"true", "false", "if" and "isZero".

aktemur · Dec 3, 2016 · 5ef5b3c · 5ef5b3c
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diff --git a/Lambda/README.md b/Lambda/README.md
@@ -94,3 +94,20 @@ Multiplication and "predecessor" function:
 - : string = "(\\f.(\\x.(f (f (f (f x))))))"
 ```
 
+Booleans, "if", and "isZero" predicate:
+
+```ocaml
+# str(run "true");;       
+- : string = "(\\a.(\\b.a))"
+# str(run "false");;
+- : string = "(\\a.(\\b.b))"
+# str(run "isZero zero");;
+- : string = "(\\a.(\\b.a))"
+# str(run "isZero one");; 
+- : string = "(\\a.(\\b.b))"
+# str(run "if (isZero (pred one)) three four");;
+- : string = "(\\f.(\\x.(f (f (f x)))))"
+# str(run "if (isZero one) three four");;       
+- : string = "(\\f.(\\x.(f (f (f (f x))))))"
+```
+
diff --git a/Lambda/grammar.mly b/Lambda/grammar.mly
@@ -11,6 +11,7 @@
 %token ZERO ONE TWO THREE FOUR
 %token SUCC ADD
 %token MULT PRED
+%token IF TRUE FALSE ISZERO
 
 %start main
 %type <expr> main
@@ -44,6 +45,11 @@ atomExpr:
                      App(App(App(Var "n", Lambda("g", Lambda("h", App(Var "h", App(Var "g", Var "f"))))),
                              Lambda("u", Var "x")),
                          Lambda("u", Var "u"))))) } 
+  | TRUE      { Lambda("a", Lambda("b", Var "a")) }
+  | FALSE     { Lambda("a", Lambda("b", Var "b")) }
+  | IF        { Lambda("cond", Lambda("then", Lambda("else", App(App(Var "cond", Var "then"), Var "else")))) }
+  | ISZERO    { Lambda("n", App(App(Var "n", Lambda("x", Lambda("a", Lambda("b", Var "b")))),
+                                Lambda("a", Lambda("b", Var "a")))) }
   | LPAR expression RPAR               { $2 }
 ;
 

diff --git a/Lambda/lexer.mll b/Lambda/lexer.mll
@@ -28,6 +28,10 @@ let keyword s =
     | "add"   -> ADD
     | "mult"  -> MULT
     | "pred"  -> PRED
+    | "if"    -> IF
+    | "true"  -> TRUE
+    | "false" -> FALSE
+    | "isZero" -> ISZERO
     | _       -> NAME s
 }