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(* Title: CTT/ex/typechk
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ID: $Id$
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1459
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory
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Copyright 1991 University of Cambridge
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Easy examples: type checking and type deduction
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*)
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writeln"Single-step proofs: verifying that a type is well-formed";
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goal CTT.thy "?A type";
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by (resolve_tac form_rls 1);
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result();
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writeln"getting a second solution";
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back();
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by (resolve_tac form_rls 1);
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by (resolve_tac form_rls 1);
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result();
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goal CTT.thy "PROD z:?A . N + ?B(z) type";
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by (resolve_tac form_rls 1);
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by (resolve_tac form_rls 1);
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by (resolve_tac form_rls 1);
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by (resolve_tac form_rls 1);
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by (resolve_tac form_rls 1);
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uresult();
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writeln"Multi-step proofs: Type inference";
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goal CTT.thy "PROD w:N. N + N type";
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by form_tac;
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result();
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goal CTT.thy "<0, succ(0)> : ?A";
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by (intr_tac[]);
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result();
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goal CTT.thy "PROD w:N . Eq(?A,w,w) type";
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by (typechk_tac[]);
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result();
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goal CTT.thy "PROD x:N . PROD y:N . Eq(?A,x,y) type";
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by (typechk_tac[]);
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result();
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writeln"typechecking an application of fst";
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goal CTT.thy "(lam u. split(u, %v w. v)) ` <0, succ(0)> : ?A";
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by (typechk_tac[]);
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result();
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writeln"typechecking the predecessor function";
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goal CTT.thy "lam n. rec(n, 0, %x y. x) : ?A";
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by (typechk_tac[]);
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result();
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writeln"typechecking the addition function";
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goal CTT.thy "lam n. lam m. rec(n, m, %x y. succ(y)) : ?A";
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by (typechk_tac[]);
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result();
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(*Proofs involving arbitrary types.
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For concreteness, every type variable left over is forced to be N*)
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val N_tac = TRYALL (rtac NF);
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goal CTT.thy "lam w. <w,w> : ?A";
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by (typechk_tac[]);
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by N_tac;
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result();
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goal CTT.thy "lam x. lam y. x : ?A";
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by (typechk_tac[]);
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by N_tac;
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result();
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writeln"typechecking fst (as a function object) ";
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goal CTT.thy "lam i. split(i, %j k. j) : ?A";
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by (typechk_tac[]);
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by N_tac;
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result();
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writeln"Reached end of file.";
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