src/CTT/Arith.thy
 author paulson Tue Nov 14 13:26:48 2000 +0100 (2000-11-14) changeset 10467 e6e7205e9e91 parent 3837 d7f033c74b38 child 12110 f8b4b11cd79d permissions -rw-r--r--
x-symbol support for Pi, Sigma, -->, : (membership)
note that "lam" is displayed as TWO lambda-symbols
```     1 (*  Title:      CTT/arith
```
```     2     ID:         \$Id\$
```
```     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 Arithmetic operators and their definitions
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```     7
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```     8 Proves about elementary arithmetic: addition, multiplication, etc.
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```     9 Tests definitions and simplifier.
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```    10 *)
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```    11
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```    12 Arith = CTT +
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```    13
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```    14 consts "#+","-","|-|"   :: "[i,i]=>i"   (infixr 65)
```
```    15        "#*",div,mod     :: "[i,i]=>i"   (infixr 70)
```
```    16
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```    17 syntax (symbols)
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```    18   "op #*"      :: [i, i] => i   (infixr "#\\<times>" 70)
```
```    19
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```    20 syntax (HTML output)
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```    21   "op #*"      :: [i, i] => i   (infixr "#\\<times>" 70)
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```    22
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```    23 rules
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```    24   add_def     "a#+b == rec(a, b, %u v. succ(v))"
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```    25   diff_def    "a-b == rec(b, a, %u v. rec(v, 0, %x y. x))"
```
```    26   absdiff_def "a|-|b == (a-b) #+ (b-a)"
```
```    27   mult_def    "a#*b == rec(a, 0, %u v. b #+ v)"
```
```    28   mod_def     "a mod b == rec(a, 0, %u v. rec(succ(v) |-| b, 0, %x y. succ(v)))"
```
```    29   div_def     "a div b == rec(a, 0, %u v. rec(succ(u) mod b, succ(v), %x y. v))"
```
```    30 end
```