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1 (* Title: CTT/ex/typechk |
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2 ID: $Id$ |
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3 Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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4 Copyright 1991 University of Cambridge |
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5 |
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6 Easy examples: type checking and type deduction |
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7 *) |
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8 |
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9 writeln"Single-step proofs: verifying that a type is well-formed"; |
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10 |
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11 goal CTT.thy "?A type"; |
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12 by (resolve_tac form_rls 1); |
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13 result(); |
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14 writeln"getting a second solution"; |
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15 back(); |
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16 by (resolve_tac form_rls 1); |
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17 by (resolve_tac form_rls 1); |
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18 result(); |
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19 |
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20 goal CTT.thy "PROD z:?A . N + ?B(z) type"; |
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21 by (resolve_tac form_rls 1); |
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22 by (resolve_tac form_rls 1); |
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23 by (resolve_tac form_rls 1); |
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24 by (resolve_tac form_rls 1); |
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25 by (resolve_tac form_rls 1); |
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26 uresult(); |
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27 |
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28 |
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29 writeln"Multi-step proofs: Type inference"; |
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30 |
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31 goal CTT.thy "PROD w:N. N + N type"; |
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32 by form_tac; |
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33 result(); |
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34 |
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35 goal CTT.thy "<0, succ(0)> : ?A"; |
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36 by (intr_tac[]); |
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37 result(); |
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38 |
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39 goal CTT.thy "PROD w:N . Eq(?A,w,w) type"; |
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40 by (typechk_tac[]); |
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41 result(); |
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42 |
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43 goal CTT.thy "PROD x:N . PROD y:N . Eq(?A,x,y) type"; |
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44 by (typechk_tac[]); |
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45 result(); |
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46 |
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47 writeln"typechecking an application of fst"; |
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48 goal CTT.thy "(lam u. split(u, %v w.v)) ` <0, succ(0)> : ?A"; |
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49 by (typechk_tac[]); |
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50 result(); |
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51 |
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52 writeln"typechecking the predecessor function"; |
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53 goal CTT.thy "lam n. rec(n, 0, %x y.x) : ?A"; |
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54 by (typechk_tac[]); |
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55 result(); |
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56 |
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57 writeln"typechecking the addition function"; |
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58 goal CTT.thy "lam n. lam m. rec(n, m, %x y.succ(y)) : ?A"; |
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59 by (typechk_tac[]); |
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60 result(); |
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61 |
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62 (*Proofs involving arbitrary types. |
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63 For concreteness, every type variable left over is forced to be N*) |
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64 val N_tac = TRYALL (rtac NF); |
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65 |
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66 goal CTT.thy "lam w. <w,w> : ?A"; |
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67 by (typechk_tac[]); |
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68 by N_tac; |
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69 result(); |
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70 |
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71 goal CTT.thy "lam x. lam y. x : ?A"; |
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72 by (typechk_tac[]); |
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73 by N_tac; |
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74 result(); |
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75 |
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76 writeln"typechecking fst (as a function object) "; |
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77 goal CTT.thy "lam i. split(i, %j k.j) : ?A"; |
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78 by (typechk_tac[]); |
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79 by N_tac; |
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80 result(); |
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81 |
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82 writeln"Reached end of file."; |