author | webertj |
Sun, 14 Nov 2004 01:40:27 +0100 | |
changeset 15283 | f21466450330 |
parent 9251 | bd57acd44fc1 |
permissions | -rw-r--r-- |
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(* Title: CTT/ex/typechk |
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ID: $Id$ |
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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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9251
bd57acd44fc1
more tidying. also generalized some tactics to prove "Type A" and
paulson
parents:
3837
diff
changeset
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Goal "?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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9251
bd57acd44fc1
more tidying. also generalized some tactics to prove "Type A" and
paulson
parents:
3837
diff
changeset
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Goal "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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9251
bd57acd44fc1
more tidying. also generalized some tactics to prove "Type A" and
paulson
parents:
3837
diff
changeset
|
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Goal "PROD w:N. N + N type"; |
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by form_tac; |
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result(); |
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9251
bd57acd44fc1
more tidying. also generalized some tactics to prove "Type A" and
paulson
parents:
3837
diff
changeset
|
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Goal "<0, succ(0)> : ?A"; |
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by (intr_tac[]); |
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result(); |
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9251
bd57acd44fc1
more tidying. also generalized some tactics to prove "Type A" and
paulson
parents:
3837
diff
changeset
|
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Goal "PROD w:N . Eq(?A,w,w) type"; |
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by (typechk_tac[]); |
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result(); |
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9251
bd57acd44fc1
more tidying. also generalized some tactics to prove "Type A" and
paulson
parents:
3837
diff
changeset
|
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Goal "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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9251
bd57acd44fc1
more tidying. also generalized some tactics to prove "Type A" and
paulson
parents:
3837
diff
changeset
|
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Goal "(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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9251
bd57acd44fc1
more tidying. also generalized some tactics to prove "Type A" and
paulson
parents:
3837
diff
changeset
|
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Goal "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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9251
bd57acd44fc1
more tidying. also generalized some tactics to prove "Type A" and
paulson
parents:
3837
diff
changeset
|
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Goal "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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9251
bd57acd44fc1
more tidying. also generalized some tactics to prove "Type A" and
paulson
parents:
3837
diff
changeset
|
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Goal "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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9251
bd57acd44fc1
more tidying. also generalized some tactics to prove "Type A" and
paulson
parents:
3837
diff
changeset
|
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Goal "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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9251
bd57acd44fc1
more tidying. also generalized some tactics to prove "Type A" and
paulson
parents:
3837
diff
changeset
|
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Goal "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."; |