Finished TidBit 3.

Added some things extra.

11-tidbit-3-tidbit-3-tidbit-3/.clang-format

@@ -0,0 +1,14 @@
+---
+AlignConsecutiveShortCaseStatements:
+  Enabled: true
+  AcrossEmptyLines: true
+  AcrossComments: true
+IndentCaseLabels: true
+AllowShortBlocksOnASingleLine: Always
+AllowShortCaseLabelsOnASingleLine: true
+AllowShortEnumsOnASingleLine: true
+AllowShortIfStatementsOnASingleLine: AllIfsAndElse
+AllowShortLoopsOnASingleLine: true
+IndentWidth: 4
+PointerAlignment: Left
+AlignAfterOpenBracket: BlockIndent

11-tidbit-3-tidbit-3-tidbit-3/main.rkt

@@ -8,6 +8,7 @@ The grammar:
             | { * <TIDBIT> <TIDBIT> }
             | { / <TIDBIT> <TIDBIT> }
             | { with { <id> <TIDBIT> } <TIDBIT> }
+            | { recur { <id> <TIDBIT> } <TIDBIT> }
             | <id>
             | { fun <id> <TIDBIT> }
             | { call <TIDBIT> <TIDBIT> }
@@ -27,6 +28,7 @@ The grammar:
   [Div TIDBIT TIDBIT]
   [Id Symbol]
   [With Symbol TIDBIT TIDBIT]
+  [Recur Symbol TIDBIT TIDBIT]
   [Fun (Listof Symbol) TIDBIT]
   [Call TIDBIT (Listof TIDBIT)]
   [Bind (Listof Symbol) (Listof TIDBIT) TIDBIT]
@@ -78,6 +80,20 @@ The grammar:
     ['() body]
     [else (With (first names) (first vals) (binds* (rest names) (rest vals) body))]))
 
+(: Z : -> TIDBIT)
+; Z combinator!
+(define (Z)
+  (Fun (list 'f)
+       (Call
+        (Fun (list 'x)
+             (Call (Id 'f)
+                   (list (Fun (list 'v)
+                              (Call (Call (Id 'x) (list (Id 'x))) (list (Id 'v)))))))
+        (list (Fun (list 'x)
+                   (Call (Id 'f)
+                         (list (Fun (list 'v)
+                                    (Call (Call (Id 'x) (list (Id 'x))) (list (Id 'v)))))))))))
+
 (: preprocess : TIDBIT BINDING-DEPTH -> CORE)
 (define (preprocess tb bd)
   (cases tb
@@ -89,6 +105,12 @@ The grammar:
     [(Id s) (CIdx (bd s))]
     [(With name value body) (CCall (CFun (preprocess body (binding-encountered bd name)))
                                    (preprocess value bd))]
+    [(Recur name value body)
+     (preprocess
+      (With name
+            (Call (Z) (list (Fun (list name) value)))
+            body)
+      bd)]
     [(Fun params body) (curryfn params body bd)]
     [(Call body args) (currycall (preprocess body bd) args bd)]
 
@@ -118,6 +140,11 @@ The grammar:
        [(list 'with (list (symbol: name) named) body)
         (With name (parse-sexpr named) (parse-sexpr body))]
        [else (error 'parse-sexpr "bad `with' syntax in ~s" sexpr)])]
+    [(cons 'recur more)
+     (match sexpr
+       [(list 'recur (list (symbol: name) named) body)
+        (Recur name (parse-sexpr named) (parse-sexpr body))]
+       [else (error 'parse-sexpr "bad `recur' syntax in ~s" sexpr)])]
 
     ; Function declaration.
     [(cons 'fun more)
@@ -207,6 +234,38 @@ The grammar:
       [else (error 'run "evaluation returned a non-number: ~s"
                    result)])))
 
+; Factorial implemented with the Z combinator implemented in SKI-logic generated
+; with C to be interpreted by TIDBIT which is built on CORE.
+(test (run "{with {I {fun {x} x}} {with {K {fun {x} {fun {y} x}}} {with {S {fun
+{f} {fun {g} {fun {x} {call {call f x} {call g x}}}}}} {with {Z {call {call S
+{call {call S {call {call S {call K S}} {call {call S {call K K}} I}}} {call
+{call S {call {call S {call K S}} {call {call S {call {call S {call K S}} {call
+{call S {call K K}} {call K S}}}} {call {call S {call {call S {call K S}} {call
+{call S {call {call S {call K S}} {call {call S {call K K}} {call K S}}}} {call
+{call S {call {call S {call K S}} {call {call S {call K K}} {call K K}}}} {call
+K I}}}}} {call {call S {call {call S {call K S}} {call {call S {call K K}} {call
+K K}}}} {call K I}}}}}} {call {call S {call K K}} {call K I}}}}} {call {call S
+{call {call S {call K S}} {call {call S {call K K}} I}}} {call {call S {call
+{call S {call K S}} {call {call S {call {call S {call K S}} {call {call S {call
+K K}} {call K S}}}} {call {call S {call {call S {call K S}} {call {call S {call
+{call S {call K S}} {call {call S {call K K}} {call K S}}}} {call {call S {call
+{call S {call K S}} {call {call S {call K K}} {call K K}}}} {call K I}}}}} {call
+{call S {call {call S {call K S}} {call {call S {call K K}} {call K K}}}} {call
+K I}}}}}} {call {call S {call K K}} {call K I}}}}}} {with {fact {call Z {fun {f}
+{fun {n} {if0 n 1 {* n {call f {- n 1}}}}}}}} {call fact 5}}}}}} ") => 120)
+; C program for generating SKI/TIDBIT code at the bottom of this file.
+
+(test (run
+       "{recur {Y {fun {n} {if0 n 1 {* n {call Y {- n 1}}}}}} {call Y 5}}")
+
+      => 120)
+(test (run
+       "{recur {fact {fun {Y} {if0 Y 1 {* Y {call fact {- Y 1}}}}}} {call fact 5}}")
+
+      => 120)
+
+(test (run "{recur {fact {fun {n} {if0 n 1 {* n {call fact {- n 1}}}}}} {call fact 5}}") => 120)
+
 (test (run "{if0 0 1 2}") => 1)
 (test (run "{if0 1 1 2}") => 2)
 
@@ -275,3 +334,138 @@ The grammar:
                         {fun {x} {fun {y} {+ x y}}}}
                   123}")
       => 124)
+
+#|
+
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+// AST; variable, application, lambda.
+typedef enum { VAR, APP, LAM } Tag;
+
+typedef struct Term {
+    Tag tag;
+    const char* name;   // For VAR.
+    struct Term *f, *a; // For APP: function and argument.
+    const char* param;  // For LAM: bound variable name.
+    struct Term* body;  // For LAM: body expression.
+} Term;
+
+static Term* var(const char* n) {
+    Term* t = malloc(sizeof *t);
+    t->tag = VAR;
+    t->name = n;
+    return t;
+}
+
+static Term* app(Term* f, Term* a) {
+    Term* t = malloc(sizeof *t);
+    t->tag = APP;
+    t->f = f;
+    t->a = a;
+    return t;
+}
+
+static Term* lam(const char* p, Term* b) {
+    Term* t = malloc(sizeof *t);
+    t->tag = LAM;
+    t->param = p;
+    t->body = b;
+    return t;
+}
+
+static Term* elim(Term* t);
+
+// [v]t → SKI
+static Term* bracket(const char* v, Term* t) {
+    if (t->tag == VAR)
+        return strcmp(v, t->name) == 0
+                   ? var("I")
+                   : app(var("K"), t); // [v]v = I, [v]x = K x
+    if (t->tag == APP)
+        return app(
+            app(var("S"), bracket(v, t->f)), bracket(v, t->a)
+        ); // [v](p q) = S ([v]p) ([v]q)
+    fprintf(stderr, "tf did you just do\n");
+    exit(1);
+}
+
+// Eliminate the λs.
+static Term* elim(Term* t) {
+    switch (t->tag) {
+        case VAR: return t;
+        case APP: return app(elim(t->f), elim(t->a));
+        case LAM: return bracket(t->param, elim(t->body));
+    }
+    return NULL;
+}
+
+// Man I love how C provides such a rich standard library for strings.
+typedef struct {
+    char* buf;
+    size_t len, cap;
+} Str;
+
+static void sb_init(Str* s) {
+    s->buf = NULL;
+    s->len = s->cap = 0;
+}
+
+static void sb_putc(Str* s, char c) {
+    if (s->len + 1 >= s->cap) {
+        s->cap = s->cap ? s->cap * 2 : 256;
+        s->buf = realloc(s->buf, s->cap);
+    }
+    s->buf[s->len++] = c;
+    s->buf[s->len] = 0;
+}
+
+static void sb_puts(Str* s, const char* p) {
+    while (*p) sb_putc(s, *p++);
+}
+
+static void spit_out(Str* s, Term* t) {
+    switch (t->tag) {
+        case VAR: sb_puts(s, t->name); return;
+        case APP:
+            sb_puts(s, "{call ");
+            spit_out(s, t->f);
+            sb_putc(s, ' ');
+            spit_out(s, t->a);
+            sb_putc(s, '}');
+            return;
+        default: fprintf(stderr, "Tried to spit out a lambda D:\n"); exit(1);
+    }
+}
+
+int main(void) {
+    // First we construct the z combinator in SKI...
+    Term* z =
+        lam("f",
+            app(lam("x", app(var("f"),
+                             lam("v", app(app(var("x"), var("x")), var("v"))))),
+                lam("x", app(var("f"), lam("v", app(app(var("x"), var("x")),
+                                                    var("v")))))));
+    Term* z_ski = elim(z);
+    Str z_txt;
+    sb_init(&z_txt);
+    spit_out(&z_txt, z_ski);
+
+    // Then print the factorial function using it.
+    printf(
+        "{with {I {fun {x} x}} "
+        "{with {K {fun {x} {fun {y} x}}} "
+        "{with {S {fun {f} {fun {g} {fun {x} {call {call f x} {call g x}}}}}} "
+        "{with {Z %s} " // <<<< Z combinator goes here.
+        "{with {fact {call Z {fun {f} {fun {n} {if0 n 1 {* n {call f {- n "
+        "1}}}}}}}} "
+        "{call fact 5}}}}}}\n",
+        z_txt.buf
+    );
+
+    free(z_txt.buf);
+    return 0;
+}
+
+|#

11-tidbit-3-tidbit-3-tidbit-3/ski.c

@@ -0,0 +1,130 @@
+#include <stdio.h>
+#include <stdlib.h>
+#include <string.h>
+
+// AST; variable, application, lambda.
+typedef enum { VAR, APP, LAM } Tag;
+
+typedef struct Term {
+    Tag tag;
+    const char* name;   // For VAR.
+    struct Term *f, *a; // For APP: function and argument.
+    const char* param;  // For LAM: bound variable name.
+    struct Term* body;  // For LAM: body expression.
+} Term;
+
+static Term* var(const char* n) {
+    Term* t = malloc(sizeof *t);
+    t->tag = VAR;
+    t->name = n;
+    return t;
+}
+
+static Term* app(Term* f, Term* a) {
+    Term* t = malloc(sizeof *t);
+    t->tag = APP;
+    t->f = f;
+    t->a = a;
+    return t;
+}
+
+static Term* lam(const char* p, Term* b) {
+    Term* t = malloc(sizeof *t);
+    t->tag = LAM;
+    t->param = p;
+    t->body = b;
+    return t;
+}
+
+static Term* elim(Term* t);
+
+// [v]t → SKI
+static Term* bracket(const char* v, Term* t) {
+    if (t->tag == VAR)
+        return strcmp(v, t->name) == 0
+                   ? var("I")
+                   : app(var("K"), t); // [v]v = I, [v]x = K x
+    if (t->tag == APP)
+        return app(
+            app(var("S"), bracket(v, t->f)), bracket(v, t->a)
+        ); // [v](p q) = S ([v]p) ([v]q)
+    fprintf(stderr, "tf did you just do\n");
+    exit(1);
+}
+
+// Eliminate the λs.
+static Term* elim(Term* t) {
+    switch (t->tag) {
+        case VAR: return t;
+        case APP: return app(elim(t->f), elim(t->a));
+        case LAM: return bracket(t->param, elim(t->body));
+    }
+    return NULL;
+}
+
+// Man I love how C provides such a rich standard library for strings.
+typedef struct {
+    char* buf;
+    size_t len, cap;
+} Str;
+
+static void sb_init(Str* s) {
+    s->buf = NULL;
+    s->len = s->cap = 0;
+}
+
+static void sb_putc(Str* s, char c) {
+    if (s->len + 1 >= s->cap) {
+        s->cap = s->cap ? s->cap * 2 : 256;
+        s->buf = realloc(s->buf, s->cap);
+    }
+    s->buf[s->len++] = c;
+    s->buf[s->len] = 0;
+}
+
+static void sb_puts(Str* s, const char* p) {
+    while (*p) sb_putc(s, *p++);
+}
+
+static void spit_out(Str* s, Term* t) {
+    switch (t->tag) {
+        case VAR: sb_puts(s, t->name); return;
+        case APP:
+            sb_puts(s, "{call ");
+            spit_out(s, t->f);
+            sb_putc(s, ' ');
+            spit_out(s, t->a);
+            sb_putc(s, '}');
+            return;
+        default: fprintf(stderr, "Tried to spit out a lambda D:\n"); exit(1);
+    }
+}
+
+int main(void) {
+    // First we construct the z combinator in SKI...
+    Term* z =
+        lam("f",
+            app(lam("x", app(var("f"),
+                             lam("v", app(app(var("x"), var("x")), var("v"))))),
+                lam("x", app(var("f"), lam("v", app(app(var("x"), var("x")),
+                                                    var("v")))))));
+    Term* z_ski = elim(z);
+    Str z_txt;
+    sb_init(&z_txt);
+    spit_out(&z_txt, z_ski);
+
+    // Then print the factorial function using it.
+    printf(
+        "{with {I {fun {x} x}} "
+        "{with {K {fun {x} {fun {y} x}}} "
+        "{with {S {fun {f} {fun {g} {fun {x} {call {call f x} {call g x}}}}}} "
+        "{with {Z %s} " // <<<< Z combinator goes here.
+        "{with {fact {call Z {fun {f} {fun {n} {if0 n 1 {* n {call f {- n "
+        "1}}}}}}}} "
+        "{call fact 5}}}}}}\n",
+        z_txt.buf
+    );
+
+    free(z_txt.buf);
+    return 0;
+}