diff --git a/src/CallBlock.css b/src/CallBlock.css
index 5200efc..907e3e7 100644
--- a/src/CallBlock.css
+++ b/src/CallBlock.css
@@ -64,13 +64,9 @@
 .outputParam {
   text-align: left;
   vertical-align: top;
-  /* margin-left: 28px; */
   padding: 0px;
-  /* padding-left: 14px; */
   display: inline-block;
-  /* border: solid 2px orange; */
   background-color: rgb(233, 224, 205);
-  /* border-radius: 10px; */
   width: 100%;
 }
 
@@ -83,28 +79,28 @@
   color: black;
 }
 .functionBlock.unifyError  > .functionParams > .outputParam > .inputParam:after {
-  border-left-color: pink;
+  background-color: pink;
 }
 .functionBlock.unifyError > .functionParams > .outputParam > .inputParam > .inputParam {
   background-color: pink;
   color: black;
 }
 .functionBlock.unifyError  > .functionParams > .outputParam > .inputParam > .inputParam:after {
-  border-left-color: pink;
+  background-color: pink;
 }
 .functionBlock.unifyError > .functionParams > .outputParam > .inputParam > .inputParam > .inputParam {
   background-color: pink;
   color: black;
 }
 .functionBlock.unifyError  > .functionParams > .outputParam > .inputParam > .inputParam > .inputParam:after {
-  border-left-color: pink;
+  background-color: pink;
 }
 .functionBlock.unifyError > .functionParams > .outputParam > .inputParam > .inputParam > .inputParam > .inputParam {
   background-color: pink;
   color: black;
 }
 .functionBlock.unifyError  > .functionParams > .outputParam > .inputParam > .inputParam > .inputParam > .inputParam:after {
-  border-left-color: pink;
+  background-color: pink;
 }
 
 .inputParam.offending {
@@ -112,5 +108,5 @@
   color: white !important;
 }
 .inputParam.offending:after {
-  border-left-color: darkred !important;
+  background-color: darkred !important;
 }
diff --git a/src/CallBlock.tsx b/src/CallBlock.tsx
index f63f58c..9ed749c 100644
--- a/src/CallBlock.tsx
+++ b/src/CallBlock.tsx
@@ -3,7 +3,7 @@ import { useContext, useInsertionEffect } from "react";
 import { Editor, type EditorState } from "./Editor";
 import { Value } from "./Value";
 import { type SetStateFn, type State2Props } from "./Editor";
-import { evalCallBlock, evalEditorBlock, scoreResolved } from "./eval";
+import { evalCallBlock, evalCallBlock2, evalEditorBlock, scoreResolved } from "./eval";
 import { type ResolvedType } from "./eval";
 import "./CallBlock.css";
 import { EnvContext } from "./EnvContext";
@@ -97,6 +97,7 @@ export function CallBlockNoSugar({ state, setState, suggestionPriority }: CallBl
                 evalEditorBlock(state.fn, env), // fn *may* be set
                 inputSuggestion[2],       // suggestions will be for input
                 suggestionPriority,       // priority function we get from parent block
+                env,
               )}
             />
         </div>
@@ -105,8 +106,8 @@ export function CallBlockNoSugar({ state, setState, suggestionPriority }: CallBl
   </span>;
 }
 
-function computePriority(fn: ResolvedType, input: ResolvedType, outPriority: (s: SuggestionType) => number) {
-  const resolved = evalCallBlock(fn, input);
+function computePriority(fn: ResolvedType, input: ResolvedType, outPriority: (s: SuggestionType) => number, env) {
+  const resolved = evalCallBlock2(fn, input, env);
   return scoreResolved(resolved, outPriority);
 }
 
@@ -131,6 +132,7 @@ function FunctionHeader({ fn, setFn, input, onFnCancel, suggestionPriority }) {
         fnSuggestion[2],
         evalEditorBlock(fn.input, env),
         suggestionPriority,
+        env,
       )}
       />;
   }
@@ -153,6 +155,7 @@ function FunctionName({fn, setFn, onFnCancel, suggestionPriority, input}) {
           fnSuggestion[2],             // suggestions will be for function
           evalEditorBlock(input, env), // input *may* be set
           suggestionPriority,          // priority function we get from parent block
+          env,
         )}
       />
     </span>;
@@ -180,6 +183,7 @@ function InputParams({ fn, setFn, input, setInput, onInputCancel, depth, errorDe
           evalEditorBlock(fn.fn, env),
           inputSuggestion[2],
           suggestionPriority,
+          env,
         )}
     />;
   }
@@ -199,6 +203,7 @@ function InputParams({ fn, setFn, input, setInput, onInputCancel, depth, errorDe
           evalEditorBlock(fn, env), // fn *may* be set
           inputSuggestion[2],       // suggestions will be for input
           suggestionPriority,       // priority function we get from parent block
+          env,
         )}
       />
   </div>;
diff --git a/src/Editor.css b/src/Editor.css
index f083c9a..5253c6f 100644
--- a/src/Editor.css
+++ b/src/Editor.css
@@ -3,10 +3,11 @@
 }
 
 .typeSignature {
-  display: none;
-  position: absolute;
+  display: inline-block;
+  /* display: none; */
+  /* position: absolute; */
   z-index: 1;
-  background-color: white;
+  /* background-color: white; */
   /* border: 1px solid black; */
 }
 
diff --git a/src/Editor.tsx b/src/Editor.tsx
index e6319be..9abc86b 100644
--- a/src/Editor.tsx
+++ b/src/Editor.tsx
@@ -71,10 +71,6 @@ export function Editor({state, setState, onCancel, suggestionPriority}: EditorPr
 
   const globalContext = useContext(CommandContext);
   const onCommand = (e: React.KeyboardEvent) => {
-    console.log(e);
-    
-    // const type = getType(state.resolved);
-    // const commands = getCommands(type);
     const commands = ['e', 't', 'Enter', 'Backspace', 'ArrowLeft', 'ArrowRight', 'Tab', 'l', 'L', '=', '.', 'c', 'a'];
     if (!commands.includes(e.key)) {
       return;
@@ -199,7 +195,7 @@ export function Editor({state, setState, onCancel, suggestionPriority}: EditorPr
   return <span className="editor">
     {renderBlock()}
     <div className="typeSignature">
-     <Type type={getType(resolved)} />
+    &nbsp;::&nbsp;<Type type={getType(resolved)} />
     </div>
     <input
       ref={commandInputRef}
diff --git a/src/InputBlock.tsx b/src/InputBlock.tsx
index c4e49af..b0a19d0 100644
--- a/src/InputBlock.tsx
+++ b/src/InputBlock.tsx
@@ -38,7 +38,7 @@ interface InputBlockProps extends State2Props<InputBlockState> {
 }
 
 const computeSuggestions = (text, env, suggestionPriority: (s: SuggestionType) => number): PrioritizedSuggestionType[] => {
-  const literals = attemptParseLiteral(text);
+  const literals = attemptParseLiteral(text, env);
 
   const ls: SuggestionType[] = [
     // literals
diff --git a/src/LambdaBlock.css b/src/LambdaBlock.css
index e69de29..208e0f1 100644
--- a/src/LambdaBlock.css
+++ b/src/LambdaBlock.css
@@ -0,0 +1,5 @@
+.lambdaExpr {
+  display: inline-block;
+  border: solid 1px darkgrey;
+  margin: 2px;
+}
\ No newline at end of file
diff --git a/src/LambdaBlock.tsx b/src/LambdaBlock.tsx
index 663e84b..abf684b 100644
--- a/src/LambdaBlock.tsx
+++ b/src/LambdaBlock.tsx
@@ -7,6 +7,7 @@ import { growEnv, TYPE_VARS } from "dope2";
 import { autoInputWidth } from "./util/dom_trickery";
 
 import "./LambdaBlock.css";
+import { getUnusedTypeVar } from "./eval";
 
 
 export interface LambdaBlockState {
@@ -31,12 +32,18 @@ export function LambdaBlock({state, setState, suggestionPriority}: LambdaBlockPr
     ...state,
     paramName,
   }));
-
   const setExpr = callback => setState(state => ({
     ...state,
     expr: callback(state.expr),
   }));
 
+  const onChangeName = (e) => {
+    if (state.paramName === "" && e.key === 'Backspace') {
+      setState(state => state.expr);
+      e.preventDefault();
+    }
+  };
+
   useEffect(() => {
     nameRef.current?.focus();
   }, []);
@@ -46,7 +53,7 @@ export function LambdaBlock({state, setState, suggestionPriority}: LambdaBlockPr
   const innerEnv = growEnv(env)(state.paramName)({
     kind: "unknown",
     i: undefined,
-    t: TYPE_VARS[0],
+    t: getUnusedTypeVar(env),
   });
   
   return <span>
@@ -58,13 +65,14 @@ export function LambdaBlock({state, setState, suggestionPriority}: LambdaBlockPr
           className='editable'
           value={state.paramName}
           placeholder="<name>"
+          onKeyDown={onChangeName}
           onChange={e => setParamName(e.target.value)}
           />
     </span>
     &nbsp;
     <span className="keyword">:</span>
     &nbsp;
-    <span className="lambdaExpr">
+    <div className="lambdaExpr">
       <EnvContext value={innerEnv}>
         <Editor
           state={state.expr}
@@ -75,6 +83,6 @@ export function LambdaBlock({state, setState, suggestionPriority}: LambdaBlockPr
           }}
           />
       </EnvContext>
-    </span>
+    </div>
   </span>
 }
diff --git a/src/eval.ts b/src/eval.ts
index 5039e88..843b52e 100644
--- a/src/eval.ts
+++ b/src/eval.ts
@@ -1,4 +1,4 @@
-import { assignFnSubstitutions, Double, fnType, getSymbol, growEnv, Int, makeGeneric, NotAFunctionError, prettyT, substitute, symbolFunction, trie, TYPE_VARS, UnifyError } from "dope2";
+import { assignFnSubstitutions, dict, Double, fnType, getSymbol, growEnv, Int, makeGeneric, NotAFunctionError, prettyT, set, substitute, symbolFunction, trie, TYPE_VARS, UnifyError } from "dope2";
 
 import type { EditorState } from "./Editor";
 import type { InputValueType, SuggestionType } from "./InputBlock";
@@ -30,7 +30,11 @@ export interface Unknown {
   substitutions: Map<Type,Type>;
 }
 
-export const entirelyUnknown: Unknown = { kind: "unknown", t: makeGeneric(a => a), substitutions: new Map() };
+export const entirelyUnknown = env => ({
+  kind: "unknown",
+  t: getUnusedTypeVar(env),
+  substitutions: new Map(),
+} as Unknown);
 
 // the value of every block is either known (Dynamic), an error, or unknown
 export type ResolvedType = Dynamic | DeepError | Unknown;
@@ -40,9 +44,7 @@ export const evalEditorBlock = (s: EditorState, env): ResolvedType => {
     return evalInputBlock(s.text, s.value, env);
   }
   if (s.kind === "call") {
-    const fn = evalEditorBlock(s.fn, env);
-    const input = evalEditorBlock(s.input, env);
-    return evalCallBlock(fn, input);
+    return evalCallBlock(s.fn, s.input, env);
   }
   if (s.kind === "let") {
     return evalLetInBlock(s.value, s.name, s.inner, env);
@@ -51,12 +53,12 @@ export const evalEditorBlock = (s: EditorState, env): ResolvedType => {
     return evalLambdaBlock(s.paramName, s.expr, env);
 
   }
-  return entirelyUnknown; // todo
+  return entirelyUnknown(env); // todo
 };
 
 export function evalInputBlock(text: string, value: InputValueType, env): ResolvedType {
   if (value.kind === "literal") {
-    return parseLiteral(text, value.type);
+    return parseLiteral(text, value.type, env);
   }
   else if (value.kind === "name") {
     const found = trie.get(env.name2dyn)(text);
@@ -67,11 +69,11 @@ export function evalInputBlock(text: string, value: InputValueType, env): Resolv
         substitutions: new Map(),
       };
     } else {
-      return entirelyUnknown;
+      return entirelyUnknown(env);
     }
   }
   else { // kind === "text" -> unresolved
-    return entirelyUnknown;
+    return entirelyUnknown(env);
   }
 }
 
@@ -79,48 +81,48 @@ const mergeMaps = (...maps: Map<Type,Type>[]) => {
   return new Map(maps.flatMap(m => [...m]));
 }
 
-export function evalCallBlock(fn: ResolvedType, input: ResolvedType): ResolvedType {
-  if (getSymbol(fn.t) !== symbolFunction) {
-    if (fn.kind === "unknown") {
-      return entirelyUnknown; // don't flash everything red, giving the user a heart attack
+export function evalCallBlock2(fnResolved: ResolvedType, inputResolved: ResolvedType, env): ResolvedType {
+  if (getSymbol(fnResolved.t) !== symbolFunction) {
+    if (fnResolved.kind === "unknown") {
+      return entirelyUnknown(env); // don't flash everything red, giving the user a heart attack
     }
-      // worst outcome: we know nothing about the result!
+    // worst outcome: we know nothing about the result!
     return {
       kind: "error",
-      e: new NotAFunctionError(`${prettyT(fn.t)} is not a function type!`),
-      t: entirelyUnknown.t,
-      substitutions: mergeMaps(fn.substitutions, input.substitutions),
+      e: new NotAFunctionError(`${prettyT(fnResolved.t)} is not a function type!`),
+      t: getUnusedTypeVar(env),
+      substitutions: mergeMaps(fnResolved.substitutions, inputResolved.substitutions),
       depth: 0,
     };
   }
   try {
     // fn is a function...
-    const [outType, substitutions] = assignFnSubstitutions(fn.t, input.t); // may throw
+    const [outType, substitutions] = assignFnSubstitutions(fnResolved.t, inputResolved.t); // may throw
   
-    const mergedSubstitutions = mergeMaps(substitutions, fn.substitutions, input.substitutions);
+    const mergedSubstitutions = mergeMaps(substitutions, fnResolved.substitutions, inputResolved.substitutions);
 
-    if (input.kind === "error") {
+    if (inputResolved.kind === "error") {
       return {
         kind: "error",
-        e: input.e, // bubble up the error
+        e: inputResolved.e, // bubble up the error
         depth: 0,
         t: outType,
         substitutions: mergedSubstitutions,
       };
     }
-    if (fn.kind === "error") {
+    if (fnResolved.kind === "error") {
       // also bubble up
       return {
         kind: "error",
-        e: fn.e,
-        depth: fn.depth+1,
+        e: fnResolved.e,
+        depth: fnResolved.depth+1,
         t: outType,
         substitutions: mergedSubstitutions,
       };
     }
     // if the above statement did not throw => types are compatible...
-    if (input.kind === "value" && fn.kind === "value") {
-      const outValue = fn.i(input.i);
+    if (inputResolved.kind === "value" && fnResolved.kind === "value") {
+      const outValue = fnResolved.i(inputResolved.i);
       return {
         kind: "value",
         i: outValue,
@@ -140,31 +142,46 @@ export function evalCallBlock(fn: ResolvedType, input: ResolvedType): ResolvedTy
   catch (e) {
     if ((e instanceof UnifyError)) {
       // even though fn was incompatible with the given parameter, we can still suppose that our output-type will be that of fn...?
-      const outType = fn.t.params[1](fn.t);
+      const outType = fnResolved.t.params[1](fnResolved.t);
       return {
         kind: "error",
         e,
         depth: 0,
         t: outType,
-        substitutions: mergeMaps(fn.substitutions, input.substitutions),
+        substitutions: mergeMaps(fnResolved.substitutions, inputResolved.substitutions),
       };
     }
     throw e;
   }
 }
 
+export function evalCallBlock(fn: EditorState, input: EditorState, env): ResolvedType {
+  const fnResolved = evalEditorBlock(fn, env);
+  const inputResolved = evalEditorBlock(input, env);
+  return evalCallBlock2(fnResolved, inputResolved, env);
+}
+
 export function evalLetInBlock(value: EditorState, name: string, inner: EditorState, env): ResolvedType {
   const valueResolved = evalEditorBlock(value, env);
   const innerEnv = makeInnerEnv(env, name, valueResolved)
   return evalEditorBlock(inner, innerEnv);
 }
 
+export function getUnusedTypeVar(env) {
+  for (let i=0; ; i++) {
+    if (!dict.has(env.typeDict)(TYPE_VARS[i])) {
+      return TYPE_VARS[i];
+    }
+  }
+}
+
 export function evalLambdaBlock(paramName: string, expr: EditorState, env): ResolvedType {
+  const paramType = getUnusedTypeVar(env);
   const fn = (x: any) => {
     const innerEnv = makeInnerEnv(env, paramName, {
       kind: "value",
       i: x,
-      t: TYPE_VARS[0],
+      t: paramType,
       substitutions: new Map(),
     });
     const result = evalEditorBlock(expr, innerEnv);
@@ -175,11 +192,11 @@ export function evalLambdaBlock(paramName: string, expr: EditorState, env): Reso
   // static env: we only know the name and the type
   const staticInnerEnv = makeInnerEnv(env, paramName, {
     kind: "unknown", // parameter value is not statically known
-    t: TYPE_VARS[0],
+    t: paramType,
     substitutions: new Map(),
   });
   const abstractOutput = evalEditorBlock(expr, staticInnerEnv);
-  const t = fnType(_ => entirelyUnknown.t)(_ => abstractOutput.t);
+  const t = fnType(_ => paramType)(_ => abstractOutput.t);
   const T = substitute(t, abstractOutput.substitutions, [])
   return {
     kind: "value",
@@ -194,18 +211,18 @@ export function haveValue(resolved: ResolvedType) {
   return resolved.kind === "value";
 }
 
-function parseLiteral(text: string, type: string): ResolvedType {
+function parseLiteral(text: string, type: string, env): ResolvedType {
   // dirty
   if (type === "Int") {
-    return parseAsInt(text);
+    return parseAsInt(text, env);
   }
   if (type === "Double") {
-    return parseAsDouble(text);
+    return parseAsDouble(text, env);
   }
-  return entirelyUnknown;
+  return entirelyUnknown(env);
 }
 
-function parseAsDouble(text: string): ResolvedType {
+function parseAsDouble(text: string, env): ResolvedType {
   if (text !== '') {
     const num = Number(text);
     if (!Number.isNaN(num)) {
@@ -217,9 +234,9 @@ function parseAsDouble(text: string): ResolvedType {
       };
     }
   }
-  return entirelyUnknown;
+  return entirelyUnknown(env);
 }
-function parseAsInt(text: string): ResolvedType {
+function parseAsInt(text: string, env): ResolvedType {
   if (text !== '') {
     try {
       return {
@@ -231,13 +248,13 @@ function parseAsInt(text: string): ResolvedType {
     }
     catch {}
   }
-  return entirelyUnknown;
+  return entirelyUnknown(env);
 }
 
 const literalParsers = [parseAsDouble, parseAsInt];
 
-export function attemptParseLiteral(text: string): Dynamic[] {
-  return literalParsers.map(parseFn => parseFn(text))
+export function attemptParseLiteral(text: string, env): Dynamic[] {
+  return literalParsers.map(parseFn => parseFn(text, env))
     .filter(resolved => (resolved.kind !== "unknown" && resolved.kind !== "error")) as unknown as Dynamic[];
 }