diff --git a/src/checker.ts b/src/checker.ts
index 01603f678..b3cf5108f 100644
--- a/src/checker.ts
+++ b/src/checker.ts
@@ -4,13 +4,21 @@ import {
   Pattern,
   Scope,
   SourceFile,
-  SourceFileElement,
-  StructDeclaration,
+  Symkind,
   Syntax,
   SyntaxKind,
   TypeExpression
 } from "./cst";
-import { ArityMismatchDiagnostic, BindingNotFoudDiagnostic, describeType, Diagnostics, FieldDoesNotExistDiagnostic, FieldMissingDiagnostic, UnificationFailedDiagnostic } from "./diagnostics";
+import {
+  describeType,
+  ArityMismatchDiagnostic,
+  BindingNotFoudDiagnostic,
+  Diagnostics,
+  FieldDoesNotExistDiagnostic,
+  FieldMissingDiagnostic,
+  UnificationFailedDiagnostic,
+  KindMismatchDiagnostic
+} from "./diagnostics";
 import { assert, isEmpty } from "./util";
 import { LabeledDirectedHashGraph, LabeledGraph, strongconnect } from "yagl"
 
@@ -30,6 +38,7 @@ export enum TypeKind {
   Tuple,
   Labeled,
   Record,
+  App,
 }
 
 abstract class TypeBase {
@@ -272,7 +281,7 @@ export class TRecord extends TypeBase {
   public nextRecord: TRecord | null = null;
 
   public constructor(
-    public decl: StructDeclaration,
+    public decl: Syntax,
     public fields: Map<string, Type>,
     public node: Syntax | null = null,
   ) {
@@ -308,6 +317,68 @@ export class TRecord extends TypeBase {
 
 }
 
+export class TApp extends TypeBase {
+
+  public readonly kind = TypeKind.App;
+
+  public constructor(
+    public operatorType: Type,
+    public argType: Type,
+    public node: Syntax | null = null
+  ) {
+    super(node);
+  }
+
+  public static build(operatorType: Type, argTypes: Type[], node: Syntax | null = null): TApp {
+    let count = argTypes.length;
+    let result = argTypes[count-1];
+    for (let i = count-2; i >= 0; i--) {
+      result = new TApp(argTypes[i], result, node);
+    }
+    return new TApp(operatorType, result, node);
+  }
+
+  public *getSequence(): Iterable<Type> {
+    if (this.operatorType.kind === TypeKind.App) {
+      yield* this.operatorType.getSequence();
+    } else {
+      yield this.operatorType;
+    }
+    if (this.argType.kind === TypeKind.App) {
+      yield* this.argType.getSequence();
+    } else {
+      yield this.argType;
+    }
+  }
+
+  public *getTypeVars(): Iterable<TVar> {
+     yield* this.operatorType.getTypeVars();
+     yield* this.argType.getTypeVars();
+  }
+
+  public shallowClone() {
+    return new TApp(
+      this.operatorType,
+      this.argType,
+      this.node
+    );
+  }
+
+  public substitute(sub: TVSub): Type {
+    let changed = false;
+    const newOperatorType = this.operatorType.substitute(sub);
+    if (newOperatorType !== this.operatorType) {
+      changed = true;
+    }
+    const newArgType = this.argType.substitute(sub);
+    if (newArgType !== this.argType) {
+      changed = true;
+    }
+    return changed ? new TApp(newOperatorType, newArgType, this.node) : this;
+  }
+
+}
+
 export type Type
   = TCon
   | TArrow
@@ -315,6 +386,7 @@ export type Type
   | TTuple
   | TLabeled
   | TRecord
+  | TApp
 
 class TVSet {
 
@@ -597,11 +669,15 @@ export class Checker {
     return context.returnType;
   }
 
-  private instantiate(scheme: Scheme, node: Syntax | null): Type {
+  private createSubstitution(scheme: Scheme): TVSub {
     const sub = new TVSub();
     for (const tv of scheme.typeVars) {
       sub.set(tv, this.createTypeVar());
     }
+    return sub;
+  }
+
+  private instantiate(scheme: Scheme, node: Syntax | null, sub = this.createSubstitution(scheme)): Type {
     for (const constraint of scheme.constraints) {
       const substituted = constraint.substitute(sub);
       substituted.node = node;
@@ -716,6 +792,8 @@ export class Checker {
         break;
       }
 
+      case SyntaxKind.TypeDeclaration:
+      case SyntaxKind.EnumDeclaration:
       case SyntaxKind.StructDeclaration:
         break;
 
@@ -820,13 +898,20 @@ export class Checker {
 
       case SyntaxKind.StructExpression:
       {
-        const scheme = this.lookup(node.name.text);
-        if (scheme === null) {
+        const scope = node.getScope();
+        const decl = scope.lookup(node.name.text, Symkind.Constructor);
+        if (decl === null) {
           this.diagnostics.add(new BindingNotFoudDiagnostic(node.name.text, node.name));
           return this.createTypeVar();
         }
-        const recordType = this.instantiate(scheme, node);
-        assert(recordType.kind === TypeKind.Record);
+        assert(decl.kind === SyntaxKind.StructDeclaration || decl.kind === SyntaxKind.EnumDeclarationStructElement);
+        const scheme = decl.scheme;
+        const sub = this.createSubstitution(scheme);
+        const declType = this.instantiate(scheme, node, sub);
+        const argTypes = [];
+        for (const typeVar of decl.tvs) {
+          argTypes.push(sub.get(typeVar)!);
+        }
         const fields = new Map();
         for (const member of node.members) {
           switch (member.kind) {
@@ -852,10 +937,10 @@ export class Checker {
               throw new Error(`Unexpected ${member}`);
           }
         }
-        const type = new TRecord(recordType.decl, fields, node);
+        const type = TApp.build(new TRecord(decl, fields, node), argTypes, node);
         this.addConstraint(
           new CEqual(
-            recordType,
+            TApp.build(declType, argTypes, node),
             type,
             node,
           )
@@ -923,6 +1008,16 @@ export class Checker {
         return scheme.type;
       }
 
+      case SyntaxKind.AppTypeExpression:
+      {
+        const operatorType = this.inferTypeExpression(node.operator);
+        const argTypes = [];
+        for (const argTypeExpr of node.args) {
+          argTypes.push(this.inferTypeExpression(argTypeExpr));
+        }
+        return TApp.build(operatorType, argTypes);
+      }
+
       case SyntaxKind.ArrowTypeExpression:
       {
         const paramTypes = [];
@@ -1145,6 +1240,7 @@ export class Checker {
         break;
       }
 
+      case SyntaxKind.TypeDeclaration:
       case SyntaxKind.EnumDeclaration:
       case SyntaxKind.StructDeclaration:
         break;
@@ -1186,6 +1282,7 @@ export class Checker {
       case SyntaxKind.IfStatement:
       case SyntaxKind.ReturnStatement:
       case SyntaxKind.ExpressionStatement:
+      case SyntaxKind.TypeDeclaration:
       case SyntaxKind.EnumDeclaration:
       case SyntaxKind.StructDeclaration:
         break;
@@ -1232,6 +1329,29 @@ export class Checker {
         break;
       }
 
+      case SyntaxKind.TypeDeclaration:
+      {
+        const env = node.typeEnv = new TypeEnv(parentEnv);
+        const constraints = new ConstraintSet();
+        const typeVars = new TVSet();
+        const context: InferContext = {
+          constraints,
+          typeVars,
+          env,
+          returnType: null,
+        };
+        this.pushContext(context);
+        for (const varExpr of node.typeVars) {
+          env.add(varExpr.text, new Forall([], [], this.createTypeVar()));
+        }
+        const type = this.inferTypeExpression(node.typeExpression);
+        this.popContext(context);
+        const scheme = new Forall(typeVars, constraints, type);
+        parentEnv.add(node.name.text, scheme); 
+        node.scheme = scheme;
+        break;
+      }
+
       case SyntaxKind.StructDeclaration:
       {
         const env = node.typeEnv = new TypeEnv(parentEnv);
@@ -1244,8 +1364,11 @@ export class Checker {
           returnType: null,
         };
         this.pushContext(context);
+        const argTypes = [];
         for (const varExpr of node.typeVars) {
-          env.add(varExpr.text, new Forall([], [], this.createTypeVar()));
+          const type = this.createTypeVar();
+          env.add(varExpr.text, new Forall([], [], type));
+          argTypes.push(type);
         }
         const fields = new Map<string, Type>();
         if (node.members !== null) {
@@ -1254,8 +1377,11 @@ export class Checker {
           }
         }
         this.popContext(context);
-        const type = new TRecord(node, fields);
-        parentEnv.add(node.name.text, new Forall(typeVars, constraints, type));
+        const type = new TRecord(node, fields, node);
+        const scheme = new Forall(typeVars, constraints, type);
+        parentEnv.add(node.name.text, scheme);
+        node.tvs = argTypes;
+        node.scheme = scheme; //new Forall(typeVars, constraints, new TApp(type, argTypes));
         break;
       }
 
@@ -1561,6 +1687,23 @@ export class Checker {
       }
     }
 
+    if (left.kind === TypeKind.App && right.kind === TypeKind.App) {
+      let leftElements = [...left.getSequence()];
+      let rightElements = [...right.getSequence()];
+      if (leftElements.length !== rightElements.length) {
+        this.diagnostics.add(new KindMismatchDiagnostic(leftElements.length-1, rightElements.length-1, constraint.node));
+        return false;
+      }
+      const count = leftElements.length;
+      let success = true;
+      for (let i = 0; i < count; i++) {
+        if (!this.unify(leftElements[i], rightElements[i], solution, constraint)) {
+          success = false;
+        }
+      }
+      return success;
+    }
+
     if (left.kind === TypeKind.Labeled && right.kind === TypeKind.Labeled) {
       let success = false;
       // This works like an ordinary union-find algorithm where an additional
@@ -1604,12 +1747,12 @@ export class Checker {
           }
           remaining.delete(fieldName);
         } else {
-          this.diagnostics.add(new FieldMissingDiagnostic(right, fieldName));
+          this.diagnostics.add(new FieldMissingDiagnostic(right, fieldName, constraint.node));
           success = false;
         }
       }
       for (const fieldName of remaining) {
-        this.diagnostics.add(new FieldDoesNotExistDiagnostic(left, fieldName));
+        this.diagnostics.add(new FieldDoesNotExistDiagnostic(left, fieldName, constraint.node));
       }
       if (success) {
         TypeBase.join(left, right);
diff --git a/src/cst.ts b/src/cst.ts
index 8d9040c1c..0163b3ab6 100644
--- a/src/cst.ts
+++ b/src/cst.ts
@@ -108,6 +108,7 @@ export const enum SyntaxKind {
   ReferenceTypeExpression,
   ArrowTypeExpression,
   VarTypeExpression,
+  AppTypeExpression,
 
   // Patterns
   BindPattern,
@@ -147,14 +148,11 @@ export const enum SyntaxKind {
   IfStatementCase,
 
   // Declarations
-  VariableDeclaration,
-  PrefixFuncDecl,
-  SuffixFuncDecl,
   LetDeclaration,
   StructDeclaration,
   EnumDeclaration,
   ImportDeclaration,
-  TypeAliasDeclaration,
+  TypeDeclaration,
 
   // Let declaration body members
   ExprBody,
@@ -185,6 +183,7 @@ export type Syntax
   | Param
   | Body
   | StructDeclarationField
+  | EnumDeclarationElement
   | TypeAssert
   | Declaration
   | Statement
@@ -207,9 +206,16 @@ function isNodeWithScope(node: Syntax): node is NodeWithScope {
       || node.kind === SyntaxKind.LetDeclaration;
 }
 
+export const enum Symkind {
+  Var = 1,
+  Type = 2,
+  Constructor = 4,
+  Any = Var | Type | Constructor
+}
+
 export class Scope {
 
-  private mapping = new Map<string, Syntax>();
+  private mapping = new Map<string, [Symkind, Syntax]>();
 
   public constructor(
     public node: NodeWithScope,
@@ -228,6 +234,10 @@ export class Scope {
     return null;
   }
 
+  private add(name: string, node: Syntax, kind: Symkind): void {
+    this.mapping.set(name, [kind, node]);
+  }
+
   private scan(node: Syntax): void {
     switch (node.kind) {
       case SyntaxKind.SourceFile:
@@ -241,9 +251,17 @@ export class Scope {
       case SyntaxKind.ReturnStatement:
       case SyntaxKind.IfStatement:
         break;
+      case SyntaxKind.TypeDeclaration:
+      {
+        this.add(node.name.text, node, Symkind.Type);
+        break;
+      }
       case SyntaxKind.EnumDeclaration:
       case SyntaxKind.StructDeclaration:
+      {
+        this.add(node.name.text, node, Symkind.Constructor);
         break;
+      }
       case SyntaxKind.LetDeclaration:
       {
         for (const param of node.params) {
@@ -257,7 +275,7 @@ export class Scope {
           }
         } else {
           if (node.pattern.kind === SyntaxKind.WrappedOperator) {
-            this.mapping.set(node.pattern.operator.text, node);
+            this.add(node.pattern.operator.text, node, Symkind.Var);
           } else {
             this.scanPattern(node.pattern, node);
           }
@@ -273,7 +291,7 @@ export class Scope {
     switch (node.kind) {
       case SyntaxKind.BindPattern:
       {
-        this.mapping.set(node.name.text, decl);
+        this.add(node.name.text, decl, Symkind.Var);
         break;
       }
       case SyntaxKind.StructPattern:
@@ -287,7 +305,7 @@ export class Scope {
             }
             case SyntaxKind.PunnedStructPatternField:
             {
-              this.mapping.set(node.name.text, decl);
+              this.add(node.name.text, decl, Symkind.Var);
               break;
             }
           }
@@ -299,12 +317,15 @@ export class Scope {
     }
   }
 
-  public lookup(name: string): Syntax | null {
+  public lookup(name: string, expectedKind = Symkind.Any): Syntax | null {
     let curr: Scope | null = this;
     do {
-      const decl = curr.mapping.get(name);
-      if (decl !== undefined) {
-        return decl;
+      const match = curr.mapping.get(name);
+      if (match !== undefined) {
+        const [kind, decl] = match;
+        if (kind & expectedKind) {
+          return decl;
+        }
       }
       curr = curr.getParent();
     } while (curr !== null);
@@ -967,6 +988,30 @@ export class ReferenceTypeExpression extends SyntaxBase {
 
 }
 
+export class AppTypeExpression extends SyntaxBase {
+
+  public readonly kind = SyntaxKind.AppTypeExpression;
+
+  public constructor(
+    public operator: TypeExpression,
+    public args: TypeExpression[],
+  ) {
+    super();
+  }
+
+  public getFirstToken(): Token {
+    return this.operator.getFirstToken();
+  }
+
+  public getLastToken(): Token {
+    if (this.args.length > 0) {
+      return this.args[this.args.length-1].getLastToken();
+    }
+    return this.operator.getLastToken();
+  }
+
+}
+
 export class VarTypeExpression extends SyntaxBase {
 
   public readonly kind = SyntaxKind.VarTypeExpression;
@@ -991,6 +1036,7 @@ export type TypeExpression
   = ReferenceTypeExpression
   | ArrowTypeExpression
   | VarTypeExpression
+  | AppTypeExpression
 
 export class BindPattern extends SyntaxBase {
 
@@ -1853,6 +1899,34 @@ export class WrappedOperator extends SyntaxBase {
 
 }
 
+export class TypeDeclaration extends SyntaxBase {
+
+  public readonly kind = SyntaxKind.TypeDeclaration;
+
+  public constructor(
+    public pubKeyword: PubKeyword | null,
+    public typeKeyword: TypeKeyword,
+    public name: IdentifierAlt,
+    public typeVars: Identifier[],
+    public equals: Equals,
+    public typeExpression: TypeExpression
+  ) {
+    super();
+  }
+
+  public getFirstToken(): Token {
+    if (this.pubKeyword !== null) {
+      return this.pubKeyword;
+    }
+    return this.typeKeyword;
+  }
+
+  public getLastToken(): Token {
+    return this.typeExpression.getLastToken();
+  }
+
+}
+
 export class LetDeclaration extends SyntaxBase {
 
   public readonly kind = SyntaxKind.LetDeclaration;
@@ -1923,6 +1997,7 @@ export type Declaration
   | ImportDeclaration
   | StructDeclaration
   | EnumDeclaration
+  | TypeDeclaration
 
 export class Initializer extends SyntaxBase {
 
diff --git a/src/diagnostics.ts b/src/diagnostics.ts
index 5ea4c1749..71856d871 100644
--- a/src/diagnostics.ts
+++ b/src/diagnostics.ts
@@ -198,19 +198,25 @@ export function describeType(type: Type): string {
     }
     case TypeKind.Record:
     {
-      let out = type.decl.name.text + ' { ';
-      let first = true;
-      for (const [fieldName, fieldType] of type.fields) {
-        if (first) first = false;
-        else out += ', ';
-        out += fieldName + ': ' + describeType(fieldType);
-      }
-      return out + ' }';
+      return type.decl.name.text;
+      // let out = type.decl.name.text + ' { ';
+      // let first = true;
+      // for (const [fieldName, fieldType] of type.fields) {
+      //   if (first) first = false;
+      //   else out += ', ';
+      //   out += fieldName + ': ' + describeType(fieldType);
+      // }
+      // return out + ' }';
     }
     case TypeKind.Labeled:
     {
+      // FIXME may need to include fields that were added during unification
       return '{ ' + type.name + ': ' + describeType(type.type) + ' }';
     }
+    case TypeKind.App:
+    {
+      return describeType(type.operatorType) + ' ' + describeType(type.argType);
+    }
   }
 }
 
@@ -294,6 +300,7 @@ export class FieldMissingDiagnostic {
   public constructor(
     public recordType: TRecord,
     public fieldName: string,
+    public node: Syntax | null,
   ) {
 
   }
@@ -302,8 +309,8 @@ export class FieldMissingDiagnostic {
     out.write(ANSI_FG_RED + ANSI_BOLD + 'error: ' + ANSI_RESET);
     out.write(`field '${this.fieldName}' is missing from `);
     out.write(describeType(this.recordType) + '\n\n');
-    if (this.recordType.node !== null) {
-      out.write(printNode(this.recordType.node) + '\n');
+    if (this.node !== null) {
+      out.write(printNode(this.node) + '\n');
     }
   }
 
@@ -316,13 +323,48 @@ export class FieldDoesNotExistDiagnostic {
   public constructor(
     public recordType: TRecord,
     public fieldName: string,
+    public node: Syntax | null,
   ) {
+
   }
 
   public format(out: IndentWriter): void {
     out.write(ANSI_FG_RED + ANSI_BOLD + 'error: ' + ANSI_RESET);
     out.write(`field '${this.fieldName}' does not exist on type `);
     out.write(describeType(this.recordType) + '\n\n');
+    if (this.node !== null) {
+      out.write(printNode(this.node) + '\n');
+    }
+  }
+
+}
+
+export class KindMismatchDiagnostic {
+
+  public readonly level = Level.Error;
+
+  public constructor(
+    public leftSize: number,
+    public rightSize: number,
+    public node: Syntax | null,
+  ) {
+  
+  }
+
+  public format(out: IndentWriter): void {
+    out.write(ANSI_FG_RED + ANSI_BOLD + 'error: ' + ANSI_RESET);
+    out.write(`kind `);
+    for (let i = 0; i < this.leftSize-1; i++) {
+      out.write(`* -> `);
+    }
+    out.write(`* does not match with `);
+    for (let i = 0; i < this.rightSize-1; i++) {
+      out.write(`* -> `);
+    }
+    out.write(`*\n\n`);
+    if (this.node !== null) {
+      out.write(printNode(this.node) + '\n');
+    }
   }
 
 }
@@ -335,6 +377,7 @@ export type Diagnostic
   | ArityMismatchDiagnostic
   | FieldMissingDiagnostic
   | FieldDoesNotExistDiagnostic
+  | KindMismatchDiagnostic
 
 export interface Diagnostics {
   add(diagnostic: Diagnostic): void;
diff --git a/src/parser.ts b/src/parser.ts
index 67703e6af..27b269a43 100644
--- a/src/parser.ts
+++ b/src/parser.ts
@@ -52,6 +52,8 @@ import {
   EnumDeclaration,
   EnumDeclarationTupleElement,
   VarTypeExpression,
+  TypeDeclaration,
+  AppTypeExpression,
 } from "./cst"
 import { Stream } from "./util";
 
@@ -181,8 +183,30 @@ export class Parser {
     }
   }
 
+  private tryParseAppTypeExpression(): TypeExpression {
+    const operator = this.parsePrimitiveTypeExpression();
+    const args = [];
+    for (;;) {
+      const t1 = this.peekToken();
+      if (t1.kind === SyntaxKind.RParen
+          || t1.kind === SyntaxKind.RBrace
+          || t1.kind === SyntaxKind.RBracket
+          || t1.kind === SyntaxKind.Equals
+          || t1.kind === SyntaxKind.BlockStart
+          || t1.kind === SyntaxKind.LineFoldEnd
+          || t1.kind === SyntaxKind.RArrow) {
+        break;
+      }
+      args.push(this.parsePrimitiveTypeExpression());
+    }
+    if (args.length === 0) {
+      return operator;
+    }
+    return new AppTypeExpression(operator, args);
+  }
+
   public parseTypeExpression(): TypeExpression {
-    let returnType = this.parsePrimitiveTypeExpression();
+    let returnType = this.tryParseAppTypeExpression();
     const paramTypes = [];
     for (;;) {
       const t1 = this.peekToken();
@@ -191,7 +215,7 @@ export class Parser {
       }
       this.getToken();
       paramTypes.push(returnType);
-      returnType = this.parsePrimitiveTypeExpression();
+      returnType = this.tryParseAppTypeExpression();
     }
     if (paramTypes.length === 0) {
       return returnType;
@@ -417,6 +441,31 @@ export class Parser {
     return this.parseBinaryOperatorAfterExpr(lhs, 0);
   }
 
+  public parseTypeDeclaration(): TypeDeclaration {
+    let pubKeyword = null;
+    let t0 = this.getToken();
+    if (t0.kind === SyntaxKind.PubKeyword) {
+      pubKeyword = t0;
+      t0 = this.getToken();
+    }
+    if (t0.kind !== SyntaxKind.TypeKeyword) {
+      this.raiseParseError(t0, [ SyntaxKind.TypeKeyword ]);
+    }
+    const name = this.expectToken(SyntaxKind.IdentifierAlt);
+    const typeVars = [];
+    let t1 = this.getToken();
+    while (t1.kind === SyntaxKind.Identifier) {
+      typeVars.push(t1);
+      t1 = this.getToken();
+    }
+    if (t1.kind !== SyntaxKind.Equals) {
+      this.raiseParseError(t1, [ SyntaxKind.Equals ]);
+    }
+    const typeExpr = this.parseTypeExpression();
+    this.expectToken(SyntaxKind.LineFoldEnd);
+    return new TypeDeclaration(pubKeyword, t0, name, typeVars, t1, typeExpr);
+  }
+
   public parseEnumDeclaration(): EnumDeclaration {
     let pubKeyword = null;
     let t0 = this.getToken();
@@ -817,7 +866,9 @@ export class Parser {
       case SyntaxKind.StructKeyword:
         return this.parseStructDeclaration();
       case SyntaxKind.EnumKeyword:
-        return this.parseEnumDeclaration();
+        return this.parseStructDeclaration();
+      case SyntaxKind.TypeKeyword:
+        return this.parseTypeDeclaration();
       case SyntaxKind.IfKeyword:
         return this.parseIfStatement();
       default: