6 files changed, 618 insertions, 65 deletions

diff --git a/src/runtime/c/pgf/expr.c b/src/runtime/c/pgf/expr.c
index 170751b8b..bcbfa0d09 100644
--- a/src/runtime/c/pgf/expr.c
+++ b/src/runtime/c/pgf/expr.c
@@ -88,7 +88,7 @@ GU_DEFINE_TYPE(PgfLiteral, GuVariant,
 GU_DECLARE_TYPE(PgfType, struct);
 
 GU_DEFINE_TYPE(PgfHypo, struct,
-	       GU_MEMBER(PgfHypo, bindtype, PgfBindType),
+	       GU_MEMBER(PgfHypo, bind_type, PgfBindType),
 	       GU_MEMBER(PgfHypo, cid, PgfCId),
 	       GU_MEMBER_P(PgfHypo, type, PgfType));
 
@@ -137,7 +137,16 @@ typedef struct PgfExprParser PgfExprParser;
 typedef enum {
 	PGF_TOKEN_LPAR,
 	PGF_TOKEN_RPAR,
+	PGF_TOKEN_LCURLY,
+	PGF_TOKEN_RCURLY,
 	PGF_TOKEN_QUESTION,
+	PGF_TOKEN_LAMBDA,
+	PGF_TOKEN_RARROW,
+	PGF_TOKEN_LTRIANGLE,
+	PGF_TOKEN_RTRIANGLE,
+	PGF_TOKEN_COMMA,
+	PGF_TOKEN_COLON,
+	PGF_TOKEN_WILD,
 	PGF_TOKEN_IDENT,
 	PGF_TOKEN_INT,
 	PGF_TOKEN_FLT,
@@ -172,11 +181,6 @@ pgf_expr_parser_token(PgfExprParser* parser)
 	while (isspace(parser->ch)) {
 		pgf_expr_parser_getc(parser);
 	}
-	
-	if (parser->tmp_pool != NULL) {
-		gu_pool_free(parser->tmp_pool);
-		parser->tmp_pool = NULL;
-	}
 
 	parser->token_tag   = PGF_TOKEN_UNKNOWN;
 	parser->token_value = gu_null_seq;
@@ -193,12 +197,50 @@ pgf_expr_parser_token(PgfExprParser* parser)
 		pgf_expr_parser_getc(parser);
 		parser->token_tag = PGF_TOKEN_RPAR;
 		break;
+	case '{':
+		pgf_expr_parser_getc(parser);
+		parser->token_tag = PGF_TOKEN_LCURLY;
+		break;
+	case '}':
+		pgf_expr_parser_getc(parser);
+		parser->token_tag = PGF_TOKEN_RCURLY;
+		break;
+	case '<':
+		pgf_expr_parser_getc(parser);
+		parser->token_tag = PGF_TOKEN_LTRIANGLE;
+		break;
+	case '>':
+		pgf_expr_parser_getc(parser);
+		parser->token_tag = PGF_TOKEN_RTRIANGLE;
+		break;
 	case '?':
 		pgf_expr_parser_getc(parser);
 		parser->token_tag = PGF_TOKEN_QUESTION;
 		break;
+	case '\\':
+		pgf_expr_parser_getc(parser);
+		parser->token_tag = PGF_TOKEN_LAMBDA;
+		break;
+	case '-':
+		pgf_expr_parser_getc(parser);
+		if (parser->ch == '>') {
+			pgf_expr_parser_getc(parser);
+			parser->token_tag = PGF_TOKEN_RARROW;
+		}
+		break;
+	case ',':
+		pgf_expr_parser_getc(parser);
+		parser->token_tag = PGF_TOKEN_COMMA;
+		break;
+	case ':':
+		pgf_expr_parser_getc(parser);
+		parser->token_tag = PGF_TOKEN_COLON;
+		break;
+	case '_':
+		pgf_expr_parser_getc(parser);
+		parser->token_tag = PGF_TOKEN_WILD;
+		break;
 	default: {
-		parser->tmp_pool = gu_new_pool();
 		GuCharBuf* chars = gu_new_buf(char, parser->tmp_pool);
 
 		if (isalpha(parser->ch)) {
@@ -249,9 +291,22 @@ pgf_expr_parser_token(PgfExprParser* parser)
 	}
 }
 
+static bool
+pgf_expr_parser_lookahead(PgfExprParser* parser, int ch)
+{
+	while (isspace(parser->ch)) {
+		pgf_expr_parser_getc(parser);
+	}
+	
+	return (parser->ch == ch);
+}
+
 static PgfExpr
 pgf_expr_parser_expr(PgfExprParser* parser);
 
+static PgfType*
+pgf_expr_parser_type(PgfExprParser* parser);
+
 static PgfExpr
 pgf_expr_parser_term(PgfExprParser* parser)
 {
@@ -266,6 +321,27 @@ pgf_expr_parser_term(PgfExprParser* parser)
 			return gu_null_variant;
 		}
 	}
+	case PGF_TOKEN_LTRIANGLE: {
+		pgf_expr_parser_token(parser);
+		PgfExpr expr = pgf_expr_parser_expr(parser);
+		
+		if (parser->token_tag != PGF_TOKEN_COLON) {
+			return gu_null_variant;
+		}
+		pgf_expr_parser_token(parser);
+
+		PgfType* type = pgf_expr_parser_type(parser);
+
+		if (parser->token_tag != PGF_TOKEN_RTRIANGLE) {
+			return gu_null_variant;
+		}
+		pgf_expr_parser_token(parser);
+
+		return gu_new_variant_i(parser->expr_pool,
+					PGF_EXPR_TYPED,
+					PgfExprTyped,
+					expr, type);
+	}
 	case PGF_TOKEN_QUESTION: {
 		pgf_expr_parser_token(parser);
 		return gu_new_variant_i(parser->expr_pool,
@@ -334,40 +410,353 @@ pgf_expr_parser_term(PgfExprParser* parser)
 }
 
 static PgfExpr
+pgf_expr_parser_arg(PgfExprParser* parser)
+{
+	PgfExpr arg;
+
+	if (parser->token_tag == PGF_TOKEN_LCURLY) {
+		pgf_expr_parser_token(parser);
+
+		arg = pgf_expr_parser_expr(parser);
+		if (gu_variant_is_null(arg))
+			return gu_null_variant;
+
+		if (parser->token_tag != PGF_TOKEN_RCURLY) {
+			return gu_null_variant;
+		}
+
+		pgf_expr_parser_token(parser);
+
+		arg = gu_new_variant_i(parser->expr_pool,
+				  PGF_EXPR_IMPL_ARG,
+				  PgfExprImplArg,
+				  arg);
+	} else {
+		arg = pgf_expr_parser_term(parser);
+	}
+
+	return arg;
+}
+
+static bool
+pgf_expr_parser_bind(PgfExprParser* parser, GuBuf* binds)
+{
+	PgfCId var;
+	PgfBindType bind_type = PGF_BIND_TYPE_EXPLICIT;
+
+	if (parser->token_tag == PGF_TOKEN_LCURLY) {
+		bind_type = PGF_BIND_TYPE_IMPLICIT;
+		pgf_expr_parser_token(parser);
+	}
+
+	for (;;) {
+		if (parser->token_tag == PGF_TOKEN_IDENT) {
+			char* str = 
+				gu_chars_str(parser->token_value, parser->tmp_pool);
+			var = gu_str_string(str, parser->expr_pool);
+			pgf_expr_parser_token(parser);
+		} else if (parser->token_tag == PGF_TOKEN_WILD) {
+			var = gu_str_string("_", parser->expr_pool);
+			pgf_expr_parser_token(parser);
+		} else {
+			return false;
+		}
+
+		PgfExpr bind =
+			gu_new_variant_i(parser->expr_pool,
+								PGF_EXPR_ABS,
+								PgfExprAbs,
+								bind_type,
+								var,
+								gu_null_variant);
+		gu_buf_push(binds, PgfExpr, bind);
+		
+		if (bind_type == PGF_BIND_TYPE_EXPLICIT ||
+		    parser->token_tag != PGF_TOKEN_COMMA) {
+			break;
+		}
+		
+		pgf_expr_parser_token(parser);
+	}
+
+	if (bind_type == PGF_BIND_TYPE_IMPLICIT) {
+		if (parser->token_tag != PGF_TOKEN_RCURLY)
+			return false;
+		pgf_expr_parser_token(parser);
+	}
+
+	return true;
+}
+
+static GuBuf*
+pgf_expr_parser_binds(PgfExprParser* parser)
+{
+	GuBuf* binds = gu_new_buf(PgfExpr, parser->tmp_pool);
+
+	for (;;) {
+		if (!pgf_expr_parser_bind(parser, binds))
+			return NULL;
+
+		if (parser->token_tag != PGF_TOKEN_COMMA)
+			break;
+
+		pgf_expr_parser_token(parser);
+	}
+
+	return binds;
+}
+
+static PgfExpr
 pgf_expr_parser_expr(PgfExprParser* parser)
 {
-	PgfExpr expr = pgf_expr_parser_term(parser);
-	if (gu_variant_is_null(expr))
+	if (parser->token_tag == PGF_TOKEN_LAMBDA) {
+		pgf_expr_parser_token(parser);
+		GuBuf* binds = pgf_expr_parser_binds(parser);
+		if (binds == NULL)
+			return gu_null_variant;
+
+		if (parser->token_tag != PGF_TOKEN_RARROW) {
+			return gu_null_variant;
+		}
+		pgf_expr_parser_token(parser);
+
+		PgfExpr expr = pgf_expr_parser_expr(parser);
+		if (gu_variant_is_null(expr))
+			return gu_null_variant;
+
+		size_t n_binds = gu_buf_length(binds);
+		for (size_t i = n_binds; i > 0; i--) {
+			PgfExpr bind = gu_buf_get(binds, PgfExpr, i-1);
+
+			((PgfExprAbs*) gu_variant_data(bind))->body = expr;
+			expr = bind;
+		}
+
 		return expr;
+	} else {
+		PgfExpr expr = pgf_expr_parser_term(parser);
+		if (gu_variant_is_null(expr))
+			return gu_null_variant;
 
-	while (true) {
-		PgfExpr arg = pgf_expr_parser_term(parser);
-		if (gu_variant_is_null(arg)) {
-			return expr;
+		while (parser->token_tag != PGF_TOKEN_EOF &&
+		       parser->token_tag != PGF_TOKEN_RPAR &&
+		       parser->token_tag != PGF_TOKEN_RCURLY &&
+		       parser->token_tag != PGF_TOKEN_RTRIANGLE &&
+		       parser->token_tag != PGF_TOKEN_COLON) {
+			PgfExpr arg = pgf_expr_parser_arg(parser);
+			if (gu_variant_is_null(arg))
+				return gu_null_variant;
+
+			expr = gu_new_variant_i(parser->expr_pool,
+						PGF_EXPR_APP,
+						PgfExprApp,
+						expr, arg);
 		}
-		expr = gu_new_variant_i(parser->expr_pool,
-					PGF_EXPR_APP,
-					PgfExprApp,
-					expr, arg);
+		
+		return expr;
 	}
 }
 
-PgfExpr
-pgf_read_expr(GuIn* in, GuPool* pool, GuExn* err)
+static bool
+pgf_expr_parser_hypos(PgfExprParser* parser, GuBuf* hypos)
+{
+	PgfCId var;
+	PgfBindType bind_type = PGF_BIND_TYPE_EXPLICIT;
+
+	for (;;) {
+		if (bind_type == PGF_BIND_TYPE_EXPLICIT &&
+		    parser->token_tag == PGF_TOKEN_LCURLY) {
+			bind_type = PGF_BIND_TYPE_IMPLICIT;
+			pgf_expr_parser_token(parser);
+		}
+
+		if (parser->token_tag == PGF_TOKEN_IDENT) {
+			char* str = 
+				gu_chars_str(parser->token_value, parser->tmp_pool);
+			var = gu_str_string(str, parser->expr_pool);
+			pgf_expr_parser_token(parser);
+		} else if (parser->token_tag == PGF_TOKEN_WILD) {
+			var = gu_str_string("_", parser->expr_pool);
+			pgf_expr_parser_token(parser);
+		} else {
+			return false;
+		}
+
+		PgfHypo* hypo = gu_buf_extend(hypos);
+		hypo->bind_type = bind_type;
+		hypo->cid = var;
+		hypo->type = NULL;
+
+		if (bind_type == PGF_BIND_TYPE_IMPLICIT &&
+			parser->token_tag == PGF_TOKEN_RCURLY) {
+			bind_type = PGF_BIND_TYPE_EXPLICIT;
+			pgf_expr_parser_token(parser);
+		}
+
+		if (parser->token_tag != PGF_TOKEN_COMMA) {
+			break;
+		}
+		
+		pgf_expr_parser_token(parser);
+	}
+
+	if (bind_type == PGF_BIND_TYPE_IMPLICIT)
+		return false;
+
+	return true;
+}
+
+static PgfType*
+pgf_expr_parser_atom(PgfExprParser* parser)
+{
+	if (parser->token_tag != PGF_TOKEN_IDENT)
+		return NULL;
+
+	char* str =
+		gu_chars_str(parser->token_value, parser->tmp_pool);
+	PgfCId cid = gu_str_string(str, parser->expr_pool);
+	pgf_expr_parser_token(parser);
+
+	GuBuf* args = gu_new_buf(PgfExpr, parser->tmp_pool);
+	while (parser->token_tag != PGF_TOKEN_EOF &&
+		   parser->token_tag != PGF_TOKEN_RPAR &&
+		   parser->token_tag != PGF_TOKEN_RTRIANGLE &&
+		   parser->token_tag != PGF_TOKEN_RARROW) {
+		PgfExpr arg =
+			pgf_expr_parser_arg(parser);
+		if (gu_variant_is_null(arg))
+			return NULL;
+			
+		gu_buf_push(args, PgfExpr, arg);
+	}
+
+	size_t n_exprs = gu_buf_length(args);
+
+	PgfType* type = gu_new_flex(parser->expr_pool, PgfType, exprs, n_exprs);
+	type->hypos   = gu_empty_seq();
+	type->cid     = cid;
+	type->n_exprs = n_exprs;
+
+	for (size_t i = 0; i < n_exprs; i++) {
+		type->exprs[i] = gu_buf_get(args, PgfExpr, i);
+	}
+	
+	return type;
+}
+
+static PgfType*
+pgf_expr_parser_type(PgfExprParser* parser)
+{
+	PgfType* type = NULL;
+	GuBuf* hypos = gu_new_buf(PgfHypo, parser->expr_pool);
+
+	for (;;) {
+		if (parser->token_tag == PGF_TOKEN_LPAR) {
+			pgf_expr_parser_token(parser);
+
+			size_t n_start = gu_buf_length(hypos);
+
+			if ((parser->token_tag == PGF_TOKEN_IDENT &&
+			     (pgf_expr_parser_lookahead(parser, ',') || 
+				  pgf_expr_parser_lookahead(parser, ':'))) ||
+				(parser->token_tag == PGF_TOKEN_LCURLY) ||
+				(parser->token_tag == PGF_TOKEN_WILD)) {
+
+				if (!pgf_expr_parser_hypos(parser, hypos))
+					return NULL;
+
+				if (parser->token_tag != PGF_TOKEN_COLON)
+					return NULL;
+
+				pgf_expr_parser_token(parser);
+			} else {
+				PgfHypo* hypo = gu_buf_extend(hypos);
+				hypo->bind_type = PGF_BIND_TYPE_EXPLICIT;
+				hypo->cid = gu_str_string("_", parser->expr_pool);
+				hypo->type = NULL;
+			}
+
+			size_t n_end = gu_buf_length(hypos);
+
+			PgfType* type = pgf_expr_parser_type(parser);
+			if (type == NULL)
+				return NULL;
+
+			if (parser->token_tag != PGF_TOKEN_RPAR)
+				return NULL;
+
+			pgf_expr_parser_token(parser);
+
+			if (parser->token_tag != PGF_TOKEN_RARROW)
+				return NULL;
+
+			pgf_expr_parser_token(parser);
+			
+			for (size_t i = n_start; i < n_end; i++) {
+				PgfHypo* hypo = gu_buf_index(hypos, PgfHypo, i);
+				hypo->type = type;
+			}
+		} else {
+			type = pgf_expr_parser_atom(parser);
+			if (type == NULL)
+				return NULL;
+
+			if (parser->token_tag != PGF_TOKEN_RARROW)
+				break;
+
+			pgf_expr_parser_token(parser);
+
+			PgfHypo* hypo = gu_buf_extend(hypos);
+			hypo->bind_type = PGF_BIND_TYPE_EXPLICIT;
+			hypo->cid = gu_str_string("_", parser->expr_pool);
+			hypo->type = type;
+		}
+	}
+
+	type->hypos = gu_buf_seq(hypos);
+
+	return type;
+}
+
+static PgfExprParser*
+pgf_new_parser(GuIn* in, GuPool* pool, GuPool* tmp_pool, GuExn* err)
 {
-	GuPool* tmp_pool = gu_new_pool();
 	PgfExprParser* parser = gu_new(PgfExprParser, tmp_pool);
 	parser->err = err;
 	parser->in = in;
 	parser->expr_pool = pool;
-	parser->tmp_pool = NULL;
+	parser->tmp_pool = tmp_pool;
 	parser->ch = ' ';
 	pgf_expr_parser_token(parser);
+	return parser;
+}
+
+PgfExpr
+pgf_read_expr(GuIn* in, GuPool* pool, GuExn* err)
+{
+	GuPool* tmp_pool = gu_new_pool();
+	PgfExprParser* parser = 
+		pgf_new_parser(in, pool, tmp_pool, err);
 	PgfExpr expr = pgf_expr_parser_expr(parser);
+	if (parser->token_tag != PGF_TOKEN_EOF)
+		return gu_null_variant;
 	gu_pool_free(tmp_pool);
 	return expr;
 }
 
+PgfType*
+pgf_read_type(GuIn* in, GuPool* pool, GuExn* err)
+{
+	GuPool* tmp_pool = gu_new_pool();
+	PgfExprParser* parser = 
+		pgf_new_parser(in, pool, tmp_pool, err);
+	PgfType* type = pgf_expr_parser_type(parser);
+	if (parser->token_tag != PGF_TOKEN_EOF)
+		return NULL;
+	gu_pool_free(tmp_pool);
+	return type;
+}
+
 bool
 pgf_literal_eq(PgfLiteral lit1, PgfLiteral lit2)
 {
@@ -470,14 +859,56 @@ pgf_print_literal(PgfLiteral lit,
 }
 
 void
-pgf_print_expr(PgfExpr expr, int prec,
-			  GuWriter* wtr, GuExn* err)
+pgf_print_expr(PgfExpr expr, PgfPrintContext* ctxt, int prec,
+               GuWriter* wtr, GuExn* err)
 {
 	GuVariantInfo ei = gu_variant_open(expr);
 	switch (ei.tag) {
-	case PGF_EXPR_FUN: {
-		PgfExprFun* fun = ei.data;
-		gu_string_write(fun->fun, wtr, err);
+	case PGF_EXPR_ABS: {
+		PgfExprAbs* abs = ei.data;
+
+		if (prec > 1) {
+			gu_puts("(", wtr, err);
+		}
+
+		gu_putc('\\', wtr, err);
+		
+		PgfPrintContext* new_ctxt = ctxt;
+
+		for (;;) {
+			if (abs->bind_type == PGF_BIND_TYPE_IMPLICIT) {
+				gu_putc('{', wtr, err);
+			}
+			gu_string_write(abs->id, wtr, err);
+			if (abs->bind_type == PGF_BIND_TYPE_IMPLICIT) {
+				gu_putc('}', wtr, err);
+			}
+
+			PgfPrintContext* c = malloc(sizeof(PgfPrintContext));
+			c->name = abs->id;
+			c->next = new_ctxt;
+			new_ctxt = c;
+
+			if (gu_variant_tag(abs->body) != PGF_EXPR_ABS)
+				break;
+				
+			gu_putc(',', wtr, err);
+			
+			abs = gu_variant_data(abs->body);
+		}
+
+		gu_puts(" -> ", wtr, err);
+		pgf_print_expr(abs->body, new_ctxt, 1, wtr, err);
+
+		while (new_ctxt != ctxt) {
+			PgfPrintContext* next = new_ctxt->next;
+			free(new_ctxt);
+			new_ctxt = next;
+		}
+
+		if (prec > 1) {
+			gu_puts(")", wtr, err);
+		}
 		break;
 	}
 	case PGF_EXPR_APP: {
@@ -485,9 +916,9 @@ pgf_print_expr(PgfExpr expr, int prec,
 		if (prec > 3) {
 			gu_puts("(", wtr, err);
 		}
-		pgf_print_expr(app->fun, 3, wtr, err);
+		pgf_print_expr(app->fun, ctxt, 3, wtr, err);
 		gu_puts(" ", wtr, err);
-		pgf_print_expr(app->arg, 4, wtr, err);
+		pgf_print_expr(app->arg, ctxt, 4, wtr, err);
 		if (prec > 3) {
 			gu_puts(")", wtr, err);
 		}
@@ -501,25 +932,57 @@ pgf_print_expr(PgfExpr expr, int prec,
 	case PGF_EXPR_META:
 		gu_putc('?', wtr, err);
 		break;
-	case PGF_EXPR_ABS:
-	case PGF_EXPR_VAR:
-	case PGF_EXPR_TYPED:
-	case PGF_EXPR_IMPL_ARG:
-		gu_impossible();
+	case PGF_EXPR_FUN: {
+		PgfExprFun* fun = ei.data;
+		gu_string_write(fun->fun, wtr, err);
+		break;
+	}
+	case PGF_EXPR_VAR: {
+		PgfExprVar* evar = ei.data;
+		
+		int var = evar->var;
+		PgfPrintContext* c = ctxt;
+		while (c != NULL && var > 0) {
+			c = ctxt->next;
+		}
+		
+		if (c == NULL) {
+			gu_printf(wtr, err, "#%d", evar->var);
+		} else {
+			gu_string_write(c->name, wtr, err);
+		}
+		break;
+	}
+	case PGF_EXPR_TYPED: {
+		PgfExprTyped* typed = ei.data;
+		gu_putc('<', wtr, err);
+		pgf_print_expr(typed->expr, ctxt, 0, wtr, err);
+		gu_puts(" : ", wtr, err);
+		pgf_print_type(typed->type, ctxt, 0, wtr, err);
+		gu_putc('>', wtr, err);
+		break;
+	}
+	case PGF_EXPR_IMPL_ARG: {
+		PgfExprImplArg* impl = ei.data;
+		gu_putc('{', wtr, err);
+		pgf_print_expr(impl->expr, ctxt, 0, wtr, err);
+		gu_putc('}', wtr, err);
 		break;
+	}
 	default:
 		gu_impossible();
 	}
 }
 
-void
-pgf_print_hypo(PgfHypo *hypo, int prec, GuWriter *wtr, GuExn *err)
+PgfPrintContext*
+pgf_print_hypo(PgfHypo *hypo, PgfPrintContext* ctxt, int prec,
+               GuWriter *wtr, GuExn *err)
 {
-    if (hypo->bindtype == PGF_BIND_TYPE_IMPLICIT) {
+    if (hypo->bind_type == PGF_BIND_TYPE_IMPLICIT) {
         gu_puts("({", wtr, err);
         gu_string_write(hypo->cid, wtr, err);
         gu_puts("} : ", wtr, err);
-        pgf_print_type(hypo->type, 0, wtr, err);
+        pgf_print_type(hypo->type, ctxt, 0, wtr, err);
         gu_puts(")", wtr, err);
     } else {
         GuPool* tmp_pool = gu_new_pool();
@@ -529,27 +992,34 @@ pgf_print_hypo(PgfHypo *hypo, int prec, GuWriter *wtr, GuExn *err)
             gu_puts("(", wtr, err);
             gu_string_write(hypo->cid, wtr, err);
             gu_puts(" : ", wtr, err);
-            pgf_print_type(hypo->type, 0, wtr, err);
+            pgf_print_type(hypo->type, ctxt, 0, wtr, err);
             gu_puts(")", wtr, err);
         } else {
-            pgf_print_type(hypo->type, prec, wtr, err);
+            pgf_print_type(hypo->type, ctxt, prec, wtr, err);
         }
         
         gu_pool_free(tmp_pool);
     }
+    
+	PgfPrintContext* new_ctxt = malloc(sizeof(PgfPrintContext));
+	new_ctxt->name = hypo->cid;
+	new_ctxt->next = ctxt;
+	return new_ctxt;
 }
 
 void
-pgf_print_type(PgfType *type, int prec, GuWriter *wtr, GuExn *err)
+pgf_print_type(PgfType *type, PgfPrintContext* ctxt, int prec,
+               GuWriter *wtr, GuExn *err)
 {
     size_t n_hypos = gu_seq_length(type->hypos);
     
     if (n_hypos > 0) {
 		if (prec > 0) gu_putc('(', wtr, err);
 		
+		PgfPrintContext* new_ctxt = ctxt;
 		for (size_t i = 0; i < n_hypos; i++) {
 			PgfHypo *hypo = gu_seq_index(type->hypos, PgfHypo, i);
-			pgf_print_hypo(hypo, 1, wtr, err);
+			new_ctxt = pgf_print_hypo(hypo, new_ctxt, 1, wtr, err);
 
 			gu_puts(" -> ", wtr, err);
 		}
@@ -558,9 +1028,15 @@ pgf_print_type(PgfType *type, int prec, GuWriter *wtr, GuExn *err)
     
 		for (size_t i = 0; i < type->n_exprs; i++) {
 			gu_puts(" ", wtr, err);
-			pgf_print_expr(type->exprs[i], 4, wtr, err);
+			pgf_print_expr(type->exprs[i], new_ctxt, 4, wtr, err);
 		}
-		
+
+		while (new_ctxt != ctxt) {
+			PgfPrintContext* next = new_ctxt->next;
+			free(new_ctxt);
+			new_ctxt = next;
+		}
+
 		if (prec > 0) gu_putc(')', wtr, err);
 	} else if (type->n_exprs > 0) {
 		if (prec > 3) gu_putc('(', wtr, err);
@@ -569,7 +1045,7 @@ pgf_print_type(PgfType *type, int prec, GuWriter *wtr, GuExn *err)
     
 		for (size_t i = 0; i < type->n_exprs; i++) {
 			gu_puts(" ", wtr, err);
-			pgf_print_expr(type->exprs[i], 4, wtr, err);
+			pgf_print_expr(type->exprs[i], ctxt, 4, wtr, err);
 		}
 		
 		if (prec > 3) gu_putc(')', wtr, err);
@@ -577,3 +1053,38 @@ pgf_print_type(PgfType *type, int prec, GuWriter *wtr, GuExn *err)
 		gu_string_write(type->cid, wtr, err);
 	}
 }
+
+bool
+pgf_type_eq(PgfType* t1, PgfType* t2)
+{
+	if (gu_seq_length(t1->hypos) != gu_seq_length(t2->hypos))
+		return false;
+
+	size_t n_hypos = gu_seq_length(t1->hypos);
+	for (size_t i = 0; i < n_hypos; i++) {
+		PgfHypo *hypo1 = gu_seq_index(t1->hypos, PgfHypo, i);
+		PgfHypo *hypo2 = gu_seq_index(t1->hypos, PgfHypo, i);
+		
+		if (hypo1->bind_type != hypo2->bind_type)
+			return false;
+			
+		if (!gu_string_eq(hypo1->cid, hypo2->cid))
+			return false;
+			
+		if (!pgf_type_eq(hypo1->type, hypo2->type))
+			return false;
+	}
+    
+	if (!gu_string_eq(t1->cid, t2->cid))
+		return false;
+
+	if (t1->n_exprs != t2->n_exprs)
+		return false;
+
+	for (size_t i = 0; i < t1->n_exprs; i++) {
+		if (!pgf_expr_eq(t1->exprs[i], t2->exprs[i]))
+			return false;
+	}
+
+	return true;
+}
diff --git a/src/runtime/c/pgf/expr.h b/src/runtime/c/pgf/expr.h
index ef2dd013c..3d07ce863 100644
--- a/src/runtime/c/pgf/expr.h
+++ b/src/runtime/c/pgf/expr.h
@@ -53,7 +53,7 @@ typedef struct {
 
 
 struct PgfHypo {
-	PgfBindType bindtype;
+	PgfBindType bind_type;
 
 	PgfCId cid;
 	/**< Locally scoped name for the parameter if dependent types
@@ -87,7 +87,7 @@ typedef enum {
 
 typedef struct {
 	PgfBindType bind_type;
-	PgfCId id; // 
+	PgfCId id;
 	PgfExpr body;
 } PgfExprAbs;
 		
@@ -154,22 +154,38 @@ pgf_expr_unapply(PgfExpr expr, GuPool* pool);
 PgfExpr
 pgf_read_expr(GuIn* in, GuPool* pool, GuExn* err);
 
+PgfType*
+pgf_read_type(GuIn* in, GuPool* pool, GuExn* err);
+
 bool
 pgf_literal_eq(PgfLiteral lit1, PgfLiteral lit2);
 
 bool
 pgf_expr_eq(PgfExpr e1, PgfExpr e2);
 
+bool
+pgf_type_eq(PgfType* t1, PgfType* t2);
+
+typedef struct PgfPrintContext PgfPrintContext;
+
+struct PgfPrintContext {
+	PgfCId name;
+	PgfPrintContext* next;
+};
+
 void
 pgf_print_literal(PgfLiteral lit, GuWriter* wtr, GuExn* err);
 
 void
-pgf_print_expr(PgfExpr expr, int prec, GuWriter* wtr, GuExn* err);
+pgf_print_expr(PgfExpr expr, PgfPrintContext* ctxt, int prec, 
+               GuWriter* wtr, GuExn* err);
 
-void
-pgf_print_hypo(PgfHypo *hypo, int prec, GuWriter *wtr, GuExn *err);
+PgfPrintContext*
+pgf_print_hypo(PgfHypo *hypo, PgfPrintContext* ctxt, int prec,
+               GuWriter *wtr, GuExn *err);
 
 void
-pgf_print_type(PgfType *type, int prec, GuWriter *wtr, GuExn *err);
+pgf_print_type(PgfType *type, PgfPrintContext* ctxt, int prec,
+               GuWriter *wtr, GuExn *err);
 
 #endif /* EXPR_H_ */
diff --git a/src/runtime/c/pgf/pgf.c b/src/runtime/c/pgf/pgf.c
index 13066927c..519dfea4a 100644
--- a/src/runtime/c/pgf/pgf.c
+++ b/src/runtime/c/pgf/pgf.c
@@ -178,6 +178,17 @@ pgf_iter_functions_by_cat(PgfPGF* pgf, PgfCId catname,
 	gu_map_iter(pgf->abstract.funs, &clo.fn, err);
 }
 
+PgfType*
+pgf_function_type(PgfPGF* pgf, PgfCId funname) 
+{
+	PgfAbsFun* absfun =
+		gu_map_get(pgf->abstract.funs, &funname, PgfAbsFun*);
+	if (absfun == NULL)
+		return NULL;
+		
+	return absfun->type;
+}
+
 GuString
 pgf_print_name(PgfConcr* concr, PgfCId id)
 {
diff --git a/src/runtime/c/pgf/pgf.h b/src/runtime/c/pgf/pgf.h
index 2e7e43584..bda70315e 100644
--- a/src/runtime/c/pgf/pgf.h
+++ b/src/runtime/c/pgf/pgf.h
@@ -107,6 +107,9 @@ void
 pgf_iter_functions_by_cat(PgfPGF* pgf, PgfCId catname,
                           GuMapItor* fn, GuExn* err);
 
+PgfType*
+pgf_function_type(PgfPGF* pgf, PgfCId funname);
+
 GuString
 pgf_print_name(PgfConcr*, PgfCId id);
 
diff --git a/src/runtime/c/pgf/printer.c b/src/runtime/c/pgf/printer.c
index 4b91a011c..71ccda1f4 100644
--- a/src/runtime/c/pgf/printer.c
+++ b/src/runtime/c/pgf/printer.c
@@ -1,4 +1,5 @@
 #include <pgf/data.h>
+#include <stdlib.h>
 
 typedef struct {
 	GuMapItor fn;
@@ -33,11 +34,18 @@ pgf_print_cat(GuMapItor* fn, const void* key, void* value,
     gu_puts("  cat ", wtr, err);
     gu_string_write(name, wtr, err);
 
+	PgfPrintContext* ctxt = NULL;
     size_t n_hypos = gu_seq_length(cat->context);
     for (size_t i = 0; i < n_hypos; i++) {
-		PgfHypo* hypo = gu_seq_get(cat->context, PgfHypo*, i);
+		PgfHypo* hypo = gu_seq_index(cat->context, PgfHypo, i);
 		gu_putc(' ', wtr, err);
-		pgf_print_hypo(hypo, 4, wtr, err);
+		ctxt = pgf_print_hypo(hypo, ctxt, 4, wtr, err);
+	}
+
+	while (ctxt != NULL) {
+		PgfPrintContext* next = ctxt->next;
+		free(ctxt);
+		ctxt = next;
 	}
 
     gu_printf(wtr, err, " ;   -- %f\n",cat->meta_prob);
@@ -55,7 +63,7 @@ pgf_print_absfun(GuMapItor* fn, const void* key, void* value,
     gu_puts(gu_seq_is_null(fun->defns) ? "  data " : "  fun ", wtr, err);
     gu_string_write(name, wtr, err);
     gu_puts(" : ", wtr, err);
-    pgf_print_type(fun->type, 0, wtr, err);
+    pgf_print_type(fun->type, NULL, 0, wtr, err);
     gu_printf(wtr, err, " ;   -- %f\n", fun->ep.prob);
 }
 static void
diff --git a/src/runtime/c/pgf/reader.c b/src/runtime/c/pgf/reader.c
index 1eccc25e0..a43ebdba0 100644
--- a/src/runtime/c/pgf/reader.c
+++ b/src/runtime/c/pgf/reader.c
@@ -188,7 +188,7 @@ pgf_read_flags(PgfReader* rdr)
 }
 
 static PgfType*
-pgf_read_type(PgfReader* rdr);
+pgf_read_type_(PgfReader* rdr);
 
 static PgfExpr
 pgf_read_expr_(PgfReader* rdr)
@@ -269,7 +269,7 @@ pgf_read_expr_(PgfReader* rdr)
 						   &expr, rdr->opool);
 		etyped->expr = pgf_read_expr_(rdr);
 		gu_return_on_exn(rdr->err, gu_null_variant);
-		etyped->type = pgf_read_type(rdr);
+		etyped->type = pgf_read_type_(rdr);
 		gu_return_on_exn(rdr->err, gu_null_variant);
 		break;
 	}
@@ -292,34 +292,38 @@ pgf_read_expr_(PgfReader* rdr)
 static void
 pgf_read_hypo(PgfReader* rdr, PgfHypo* hypo)
 {
-	hypo->bindtype = pgf_read_tag(rdr);
+	hypo->bind_type = pgf_read_tag(rdr);
 	gu_return_on_exn(rdr->err, );
 	
 	hypo->cid = pgf_read_cid(rdr);
 	gu_return_on_exn(rdr->err, );
 	
-	hypo->type = pgf_read_type(rdr);
+	hypo->type = pgf_read_type_(rdr);
 	gu_return_on_exn(rdr->err, );
 }
 
 static PgfType*
-pgf_read_type(PgfReader* rdr)
+pgf_read_type_(PgfReader* rdr)
 {
-	PgfType* type = gu_new(PgfType, rdr->opool);
-
 	size_t n_hypos = pgf_read_len(rdr);
 	gu_return_on_exn(rdr->err, NULL);
-	type->hypos = gu_new_seq(PgfHypo, n_hypos, rdr->opool);
+	GuSeq hypos = gu_new_seq(PgfHypo, n_hypos, rdr->opool);
 	for (size_t i = 0; i < n_hypos; i++) {
-		PgfHypo* hypo = gu_seq_index(type->hypos, PgfHypo, i);
+		PgfHypo* hypo = gu_seq_index(hypos, PgfHypo, i);
 		pgf_read_hypo(rdr, hypo);
 		gu_return_on_exn(rdr->err, NULL);
 	}
 
-	type->cid = pgf_read_cid(rdr);
+	PgfCId cid = pgf_read_cid(rdr);
 	gu_return_on_exn(rdr->err, NULL);
 
-	type->n_exprs = pgf_read_len(rdr);
+	size_t n_exprs = pgf_read_len(rdr);
+
+	PgfType* type = gu_new_flex(rdr->opool, PgfType, exprs, n_exprs);
+	type->hypos   = hypos;
+	type->cid     = cid;
+	type->n_exprs = n_exprs;
+
 	for (size_t i = 0; i < type->n_exprs; i++) {
 		type->exprs[i] = pgf_read_expr_(rdr);
 		gu_return_on_exn(rdr->err, NULL);
@@ -423,7 +427,7 @@ pgf_read_absfun(PgfReader* rdr)
 	absfun->name = pgf_read_cid(rdr);
 	gu_return_on_exn(rdr->err, NULL);
 
-	absfun->type = pgf_read_type(rdr);
+	absfun->type = pgf_read_type_(rdr);
 	gu_return_on_exn(rdr->err, NULL);
 
 	absfun->arity = pgf_read_int(rdr);