author | wenzelm |
Mon, 05 Jun 2006 21:54:20 +0200 | |
changeset 19774 | 5fe7731d0836 |
parent 19761 | 5cd82054c2c6 |
child 35762 | af3ff2ba4c54 |
permissions | -rw-r--r-- |
19761 | 1 |
(* Title: CTT/ex/Synthesis.thy |
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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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*) |
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header "Synthesis examples, using a crude form of narrowing" |
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theory Synthesis |
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imports Arith |
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begin |
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text "discovery of predecessor function" |
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allow non-trivial schematic goals (via embedded term vars);
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parents:
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lemma "?a : SUM pred:?A . Eq(N, pred`0, 0) |
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* (PROD n:N. Eq(N, pred ` succ(n), n))" |
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apply (tactic "intr_tac []") |
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apply (tactic eqintr_tac) |
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apply (rule_tac [3] reduction_rls) |
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apply (rule_tac [5] comp_rls) |
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apply (tactic "rew_tac []") |
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done |
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text "the function fst as an element of a function type" |
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lemma [folded basic_defs]: |
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"A type ==> ?a: SUM f:?B . PROD i:A. PROD j:A. Eq(A, f ` <i,j>, i)" |
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apply (tactic "intr_tac []") |
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apply (tactic eqintr_tac) |
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apply (rule_tac [2] reduction_rls) |
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apply (rule_tac [4] comp_rls) |
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apply (tactic "typechk_tac []") |
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txt "now put in A everywhere" |
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apply assumption+ |
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done |
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text "An interesting use of the eliminator, when" |
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(*The early implementation of unification caused non-rigid path in occur check |
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See following example.*) |
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parents:
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lemma "?a : PROD i:N. Eq(?A, ?b(inl(i)), <0 , i>) |
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* Eq(?A, ?b(inr(i)), <succ(0), i>)" |
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apply (tactic "intr_tac []") |
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apply (tactic eqintr_tac) |
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apply (rule comp_rls) |
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apply (tactic "rew_tac []") |
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allow non-trivial schematic goals (via embedded term vars);
wenzelm
parents:
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done |
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allow non-trivial schematic goals (via embedded term vars);
wenzelm
parents:
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(*Here we allow the type to depend on i. |
5fe7731d0836
allow non-trivial schematic goals (via embedded term vars);
wenzelm
parents:
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This prevents the cycle in the first unification (no longer needed). |
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Requires flex-flex to preserve the dependence. |
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Simpler still: make ?A into a constant type N*N.*) |
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lemma "?a : PROD i:N. Eq(?A(i), ?b(inl(i)), <0 , i>) |
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* Eq(?A(i), ?b(inr(i)), <succ(0),i>)" |
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oops |
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text "A tricky combination of when and split" |
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(*Now handled easily, but caused great problems once*) |
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lemma [folded basic_defs]: |
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allow non-trivial schematic goals (via embedded term vars);
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parents:
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"?a : PROD i:N. PROD j:N. Eq(?A, ?b(inl(<i,j>)), i) |
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* Eq(?A, ?b(inr(<i,j>)), j)" |
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apply (tactic "intr_tac []") |
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apply (tactic eqintr_tac) |
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apply (rule PlusC_inl [THEN trans_elem]) |
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apply (rule_tac [4] comp_rls) |
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apply (rule_tac [7] reduction_rls) |
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apply (rule_tac [10] comp_rls) |
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apply (tactic "typechk_tac []") |
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done |
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(*similar but allows the type to depend on i and j*) |
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lemma "?a : PROD i:N. PROD j:N. Eq(?A(i,j), ?b(inl(<i,j>)), i) |
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* Eq(?A(i,j), ?b(inr(<i,j>)), j)" |
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oops |
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(*similar but specifying the type N simplifies the unification problems*) |
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lemma "?a : PROD i:N. PROD j:N. Eq(N, ?b(inl(<i,j>)), i) |
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* Eq(N, ?b(inr(<i,j>)), j)" |
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oops |
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text "Deriving the addition operator" |
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lemma [folded arith_defs]: |
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"?c : PROD n:N. Eq(N, ?f(0,n), n) |
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* (PROD m:N. Eq(N, ?f(succ(m), n), succ(?f(m,n))))" |
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apply (tactic "intr_tac []") |
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apply (tactic eqintr_tac) |
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apply (rule comp_rls) |
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apply (tactic "rew_tac []") |
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parents:
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done |
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text "The addition function -- using explicit lambdas" |
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lemma [folded arith_defs]: |
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"?c : SUM plus : ?A . |
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PROD x:N. Eq(N, plus`0`x, x) |
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* (PROD y:N. Eq(N, plus`succ(y)`x, succ(plus`y`x)))" |
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apply (tactic "intr_tac []") |
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apply (tactic eqintr_tac) |
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apply (tactic "resolve_tac [TSimp.split_eqn] 3") |
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apply (tactic "SELECT_GOAL (rew_tac []) 4") |
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apply (tactic "resolve_tac [TSimp.split_eqn] 3") |
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apply (tactic "SELECT_GOAL (rew_tac []) 4") |
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apply (rule_tac [3] p = "y" in NC_succ) |
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(** by (resolve_tac comp_rls 3); caused excessive branching **) |
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apply (tactic "rew_tac []") |
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done |
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end |
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