Finished TidBit 3.

Added some things extra.
2026-02-28 22:32:31 -05:00
parent 778784e30d
commit 4f5a34efaa
3 changed files with 399 additions and 61 deletions
@@ -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;
+}