diff --git a/src/python/flowmetal/syntax_analyzer.py b/src/python/flowmetal/syntax_analyzer.py
index 81d0717..e2a4c2d 100644
--- a/src/python/flowmetal/syntax_analyzer.py
+++ b/src/python/flowmetal/syntax_analyzer.py
@@ -5,11 +5,13 @@ The [syntax] analyzer interprets a parse sequence into a syntax tree which can b
 """
 
 from abc import ABC, abstractmethod
-from io import StringIO, IO
-from typing import NamedTuple
+from io import StringIO
+from typing import NamedTuple, List, Union, Any, IO, Tuple
+from enum import Enum
 
 import flowmetal.parser as p
 
+
 ### Types
 ## We are not, in fact, sponsored by Typelevel LLC.
 class TypeLevelExpr(object):
@@ -24,135 +26,289 @@ class GenericExpr(TypeLevelExpr, NamedTuple):
 
 class TypeExpr(TypeLevelExpr, NamedTuple):
     """A bound (or yet to be bound) type level symbol."""
+    pass
 
 
-## Now down to reality
+class BuiltinType(TypeLevelExpr, Enum):
+    """Built in types for atoms."""
+    BOOLEAN = 'Boolean'
+    SYMBOL = 'Symbol'
+    KEYWORD = 'Keyword'
+    STRING = 'String'
+    INTEGER = 'Integer'
+    FRACTION = 'Fraction'
+    FLOAT = 'Float'
+
+
+class ConstraintExpr(TypeLevelExpr, NamedTuple):
+    """A value-level constraint (predicate) as a type."""
+
+
+## Terms
+# Now down to reality
 class ValueLevelExpr(object):
     """A base class for value-level expressions."""
-    pass
+
+    @property
+    def type(self) -> TypeExpr:
+        """The type of an expression."""
 
 
-class AscribeExpr(ValueLevelExpr, NamedTuple):
-    """Ascribe a type (via type-level expression) to a value-level expression."""
-    pass
+class AscribeExpr(TypeLevelExpr):
+    value: ValueLevelExpr
+    type: TypeLevelExpr
 
 
-class InvokeExpr(ValueLevelExpr, NamedTuple):
-    """(a ⊢ (fn A ⊢ B) [...] ⊢ A) ⊢ B"""
-    pass
+class ConstExpr(ValueLevelExpr, NamedTuple):
+    """Constant expressions. Keywords, strings, numbers, that sort of thing."""
+
+    token: p.ConstTokenBase
+
+    @property
+    def data(self) -> Any:
+        """The value of the constant."""
+        # The parser gives us this data
+        return self.token.data
+
+    @abstractmethod
+    def type(self):
+        raise NotImplementedError()
 
 
-class IfExpr(ValueLevelExpr, NamedTuple):
-    """(if test a ⊢ A b ⊢ B) ⊢ (Variant A B)."""
-    pass
+class BooleanExpr(ConstExpr):
+    @property
+    def type(self):
+        return BuiltinType.BOOLEAN
 
 
-class LetExpr(ValueLevelExpr, NamedTuple):
-    """Let a single binding and wrap a body. Yes one. N-ary let is an abstraction."""
-    pass
+class IntegerExpr(ConstExpr):
+    @property
+    def type(self):
+        return BuiltinType.INTEGER
 
 
-class DoExpr(ValueError, NamedTuple):
-    """do a procedure ahem sequence of things.
-
-    (do a b c ... ω ⊢ Ω) ⊢ Ω
-    """
-    pass
+class FractionExpr(ConstExpr):
+    @property
+    def type(self):
+        return BuiltinType.FRACTION
 
 
-ProcExpr = DoExpr  # ain't broke don't fix it
+class FloatExpr(ConstExpr):
+    @property
+    def type(self):
+        return BuiltinType.FLOAT
 
 
-class MappingExpr(ValueLevelExpr, NamedTuple):
-    """Mappings require their own constructor expression due to local/symbol references."""
-    pass
+class KeywordExpr(ConstExpr):
+    @property
+    def type(self):
+        return BuiltinType.KEYWORD
 
 
-class SetExpr(ValueLevelExpr, NamedTuple):
-    """Sets require their own constructor expression due to local/symbol references."""
-    pass
+class StringExpr(ConstExpr):
+    @property
+    def type(self):
+        return BuiltinType.STRING
 
 
 class ListExpr(ValueLevelExpr, NamedTuple):
-    """While round () lists are generally InvokeExprs, [] lists are constructors like sets and maps."""
-    pass
+    elements: List[ValueLevelExpr]
+
+    # FIXME (arrdem 2020-07-18):
+    #  Probably typed? Not sure.
+
+    @property
+    def type(self) -> TypeExpr:
+        if self.elements:
+            return self.elements[-1].type
+
+
+## 'real' AST nodes
+class DoExpr(ValueLevelExpr, NamedTuple):
+    effect_exprs: List[ValueLevelExpr]
+    ret_expr: ValueLevelExpr
+
+    @property
+    def type(self) -> TypeExpr:
+        return self.ret_expr.type
+
+
+class LetExpr(ValueLevelExpr, NamedTuple):
+    binding_exprs: List[Tuple]
+    ret_expr: DoExpr
+
+    @property
+    def type(self) -> TypeExpr:
+        return self.ret_expr.type
+
+
+class FnExpr(ValueLevelExpr, NamedTuple):
+    arguments: List
+    ret_expr: DoExpr
+
+    @property
+    def type(self) -> TypeExpr:
+        """This is where the fun begins."""
+        return
 
 
 ## Reader implementation
-class SexpAnalyzer(ABC):
-    """A base class for Analyzers."""
-    pass
+class AnalyzerBase(ABC):
+    """Analyzer interface."""
+
+    @classmethod
+    @abstractmethod
+    def analyze(cls, token: p.TokenBase) -> ValueLevelExpr:
+        """Analyze a token tree, returning an expr tree."""
 
 
-class Analyzer(SexpAnalyzer):
+class Analyzer(AnalyzerBase):
     """A reference Analyzer implementation.
 
     Walks a parsed token tree, building up a syntax tree.
     """
 
     @classmethod
-    def read(cls, token: p.TokenBase):
-        if isinstance(token, p.WhitespaceToken):
-            ## Whitespace tokens are discarded when considering syntax
-            pass
+    def _nows(cls, tokens):
+        return [t for t in tokens if not isinstance(t, p.WhitespaceToken)]
 
-        elif isinstance(token, (p.StringToken, p.KeywordToken,
-                                p.IntegerToken, p.RationalToken, p.FloatToken)):
-            ## These are atoms we don't do much with
-            pass
-
-        elif isinstance(token, p.SetToken):
-            ## Set tokens have their own syntax object to allow for lexical sets
-            pass
-
-        elif isinstance(token, p.MappingToken):
-            ## As with sets, mappings have their own syntax object
-            pass
-
-        elif isinstance(token, p.ListToken):
-            ## This is the fun one because it's where most of the notation is implemented
-            pass
+    TACK0 = p.SymbolToken('⊢', '/⊢', None)
+    TACK1 = p.SymbolToken('|-', '|-', None)
 
     @classmethod
-    def read_symexpr(cls, token: p.SymbolToken):
-        """Emit a representation of using a binding."""
+    def _chomp(cls, tokens):
+        """'chomp' an expression and optional ascription off the tokens, returning an expression and the remaining tokens."""
+
+        print(tokens)
+        if len(tokens) == 1:
+            return cls.analyze(tokens[0]), []
+        elif tokens[1] in [cls.TACK0, cls.TACK1]:
+            if len(tokens) >= 3:
+                return AscribeExpr(cls.analyze(tokens[0]), cls.analyze(tokens[2])), tokens[3:]
+            else:
+                raise SyntaxError(f"Analyzing tack at {tokens[1].pos}, did not find following type ascription!")
+        else:
+            return cls.analyze(tokens[0]), tokens[1::]
 
     @classmethod
-    def read_setexpr(cls, token: p.SetToken):
-        """Emit a SetExpr """
+    def _terms(cls, tokens):
+        terms = []
+        tokens = cls._nows(tokens)
+        while tokens:
+            term, tokens = cls._chomp(tokens)
+            terms.append(term)
+        return terms
 
     @classmethod
-    def
+    def analyze(cls, token: p.TokenBase):
+        if isinstance(token, p.BooleanToken):
+            return BooleanExpr(token)
 
+        if isinstance(token, p.KeywordToken):
+            return KeywordExpr(token)
+
+        if isinstance(token, p.IntegerToken):
+            return IntegerExpr(token)
+
+        if isinstance(token, p.FractionToken):
+            return FractionExpr(token)
+
+        if isinstance(token, p.FloatToken):
+            return FloatExpr(token)
+
+        if isinstance(token, p.StringToken):
+            return StringExpr(token)
+
+        if isinstance(token, p.ListToken):
+            return cls.analyze_list(token)
+
+    LET = p.SymbolToken('let', 'let', None)
+    DO = p.SymbolToken('do', 'do', None)
+    FN = p.SymbolToken('fn', 'fn', None)
+    LIST = p.SymbolToken('list', 'list', None)
+    QUOTE = p.SymbolToken('quote', 'quote', None)
+
+    @classmethod
+    def analyze_list(cls, token: p.ListToken):
+        """Analyze a list, for which there are several 'ground' forms."""
+
+        # Expunge any whitespace tokens
+        tokens = cls._nows(token.data)
+
+        if len(tokens) == 0:
+            return ListExpr([])
+
+        if tokens[0] == cls.QUOTE:
+            raise NotImplementedError("Quote isn't quite there!")
+
+        if tokens[0] == cls.LIST:
+            return ListExpr(cls._terms(tokens[1::]))
+
+        if tokens[0] == cls.DO:
+            return cls.analyze_do(tokens[1::])
+
+        if tokens[0] == cls.LET:
+            return cls.analyze_let(tokens[1::])
+
+        if tokens[0] == cls.FN:
+            return cls.analyze_fn(tokens[1::])
+
+        cls.analyze_invoke(tokens)
+
+    @classmethod
+    def analyze_let(cls, tokens):
+        assert len(tokens) >= 2
+        assert isinstance(tokens[0], p.ListToken)
+        bindings = []
+        binding_tokens = cls._nows(tokens[0].data)
+        while binding_tokens:
+            print("analyze_let", binding_tokens)
+            bindexpr, binding_tokens = cls._chomp(binding_tokens)
+            valexpr, binding_tokens = cls._chomp(binding_tokens)
+            bindings.append((bindexpr, valexpr))
+
+        return LetExpr(bindings, cls.analyze_do(tokens[1::]))
+
+    @classmethod
+    def analyze_do(cls, tokens):
+        exprs = cls._terms(tokens)
+        return DoExpr(exprs[::-1], exprs[-1])
+
+    @classmethod
+    def analyze_fn(cls, tokens):
+        assert len(tokens) >= 2
+        assert isinstance(tokens[0], p.ListToken)
+        args = []
+        arg_tokens = cls._nows(tokens[0].data)
+        while arg_tokens:
+            argexpr, arg_tokens = cls._chomp(arg_tokens)
+            args.append(argexpr)
+
+        return FnExpr(args, cls.analyze_do(tokens[1::]))
 
 ## Analysis interface
-def reads(buff: str,
-          reader: SexpReader = Reader,
-          parser: p.SexpParser = p.Parser,
-          source_name=None):
+def analyzes(buff: str,
+             analyzer: AnalyzerBase = Analyzer,
+             parser: p.SexpParser = p.Parser,
+             source_name = None):
     """Parse a single s-expression from a string, returning its token tree."""
 
-    return read(StringIO(buff), parser, source_name or f"<string {id(buff):x}>")
+    return analyze(StringIO(buff), analyzer, parser, source_name or f"<string {id(buff):x}>")
 
 
-def readf(path: str,
-          reader: SexpReader = Reader,
-          parser: p.SexpParser = p.Parser):
+def analyzef(path: str,
+             analyzer: AnalyzerBase = Analyzer,
+             parser: p.SexpParser = p.Parser):
     """Parse a single s-expression from the file named by a string, returning its token tree."""
 
     with open(path, "r") as f:
-        return read(f, parser, path)
+        return analyze(f, analyzer, parser, path)
 
 
-def read(file: IO,
-         reader: SexpReader = Reader,
-         parser: p.SexpParser = p.Parser,
-         source_name=None):
+def analyze(file: IO,
+            analyzer: AnalyzerBase = Analyzer,
+            parser: p.SexpParser = p.Parser,
+            source_name = None):
     """Parse a single sexpression from a file-like object, returning its token tree."""
 
-    return parser.parse(
-        PosTrackingBufferedReader(
-            file,
-            source_name=source_name
-        )
-    )
+    return analyzer.analyze(p.parse(file, parser, source_name))
diff --git a/test/python/flowmetal/test_syntax_analyzer.py b/test/python/flowmetal/test_syntax_analyzer.py
new file mode 100644
index 0000000..f6e419a
--- /dev/null
+++ b/test/python/flowmetal/test_syntax_analyzer.py
@@ -0,0 +1,46 @@
+"""
+Tests covering the Flowmetal analyzer.
+"""
+
+import flowmetal.parser as p
+import flowmetal.syntax_analyzer as a
+
+import pytest
+
+
+@pytest.mark.parametrize('txt, exprtype', [
+    # Booleans
+    ('true', a.ConstExpr),
+    ('false', a.BooleanExpr),
+    # Integers
+    ('1', a.ConstExpr),
+    ('1', a.IntegerExpr),
+    # Fractions
+    ('1/2', a.ConstExpr),
+    ('1/2', a.FractionExpr),
+    # Floats
+    ('1.0', a.ConstExpr),
+    ('1.0', a.FloatExpr),
+    # Keywords
+    (':foo', a.ConstExpr),
+    (':foo', a.KeywordExpr),
+    # Strings
+    ('"foo"', a.ConstExpr),
+    ('"foo"', a.StringExpr),
+])
+def test_analyze_constants(txt, exprtype):
+    """Make sure the analyzer can chew on constants."""
+    assert isinstance(a.analyzes(txt), exprtype)
+
+
+@pytest.mark.parametrize('txt, exprtype, rettype', [
+    ('()', a.ListExpr, None),
+    ('(list)', a.ListExpr, None),
+    ('(list 1)', a.ListExpr, a.BuiltinType.INTEGER),
+    ('(do foo bar 1)', a.DoExpr, a.BuiltinType.INTEGER),
+    ('(let [a 1] 1)', a.LetExpr, a.BuiltinType.INTEGER),
+])
+def test_analyze_rettype(txt, exprtype, rettype):
+    """Make sure that do exprs work."""
+    assert isinstance(a.analyzes(txt), exprtype)
+    assert a.analyzes(txt).type == rettype