path: RelativePath
     data: bytes
 
 
@@ -45,7 +46,7 @@ def get_includes_for_language(self, language: str) -> LanguageIncludes:
 
 
 def load_includes(probdir: Path, language_config: Languages) -> Includes:
-    include_dir = probdir / 'include'
+    include_dir = resolve(probdir) / 'include'
     includes = Includes()
     if not include_dir.is_dir():
         return includes
@@ -59,7 +60,7 @@ def load_includes(probdir: Path, language_config: Languages) -> Includes:
 
 def _load_language_includes(lang_dir: Path, language: Language | None) -> LanguageIncludes:
     paths = sorted(p for p in lang_dir.rglob('*') if p.is_file())
-    files = [IncludeFile(path=path.relative_to(lang_dir), data=path.read_bytes()) for path in paths]
+    files = [IncludeFile(path=relpath(path.relative_to(lang_dir)), data=path.read_bytes()) for path in paths]
 
     mainfile = None
     if language is not None:
diff --git a/problemtools/model/paths.py b/problemtools/model/paths.py
new file mode 100644
index 00000000..9daf9261
--- /dev/null
+++ b/problemtools/model/paths.py
@@ -0,0 +1,29 @@
+"""Type-level distinction between absolute and relative paths.
+
+`AbsolutePath`/`RelativePath` are used to communicate which paths
+in our models are absolute, and which are relative, with type
+system enforcement. For relative paths, the model should document
+what they are relative to."""
+
+from pathlib import Path
+from typing import NewType
+
+AbsolutePath = NewType('AbsolutePath', Path)
+RelativePath = NewType('RelativePath', Path)
+
+
+def abspath(path: Path) -> AbsolutePath:
+    """Assert that `path` is already absolute."""
+    assert path.is_absolute(), f'expected an absolute path, got {path}'
+    return AbsolutePath(path)
+
+
+def relpath(path: Path) -> RelativePath:
+    """Assert that `path` is relative."""
+    assert not path.is_absolute(), f'expected a relative path, got {path}'
+    return RelativePath(path)
+
+
+def resolve(path: Path) -> AbsolutePath:
+    """Canonicalize `path` to an `AbsolutePath`."""
+    return AbsolutePath(path.resolve())
diff --git a/problemtools/model/problem.py b/problemtools/model/problem.py
index 4933390e..3f9b31a4 100644
--- a/problemtools/model/problem.py
+++ b/problemtools/model/problem.py
@@ -12,6 +12,7 @@
 from .attachments import Attachments, load_attachments
 from .graders import Graders, load_graders
 from .includes import Includes, load_includes
+from .paths import AbsolutePath, resolve
 from .statements import Statements, load_statements
 from .submissions import Submissions, load_submissions
 from .testdata import TestDataGroup, load_testdata
@@ -27,7 +28,7 @@ class Problem:
     checks that should be run on top of a loaded Problem.
     """
 
-    probdir: Path
+    probdir: AbsolutePath
     language_config: Languages
     metadata: Metadata
     statements: Statements
@@ -54,6 +55,7 @@ def load_problem(probdir: Path, diag: Diagnostics) -> Problem:
     On failure, reports errors via `diag` and raises VerifyError.
     """
     try:
+        probdir = resolve(probdir)
         language_config = load_language_config(probdir.parent)
         problem_metadata = load_metadata(probdir)
         format_version = problem_metadata.problem_format_version
diff --git a/problemtools/model/statements.py b/problemtools/model/statements.py
index 18d0f9df..97a57328 100644
--- a/problemtools/model/statements.py
+++ b/problemtools/model/statements.py
@@ -5,6 +5,7 @@
 
 from .. import statement_util
 from ..formatversion import FormatVersion
+from .paths import AbsolutePath, abspath, resolve
 
 
 @dataclass(frozen=True)
@@ -14,8 +15,10 @@ class Statements:
     Well-formed packages have exactly one statement per language; this keeps every
     file found (rather than just the first) so checks can report duplicates."""
 
-    by_language: dict[str, list[Path]] = field(default_factory=dict)
+    by_language: dict[str, list[AbsolutePath]] = field(default_factory=dict)
 
 
 def load_statements(probdir: Path, format_version: FormatVersion) -> Statements:
-    return Statements(by_language=statement_util.find_statements(probdir, format_version))
+    probdir = resolve(probdir)
+    found = statement_util.find_statements(probdir, format_version)
+    return Statements(by_language={lang: [abspath(p) for p in paths] for lang, paths in found.items()})
diff --git a/problemtools/model/submissions.py b/problemtools/model/submissions.py
index 6d82e7af..b343b397 100644
--- a/problemtools/model/submissions.py
+++ b/problemtools/model/submissions.py
@@ -7,6 +7,7 @@
 from ..run import Program, find_programs
 from . import Verdict
 from .includes import Includes
+from .paths import RelativePath, relpath, resolve
 
 
 @dataclass(frozen=True)
@@ -17,7 +18,7 @@ class Submission:
     submissions/accepted/hello.java, path is accepted/hello.java."""
 
     program: Program
-    path: Path
+    path: RelativePath
 
     def __post_init__(self) -> None:
         if len(self.path.parts) != 2:
@@ -74,7 +75,7 @@ class Submissions:
 
 
 def load_submissions(probdir: Path, language_config: Languages, includes: Includes) -> Submissions:
-    subs_root = probdir / 'submissions'
+    subs_root = resolve(probdir) / 'submissions'
     if not subs_root.is_dir():
         return Submissions()
 
@@ -82,5 +83,5 @@ def load_submissions(probdir: Path, language_config: Languages, includes: Includ
     for entry in sorted(subs_root.iterdir()):
         if entry.is_dir():
             for program in find_programs(str(entry), language_config=language_config, includes=includes):
-                submissions.append(Submission(program=program, path=Path(entry.name) / program.name))
+                submissions.append(Submission(program=program, path=relpath(Path(entry.name) / program.name)))
     return Submissions(submissions=submissions)
diff --git a/problemtools/model/testdata.py b/problemtools/model/testdata.py
index 5c1bb795..a1add264 100644
--- a/problemtools/model/testdata.py
+++ b/problemtools/model/testdata.py
@@ -10,6 +10,7 @@
 
 from .. import config
 from ..metadata import Metadata
+from .paths import AbsolutePath, RelativePath, abspath, relpath, resolve
 
 DEFAULT_CONFIG = config.load_config('testdata.yaml')
 SCORING_ONLY_KEYS = ['accept_score', 'reject_score', 'range']
@@ -22,9 +23,9 @@ class TestCase:
     `path` is relative to the data directory and has no extension, e.g. for
     data/secret/hello.in, path is secret/hello."""
 
-    infile: Path
-    ansfile: Path
-    path: Path
+    infile: AbsolutePath
+    ansfile: AbsolutePath
+    path: RelativePath
     input_validator_flags: list[str]
     output_validator_flags: list[str]
 
@@ -50,7 +51,7 @@ class TestDataGroup:
     package defaults."""
 
     name: str
-    datadir: Path
+    datadir: AbsolutePath
     config: dict[str, Any]
     is_root: bool
     items: list[TestCase | TestDataGroup] = field(default_factory=list)
@@ -87,10 +88,11 @@ def get_score_range(self) -> tuple[float, float]:
 
 def load_testdata(probdir: Path, metadata: Metadata) -> TestDataGroup:
     """Load the full testdata tree rooted at <probdir>/data."""
-    return _load_group(probdir, probdir / 'data', {}, metadata, is_root=True)
+    root = resolve(probdir)
+    return _load_group(root, abspath(root / 'data'), {}, metadata, is_root=True)
 
 
-def _load_group_config(datadir: Path) -> dict[str, Any]:
+def _load_group_config(datadir: AbsolutePath) -> dict[str, Any]:
     configfile = datadir / 'testdata.yaml'
     if not configfile.is_file():
         return {}
@@ -98,7 +100,9 @@ def _load_group_config(datadir: Path) -> dict[str, Any]:
     return loaded if loaded is not None else {}
 
 
-def _load_group(probdir: Path, datadir: Path, parent_config: dict[str, Any], metadata: Metadata, is_root: bool) -> TestDataGroup:
+def _load_group(
+    probdir: AbsolutePath, datadir: AbsolutePath, parent_config: dict[str, Any], metadata: Metadata, is_root: bool
+) -> TestDataGroup:
     name = os.path.relpath(datadir, probdir).replace(os.sep, '.')
 
     merged_config = _load_group_config(datadir)
@@ -130,18 +134,18 @@ def _load_group(probdir: Path, datadir: Path, parent_config: dict[str, Any], met
     if datadir.is_dir():
         for entry in sorted(datadir.iterdir()):
             if entry.is_dir():
-                items.append(_load_group(probdir, entry, merged_config, metadata, is_root=False))
+                items.append(_load_group(probdir, abspath(entry), merged_config, metadata, is_root=False))
             elif entry.suffix == '.ans' and entry.with_suffix('.in').is_file():
-                items.append(_load_testcase(entry, probdir / 'data', merged_config, metadata))
+                items.append(_load_testcase(abspath(entry), abspath(probdir / 'data'), merged_config, metadata))
     return TestDataGroup(name=name, datadir=datadir, config=merged_config, is_root=is_root, items=items)
 
 
-def _load_testcase(ansfile: Path, data_root: Path, group_config: dict[str, Any], metadata: Metadata) -> TestCase:
-    infile = ansfile.with_suffix('.in')
+def _load_testcase(ansfile: AbsolutePath, data_root: AbsolutePath, group_config: dict[str, Any], metadata: Metadata) -> TestCase:
+    infile = abspath(ansfile.with_suffix('.in'))
     return TestCase(
         infile=infile,
         ansfile=ansfile,
-        path=infile.with_suffix('').relative_to(data_root),
+        path=relpath(infile.with_suffix('').relative_to(data_root)),
         input_validator_flags=group_config['input_validator_flags'].split(),
         output_validator_flags=(metadata.legacy_validator_flags.split() + group_config.get('output_validator_flags', '').split()),
     )
diff --git a/problemtools/model/validators.py b/problemtools/model/validators.py
index 36034920..996e89b2 100644
--- a/problemtools/model/validators.py
+++ b/problemtools/model/validators.py
@@ -6,7 +6,8 @@
 from ..formatversion import FormatVersion
 from ..languages import Languages
 from ..metadata import Metadata
-from ..run import Program, find_programs, get_tool
+from ..run import BuildRun, Program, SourceCode, as_source_or_buildrun, find_programs, get_tool
+from .paths import resolve
 
 #: The problemtools-provided validator used when a problem doesn't ship a custom output validator.
 DEFAULT_VALIDATOR = get_tool('default_validator')
@@ -20,6 +21,7 @@ class InputValidators:
 
 
 def load_input_validators(probdir: Path, language_config: Languages) -> InputValidators:
+    probdir = resolve(probdir)
     # input_format_validators is a deprecated name for input_validators. We just load
     # from both and let _check_root_directory_names warn about the deprecated directory
     validators = [
@@ -34,7 +36,7 @@ def load_input_validators(probdir: Path, language_config: Languages) -> InputVal
 class OutputValidators:
     """A problem's output validators: custom validator programs found on disk, if any."""
 
-    validators: list[Program] = field(default_factory=list)
+    validators: list[SourceCode | BuildRun] = field(default_factory=list)
 
     def uses_default(self, format_version: FormatVersion, metadata: Metadata) -> bool:
         """Whether the default validator is used, rather than a custom one."""
@@ -51,5 +53,8 @@ def select(self, format_version: FormatVersion, metadata: Metadata) -> Program |
 
 
 def load_output_validators(probdir: Path, format_version: FormatVersion, language_config: Languages) -> OutputValidators:
-    validators = find_programs(str(probdir / format_version.output_validator_directory), language_config=language_config)
+    probdir = resolve(probdir)
+    validators = as_source_or_buildrun(
+        find_programs(str(probdir / format_version.output_validator_directory), language_config=language_config)
+    )
     return OutputValidators(validators=validators)
diff --git a/problemtools/run/__init__.py b/problemtools/run/__init__.py
index 6391c546..0f95f69a 100644
--- a/problemtools/run/__init__.py
+++ b/problemtools/run/__init__.py
@@ -115,3 +115,17 @@ def get_program(
     if lang is not None:
         return SourceCode(path, lang, includes=includes.get_includes_for_language(lang.lang_id))
     return None
+
+
+def as_source_or_buildrun(programs: list[Program]) -> list[SourceCode | BuildRun]:
+    """Narrow a list of Programs to SourceCode | BuildRun.
+
+    Use on the result of find_programs(allow_validation_script=False) (the default) if
+    you need to narrow the type."""
+    result: list[SourceCode | BuildRun] = []
+    for program in programs:
+        assert isinstance(program, SourceCode | BuildRun), (
+            f'{program} is a {type(program).__name__}, expected SourceCode or BuildRun'
+        )
+        result.append(program)
+    return result
diff --git a/problemtools/statement_util.py b/problemtools/statement_util.py
index 649e2987..b92c0bdf 100644
--- a/problemtools/statement_util.py
+++ b/problemtools/statement_util.py
@@ -21,7 +21,7 @@
 
 
 def find_statements(problem_root: Path, version: FormatVersion) -> dict[str, list[Path]]:
-    """Returns a dict mapping language code to a list of paths to statements (relative to problem_root)
+    """Returns a dict mapping language code to a list of paths to statements, under problem_root.
 
     Note that in well-formed problem packages, there should only be a single
     statement for each language, but this function returns all found
diff --git a/tests/test_score_range.py b/tests/test_score_range.py
index 6127505a..a3e832e5 100644
--- a/tests/test_score_range.py
+++ b/tests/test_score_range.py
@@ -1,21 +1,22 @@
 from pathlib import Path
 
 from problemtools.checks.testdata import _check_score_range
+from problemtools.model.paths import abspath, relpath
 from problemtools.model.testdata import TestCase, TestDataGroup
 
 # Not test classes -- just named that way by the model. Tell pytest not to collect them.
-TestCase.__test__ = False
-TestDataGroup.__test__ = False
+TestCase.__test__ = False  # type: ignore[attr-defined]
+TestDataGroup.__test__ = False  # type: ignore[attr-defined]
 
 INF = float('inf')
 
 
 def make_testcase(name: str) -> TestCase:
-    path = Path(name)
+    path = Path('/' + name)
     return TestCase(
-        infile=path.with_suffix('.in'),
-        ansfile=path.with_suffix('.ans'),
-        path=path,
+        infile=abspath(path.with_suffix('.in')),
+        ansfile=abspath(path.with_suffix('.ans')),
+        path=relpath(Path(name)),
         input_validator_flags=[],
         output_validator_flags=[],
     )
@@ -34,7 +35,7 @@ def make_group(
 ) -> TestDataGroup:
     return TestDataGroup(
         name=name,
-        datadir=Path(name),
+        datadir=abspath(Path('/' + name)),
         config={
             'grading': grading,
             'grader_flags': grader_flags,